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Telecommunications in the Comoros
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In large part thanks to international aid programs, Moroni has international telecommunications service. Telephone service, however, is largely limited to the islands\' few towns.
## Overview
Telephones -- main lines in use: 5,000 (1995)
Telephones -- mobile cellular: 0 (1995)
Telephone system: sparse system of microwave radio relay and HF radiotelephone communication stations\
*domestic:* HF radiotelephone communications and microwave radio relay\
CMDA mobile network (Huri, operated by Comores Telecom)\
*international:* HF radiotelephone communications to Madagascar and Réunion
Radio broadcast stations: AM 1, FM 2, shortwave 1 (1998)
Radios: 90,000 (1997)
Television broadcast stations: 0 (1998)
Televisions: 1,000 (1997)
Internet Service Providers (ISPs): 1 (1999)
Country code (Top-level domain): .km
## Special projects {#special_projects}
In October 2011 the State of Qatar launched a special program for the construction of a wireless network to interconnect the three islands of the archipelago, by means of low cost, repeatable technology. The project has been developed by Qatar University and Politecnico di Torino, under the supervision of prof. Mazen Hasna and prof. Daniele Trinchero, with a major participation of local actors (Comorian Government, NRTIC, University of the Comoros). The project has been referred as an example of technology transfer and Sustainable Inclusion in developing countries
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6,006 |
Transport in the Comoros
|
There are a number of systems of **transport in the Comoros**. The Comoros possesses 880 km of road, of which 673 km are paved. It has three seaports: Fomboni, Moroni and Moutsamoudou, but does not have a merchant marine, and no longer has any railway network. It has four airports, all with paved runways, one with runways over 2438 m long, with the others having runways shorter than 1523 m.
The isolation of the Comoros had made air traffic a major means of transportation. One of President Abdallah\'s accomplishments was to make the Comoros more accessible by air. During his administration, he negotiated agreements to initiate or enhance commercial air links with Tanzania and Madagascar. The Djohar regime reached an agreement in 1990 to link Moroni and Brussels by air. By the early 1990s, commercial flights connected the Comoros with France, Mauritius, Kenya, South Africa, Tanzania, and Madagascar. The national airline was Air Comores. Daily flights linked the three main islands, and air service was also available to Mahoré; each island had airstrips. In 1986 the republic received a grant from the French government\'s CCCE to renovate and expand Hahaya airport, near Moroni. Because of the absence of scheduled sea transport between the islands, nearly all interisland passenger traffic is by air.
More than 99% of freight is transported by sea. Both Moroni on Njazidja and Mutsamudu on Nzwani have artificial harbors. There is also a harbor at Fomboni, on Mwali. Despite extensive internationally financed programs to upgrade the harbors at Moroni and Mutsamudu, by the early 1990s only Mutsamudu was operational as a deepwater facility. Its harbor could accommodate vessels of up to eleven meters\' draught. At Moroni, ocean-going vessels typically lie offshore and are loaded or unloaded by smaller craft, a costly and sometimes dangerous procedure. Most freight continues to be sent to Tanzania, Kenya, Reunion, or Madagascar for transshipment to the Comoros. Use of Comoran ports is further restricted by the threat of cyclones from December through March. The privately operated Comoran Navigation Company (*Société Comorienne de Navigation*) is based in Moroni, and provides services to Madagascar.
Roads serve the coastal areas, rather than the interior, and the mountainous terrain makes surface travel difficult.
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6,008 |
Army of National Development
|
The **Comorian Armed Forces** (*Armée nationale de développement, AND*; `{{literally|Army of National Development}}`{=mediawiki}) are the national military of the Comoros. The armed forces consist of a small standing army and a 500-member police force, as well as a 500-member defense force. A defense treaty with France provides naval resources for protection of territorial waters, training of Comorian military personnel, and air surveillance. France maintains a small troop presence in the Comoros at government request. France maintains a small Navy base and a Foreign Legion Detachment (DLEM) in Mayotte.
## Structure
The AND consists of the following components:
- Comorian Ground Defense Force
- Comorian National Gendarmerie
- National School of the Armed Forces and Gendarmerie
- Comorian Air Force
- Comorian Presidential Guard
- Comorian Military Health Services
- Comorian Coast Guard
## Equipment inventory {#equipment_inventory}
- FN FAL battle rifle
- AK-47 assault rifle
- Type 81 assault rifle
- NSV HMG
- RPG-7 anti-tank weapon
- Mitsubishi L200 pickup truck
## Aircraft
Note: The last comprehensive aircraft inventory list was from *Aviation Week & Space Technology* in 2007.
Aircraft Origin Type Variant In service Notes
--------------------------- ---------------- --------------------- ---------- ------------ -------
Transport
Cessna 402 United States Transport 1
L-410 Turbolet Czech Republic Transport 1
Aérospatiale Corvette France VIP transport 1
Helicopters
Mil Mi-14 Russia Transport / Utility Mi-14PZh 2
Eurocopter AS350 Écureuil France Utility 1
Trainer aircraft
SIAI-Marchetti SF.260 Italy Patrol / Trainer 5
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6,015 |
Crystal
|
thumb\|upright=1.25\|Crystals of amethyst quartz thumb\|upright=1.25\|Microscopically, a single crystal has atoms in a near-perfect periodic arrangement; a polycrystal is composed of many microscopic crystals (called \"crystallites\" or \"grains\"); and an amorphous solid (such as glass) has no periodic arrangement even microscopically.
A **crystal** or **crystalline solid** is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.
The word *crystal* derives from the Ancient Greek word *κρύσταλλος* (`{{transliteration|grc|''krustallos''}}`{=mediawiki}), meaning both \"ice\" and \"rock crystal\", from *κρύος* (`{{transliteration|grc|''kruos''}}`{=mediawiki}), \"icy cold, frost\".
Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass, wax, and many plastics.
Despite the name, lead crystal, crystal glass, and related products are *not* crystals, but rather types of glass, i.e. amorphous solids.
Crystals, or crystalline solids, are often used in pseudoscientific practices such as crystal therapy, and, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements.
## Crystal structure (microscopic) {#crystal_structure_microscopic}
The scientific definition of a \"crystal\" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement. (Quasicrystals are an exception, see below).
Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a *polycrystalline* structure. In the final block of ice, each of the small crystals (called \"crystallites\" or \"grains\") is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does *not* have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries. Most macroscopic inorganic solids are polycrystalline, including almost all metals, ceramics, ice, rocks, etc. Solids that are neither crystalline nor polycrystalline, such as glass, are called *amorphous solids*, also called glassy, vitreous, or noncrystalline. These have no periodic order, even microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does.
A crystal structure (an arrangement of atoms in a crystal) is characterized by its *unit cell*, a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are stacked in three-dimensional space to form the crystal.
The symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries (230 is commonly cited, but this treats chiral equivalents as separate entities), called crystallographic space groups. These are grouped into 7 crystal systems, such as cubic crystal system (where the crystals may form cubes or rectangular boxes, such as halite shown at right) or hexagonal crystal system (where the crystals may form hexagons, such as ordinary water ice).
## Crystal faces, shapes and crystallographic forms {#crystal_faces_shapes_and_crystallographic_forms}
thumb\|upright=1.6\|As a halite crystal is growing, new atoms can very easily attach to the parts of the surface with rough atomic-scale structure and many dangling bonds. Therefore, these parts of the crystal grow out very quickly (yellow arrows). Eventually, the whole surface consists of smooth, stable faces, where new atoms cannot as easily attach themselves. Crystals are commonly recognized, macroscopically, by their shape, consisting of flat faces with sharp angles. These shape characteristics are not *necessary* for a crystal---a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape---but the characteristic macroscopic shape is often present and easy to see.
Euhedral crystals are those that have obvious, well-formed flat faces. Anhedral crystals do not, usually because the crystal is one grain in a polycrystalline solid.
The flat faces (also called facets) of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of relatively low Miller index. This occurs because some surface orientations are more stable than others (lower surface energy). As a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. (See diagram on right.)
One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, and using them to infer the underlying crystal symmetry.
A crystal\'s **crystallographic forms** are sets of possible faces of the crystal that are related by one of the symmetries of the crystal. For example, crystals of galena often take the shape of cubes, and the six faces of the cube belong to a crystallographic form that displays one of the symmetries of the isometric crystal system. Galena also sometimes crystallizes as octahedrons, and the eight faces of the octahedron belong to another crystallographic form reflecting a different symmetry of the isometric system. A crystallographic form is described by placing the Miller indices of one of its faces within brackets. For example, the octahedral form is written as {111}, and the other faces in the form are implied by the symmetry of the crystal.
Forms may be closed, meaning that the form can completely enclose a volume of space, or open, meaning that it cannot. The cubic and octahedral forms are examples of closed forms. All the forms of the isometric system are closed, while all the forms of the monoclinic and triclinic crystal systems are open. A crystal\'s faces may all belong to the same closed form, or they may be a combination of multiple open or closed forms.
A crystal\'s habit is its visible external shape. This is determined by the crystal structure (which restricts the possible facet orientations), the specific crystal chemistry and bonding (which may favor some facet types over others), and the conditions under which the crystal formed.
## Occurrence in nature {#occurrence_in_nature}
### Rocks
By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock. Crystals found in rocks typically range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are occasionally found. `{{As of|1999}}`{=mediawiki}, the world\'s largest known naturally occurring crystal is a crystal of beryl from Malakialina, Madagascar, 18 m long and 3.5 m in diameter, and weighing 380,000 kg.
Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock. The vast majority of igneous rocks are formed from molten magma and the degree of crystallization depends primarily on the conditions under which they solidified. Such rocks as granite, which have cooled very slowly and under great pressures, have completely crystallized; but many kinds of lava were poured out at the surface and cooled very rapidly, and in this latter group a small amount of amorphous or glassy matter is common. Other crystalline rocks, the metamorphic rocks such as marbles, mica-schists and quartzites, are recrystallized. This means that they were at first fragmental rocks like limestone, shale and sandstone and have never been in a molten condition nor entirely in solution, but the high temperature and pressure conditions of metamorphism have acted on them by erasing their original structures and inducing recrystallization in the solid state.
Other rock crystals have formed out of precipitation from fluids, commonly water, to form druses or quartz veins. Evaporites such as halite, gypsum and some limestones have been deposited from aqueous solution, mostly owing to evaporation in arid climates.
### Ice
Water-based ice in the form of snow, sea ice, and glaciers are common crystalline/polycrystalline structures on Earth and other planets. A single snowflake is a single crystal or a collection of crystals, while an ice cube is a polycrystal. Ice crystals may form from cooling liquid water below its freezing point, such as ice cubes or a frozen lake. Frost, snowflakes, or small ice crystals suspended in the air (ice fog) more often grow from a supersaturated gaseous-solution of water vapor and air, when the temperature of the air drops below its dew point, without passing through a liquid state. Another unusual property of water is that it expands rather than contracts when it crystallizes.
### Organigenic crystals {#organigenic_crystals}
Many living organisms are able to produce crystals grown from an aqueous solution, for example calcite and aragonite in the case of most molluscs or hydroxylapatite in the case of bones and teeth in vertebrates.
## Polymorphism and allotropy {#polymorphism_and_allotropy}
The same group of atoms can often solidify in many different ways. Polymorphism is the ability of a solid to exist in more than one crystal form. For example, water ice is ordinarily found in the hexagonal form Ice I~h~, but can also exist as the cubic Ice I~c~, the rhombohedral ice II, and many other forms. The different polymorphs are usually called different *phases*.
In addition, the same atoms may be able to form noncrystalline phases. For example, water can also form amorphous ice, while SiO~2~ can form both fused silica (an amorphous glass) and quartz (a crystal). Likewise, if a substance can form crystals, it can also form polycrystals.
For pure chemical elements, polymorphism is referred to as allotropy. For example, diamond and graphite are two crystalline forms of carbon, while amorphous carbon is a noncrystalline form. Polymorphs, despite having the same atoms, may have very different properties. For example, diamond is the hardest substance known, while graphite is so soft that it is used as a lubricant. Chocolate can form six different types of crystals, but only one has the suitable hardness and melting point for candy bars and confections. Polymorphism in steel is responsible for its ability to be heat treated, giving it a wide range of properties.
Polyamorphism is a similar phenomenon where the same atoms can exist in more than one amorphous solid form.
## Crystallization
Crystallization is the process of forming a crystalline structure from a fluid or from materials dissolved in a fluid. (More rarely, crystals may be deposited directly from gas; see: epitaxy and frost.)
Crystallization is a complex and extensively-studied field, because depending on the conditions, a single fluid can solidify into many different possible forms. It can form a single crystal, perhaps with various possible phases, stoichiometries, impurities, defects, and habits. Or, it can form a polycrystal, with various possibilities for the size, arrangement, orientation, and phase of its grains. The final form of the solid is determined by the conditions under which the fluid is being solidified, such as the chemistry of the fluid, the ambient pressure, the temperature, and the speed with which all these parameters are changing.
Specific industrial techniques to produce large single crystals (called *boules*) include the Czochralski process and the Bridgman technique. Other less exotic methods of crystallization may be used, depending on the physical properties of the substance, including hydrothermal synthesis, sublimation, or simply solvent-based crystallization.
Large single crystals can be created by geological processes. For example, selenite crystals in excess of 10 m are found in the Cave of the Crystals in Naica, Mexico. For more details on geological crystal formation, see above.
Crystals can also be formed by biological processes, see above. Conversely, some organisms have special techniques to *prevent* crystallization from occurring, such as antifreeze proteins.
## Defects, impurities, and twinning {#defects_impurities_and_twinning}
thumb\|left\|upright=1.25\|Two types of crystallographic defects. Top right: edge dislocation. Bottom right: screw dislocation. An *ideal* crystal has every atom in a perfect, exactly repeating pattern. However, in reality, most crystalline materials have a variety of crystallographic defects: places where the crystal\'s pattern is interrupted. The types and structures of these defects may have a profound effect on the properties of the materials.
A few examples of crystallographic defects include vacancy defects (an empty space where an atom should fit), interstitial defects (an extra atom squeezed in where it does not fit), and dislocations (see figure at right). Dislocations are especially important in materials science, because they help determine the mechanical strength of materials.
Another common type of crystallographic defect is an impurity, meaning that the \"wrong\" type of atom is present in a crystal. For example, a perfect crystal of diamond would only contain carbon atoms, but a real crystal might perhaps contain a few boron atoms as well. These boron impurities change the diamond\'s color to slightly blue. Likewise, the only difference between ruby and sapphire is the type of impurities present in a corundum crystal.
In semiconductors, a special type of impurity, called a dopant, drastically changes the crystal\'s electrical properties. Semiconductor devices, such as transistors, are made possible largely by putting different semiconductor dopants into different places, in specific patterns.
Twinning is a phenomenon somewhere between a crystallographic defect and a grain boundary. Like a grain boundary, a twin boundary has different crystal orientations on its two sides. But unlike a grain boundary, the orientations are not random, but related in a specific, mirror-image way.
Mosaicity is a spread of crystal plane orientations. A mosaic crystal consists of smaller crystalline units that are somewhat misaligned with respect to each other.
## Chemical bonds {#chemical_bonds}
In general, solids can be held together by various types of chemical bonds, such as metallic bonds, ionic bonds, covalent bonds, van der Waals bonds, and others. None of these are necessarily crystalline or non-crystalline. However, there are some general trends as follows:
Metals crystallize rapidly and are almost always polycrystalline, though there are exceptions like amorphous metal and single-crystal metals. The latter are grown synthetically, for example, fighter-jet turbines are typically made by first growing a single crystal of titanium alloy, increasing its strength and melting point over polycrystalline titanium. A small piece of metal may naturally form into a single crystal, such as Type 2 telluric iron, but larger pieces generally do not unless extremely slow cooling occurs. For example, iron meteorites are often composed of single crystal, or many large crystals that may be several meters in size, due to very slow cooling in the vacuum of space. The slow cooling may allow the precipitation of a separate phase within the crystal lattice, which form at specific angles determined by the lattice, called Widmanstatten patterns.
Ionic compounds typically form when a metal reacts with a non-metal, such as sodium with chlorine. These often form substances called salts, such as sodium chloride (table salt) or potassium nitrate (saltpeter), with crystals that are often brittle and cleave relatively easily. Ionic materials are usually crystalline or polycrystalline. In practice, large salt crystals can be created by solidification of a molten fluid, or by crystallization out of a solution. Some ionic compounds can be very hard, such as oxides like aluminium oxide found in many gemstones such as ruby and synthetic sapphire.
Covalently bonded solids (sometimes called covalent network solids) are typically formed from one or more non-metals, such as carbon or silicon and oxygen, and are often very hard, rigid, and brittle. These are also very common, notable examples being diamond and quartz respectively.
Weak van der Waals forces also help hold together certain crystals, such as crystalline molecular solids, as well as the interlayer bonding in graphite. Substances such as fats, lipids and wax form molecular bonds because the large molecules do not pack as tightly as atomic bonds. This leads to crystals that are much softer and more easily pulled apart or broken. Common examples include chocolates, candles, or viruses. Water ice and dry ice are examples of other materials with molecular bonding.Polymer materials generally will form crystalline regions, but the lengths of the molecules usually prevent complete crystallization---and sometimes polymers are completely amorphous.
## Quasicrystals
`{{Main article|Quasicrystal}}`{=mediawiki} A quasicrystal consists of arrays of atoms that are ordered but not strictly periodic. They have many attributes in common with ordinary crystals, such as displaying a discrete pattern in x-ray diffraction, and the ability to form shapes with smooth, flat faces.
Quasicrystals are most famous for their ability to show five-fold symmetry, which is impossible for an ordinary periodic crystal (see crystallographic restriction theorem).
The International Union of Crystallography has redefined the term \"crystal\" to include both ordinary periodic crystals and quasicrystals (\"any solid having an essentially discrete diffraction diagram\").
Quasicrystals, first discovered in 1982, are quite rare in practice. Only about 100 solids are known to form quasicrystals, compared to about 400,000 periodic crystals known in 2004. The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for the discovery of quasicrystals.
## Special properties from anisotropy {#special_properties_from_anisotropy}
Crystals can have certain special electrical, optical, and mechanical properties that glass and polycrystals normally cannot. These properties are related to the anisotropy of the crystal, i.e. the lack of rotational symmetry in its atomic arrangement. One such property is the piezoelectric effect, where a voltage across the crystal can shrink or stretch it. Another is birefringence, where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including electrical conductivity, electrical permittivity, and Young\'s modulus, may be different in different directions in a crystal. For example, graphite crystals consist of a stack of sheets, and although each individual sheet is mechanically very strong, the sheets are rather loosely bound to each other. Therefore, the mechanical strength of the material is quite different depending on the direction of stress.
Not all crystals have all of these properties. Conversely, these properties are not quite exclusive to crystals. They can appear in glasses or polycrystals that have been made anisotropic by working or stress---for example, stress-induced birefringence.
## Crystallography
*Crystallography* is the science of measuring the crystal structure (in other words, the atomic arrangement) of a crystal. One widely used crystallography technique is X-ray diffraction. Large numbers of known crystal structures are stored in crystallographic databases.
## Image gallery {#image_gallery}
<File:Insulincrystals.jpg>\|Insulin crystals grown in earth orbit. The low gravity allows crystals to be grown with minimal defects. <File:Hoar> frost macro2.jpg\|Hoar frost: A type of ice crystal (picture taken from a distance of about 5 cm). <File:Gallium> crystals.jpg\|Gallium, a metal that easily forms large crystals. <File:Apatite-Rhodochrosite-Fluorite-169799.jpg%7CAn> apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes. <File:Monokristalines> Silizium für die Waferherstellung.jpg\|Boules of silicon, like this one, are an important type of industrially-produced single crystal. <File:Bornite-Chalcopyrite-Pyrite-180794.jpg%7CA> specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across. <File:Calcite-millerite> association.jpg\|Needle-like millerite crystals partially encased in calcite crystal and oxidized on their surfaces to zaratite; from the Devonian Milwaukee Formation of Wisconsin <File:Crystallized> sugar, multiple crystals and a single crystal grown from seed.jpg\|Crystallized sugar. Crystals on the right were grown from a sugar cube, while the left from a single seed crystal taken from the right. Red dye was added to the solution when growing the larger crystal, but, insoluble with the solid sugar, all but small traces were forced to precipitate out as it grew.
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Cytosine
|
**Cytosine** (`{{IPAc-en|ˈ|s|aɪ|t|ə|ˌ|s|iː|n|,_|-|ˌ|z|iː|n|,_|-|ˌ|s|ɪ|n}}`{=mediawiki}) (symbol **C** or **Cyt**) is one of the four nucleotide bases found in DNA and RNA, along with adenine, guanine, and thymine (uracil in RNA). It is a pyrimidine derivative, with a heterocyclic aromatic ring and two substituents attached (an amine group at position 4 and a keto group at position 2). The nucleoside of cytosine is cytidine. In Watson--Crick base pairing, it forms three hydrogen bonds with guanine.
## History
Cytosine was discovered and named by Albrecht Kossel and Albert Neumann in 1894 when it was hydrolyzed from calf thymus tissues. A structure was proposed in 1903, and was synthesized (and thus confirmed) in the laboratory in the same year.
In 1998, cytosine was used in an early demonstration of quantum information processing when Oxford University researchers implemented the Deutsch--Jozsa algorithm on a two qubit nuclear magnetic resonance quantum computer (NMRQC).
In March 2015, NASA scientists reported the formation of cytosine, along with uracil and thymine, from pyrimidine under the space-like laboratory conditions, which is of interest because pyrimidine has been found in meteorites although its origin is unknown.
## Chemical reactions {#chemical_reactions}
Cytosine can be found as part of DNA, as part of RNA, or as a part of a nucleotide. As cytidine triphosphate (CTP), it can act as a co-factor to enzymes, and can transfer a phosphate to convert adenosine diphosphate (ADP) to adenosine triphosphate (ATP).
In DNA and RNA, cytosine is paired with guanine. However, it is inherently unstable, and can change into uracil (spontaneous deamination). This can lead to a point mutation if not repaired by the DNA repair enzymes such as uracil glycosylase, which cleaves a uracil in DNA.
Cytosine can also be methylated into 5-methylcytosine by an enzyme called DNA methyltransferase or be methylated and hydroxylated to make 5-hydroxymethylcytosine. The difference in rates of deamination of cytosine and 5-methylcytosine (to uracil and thymine) forms the basis of bisulfite sequencing.
## Biological function {#biological_function}
When found third in a codon of RNA, cytosine is synonymous with uracil, as they are interchangeable as the third base. When found as the second base in a codon, the third is always interchangeable. For example, UCU, UCC, UCA and UCG are all serine, regardless of the third base.
Active enzymatic deamination of cytosine or 5-methylcytosine by the APOBEC family of cytosine deaminases could have both beneficial and detrimental implications on various cellular processes as well as on organismal evolution. The implications of deamination on 5-hydroxymethylcytosine, on the other hand, remains less understood.
## Theoretical aspects {#theoretical_aspects}
Until October 2021, Cytosine had not been found in meteorites, which suggested the first strands of RNA and DNA had to look elsewhere to obtain this building block. Cytosine likely formed within some meteorite parent bodies, however did not persist within these bodies due to an effective deamination reaction into uracil.
In October 2021, Cytosine was announced as having been found in meteorites by researchers in a joint Japan/NASA project, that used novel methods of detection which avoided damaging nucleotides as they were extracted from meteorites.
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Castle of the Winds
|
***Castle of the Winds*** is a tile-based roguelike video game for Microsoft Windows. It was developed by Rick Saada in 1989 and distributed by Epic MegaGames in 1993. The game was released around 1998 as a freeware download by the author. Though it is secondary to its hack and slash gameplay, *Castle of the Winds* has a plot loosely based on Norse mythology, told with setting changes, unique items, and occasional passages of text. The game is composed of two parts: ***A Question of Vengeance**\'\', released as shareware, and***Lifthransir\'s Bane**\'\', sold commercially. A combined license for both parts was also sold.
## Gameplay
The game differs from most roguelikes in a number of ways. Its interface is mouse-dependent, but supports keyboard shortcuts (such as \'g\' to get an item). *Castle of the Winds* also allows the player to restore saved games after dying.
The game favors the use of magic in combat, as spells are the only weapons that work from a distance. The player character automatically gains a spell with each experience level, and can permanently gain others using corresponding books, until all thirty spells available are learned. There are two opposing pairs of elements: cold vs. fire and lightning vs. acid/poison. Spells are divided into six categories: attack, defense, healing, movement, divination, and miscellaneous.
*Castle of the Winds* possesses an inventory system that limits a player\'s load based on weight and bulk, rather than by number of items. It allows the character to use different containers, including packs, belts, chests, and bags. Other items include weapons, armor, protective clothing, purses, and ornamental jewellery. Almost every item in the game can be normal, cursed, or enchanted, with curses and enchantments working in a manner similar to *NetHack*. Although items do not break with use, they may already be broken or rusted when found. Most objects that the character currently carries can be renamed.
Wherever the player goes before entering the dungeon, there is always a town which offers the basic services of a temple for healing and curing curses, a junk store where anything can be sold for a few copper coins, a sage who can identify items and (from the second town onwards) a bank for storing the total capacity of coins to lighten the player\'s load. Other services that differ and vary in what they sell are outfitters, weaponsmiths, armoursmiths, magic shops and general stores.
The game tracks how much time has been spent playing the game. Although story events are not triggered by the passage of time, it does determine when merchants rotate their stock. Victorious players are listed as \"Valhalla\'s Champions\" in the order of time taken, from fastest to slowest. If the player dies, they are still put on the list, but are categorized as \"Dead\", with their experience point total listed as at the final killing blow. The amount of time spent also determines the difficulty of the last boss.
## Plot
The player begins in a tiny hamlet, near which they used to live. Their farm has been destroyed and godparents killed. After clearing out an abandoned mine, the player finds a scrap of parchment that reveals the death of the player\'s godparents was ordered by an unknown enemy. The player then returns to the hamlet to find it pillaged, and decides to travel to Bjarnarhaven.
Once in Bjarnarhaven, the player explores the levels beneath a nearby fortress, eventually facing Hrungnir, the Hill Giant Lord, responsible for ordering the player\'s godparents\' death. Hrungnir carries the Enchanted Amulet of Kings. Upon activating the amulet, the player is informed of their past by their dead father, after which the player is transported to the town of Crossroads, and *Part I* ends. The game can be imported or started over in *Part II*.
The town of Crossroads is run by a Jarl who at first does not admit the player, but later (on up to three occasions) provides advice and rewards. The player then enters the nearby ruined titular Castle of the Winds. There the player meets his/her deceased grandfather, who instructs them to venture into the dungeons below, defeat Surtur, and reclaim their birthright. Venturing deeper, the player encounters monsters run rampant, a desecrated crypt, a necromancer, and the installation of various special rooms for elementals. The player eventually meets and defeats the Wolf-Man leader, Bear-Man leader, the four Jotun kings, a Demon Lord, and finally Surtur. Upon defeating Surtur and escaping the dungeons, the player sits upon the throne, completing the game.
## Development
Inspired by his love of RPGs and while learning Windows programming in the 80s, Rick Saada designed and completed *Castle of the Winds*. The game sold 13,500 copies. By 1998, the game\'s author, Rick Saada, decided to distribute the entirety of *Castle of the Winds* free of charge.
The game is public domain per Rick Saada\'s words: `{{Blockquote|Rick Saada, creator of ''Castle of the Winds'', decided to give permission for anyone to distribute it for free. Epic doesn't have an ''exclusive'' license to sell it.<ref name="odin-downloads"/>}}`{=mediawiki}
### Graphics
All terrain tiles, some landscape features, all monsters and objects, and some spell/effect graphics take the form of Windows 3.1 icons and were done by Paul Canniff. Multi-tile graphics, such as ball spells and town buildings, are bitmaps included in the executable file. No graphics use colors other than the Windows-standard 16-color palette, plus transparency. They exist in monochrome versions as well, meaning that the game will display well on monochrome monitors.
The map view is identical to the playing-field view, except for scaling to fit on one screen. A simplified map view is available to improve performance on slower computers. The latter functionality also presents a cleaner display, as the aforementioned scaling routine does not always work correctly.
## Reception
*Computer Gaming World* rated the gameplay as good and the graphics simple but effective, while noticing the lack of audio, but regarded the game itself enjoyable.
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6,026 |
Countable set
|
In mathematics, a set is **countable** if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is *countable* if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
In more technical terms, assuming the axiom of countable choice, a set is *countable* if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said to be **countably infinite**.
The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers.
## A note on terminology {#a_note_on_terminology}
Although the terms \"countable\" and \"countably infinite\" as defined here are quite common, the terminology is not universal. An alternative style uses *countable* to mean what is here called countably infinite, and *at most countable* to mean what is here called countable.
The terms *enumerable* and **denumerable** may also be used, e.g. referring to countable and countably infinite respectively, definitions vary and care is needed respecting the difference with recursively enumerable.
## Definition
A set $S$ is *countable* if:
- Its cardinality $|S|$ is less than or equal to $\aleph_0$ (aleph-null), the cardinality of the set of natural numbers $\N$.
- There exists an injective function from $S$ to $\N$.
- $S$ is empty or there exists a surjective function from $\N$ to $S$.
- There exists a bijective mapping between $S$ and a subset of $\N$.
- $S$ is either finite ($|S|<\aleph_0$) or countably infinite.
All of these definitions are equivalent.
A set $S$ is *countably infinite* if:
- Its cardinality $|S|$ is exactly $\aleph_0$.
- There is an injective and surjective (and therefore bijective) mapping between $S$ and $\N$.
- $S$ has a one-to-one correspondence with $\N$.
- The elements of $S$ can be arranged in an infinite sequence $a_0, a_1, a_2, \ldots$, where $a_i$ is distinct from $a_j$ for $i\neq j$ and every element of $S$ is listed.
A set is *uncountable* if it is not countable, i.e. its cardinality is greater than $\aleph_0$.
## History
In 1874, in his first set theory article, Cantor proved that the set of real numbers is uncountable, thus showing that not all infinite sets are countable. In 1878, he used one-to-one correspondences to define and compare cardinalities. In 1883, he extended the natural numbers with his infinite ordinals, and used sets of ordinals to produce an infinity of sets having different infinite cardinalities.
## Introduction
A *set* is a collection of *elements*, and may be described in many ways. One way is simply to list all of its elements; for example, the set consisting of the integers 3, 4, and 5 may be denoted $\{3, 4, 5\}$, called roster form. This is only effective for small sets, however; for larger sets, this would be time-consuming and error-prone. Instead of listing every single element, sometimes an ellipsis (\"\...\") is used to represent many elements between the starting element and the end element in a set, if the writer believes that the reader can easily guess what \... represents; for example, $\{1, 2, 3, \dots, 100\}$ presumably denotes the set of integers from 1 to 100. Even in this case, however, it is still *possible* to list all the elements, because the number of elements in the set is finite. If we number the elements of the set 1, 2, and so on, up to $n$, this gives us the usual definition of \"sets of size $n$\".
Some sets are *infinite*; these sets have more than $n$ elements where $n$ is any integer that can be specified. (No matter how large the specified integer $n$ is, such as $n=10^{1000}$, infinite sets have more than $n$ elements.) For example, the set of natural numbers, denotable by $\{0, 1, 2, 3, 4, 5,\dots\}$, has infinitely many elements, and we cannot use any natural number to give its size. It might seem natural to divide the sets into different classes: put all the sets containing one element together; all the sets containing two elements together; \...; finally, put together all infinite sets and consider them as having the same size. This view works well for countably infinite sets and was the prevailing assumption before Georg Cantor\'s work. For example, there are infinitely many odd integers, infinitely many even integers, and also infinitely many integers overall. We can consider all these sets to have the same \"size\" because we can arrange things such that, for every integer, there is a distinct even integer: $\ldots \, -\! 2\! \rightarrow \! - \! 4, \, -\! 1\! \rightarrow \! - \! 2, \, 0\! \rightarrow \! 0, \, 1\! \rightarrow \! 2, \, 2\! \rightarrow \! 4 \, \cdots$ or, more generally, $n \rightarrow 2n$ (see picture). What we have done here is arrange the integers and the even integers into a *one-to-one correspondence* (or *bijection*), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set. This mathematical notion of \"size\", cardinality, is that two sets are of the same size if and only if there is a bijection between them. We call all sets that are in one-to-one correspondence with the integers *countably infinite* and say they have cardinality $\aleph_0$.
Georg Cantor showed that not all infinite sets are countably infinite. For example, the real numbers cannot be put into one-to-one correspondence with the natural numbers (non-negative integers). The set of real numbers has a greater cardinality than the set of natural numbers and is said to be uncountable.
## Formal overview {#formal_overview}
By definition, a set $S$ is *countable* if there exists a bijection between $S$ and a subset of the natural numbers $\N=\{0,1,2,\dots\}$. For example, define the correspondence $a \leftrightarrow 1,\ b \leftrightarrow 2,\ c \leftrightarrow 3$ Since every element of $S=\{a,b,c\}$ is paired with *precisely one* element of $\{1,2,3\}$, *and* vice versa, this defines a bijection, and shows that $S$ is countable. Similarly we can show all finite sets are countable.
As for the case of infinite sets, a set $S$ is countably infinite if there is a bijection between $S$ and all of $\N$. As examples, consider the sets $A=\{1,2,3,\dots\}$, the set of positive integers, and $B=\{0,2,4,6,\dots\}$, the set of even integers. We can show these sets are countably infinite by exhibiting a bijection to the natural numbers. This can be achieved using the assignments $n \leftrightarrow n+1$ and $n \leftrightarrow 2n$, so that $\begin{matrix}
0 \leftrightarrow 1, & 1 \leftrightarrow 2, & 2 \leftrightarrow 3, & 3 \leftrightarrow 4, & 4 \leftrightarrow 5, & \ldots \\[6pt]
0 \leftrightarrow 0, & 1 \leftrightarrow 2, & 2 \leftrightarrow 4, & 3 \leftrightarrow 6, & 4 \leftrightarrow 8, & \ldots
\end{matrix}$ Every countably infinite set is countable, and every infinite countable set is countably infinite. Furthermore, any subset of the natural numbers is countable, and more generally: `{{math theorem | math_statement = A subset of a countable set is countable.<ref>{{harvnb|Halmos|1960|page=91}}</ref>}}`{=mediawiki}
The set of all ordered pairs of natural numbers (the Cartesian product of two sets of natural numbers, $\N\times\N$ is countably infinite, as can be seen by following a path like the one in the picture: The resulting mapping proceeds as follows: $0 \leftrightarrow (0, 0), 1 \leftrightarrow (1, 0), 2 \leftrightarrow (0, 1), 3 \leftrightarrow (2, 0), 4 \leftrightarrow (1, 1), 5 \leftrightarrow (0, 2), 6 \leftrightarrow (3, 0), \ldots$ This mapping covers all such ordered pairs.
This form of triangular mapping recursively generalizes to $n$-tuples of natural numbers, i.e., $(a_1,a_2,a_3,\dots,a_n)$ where $a_i$ and $n$ are natural numbers, by repeatedly mapping the first two elements of an $n$-tuple to a natural number. For example, $(0, 2, 3)$ can be written as $((0, 2), 3)$. Then $(0, 2)$ maps to 5 so $((0, 2), 3)$ maps to $(5, 3)$, then $(5, 3)$ maps to 39. Since a different 2-tuple, that is a pair such as $(a,b)$, maps to a different natural number, a difference between two n-tuples by a single element is enough to ensure the n-tuples being mapped to different natural numbers. So, an injection from the set of $n$-tuples to the set of natural numbers $\N$ is proved. For the set of $n$-tuples made by the Cartesian product of finitely many different sets, each element in each tuple has the correspondence to a natural number, so every tuple can be written in natural numbers then the same logic is applied to prove the theorem.
The set of all integers $\Z$ and the set of all rational numbers $\Q$ may intuitively seem much bigger than $\N$. But looks can be deceiving. If a pair is treated as the numerator and denominator of a vulgar fraction (a fraction in the form of $a/b$ where $a$ and $b\neq 0$ are integers), then for every positive fraction, we can come up with a distinct natural number corresponding to it. This representation also includes the natural numbers, since every natural number $n$ is also a fraction $n/1$. So we can conclude that there are exactly as many positive rational numbers as there are positive integers. This is also true for all rational numbers, as can be seen below.
In a similar manner, the set of algebraic numbers is countable.\^{a_n}, where $p_n$ is the $n$-th prime.}}
Sometimes more than one mapping is useful: a set $A$ to be shown as countable is one-to-one mapped (injection) to another set $B$, then $A$ is proved as countable if $B$ is one-to-one mapped to the set of natural numbers. For example, the set of positive rational numbers can easily be one-to-one mapped to the set of natural number pairs (2-tuples) because $p/q$ maps to $(p,q)$. Since the set of natural number pairs is one-to-one mapped (actually one-to-one correspondence or bijection) to the set of natural numbers as shown above, the positive rational number set is proved as countable.
With the foresight of knowing that there are uncountable sets, we can wonder whether or not this last result can be pushed any further. The answer is \"yes\" and \"no\", we can extend it, but we need to assume a new axiom to do so.
For example, given countable sets $\textbf{a},\textbf{b},\textbf{c},\dots$, we first assign each element of each set a tuple, then we assign each tuple an index using a variant of the triangular enumeration we saw above: $\begin{array}{ c|c|c }
\text{Index} & \text{Tuple} & \text {Element} \\ \hline
0 & (0,0) & \textbf{a}_0 \\
1 & (0,1) & \textbf{a}_1 \\
2 & (1,0) & \textbf{b}_0 \\
3 & (0,2) & \textbf{a}_2 \\
4 & (1,1) & \textbf{b}_1 \\
5 & (2,0) & \textbf{c}_0 \\
6 & (0,3) & \textbf{a}_3 \\
7 & (1,2) & \textbf{b}_2 \\
8 & (2,1) & \textbf{c}_1 \\
9 & (3,0) & \textbf{d}_0 \\
10 & (0,4) & \textbf{a}_4 \\
\vdots & &
\end{array}$
We need the axiom of countable choice to index *all* the sets $\textbf{a},\textbf{b},\textbf{c},\dots$ simultaneously.
This set is the union of the length-1 sequences, the length-2 sequences, the length-3 sequences, and so on, each of which is a countable set (finite Cartesian product). Thus the set is a countable union of countable sets, which is countable by the previous theorem.
The elements of any finite subset can be ordered into a finite sequence. There are only countably many finite sequences, so also there are only countably many finite subsets.
These follow from the definitions of countable set as injective / surjective functions.
**Cantor\'s theorem** asserts that if $A$ is a set and $\mathcal{P}(A)$ is its power set, i.e. the set of all subsets of $A$, then there is no surjective function from $A$ to $\mathcal{P}(A)$. A proof is given in the article Cantor\'s theorem. As an immediate consequence of this and the Basic Theorem above we have: `{{math theorem | name = Proposition | math_statement = The set <math>\mathcal{P}(\N)</math> is not countable; i.e. it is [[uncountable]].}}`{=mediawiki}
For an elaboration of this result see Cantor\'s diagonal argument.
The set of real numbers is uncountable, and so is the set of all infinite sequences of natural numbers.
## Minimal model of set theory is countable {#minimal_model_of_set_theory_is_countable}
If there is a set that is a standard model (see inner model) of ZFC set theory, then there is a minimal standard model (see Constructible universe). The Löwenheim--Skolem theorem can be used to show that this minimal model is countable. The fact that the notion of \"uncountability\" makes sense even in this model, and in particular that this model *M* contains elements that are:
- subsets of *M*, hence countable,
- but uncountable from the point of view of *M*,
was seen as paradoxical in the early days of set theory; see Skolem\'s paradox for more.
The minimal standard model includes all the algebraic numbers and all effectively computable transcendental numbers, as well as many other kinds of numbers.
## Total orders {#total_orders}
Countable sets can be totally ordered in various ways, for example:
- Well-orders (see also ordinal number):
- The usual order of natural numbers (0, 1, 2, 3, 4, 5, \...)
- The integers in the order (0, 1, 2, 3, \...; −1, −2, −3, \...)
- Other (*not* well orders):
- The usual order of integers (\..., −3, −2, −1, 0, 1, 2, 3, \...)
- The usual order of rational numbers (Cannot be explicitly written as an ordered list!)
In both examples of well orders here, any subset has a *least element*; and in both examples of non-well orders, *some* subsets do not have a *least element*. This is the key definition that determines whether a total order is also a well order.
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6,047 |
Consul
|
**Consul** (abbrev. *cos.*; Latin plural *consules*) was the title of one of the two chief magistrates of the Roman Republic, and subsequently also an important title under the Roman Empire. The title was used in other European city-states through antiquity and the Middle Ages, in particular in the Republics of Genoa and Pisa, then revived in modern states, notably in the First French Republic. The related adjective is **consular**, from the Latin *consularis*.
This usage contrasts with modern terminology, where a consul is a type of diplomat.
## Roman consul {#roman_consul}
A consul held the highest elected political office of the Roman Republic (509 to 27 BC), and ancient Romans considered the consulship the highest level of the *cursus honorum* (an ascending sequence of public offices to which politicians aspired). Consuls were elected to office and held power for one year. There were always two consuls in power at any time.
## Other uses in antiquity {#other_uses_in_antiquity}
### Private sphere {#private_sphere}
It was not uncommon for an organization under Roman private law to copy the terminology of state and city institutions for its own statutory agents. The founding statute, or contract, of such an organisation was called *lex*, \'law\'. The people elected each year were patricians, members of the upper class.
### City-states {#city_states}
While many cities, including the Gallic states and the Carthaginian Republic, had a double-headed chief magistracy, another title was often used, such as the Punic *sufet*, *Duumvir*, or native styles like *Meddix*.
## Medieval city-states, communes and municipalities {#medieval_city_states_communes_and_municipalities}
### Republic of Genoa {#republic_of_genoa}
The city-state of Genoa, unlike ancient Rome, bestowed the title of *consul* on various state officials, not necessarily restricted to the highest. Among these were Genoese officials stationed in various Mediterranean ports, whose role included helping Genoese merchants and sailors in difficulties with the local authorities. Great Britain reciprocated by appointing consuls to Genoa from 1722. This institution, with its name, was later emulated by other powers and is reflected in the modern usage of the word (see Consul (representative)).
### Republic of Pisa {#republic_of_pisa}
In addition to the Genoese Republic, the Republic of Pisa also took the form of \"Consul\" in the early stages of its government. The Consulate of the Republic of Pisa was the major government institution present in Pisa from 1087 to 1189. Despite losing space within the government since 1190 in favor of the Podestà, for some periods of the 13th century some citizens were again elected as consuls.
### Other uses in the Medieval period {#other_uses_in_the_medieval_period}
Throughout most of southern France, a consul (*consul* or **consule**) was an office equivalent to the `{{Interlanguage link multi|Échevin (France)|fr|3=Échevin|lt=échevins}}`{=mediawiki} of the north and roughly similar with English aldermen. The most prominent were those of Bordeaux and Toulouse, which came to be known as jurats and capitouls, respectively. The capitouls of Toulouse were granted transmittable nobility. In many other smaller towns the first consul was the equivalent of a mayor today, assisted by a variable number of secondary consuls and jurats. His main task was to levy and collect tax.
The Dukes of Gaeta often used also the title of \"consul\" in its Greek form \"Hypatos\" (see List of Hypati and Dukes of Gaeta).
## French Revolution {#french_revolution}
### French Republic 1799--1804 {#french_republic_17991804}
After Napoleon Bonaparte staged a coup against the Directory government in November 1799, the French Republic adopted a constitution which conferred executive powers upon three consuls, elected for a period of ten years. In reality, the first consul, Bonaparte, dominated his two colleagues and held supreme power, soon making himself consul for life (1802) and eventually, in 1804, emperor.
The office was held by:
- Napoleon Bonaparte, Emmanuel-Joseph Sieyès, Roger Ducos, provisional consuls (10 November -- 12 December 1799)
- Napoleon Bonaparte (first consul), Jean-Jacques Cambacérès (second consul), Charles-François Lebrun (third consul), consuls (12 December 1799 -- 18 May 1804)
### Bolognese Republic, 1796 {#bolognese_republic_1796}
The short-lived Bolognese Republic, proclaimed in 1796 as a French client republic in the Central Italian city of Bologna, had a government consisting of nine consuls and its head of state was the *Presidente del Magistrato*, i.e., chief magistrate, a presiding office held for four months by one of the consuls. Bologna already had consuls at some parts of its Medieval history.
### Roman Republic, 1798--1800 {#roman_republic_17981800}
The French-sponsored Roman Republic (15 February 1798 -- 23 June 1800) was headed by multiple consuls:
- Francesco Riganti, Carlo Luigi Costantini, Duke Bonelli-Crescenzi, Antonio Bassi, Gioacchino Pessuti, Angelo Stampa, Domenico Maggi, provisional consuls (15 February -- 20 March 1798)
- Liborio Angelucci, Giacomo De Mattheis, Panazzi, Reppi, Ennio Quirino Visconti, consuls (20 March -- September 1798)
- Brigi, Calisti, Francesco Pierelli, Giuseppe Rey, Federico Maria Domenico Michele, Zaccaleoni, consuls (September -- 24 July 1799)
Consular rule was interrupted by the Neapolitan occupation (27 November -- 12 December 1798), which installed a Provisional Government:
- Prince Giambattista Borghese, Prince Paolo-Maria Aldobrandini, Prince Gibrielli, Marchese Camillo Massimo, Giovanni Ricci (29 November 1798 - 12 December 1798)
Rome was occupied by France (11 July -- 28 September 1799) and again by Naples (30 September 1799 -- 23 June 1800), bringing an end to the Roman Republic.
## Revolutionary Greece, 1821 {#revolutionary_greece_1821}
Among the many petty local republics that were formed during the first year of the Greek Revolution, prior to the creation of a unified Provisional Government at the First National Assembly at Epidaurus, were:
- The Consulate of Argos (from 26 May 1821, under the Senate of the Peloponnese) had a *single* head of state, styled consul, 28 March 1821 -- 26 May 1821: Stamatellos Antonopoulos
- The Consulate of East Greece (Livadeia) (from 15 November 1821, under the Areopagus of East Greece) was headed 1 April 1821 -- 15 November 1821 by three consuls: Lambros Nakos, Ioannis Logothetis & Ioannis Filon
*Note: in Greek, the term for \"consul\" is \"hypatos\" (ὕπατος), which translates as \"supreme one\", and hence does not necessarily imply a joint office.*
## Paraguay, 1813--1844 {#paraguay_18131844}
In between a series of juntas and various other short-lived regimes, the young republic was governed by \"consuls of the republic\", with two consuls alternating in power every 4 months:
- 12 October 1813 -- 12 February 1814, José Gaspar Rodríguez de Francia y Velasco
- 12 February 1814 -- 12 June 1814, Fulgencio Yegros y Franco de Torres
- 12 June 1814 -- 3 October 1814, José Gaspar Rodríguez de Francia y Velasco; he stayed on as \"supreme dictator\" 3 October 1814 -- 20 September 1840 (from 6 June 1816 styled \"perpetual supreme dictator\")
After a few presidents of the Provisional Junta, there were again consuls of the republic, 14 March 1841 -- 13 March 1844 (ruling jointly, but occasionally styled \"first consul\", \"second consul\"): Carlos Antonio López Ynsfrán (b. 1792 -- d. 1862) + Mariano Roque Alonzo Romero (d. 1853) (the lasts of the aforementioned juntistas, Commandant-General of the Army) Thereafter all republican rulers were styled \"president\".
## Modern uses of the term {#modern_uses_of_the_term}
In modern terminology, a consul is a type of diplomat. The *American Heritage Dictionary* defines **consul** as \"an official appointed by a government to reside in a foreign country and represent its interests there.\" *The Devil\'s Dictionary* defines **Consul** as \"in American politics, a person who having failed to secure an office from the people is given one by the Administration on condition that he leave the country\".
In most governments, the consul is the head of the consular section of an embassy, and is responsible for all consular services such as immigrant and non-immigrant visas, passports, and citizen services for expatriates living or traveling in the host country.
A less common modern usage is when the consul of one country takes a governing role in the host country.
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6,050 |
List of equations in classical mechanics
|
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of reference. The point of concurrency of the three axes is known as the origin of the particular space.
Classical mechanics utilises many equations---as well as other mathematical concepts---which relate various physical quantities to one another. These include differential equations, manifolds, Lie groups, and ergodic theory. This article gives a summary of the most important of these.
This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics).
## Classical mechanics {#classical_mechanics}
### Mass and inertia {#mass_and_inertia}
+--------------------------------------------------------+----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------+-----------+
| Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
+========================================================+==============================================================================================+=================================================================================================================================================================================+===========================+===========+
| Linear, surface, volumetric mass density | *λ* or *μ* (especially in acoustics, see below) for Linear, *σ* for surface, *ρ* for volume. | $m = \int \lambda \, \mathrm{d} \ell$ $m = \iint \sigma \, \mathrm{d} S$ | kg m^−*n*^, *n* = 1, 2, 3 | M L^−*n*^ |
| | | | | |
| | | $m = \iiint \rho \, \mathrm{d} V$ | | |
+--------------------------------------------------------+----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------+-----------+
| Moment of mass`{{Anchor|Moment of mass}}`{=mediawiki} | **m** (No common symbol) | Point mass: $\mathbf{m} = \mathbf{r}m$ | kg m | M L |
| | | | | |
| | | Discrete masses about an axis $x_i$: $\mathbf{m} = \sum_{i=1}^N \mathbf{r}_i m_i$ | | |
| | | | | |
| | | Continuum of mass about an axis $x_i$: $\mathbf{m} = \int \rho \left ( \mathbf{r} \right ) x_i \mathrm{d} \mathbf{r}$ | | |
+--------------------------------------------------------+----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------+-----------+
| Center of mass | **r**~com~ (Symbols vary) | *i*-th moment of mass $\mathbf{m}_i = \mathbf{r}_i m_i$ | m | L |
| | | | | |
| | | Discrete masses: $\mathbf{r}_\mathrm{com} = \frac{1}{M} \sum_i \mathbf{r}_i m_i = \frac{1}{M} \sum_i \mathbf{m}_i$ | | |
| | | | | |
| | | Mass continuum: $\mathbf{r}_\mathrm{com} = \frac{1}{M} \int \mathrm{d}\mathbf{m} = \frac{1}{M} \int \mathbf{r} \, \mathrm{d}m = \frac{1}{M}\int \mathbf{r} \rho \, \mathrm{d}V$ | | |
+--------------------------------------------------------+----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------+-----------+
| 2-Body reduced mass | *m*~12~, *μ* Pair of masses = *m*~1~ and *m*~2~ | $\mu = \frac{m_1 m_2}{m_1 + m_2}$ | kg | M |
+--------------------------------------------------------+----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------+-----------+
| Moment of inertia (MOI) | *I* | Discrete Masses: $I = \sum_i \mathbf{m}_i \cdot \mathbf{r}_i = \sum_i \left | \mathbf{r}_i \right | ^2 m$ | kg m^2^ | M L^2^ |
| | | | | |
| | | Mass continuum: $I = \int \left | \mathbf{r} \right | ^2 \mathrm{d} m = \int \mathbf{r} \cdot \mathrm{d} \mathbf{m} = \int \left | \mathbf{r} \right | ^2 \rho \, \mathrm{d}V$ | | |
+--------------------------------------------------------+----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------+-----------+
### Derived kinematic quantities {#derived_kinematic_quantities}
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension
-------------------------- ------------------- ------------------------------------------------------------------------------------------------------------------------------------------- ----------- -----------
Velocity **v** $\mathbf{v} = \frac{\mathrm{d} \mathbf{r}}{\mathrm{d} t}$ m s^−1^ L T^−1^
Acceleration **a** $\mathbf{a} = \frac{\mathrm{d} \mathbf{v}}{\mathrm{d} t} = \frac{\mathrm{d}^2 \mathbf{r}}{\mathrm{d} t^2 }$ m s^−2^ L T^−2^
Jerk **j** $\mathbf{j} = \frac{\mathrm{d} \mathbf{a}}{\mathrm{d} t} = \frac{\mathrm{d}^3 \mathbf{r}}{\mathrm{d} t^3}$ m s^−3^ L T^−3^
Jounce **s** $\mathbf{s} = \frac{\mathrm{d} \mathbf{j}}{\mathrm{d} t} = \frac{\mathrm{d}^4 \mathbf{r}}{\mathrm{d} t^4}$ m s^−4^ L T^−4^
Angular velocity **ω** $\boldsymbol{\omega} = \mathbf{\hat{n}} \frac{ \mathrm{d} \theta }{\mathrm{d} t}$ rad s^−1^ T^−1^
Angular Acceleration **α** $\boldsymbol{\alpha} = \frac{\mathrm{d} \boldsymbol{\omega}}{\mathrm{d} t} = \mathbf{\hat{n}} \frac{\mathrm{d}^2 \theta}{\mathrm{d} t^2}$ rad s^−2^ T^−2^
Angular jerk **ζ** $\boldsymbol{\zeta} = \frac{\mathrm{d} \boldsymbol{\alpha}}{\mathrm{d} t} = \mathbf{\hat{n}} \frac{ \mathrm{d}^3 \theta}{\mathrm{d} t^3}$ rad s^−3^ T^−3^
### Derived dynamic quantities {#derived_dynamic_quantities}
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
| Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
+===========================================================+===========================+=================================================================================================================================+=====================+==============+
| Momentum | **p** | $\mathbf{p} = m\mathbf{v}$ | kg m s^−1^ | M L T^−1^ |
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
| Force | **F** | $\mathbf{F} = \mathrm{d} \mathbf{p}/\mathrm{d} t$ | N = kg m s^−2^ | M L T^−2^ |
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
| Impulse | **J**, Δ**p**, **I** | $\mathbf{J} = \Delta \mathbf{p} = \int_{t_1}^{t_2} \mathbf{F} \, \mathrm{d} t$ | kg m s^−1^ | M L T^−1^ |
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
| Angular momentum about a position point **r**~0~, | **L**, **J**, **S** | $\mathbf{L} = \left ( \mathbf{r} - \mathbf{r}_0 \right ) \times \mathbf{p}$ | kg m^2^ s^−1^ | M L^2^ T^−1^ |
| | | | | |
| | | Most of the time we can set **r**~0~ = **0** if particles are orbiting about axes intersecting at a common point. | | |
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
| Moment of a force about a position point **r**~0~, Torque | **τ**, **M** | $\boldsymbol{\tau} = \left ( \mathbf{r} - \mathbf{r}_0 \right ) \times \mathbf{F} = \frac{\mathrm{d} \mathbf{L}}{\mathrm{d} t}$ | N m = kg m^2^ s^−2^ | M L^2^ T^−2^ |
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
| Angular impulse | Δ**L** (no common symbol) | $\Delta \mathbf{L} = \int_{t_1}^{t_2} \boldsymbol{\tau} \, \mathrm{d} t$ | kg m^2^ s^−1^ | M L^2^ T^−1^ |
+-----------------------------------------------------------+---------------------------+---------------------------------------------------------------------------------------------------------------------------------+---------------------+--------------+
### General energy definitions {#general_energy_definitions}
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension
---------------------------------------------- -------------------------- ----------------------------------------------------- ------------------------- --------------
Mechanical work due to a Resultant Force *W* $W = \int_C \mathbf{F} \cdot \mathrm{d} \mathbf{r}$ J = N m = kg m^2^ s^−2^ M L^2^ T^−2^
Work done ON mechanical system, Work done BY *W*~ON~, *W*~BY~ $\Delta W_\mathrm{ON} = - \Delta W_\mathrm{BY}$ J = N m = kg m^2^ s^−2^ M L^2^ T^−2^
Potential energy *φ*, Φ, *U*, *V*, *E~p~* $\Delta W = - \Delta V$ J = N m = kg m^2^ s^−2^ M L^2^ T^−2^
Mechanical power *P* $P = \frac{\mathrm{d}E}{\mathrm{d}t}$ W = J s^−1^ M L^2^ T^−3^
Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to *U*:
- Wherever the force is zero, its potential energy is defined to be zero as well.
- Whenever the force does work, potential energy is lost.
### Generalized mechanics {#generalized_mechanics}
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
+========================================+==================================+===================================================================================================================================+====================+====================+
| Generalized coordinates | *q, Q* | | varies with choice | varies with choice |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Generalized velocities | $\dot{q},\dot{Q}$ | $\dot{q}\equiv \mathrm{d}q/\mathrm{d}t$ | varies with choice | varies with choice |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Generalized momenta | *p, P* | $p = \partial L /\partial \dot{q}$ | varies with choice | varies with choice |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Lagrangian | *L* | $L(\mathbf{q},\mathbf{\dot{q}},t) = T(\mathbf{\dot{q}}) - V(\mathbf{q},\mathbf{\dot{q}},t)$ | J | M L^2^ T^−2^ |
| | | | | |
| | | where $\mathbf{q} = \mathbf{q}(t)$ and **p** = **p**(*t*) are vectors of the generalized coords and momenta, as functions of time | | |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Hamiltonian | *H* | $H(\mathbf{p},\mathbf{q},t) = \mathbf{p}\cdot\mathbf{\dot{q}} - L(\mathbf{q},\mathbf{\dot{q}},t)$ | J | M L^2^ T^−2^ |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Action, Hamilton\'s principal function | *S*, $\scriptstyle{\mathcal{S}}$ | $\mathcal{S} = \int_{t_1}^{t_2} L(\mathbf{q},\mathbf{\dot{q}},t) \mathrm{d}t$ | J s | M L^2^ T^−1^ |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
## Kinematics
In the following rotational definitions, the angle can be any angle about the specified axis of rotation. It is customary to use *θ*, but this does not have to be the polar angle used in polar coordinate systems. The unit axial vector
$\mathbf{\hat{n}} = \mathbf{\hat{e}}_r\times\mathbf{\hat{e}}_\theta$
defines the axis of rotation, $\scriptstyle \mathbf{\hat{e}}_r$ = unit vector in direction of `{{math|'''r'''}}`{=mediawiki}, $\scriptstyle \mathbf{\hat{e}}_\theta$ = unit vector tangential to the angle.
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | Translation | Rotation |
+==============+=================================================================================================+====================================================================================================================================================================================+
| Velocity | Average: $\mathbf{v}_{\mathrm{average}} = {\Delta \mathbf{r} \over \Delta t}$ Instantaneous: | Angular velocity$\boldsymbol{\omega} = \mathbf{\hat{n}}\frac{{\rm d} \theta}{{\rm d} t}$Rotating rigid body$$\mathbf{v} = \boldsymbol{\omega} \times \mathbf{r}$$ |
| | | |
| | $\mathbf{v} = {d\mathbf{r} \over dt}$ | |
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Acceleration | Average: $\mathbf{a}_{\mathrm{average}} = \frac{\Delta\mathbf{v}}{\Delta t}$ | Angular acceleration |
| | | |
| | Instantaneous: | $\boldsymbol{\alpha} = \frac{{\rm d} \boldsymbol{\omega}}{{\rm d} t} = \mathbf{\hat{n}}\frac{{\rm d}^2 \theta}{{\rm d} t^2}$ |
| | | |
| | $\mathbf{a} = \frac{d\mathbf{v}}{dt} = \frac{d^2\mathbf{r}}{dt^2}$ | Rotating rigid body: |
| | | |
| | | $\mathbf{a} = \boldsymbol{\alpha} \times \mathbf{r} + \boldsymbol{\omega} \times \mathbf{v}$ |
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Jerk | Average: $\mathbf{j}_{\mathrm{average}} = \frac{\Delta\mathbf{a}}{\Delta t}$ | Angular jerk |
| | | |
| | Instantaneous: | $\boldsymbol{\zeta} = \frac{{\rm d} \boldsymbol{\alpha}}{{\rm d} t} = \mathbf{\hat{n}}\frac{{\rm d}^2 \omega}{{\rm d} t^2} = \mathbf{\hat{n}}\frac{{\rm d}^3 \theta}{{\rm d} t^3}$ |
| | | |
| | $\mathbf{j} = \frac{d\mathbf{a}}{dt} = \frac{d^2\mathbf{v}}{dt^2} = \frac{d^3\mathbf{r}}{dt^3}$ | Rotating rigid body: |
| | | |
| | | $\mathbf{j} = \boldsymbol{\zeta} \times \mathbf{r} + \boldsymbol{\alpha} \times \mathbf{a}$ |
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
## Dynamics
+-----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------+
| | Translation | Rotation |
+=============================+===============================================================================================================================================================================================================================================+========================================================================================================================================================+
| Momentum | Momentum is the \"amount of translation\" | Angular momentum |
| | | |
| | $\mathbf{p} = m\mathbf{v}$ | Angular momentum is the \"amount of rotation\": |
| | | |
| | For a rotating rigid body: | $\mathbf{L} = \mathbf{r} \times \mathbf{p} = \mathbf{I} \cdot \boldsymbol{\omega}$ |
| | | |
| | $\mathbf{p} = \boldsymbol{\omega} \times \mathbf{m}$ | and the cross-product is a pseudovector i.e. if **r** and **p** are reversed in direction (negative), **L** is not. |
| | | |
| | | In general **I** is an order-2 tensor, see above for its components. The dot **·** indicates tensor contraction. |
+-----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------+
| Force and Newton\'s 2nd law | Resultant force acts on a system at the center of mass, equal to the rate of change of momentum: | Torque |
| | | |
| | $\begin{align} \mathbf{F} & = \frac{d\mathbf{p}}{dt} = \frac{d(m\mathbf{v})}{dt} \\ | Torque **τ** is also called moment of a force, because it is the rotational analogue to force: |
| | & = m\mathbf{a} + \mathbf{v}\frac{{\rm d}m}{{\rm d}t} \\ | |
| | \end{align}$ | $\boldsymbol{\tau} = \frac{{\rm d}\mathbf{L}}{{\rm d}t} = \mathbf{r}\times\mathbf{F} = \frac{{\rm d}(\mathbf{I} \cdot \boldsymbol{\omega})}{{\rm d}t}$ |
| | | |
| | For a number of particles, the equation of motion for one particle *i* is: | For rigid bodies, Newton\'s 2nd law for rotation takes the same form as for translation: |
| | | |
| | $\frac{\mathrm{d}\mathbf{p}_i}{\mathrm{d}t} = \mathbf{F}_{E} + \sum_{i \neq j} \mathbf{F}_{ij}$ | $\begin{align} |
| | | \boldsymbol{\tau} & = \frac{{\rm d}\mathbf{L}}{{\rm d}t} = \frac{{\rm d}(\mathbf{I}\cdot\boldsymbol{\omega})}{{\rm d}t} \\ |
| | where **p**~*i*~ = momentum of particle *i*, **F**~*ij*~ = force ***on*** particle *i* ***by*** particle *j*, and **F**~*E*~ = resultant external force (due to any agent not part of system). Particle *i* does not exert a force on itself. | & = \frac{{\rm d}\mathbf{I}}{{\rm d}t}\cdot\boldsymbol{\omega} + \mathbf{I}\cdot\boldsymbol{\alpha} \\ |
| | | \end{align}$ |
| | | |
| | | Likewise, for a number of particles, the equation of motion for one particle *i* is: |
| | | |
| | | $\frac{\mathrm{d}\mathbf{L}_i}{\mathrm{d}t} = \boldsymbol{\tau}_E + \sum_{i \neq j} \boldsymbol{\tau}_{ij}$ \|- valign=\"top\"\|-valign=\"top\" |
+-----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------+
### Precession
The precession angular speed of a spinning top is given by:
$\boldsymbol{\Omega} = \frac{wr}{I\boldsymbol{\omega}}$
where *w* is the weight of the spinning flywheel.
## Energy
The mechanical work done by an external agent on a system is equal to the change in kinetic energy of the system:
### General work-energy theorem (translation and rotation) {#general_work_energy_theorem_translation_and_rotation}
The work done *W* by an external agent which exerts a force **F** (at **r**) and torque **τ** on an object along a curved path *C* is:
$W = \Delta T = \int_C \left ( \mathbf{F} \cdot \mathrm{d} \mathbf{r} + \boldsymbol{\tau} \cdot \mathbf{n} \, {\mathrm{d} \theta} \right )$
where θ is the angle of rotation about an axis defined by a unit vector **n**.
### Kinetic energy {#kinetic_energy}
The change in kinetic energy for an object initially traveling at speed $v_0$ and later at speed $v$ is: $\Delta E_k = W = \frac{1}{2} m(v^2 - {v_0}^2)$
### Elastic potential energy {#elastic_potential_energy}
For a stretched spring fixed at one end obeying Hooke\'s law, the elastic potential energy is
$\Delta E_p = \frac{1}{2} k(r_2-r_1)^2$
where *r*~2~ and *r*~1~ are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
## Euler\'s equations for rigid body dynamics {#eulers_equations_for_rigid_body_dynamics}
Euler also worked out analogous laws of motion to those of Newton, see Euler\'s laws of motion. These extend the scope of Newton\'s laws to rigid bodies, but are essentially the same as above. A new equation Euler formulated is:
$\mathbf{I} \cdot \boldsymbol{\alpha} + \boldsymbol{\omega} \times \left ( \mathbf{I} \cdot \boldsymbol{\omega} \right ) = \boldsymbol{\tau}$
where **I** is the moment of inertia tensor.
## General planar motion {#general_planar_motion}
The previous equations for planar motion can be used here: corollaries of momentum, angular momentum etc. can immediately follow by applying the above definitions. For any object moving in any path in a plane,
$\mathbf{r} = \mathbf{r}(t) = r\hat\mathbf r$
the following general results apply to the particle.
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Kinematics | Dynamics |
+==================================================================================================================================================================================+===========================================================================================================================================+
| Position $\mathbf{r} =\mathbf{r}\left ( r,\theta, t \right ) = r \hat\mathbf r$ | |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Velocity | Momentum $\mathbf{p} = m \left(\hat\mathbf r \frac{\mathrm{d} r}{\mathrm{d}t} + r \omega \hat\mathbf\theta \right)$ |
| | |
| $\mathbf{v} = \hat\mathbf r \frac{\mathrm{d} r}{\mathrm{d}t} + r \omega \hat\mathbf\theta$ | Angular momenta $\mathbf{L} = m \mathbf{r}\times \left(\hat\mathbf{r} \frac{\mathrm{d} r}{\mathrm{d}t} + r\omega\hat\mathbf\theta\right)$ |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Acceleration | The centripetal force is |
| | |
| $\mathbf{a} =\left ( \frac{\mathrm{d}^2 r}{\mathrm{d}t^2} - r\omega^2\right )\hat\mathbf r + \left ( r \alpha + 2 \omega \frac{\mathrm{d}r}{{\rm d}t} \right )\hat\mathbf\theta$ | $\mathbf{F}_\bot = - m \omega^2 R \hat\mathbf r= - \omega^2 \mathbf{m}$ |
| | |
| | where again **m** is the mass moment, and the Coriolis force is |
| | |
| | $\mathbf{F}_c = 2\omega m \frac{{\rm d}r}{{\rm d}t} \hat\mathbf\theta = 2\omega m v \hat\mathbf\theta$ |
| | |
| | The Coriolis acceleration and force can also be written: |
| | |
| | $\mathbf{F}_c = m\mathbf{a}_c = -2 m \boldsymbol{ \omega \times v}$ |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
### Central force motion {#central_force_motion}
For a massive body moving in a central potential due to another object, which depends only on the radial separation between the centers of masses of the two objects, the equation of motion is:
$\frac{d^2}{d\theta^2}\left(\frac{1}{\mathbf{r}}\right) + \frac{1}{\mathbf{r}} = -\frac{\mu\mathbf{r}^2}{\mathbf{l}^2}\mathbf{F}(\mathbf{r})$
## Equations of motion (constant acceleration) {#equations_of_motion_constant_acceleration}
These equations can be used only when acceleration is constant. If acceleration is not constant then the general calculus equations above must be used, found by integrating the definitions of position, velocity and acceleration (see above).
Linear motion Angular motion
-------------------------------------------------------------- ------------------------------------------------------------------------------------------------
$\mathbf{v-v_0}=\mathbf at$ $\boldsymbol{\omega - \omega_0} = \boldsymbol\alpha t$
$\mathbf{x - x_0} = \tfrac{1}{2}(\mathbf{v_0+v})t$ $\boldsymbol{\theta - \theta_0} = \tfrac{1}{2}(\boldsymbol{\omega_0 + \omega})t$
$\mathbf{x - x_0} = \mathbf v_0t+\tfrac{1}{2}\mathbf at^2$ $\boldsymbol{\theta - \theta_0} = \boldsymbol\omega _0 t + \tfrac{1}{2} \boldsymbol\alpha t^2$
$\mathbf x_{n^{th}} = \mathbf v_0+\mathbf a(n-\tfrac{1}{2})$ $\boldsymbol\theta_{n^{th}} =\boldsymbol\omega_0+\boldsymbol\alpha(n-\tfrac{1}{2})$
$v^2 - v_0^2 = 2\mathbf{a(x-x_0)}$ $\omega^2 - \omega_0^2 = 2\boldsymbol{\alpha(\theta-\theta_0)}$
## Galilean frame transforms {#galilean_frame_transforms}
For classical (Galileo-Newtonian) mechanics, the transformation law from one inertial or accelerating (including rotation) frame (reference frame traveling at constant velocity - including zero) to another is the Galilean transform.
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F\' moving at translational velocity **V** or angular velocity **Ω** relative to F. Conversely F moves at velocity (---**V** or ---**Ω**) relative to F\'. The situation is similar for relative accelerations.
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
| Motion of entities | Inertial frames | Accelerating frames |
+=============================================================================================+===========================================================================================================================================================================+=======================================================================================================+
| **Translation** | Relative position $\mathbf{r}' = \mathbf{r} + \mathbf{V}t$ | Relative accelerations $\mathbf{a}' = \mathbf{a} + \mathbf{A}$ |
| | | |
| **V** = Constant relative velocity between two inertial frames F and F\'.\ | Relative velocity $\mathbf{v}' = \mathbf{v} + \mathbf{V}$ | Apparent/fictitious forces $\mathbf{F}' = \mathbf{F} - \mathbf{F}_\mathrm{app}$ |
| **A** = (Variable) relative acceleration between two accelerating frames F and F\'.\ | | |
| | Equivalent accelerations $\mathbf{a}' = \mathbf{a}$ | |
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
| **Rotation** | Relative angular position $\theta' = \theta + \Omega t$ Relative velocity $\boldsymbol{\omega}' = \boldsymbol{\omega} + \boldsymbol{\Omega}$ | Relative accelerations $\boldsymbol{\alpha}' = \boldsymbol{\alpha} + \boldsymbol{\Lambda}$ |
| | | |
| **Ω** = Constant relative angular velocity between two frames F and F\'.\ | Equivalent accelerations $\boldsymbol{\alpha}' = \boldsymbol{\alpha}$ | Apparent/fictitious torques $\boldsymbol{\tau}' = \boldsymbol{\tau} - \boldsymbol{\tau}_\mathrm{app}$ |
| **Λ** = (Variable) relative angular acceleration between two accelerating frames F and F\'. | | |
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
| | Transformation of any vector **T** to a rotating frame $\frac{{\rm d}\mathbf{T}'}{{\rm d}t} = \frac{{\rm d}\mathbf{T}}{{\rm d}t} - \boldsymbol{\Omega} \times \mathbf{T}$ | |
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
## Mechanical oscillators {#mechanical_oscillators}
SHM, DHM, SHO, and DHO refer to simple harmonic motion, damped harmonic motion, simple harmonic oscillator and damped harmonic oscillator respectively.
+--------------------+-----------------------------------+------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
| Physical situation | Nomenclature | Translational equations | Angular equations |
+====================+===================================+================================================================================================+============================================================================================================+
| SHM | - *x* = Transverse displacement | $\frac{\mathrm{d}^2 x}{\mathrm{d}t^2} = - \omega^2 x$ | $\frac{\mathrm{d}^2 \theta}{\mathrm{d}t^2} = - \omega^2 \theta$ |
| | - *θ* = Angular displacement | | |
| | - *A* = Transverse amplitude | Solution: $x = A \sin\left ( \omega t + \phi \right )$ | Solution: $\theta = \Theta \sin\left ( \omega t + \phi \right )$ |
| | - Θ = Angular amplitude | | |
+--------------------+-----------------------------------+------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
| Unforced DHM | - *b* = damping constant | $\frac{\mathrm{d}^2 x}{\mathrm{d}t^2} + b \frac{\mathrm{d}x}{\mathrm{d}t} + \omega^2 x = 0$ | $\frac{\mathrm{d}^2 \theta}{\mathrm{d}t^2} + b \frac{\mathrm{d}\theta}{\mathrm{d}t} + \omega^2 \theta = 0$ |
| | - *κ* = torsion constant | | |
| | | Solution (see below for *ω*\'): $x=Ae^{-bt/2m}\cos\left ( \omega' \right )$ | Solution: $\theta=\Theta e^{-\kappa t/2m}\cos\left ( \omega \right )$ |
| | | | |
| | | Resonant frequency: $\omega_\mathrm{res} = \sqrt{\omega^2 - \left ( \frac{b}{4m} \right )^2 }$ | Resonant frequency: $\omega_\mathrm{res} = \sqrt{\omega^2 - \left ( \frac{\kappa}{4m} \right )^2 }$ |
| | | | |
| | | Damping rate: $\gamma = b/m$ | Damping rate: $\gamma = \kappa/m$ |
| | | | |
| | | Expected lifetime of excitation: $\tau = 1/\gamma$ | Expected lifetime of excitation: $\tau = 1/\gamma$ |
+--------------------+-----------------------------------+------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
: Equations of motion
+-------------------------------+----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Physical situation | Nomenclature | Equations |
+===============================+====================================================+=====================================================================================================================================================================================================+
| Linear undamped unforced SHO | - *k* = spring constant | $\omega = \sqrt{\frac{k}{m}}$ |
| | - *m* = mass of oscillating bob | |
+-------------------------------+----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Linear unforced DHO | - *k* = spring constant | $\omega' = \sqrt{\frac{k}{m}-\left ( \frac{b}{2m} \right )^2 }$ |
| | - *b* = Damping coefficient | |
+-------------------------------+----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Low amplitude angular SHO | - *I* = Moment of inertia about oscillating axis | $\omega = \sqrt{\frac{\kappa}{I}}$ |
| | - *κ* = torsion constant | |
+-------------------------------+----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Low amplitude simple pendulum | - *L* = Length of pendulum | Approximate value $\omega = \sqrt{\frac{g}{L}}$ |
| | - *g* = Gravitational acceleration | |
| | - Θ = Angular amplitude | Exact value can be shown to be: $\omega = \sqrt{\frac{g}{L}} \left [ 1 + \sum_{k=1}^\infty \frac{\prod_{n=1}^k \left ( 2n-1 \right )}{\prod_{n=1}^m \left ( 2n \right )} \sin^{2n} \Theta \right ]$ |
+-------------------------------+----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
: Angular frequencies
+--------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Physical situation | Nomenclature | Equations |
+====================+============================+=================================================================================================================================================================================================================+
| SHM energy | - *T* = kinetic energy | Potential energy $U = \frac{m}{2} \left ( x \right )^2 = \frac{m \left( \omega A \right )^2}{2} \cos^2(\omega t + \phi)$ Maximum value at *x* = *A*: $U_\mathrm{max} = \frac{m}{2} \left ( \omega A \right )^2$ |
| | - *U* = potential energy | |
| | - *E* = total energy | Kinetic energy $T = \frac{\omega^2 m}{2} \left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )^2 = \frac{m \left ( \omega A \right )^2}{2}\sin^2\left ( \omega t + \phi \right )$ |
| | | |
| | | Total energy $E = T + U$ |
+--------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| DHM energy | | $E = \frac{m \left ( \omega A \right )^2}{2}e^{-bt/m}$ |
+--------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
: Energy in mechanical oscillations
| 2025-06-20T00:00:00 |
6,051 |
Cursus honorum
|
The `{{langnf|la|'''cursus honorum'''|course of honors|paren=left}}`{=mediawiki}, or more colloquially \'ladder of offices\'; `{{IPA|la|ˈkʊrsʊs hɔˈnoːrũː|lang}}`{=mediawiki}) was the sequential order of public offices held by aspiring politicians in the Roman Republic and the early Roman Empire. It was designed for men of senatorial rank. The *cursus honorum* comprised a mixture of military and political administration posts; the ultimate prize for winning election to each \"rung\" in the sequence was to become one of the two consuls in a given year.
These rules were altered and flagrantly ignored in the course of the last century of the Republic. For example, Gaius Marius held consulships for five years in a row between 104 and 100 BC. He was consul seven times in all, also serving in 107 and 86. Officially presented as opportunities for public service, the offices often became mere opportunities for self-aggrandizement. The constitutional reforms of Sulla between 82 and 79 BC required a ten-year interval before holding the same office again for another term.
To have held each office at the youngest possible age (*suo anno*, \'in his year\') was considered a great political success. For instance, to miss out on a praetorship at 39 meant that one could not become consul at 42. Cicero expressed extreme pride not only in being a *\[\[novus homo\]\]* (\'new man\'; comparable to a \"self-made man\") who became consul even though none of his ancestors had ever served as a consul, but also in having become consul \"in his year\".
thumb\|upright=1.2\|The Roman *cursus honorum*
## Military service {#military_service}
Prior to entering political life and the *cursus honorum*, a young man of senatorial rank was expected to serve around ten years of military duty. The years of service were intended to be mandatory in order to qualify for political office.
Advancement and honors would improve his political prospects, and a successful military career might culminate in the office of military tribune, to which 24 men were elected by the Tribal Assembly each year. The rank of military tribune is sometimes described as the first office of the *cursus honorum*.
## Quaestor
The first official post was that of quaestor. Ever since the reforms of Sulla, candidates had to be at least 30 years old to hold the office. From the time of Augustus onwards, twenty quaestors served in the financial administration at Rome or as second-in-command to a governor in the provinces. They could also serve as the paymaster for a legion.
## Aedile
At 36 years of age, a promagistrate could stand for election to one of the aediles (pronounced `{{IPAc-en|ˈ|iː|d|aɪ|l}}`{=mediawiki} `{{respell|EE|dyle}}`{=mediawiki}, from *aedes*, \"temple edifice\") positions. Of these aediles, two were plebeian and two were patrician, with the patrician aediles called curule aediles. The plebeian aediles were elected by the Plebeian Council and the curule aediles were either elected by the Tribal Assembly or appointed by the reigning consul. The aediles had administrative responsibilities in Rome. They had to take care of the temples (whence their title, from the Latin *aedes*, \"temple\"), organize games, and be responsible for the maintenance of the public buildings in Rome. Moreover, they took charge of Rome\'s water and food supplies; in their capacity as market superintendents, they served sometimes as judges in mercantile affairs.
The aedile was the supervisor of public works; the words \"edifice\" and \"edification\" stem from the same root. He oversaw the public works, temples and markets. Therefore, the aediles would have been in some cooperation with the current censors, who had similar or related duties. Also, they oversaw the organization of festivals and games (*ludi*), which made this a very sought-after office for a career minded politician of the late Republic, as it was a good means of gaining popularity by staging spectacles. Curule aediles were added at a later date in the 4th century BC; their duties do not differ substantially from plebeian aediles. However, unlike plebeian aediles, curule aediles were allowed certain symbols of rank---the *sella curulis* or curule chair, for example---and only patricians could stand for election to curule aedile. This later changed, and both plebeians and patricians could stand for curule aedileship.
The elections for curule aedile were at first alternated between patricians and plebeians, until late in the 2nd century BC, when the practice was abandoned and both classes became free to run during all years.
While part of the *cursus honorum*, this step was optional and not required to hold future offices. Though the office was usually held after the quaestorship and before the praetorship, there are some cases with former praetors serving as aediles.
## Praetor
After serving either as quaestor or as aedile, a man of 39 years could run for praetor. During the reign of Augustus this requirement was lowered to 30, at the request of Gaius Maecenas. The number of praetors elected varied through history, generally increasing with time. During the republic, six or eight were generally elected each year to serve judicial functions throughout Rome and other governmental responsibilities. In the absence of the consuls, a praetor would be given command of the garrison in Rome or in Italy. Also, a praetor could exercise the functions of the consuls throughout Rome, but their main function was that of a judge. They would preside over trials involving criminal acts, grant court orders and validate \"illegal\" acts as acts of administering justice. A praetor was escorted by six lictors, and wielded *imperium*. After a term as praetor, the magistrate could serve as a provincial governor with the title of propraetor, wielding *propraetor imperium*, commanding the province\'s legions, and possessing ultimate authority within his province(s).
Two of the praetors were more prestigious than the others. The first was the Praetor Peregrinus, who was the chief judge in trials involving one or more foreigners. The other was the Praetor Urbanus, the chief judicial office in Rome. He had the power to overturn any verdict by any other courts, and served as judge in cases involving criminal charges against provincial governors. The Praetor Urbanus was not allowed to leave the city for more than ten days. If one of these two praetors was absent from Rome, the other would perform the duties of both.
## Consul
The office of consul was the most prestigious of all of the offices on the *cursus honorum*, and represented the summit of a successful career. The minimum age was 42. Years were identified by the names of the two consuls elected for a particular year; for instance, *M. Messalla et M. Pisone consulibus*, \"in the consulship of Messalla and Piso\", dates an event to 61 BC. Consuls were responsible for the city\'s political agenda, commanded large-scale armies and controlled important provinces. The consuls served for only a year (a restriction intended to limit the amassing of power by individuals) and could only rule when they agreed, because each consul could veto the other\'s decision.
The consuls would alternate monthly as the chairman of the Senate. They also were the supreme commanders in the Roman army, with each being granted two legions during their consular year. Consuls also exercised the highest juridical power in the Republic, being the only office with the power to override the decisions of the Praetor Urbanus. Only laws and the decrees of the Senate or the People\'s assembly limited their powers, and only the veto of a fellow consul or a tribune of the plebs could supersede their decisions.
A consul was escorted by twelve lictors, held *imperium* and wore the toga *praetexta*. Because the consul was the highest executive office within the Republic, they had the power to veto any action or proposal by any other magistrate, save that of the Tribune of the Plebs. After a consulship, a consul was assigned one of the more important provinces and acted as the governor in the same way that a propraetor did, only owning proconsular *imperium*. A second consulship could only be attempted after an interval of 10 years to prevent one man holding too much power.
## Governor
Although not part of the *cursus honorum*, upon completing a term as either praetor or consul, an officer was required to serve a term as propraetor and proconsul, respectively, in one of Rome\'s many provinces. These propraetors and proconsuls held near autocratic authority within their selected province or provinces. Because each governor held equal *imperium* to the equivalent magistrate, they were escorted by the same number of lictors (12) and could only be vetoed by a reigning consul or praetor. Their abilities to govern were only limited by the decrees of the Senate or the people\'s assemblies, and the Tribune of the Plebs was unable to veto their acts as long as the governor remained at least a mile outside of Rome.
## Censor
After a term as consul, the final step in the *cursus honorum* was the office of *censor*. This was the only office in the Roman Republic whose term was a period of eighteen months instead of the usual twelve. Censors were elected every five years and although the office held no military *imperium*, it was considered a great honour. The censors took a regular census of the people and then apportioned the citizens into voting classes on the basis of income and tribal affiliation. The censors enrolled new citizens in tribes and voting classes as well. The censors were also in charge of the membership roll of the Senate, every five years adding new senators who had been elected to the requisite offices. Censors could also remove unworthy members from the Senate. This ability was lost during the dictatorship of Sulla. Censors were also responsible for construction of public buildings and the moral status of the city.
Censors also had financial duties, in that they had to put out to tender projects that were to be financed by the state. Also, the censors were in charge of the leasing out of conquered land for public use and auction. Though this office owned no *imperium*, meaning no lictors for protection, they were allowed to wear the toga *praetexta*.
## Tribune of the Plebs {#tribune_of_the_plebs}
The office of Tribune of the Plebs was an important step in the political career of plebeians. Patricians could not hold the office. They were not an official step in the *cursus honorum*. The Tribune was an office first created to protect the right of the common man in Roman politics and served as the head of the Plebeian Council. In the mid-to-late Republic, however, plebeians were often just as, and sometimes more, wealthy and powerful than patricians. Those who held the office were granted sacrosanctity (the right to be legally protected from any physical harm), the power to rescue any plebeian from the hands of a patrician magistrate, and the right to veto any act or proposal of any magistrate, including another tribune of the people and the consuls. The tribune also had the power to exercise capital punishment against any person who interfered in the performance of his duties. The tribunes could even convene a Senate meeting and lay legislation before it and arrest magistrates. Their houses had to remain open for visitors even during the night, and they were not allowed to be more than a day\'s journey from Rome. Due to their unique power of sacrosanctity, the Tribune had no need for lictors for protection and owned no *imperium*, nor could they wear the toga *praetexta*. For a period after Sulla\'s reforms, a person who had held the office of Tribune of the Plebs could no longer qualify for any other office, and the powers of the tribunes were more limited, but these restrictions were subsequently lifted.
## *Princeps senatus* {#princeps_senatus}
Another office not officially a step in the *cursus honorum* was the *princeps senatus*, an extremely prestigious office for a patrician. The *princeps senatus* served as the leader of the Senate and was chosen to serve a five-year term by each pair of Censors every five years. Censors could, however, confirm a *princeps senatus* for a period of another five years. The *princeps senatus* was chosen from all Patricians who had served as a Consul, with former Censors usually holding the office. The office originally granted the holder the ability to speak first at session on the topic presented by the presiding magistrate, but eventually gained the power to open and close the senate sessions, decide the agenda, decide where the session should take place, impose order and other rules of the session, meet in the name of the senate with embassies of foreign countries, and write in the name of the senate letters and dispatches. This office, like the Tribune, did not own *imperium*, was not escorted by lictors, and could not wear the *toga praetexta*.
## Dictator and *magister equitum* {#dictator_and_magister_equitum}
Of all the offices within the Roman Republic, none granted as much power and authority as the position of dictator, known as the Master of the People. In times of emergency, the Senate would declare that a dictator was required, and the current consuls would appoint a dictator. This was the only decision that could not be vetoed by the Tribune of the Plebs. The dictator was the sole exception to the Roman legal principles of having multiple magistrates in the same office and being legally able to be held to answer for actions in office. Essentially by definition, only one dictator could serve at a time, and no dictator could ever be held legally responsible for any action during his time in office for any reason.
The dictator was the highest magistrate in degree of *imperium* and was attended by twenty-four lictors (as were the former Kings of Rome). Although his term lasted only six months instead of twelve (except for the Dictatorships of Sulla and Caesar), all other magistrates reported to the dictator (except for the tribunes of the plebs -- although they could not veto any of the dictator\'s acts), granting the dictator absolute authority in both civil and military matters throughout the Republic. The dictator was free from the control of the Senate in all that he did, could execute anyone without a trial for any reason, and could ignore any law in the performance of his duties. The dictator was the sole magistrate under the Republic that was truly independent in discharging his duties. All of the other offices were extensions of the Senate\'s executive authority and thus answerable to the Senate. Since the dictator exercised his own authority, he did not suffer this limitation, which was the cornerstone of the office\'s power.
When a dictator entered office, he appointed to serve as his second-in-command a *magister equitum*, the Master of the Horse, whose office ceased to exist once the dictator left office. The *magister equitum* held *praetorian imperium*, was attended by six lictors, and was charged with assisting the dictator in managing the State. When the dictator was away from Rome, the *magister equitum* usually remained behind to administer the city. The *magister equitum*, like the dictator, had unchallengeable authority in all civil and military affairs, with his decisions only being overturned by the dictator himself.
The dictatorship was definitively abolished in 44 BC after the assassination of Gaius Julius Caesar (*Lex Antonia*).
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Craps
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crap}} `{{redirect|Snake-eyes|other uses|Snake Eyes (disambiguation)}}`{=mediawiki} `{{Multiple issues|
{{Overly detailed|date=May 2020}}
{{Cleanup MOS|article|, , |date=December 2022}}
}}`{=mediawiki} `{{Infobox game
| title = Craps
| subtitle =
| image_link = Marines_and_sailors_attended_5th_annual_Casino_Royale_event_130928-M-WI309-003.jpg
| image_caption = A craps table with a game in progress
| image_size = 350px
| other_names = Seven-Eleven
| players =
| genre = [[Dice game]]
| ages =
| deck =
| origin =
| related =
| playing_time =
| random_chance = High
| skills =
| footnotes =
}}`{=mediawiki}
**Craps** is a dice game in which players bet on the outcomes of the roll of a pair of dice. Players can wager money against each other (playing \"street craps\") or against a bank (\"casino craps\"). Because it requires little equipment, \"street craps\" can be played in informal settings. While shooting craps, players may use slang terminology to place bets and actions.
## History
Craps developed in the United States from a simplification of the western European game of Hazard, also spelled Hazzard or Hasard. The origins of Hazard are obscure and may date to the Crusades; a detailed description of Hazard was provided by Edmond Hoyle in *Hoyle\'s Games, Improved* (1790). At approximately the same time (1788), \"Krabs\" was documented as a French variation on Hazard.
In aristocratic London, crabs was the epithet for the sum combinations of two and three for two rolled dice, which in Hazard are instant-losing numbers for the first dice roll, regardless of the shooter\'s selected main number. The name craps is derived from the corruption of this term crabs (or Krabs) to creps and then craps.
According to some accounts, Hazard was brought from London to New Orleans in approximately 1805 by the returning Bernard Xavier Philippe de Marigny de Mandeville, the young gambler and scion of a family of wealthy landowners in colonial Louisiana. Hazard allows the dice shooter to choose any number from five to nine as their \"main\" number; in a pamphlet published in 1933, Edward Tinker claimed that Marigny simplified the game by making the main always seven, which is the mathematically optimal choice, i.e., the choice with the lowest disadvantage for the shooter. However, more recent research indicates that Marigny played an unmodified version of Hazard, which had been played in America since at least the 1600s. Instead, John Scarne credits anonymous Black American inventors with simplifying and streamlining Hazard, increasing the pace of the game and adding a variety of wagers.
Regardless of who deserves credit for simplifying Hazard, the game initially was called Pass from the French word *pas* (meaning \"pace\" or \"step\"), and was popularized by the underclass starting in the early 19th century. Field hands taught their friends and deckhands, who carried the new game up the Mississippi River and its tributaries, although the game was never popular amongst the riverboat gamblers. Marigny gave the name Rue de Craps to a street in his new subdivision in New Orleans; in that city, craps experienced a resurgence of popularity in the late 1830s, but was not played in gaming houses until the 1890s. Budd Theobald credits the cultural exchange between attendants and railroad passengers on Pullman cars for popularizing the game, which eventually spread throughout America by the 1910s, when it was described as \"the gambling game of \[the country\]\" in *Foster\'s Complete Hoyle* (1914).
The craps numbers of 2, 3, and 12 are similarly derived from Hazard. If the main is seven, then the two-dice sum of twelve is added to the crabs as a losing number on the first dice roll. This condition is retained in the simplified game called Pass. All three losing numbers (2, 3, and 12) on the first roll of Pass are jointly called the craps numbers. The central game Pass gradually has been supplemented over the decades by many companion games and wagers which can be played simultaneously with Pass; these are now collectively known as craps.
Early versions of bank craps played in casinos made money either by charging a commission to shooters or offering short odds on the various wagers, primarily on the \"Pass line\" bet for the shooter to win against the house. In approximately 1907, a dicemaker named John H. Winn in Philadelphia introduced a layout which featured a space to wager on \"Don\'t Pass\" (i.e., for the shooter to lose) in addition to \"Pass\". Virtually all modern casinos use his innovation, which incentivizes casinos to use fair dice. As introduced by Winn, \"Don\'t Pass\" bets were taken with a 5 percent commission to ensure the house retained an edge in running the game; this was replaced by the Bar-3 push for \"Don\'t Pass\", and later by the Bar-12 (or Bar-2) push.
Craps exploded in popularity during World War II, which brought most young American men of every social class into the military. The street version of craps was popular among service members who often played it using a blanket as a shooting surface. Their military memories led to craps becoming the dominant casino game in postwar Las Vegas and the Caribbean.
After 1960, a few casinos in Europe, Australia, and Macau began offering craps, and, after 2004, online casinos extended the game\'s spread globally. Craps has been featured in a number of newer casinos, including the idea of expanding into formerly unavailable locals on the coastline.
## Bank craps {#bank_craps}
Bank craps or casino craps is played by one or more players betting against the casino rather than each other. Both the players and the dealers stand around a large rectangular craps table. Sitting is discouraged by most casinos unless a player has medical reasons for requiring a seat.
The basic flow of a single game is:
1. The *shooter* wagers to *pass* (win) and then makes an initial *come-out* roll with two six-sided dice.
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1. If the come-out roll is 7 or 11, that is a *natural* and the shooter has a *pass* (wins); the game is over.
2. If the come-out roll is 2, 3, or 12, that is a *crap* and the shooter has a *missout* (loses); the game is over.
3. If the come-out roll is any other number (4, 5, 6, 8, 9, or 10), that value becomes the shooter\'s *point*.
If a point has been set, the shooter continues to roll until either:
1. A subsequent roll matches the point and the shooter has a *pass* (wins); or
2. A subsequent roll is 7 and the shooter has a *missout* (loses).
Once a point is set and a missout occurs, the dice are passed to the person on the shooter\'s left, who becomes the new shooter.
### Craps table {#craps_table}
thumb\|center\|upright=4\|The layout of a craps table, sometimes called a *double-side dealer* Players use casino chips rather than cash to bet on the Craps \"layout\", a fabric surface which displays the various bets. The bets vary somewhat among casinos in availability, locations, and payouts. The tables roughly resemble bathtubs and come in various sizes. In some locations, chips may be called checks, tokens, or plaques.
Against one long side is the casino\'s table bank: as many as two thousand casino chips in stacks of 20. The opposite long side is usually a long mirror. The U-shaped ends of the table have duplicate layouts and standing room for approximately eight players. In the center of the layout is an additional group of side bets which are used by players from both ends. The vertical walls at each end are usually covered with a rubberized target surface covered with small pyramid shapes to randomize the dice which strike them. The top edges of the table walls have one or two horizontal grooves in which players may store their reserve chips.
The table is run by up to four casino employees: a ***boxman*** seated (usually the only seated employee) behind the casino\'s bank, who manages the chips, supervises the dealers, and handles \"coloring up\" players (exchanging small chip denominations for larger denominations in order to preserve the chips at a table); two ***base dealers**\'\' who stand to either side of the boxman and collect and pay bets to players around their half of the table; and a***stickman**\'\' who stands directly across the table from the boxman, takes and pays (or directs the base dealers to do so) the bets in the center of the table, announces the results of each roll (usually with a distinctive patter), and moves the dice across the layout with an elongated wooden stick.
Each employee also watches for mistakes by the others because of the sometimes large number of bets and frantic pace of the game. In smaller casinos or at quiet times of day, one or more of these employees may be missing, and have their job covered by another, or cause player capacity to be reduced.
Some smaller casinos have introduced \"mini-craps\" tables which are operated with only two dealers; rather than being two essentially identical sides and the center area, a single set of major bets is presented, split by the center bets. Responsibility of the dealers is adjusted: while the stickman continues to handle the center bets, it is the base dealer who handles all other bets (as well as cash and chip exchanges).
By contrast, in \"street craps\", there is no marked table and often the game is played with no back-stop against which the dice are to hit. Despite the name \"street craps\", this game is often played in houses, usually on an un-carpeted garage or kitchen floor. The wagers are made in cash, never in chips, and are usually thrown down onto the ground or floor by the players. There are no attendants, and so the progress of the game, fairness of the throws, and the way that the payouts are made for winning bets are self-policed by the players.
### Dice
thumb\|right\|upright=1.2\|These *perfect dice* from the Tropicana Atlantic City have been retired by drilling a hole completely through between the 1-6 faces; the four-digit serial number on the 6 face has been partially obliterated, but it started and ended with a 4. The dice used at casinos for craps and many other games are sometimes called *perfect* or *gambling house dice*. These are generally made from translucent extruded cellulose, with perfectly square edges each 3/4 ± in length, with pips drilled 17 ± deep and filled with opaque paint matching the density of cellulose, which ensures the dice remain balanced. The dice are buffed and polished to a high glossy finish after the pips are set, and the edges usually are left sharp, also called square or razor edge. To discourage cheating and dice substitution, each die carries a serial number and the casino\'s logo or name. New Jersey specifies the maximum size of the die is 0.775 in on a side.
Under New Jersey regulations, the shooter selects two dice from a set of at least five.
### Rules of play {#rules_of_play}
Each casino may set which bets are offered and different payouts for them, though a core set of bets and payouts is typical. Players take turns rolling two dice and whoever is throwing the dice is called the \"shooter\". Players can bet on the various options by placing chips directly on the appropriately-marked sections of the layout, or asking the base dealer or stickman to do so, depending on which bet is being made.
While acting as the shooter, a player must have a bet on either the \"Pass\" or the \"Don\'t Pass\" line or both. \"Pass\" and \"Don\'t Pass\" are sometimes called \"Win\" and \"Lose\", \"Do\" and \"Don\'t\", or \"Right\" and \"Wrong\". The game is played in rounds and these \"Pass\" and \"Don\'t Pass\" bets are betting on the outcome of a single round. The shooter is presented with multiple dice (typically five) by the \"stickman\", and must choose two for the round. The remaining dice are returned to the stickman\'s bowl and are not used.
Each round has two phases: \"come-out\" and \"point\". Dice are passed to the left.
#### Phase 1 (Come-out) {#phase_1_come_out}
To start a round, the shooter makes one or more \"come-out\" rolls. While the come-out roll may specifically refer to the first roll of a new shooter, any roll where no point is established may be referred to as a come-out. By this definition the start of any new round regardless of whether it is the shooter\'s first toss can be referred to as a come-out roll. The shooter must shoot toward the farther back wall and is generally required to hit the farther back wall with both dice. Casinos may allow a few warnings before enforcing the dice to hit the back wall and are generally lenient if at least one die hits the back wall. Both dice must be tossed in one throw. If only one die is thrown the shot is invalid.
A come-out roll of 2, 3, or 12 is called \"craps\" or \"crapping out\", and anyone betting the Pass line loses. On the other hand, anyone betting the Don\'t Pass line on come out wins with a roll of 2 or 3 and ties (pushes) if a 12 is rolled; in some rules, the 2 pushes instead of the 12, in which case the 3 and 12 win a Don\'t Pass bet. Shooters may keep rolling after crapping out; the dice are only required to be passed if a shooter sevens out (rolls a seven after a point has been established). A come-out roll of 7 or 11 is a \"natural\"; the Pass line wins and Don\'t Pass loses. The other possible numbers are the point numbers: 4, 5, 6, 8, 9, and 10. If the shooter rolls one of these numbers on the come-out roll, this establishes the \"point\" -- to \"pass\" or \"win\", the point number must be rolled again before a seven.
#### Phase 2 (Point) {#phase_2_point}
The dealer flips a button to the \"On\" side and moves it to the point number signifying the second phase of the round. If the shooter \"hits\" the point value again (any value of the dice that sum to the point will do; the shooter does not have to exactly repeat the exact combination of the come-out roll) before rolling a seven, the Pass line wins and a new round starts. If the shooter rolls any seven before repeating the point number (a \"seven-out\"), the Pass line loses, the Don\'t Pass line wins, and the dice pass clockwise to the next new shooter for the next round. Once a point has been established, any multi-roll bets (including line bets and odds for Pass, Don\'t Pass, or both) are unaffected by the 2, 3, 11, or 12; the only numbers which affect the round are the established point, any specific bet on a number, or any 7. Any single roll bet is always affected (win or lose) by the outcome of any roll.
Phase 1 (\"Come-out\")
------------------------ --------------------- -------------------------------------------------------------
Come-out roll Initial outcome Subsequent roll(s), after point is established
2
2 Craps (Don\'t Pass) colspan=11 style=\"background:#faa;\" `{{N/A}}`{=mediawiki}
3 Craps (Don\'t Pass) colspan=11 style=\"background:#faa;\" `{{N/A}}`{=mediawiki}
4 Point 4 Reroll
5 Point 5 Reroll
6 Point 6 Reroll
7 Natural (Pass) colspan=11 style=\"background:#afa;\" `{{N/A}}`{=mediawiki}
8 Point 8 Reroll
9 Point 9 Reroll
10 Point 10 Reroll
11 Natural (Pass) colspan=11 style=\"background:#afa;\" `{{N/A}}`{=mediawiki}
12 Craps (Don\'t Pass) colspan=11 style=\"background:#faa;\" `{{N/A}}`{=mediawiki}
: Summary of rolls during a single round
#### Basic wagering rules {#basic_wagering_rules}
Any player can make a bet on Pass or Don\'t Pass as long as a point has not been established, or Come or Don\'t Come as long as a point is established. All other bets, including an increase in odds behind the Pass and Don\'t Pass lines, may be made at any time. All bets other than Pass line and Come may be removed or reduced any time before the bet loses. This is known as \"taking it down\" in craps.
The maximum bet for Place, Buy, Lay, Pass, and Come bets are generally equal to table maximum. Lay bet maximum are equal to the table maximum win, so players wishing to lay the 4 or 10 may bet twice that amount of the table maximum for the win to be table maximum. Odds behind Pass, Come, Don\'t Pass, and Don\'t Come may be however larger than the odds offered allows and can be greater than the table maximum in some casinos. Don\'t odds are capped on the maximum allowed win. Some casino allow the odds bet itself to be larger than the maximum bet allowed as long as the win is capped at maximum odds. Single rolls bets can be lower than the table minimum, but the maximum bet allowed is also lower than the table maximum. The maximum allowed single roll bet is based on the maximum allowed win from a single roll.
In all the above scenarios, whenever the Pass line wins, the Don\'t Pass line loses, and vice versa, with one exception: on the come-out roll, a roll of 12 will cause Pass Line bets to lose, but Don\'t Pass bets are pushed (or \"barred\"), neither winning nor losing; this is done to establish a house edge for Don\'t Pass bets. (The same applies to \"Come\" and \"Don\'t Come\" bets, discussed below.)
### Joining a game {#joining_a_game}
A player wishing to play craps without being the shooter should approach the craps table and first check to see if the dealer\'s \"On\" button is on any of the point numbers.
- If the button has been turned to \"Off\", then the table is in the come-out phase, and a point has not been established.
- If the dealer\'s button is \"On\", the table is in the point phase where casinos will allow odds behind an existing Pass line to be bet. Some casino do not allow new Pass line bets while a point has been established. Some casinos will place the bet straddling the outer border of the Pass line so as to indicate that it is to be paid the same odds as a place bet, instead of just even money. Other casinos will take the bet on the Pass line after a point has been established, known as put betting, which is a disadvantage to the player (since the seven is the most common roll and likely to happen before the \"point\").
In either case, all single or multi-roll proposition bets may be placed in either of the two phases.
Between dice rolls there is a period for dealers to make payouts and collect losing bets, after which players can place new bets. The stickman monitors the action at a table and decides when to give the shooter the dice, after which no more betting is allowed.
When joining the game, one should place money on the table rather than passing it directly to a dealer. The dealer\'s exaggerated movements during the process of \"making change\" or \"change only\" (converting currency to an equivalent in casino cheques) are required so that any disputes can be later reviewed against security camera footage.
### Rolling
The dealers will insist that the shooter roll with one hand and that the dice bounce off the far wall surrounding the table. These requirements are meant to keep the game fair (preventing switching the dice or making a \"controlled shot\"). If a die leaves the table, the shooter will usually be asked to select another die from the remaining three but can request permission to use the same die if it passes the boxman\'s inspection. This requirement exists to keep the game fair and reduce the chance of loaded dice.
### Names of rolls {#names_of_rolls}
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| | B:1\ | B:2\ | B:3\ | B:4\ | B:5\ | B:6\ |
| | `{{die|1}}`{=mediawiki} | `{{die|2}}`{=mediawiki} | `{{die|3}}`{=mediawiki} | `{{die|4}}`{=mediawiki} | `{{die|5}}`{=mediawiki} | `{{die|6}}`{=mediawiki} |
+=========================+=========================+=========================+=========================+=========================+=========================+=========================+
| A:1\ | Snake Eyes | | | | | |
| `{{die|1}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:2\ | Ace Deuce | Hard Four | | | | |
| `{{die|2}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:3\ | Easy Four | Five (Fever Five) | Hard Six | | | |
| `{{die|3}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:4\ | Five (Fever Five) | Easy Six | Natural/Seven Out | Hard Eight | | |
| `{{die|4}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:5\ | Easy Six | Natural/Seven Out | Easy Eight | Nine (Nina) | Hard Ten | \| |
| `{{die|5}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:6\ | Natural/Seven Out | Easy Eight | Nine (Nina) | Easy Ten | Yo (Yo-leven) | Boxcars/Midnight |
| `{{die|6}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
: Names of Rolls in Craps
There are many local variants of the calls made by the stickman for rolls during a craps game. These frequently incorporate a reminder to the dealers as to which bets to pay or collect.
Two --- \"Snake Eyes\", \"Two Craps Two\", \"Double Aces\", \"Loose Deuce\", \"Snickies\"
: The two ones that compose it look like a pair of small, beady eyes. During actual play, more common terms are \"two craps two\" during the comeout roll because the Pass line bet is lost on a comeout crap roll and/or because a bet on any craps would win. \"Aces; double the field\" would be a more common call when not on the comeout roll to remind the dealers to pay double on the field bets and encourage the field bettor to place subsequent bets and/or when no crap bets have been placed. Another name for the two is \"loose deuce\" or \"Snickies\" due to it sounding like \"Snake eyes\" but spoken with an accent.
Three --- \"Three Craps Three\", \"Ace Deuce\", \"Tracy\", \"Acey Deucy\"
: Typically called as \"three craps three\" during the comeout roll, or \"three, ace deuce, come away single\" when not on the comeout to signify the come bet has been lost and to pay single to any field bettors. Three may also be referred to as \"ace caught a deuce\", \"Tracy\", or even less often \"acey deucey\".
Four (hard) --- \"Little Joe\", \"Joe\", \"Little Dick\", \"Little Joe from Kokomo\", \"Little Joe on the Front Row\", \"Ballerina\"
: usually hard, is sometimes referred to as \"Little Joe from Kokomo\" or \"Little Joe on the front row\" or just \"Little Joe\". A hard four can be called a \"ballerina\" because it is two-two (\"tutu\").
Five --- \"Phoebe\", \"Fever in the South\", \"West Kentucky\", \"No Field Five\", \"Fever\"
: is frequently called \"no field five\" in casinos in which five is not one of the field rolls and thus not paid in the field bets. Other names for a five are \"fever\" and \"little Phoebe\".
Six --- \"Jimmie Hicks\", \"Jimmie Hicks from the Sticks\", \"666 Winner 6\", \"Sixty Days\", \"Sice\"
: may be referred to as \"Jimmie Hicks\" or \"Jimmie Hicks from the sticks\", examples of rhyming slang. On a win, the six is often called \"666 winner 6\" followed by \"came hard\" or \"came easy\".
Seven --- \"Six Ace\", \"Up Pops the Devil\", \"Up Jumped the Devil\", \"Big Red\", \"Seven Out\", \"Seven Out Seven\"
: rolled as 6--1 is sometimes called \"six ace\" or \"up pops the Devil\". Older dealers and players may use the term \"Big Red\" because craps tables once prominently featured a large red \"7\" in the center of the layout for the one-roll seven bet. During the comeout, the seven is called \"seven, front line winner\", frequently followed by \"pay the line\" and/or \"take the don\'ts\". After the point is established, a seven is typically called by simply \"7 out\" or \"7 out 7\"..
Eight (hard) --- \"Eighter from Decatur\", \"Ada from Decatur\", \"Square Pair\", \"Mom and Dad\", \"Ozzie and Harriet\"
: rolled the hard way, as opposed to an \"easy eight\", is sometimes called an \"eighter from Decatur\". It can also be known as a \"square pair\", \"mom and dad\", or \"Ozzie and Harriet\".
Nine --- \"Centerfield Nine\", \"Railroad Nine\", \"Jesse James\", \"Nina from Pasadena\", \"Nina at the Marina\", \"Niner from Carolina\", Old Mike\"
: is called a \"centerfield nine\" in casinos in which nine is one of the field rolls, because nine is the center number shown on the layout in such casinos (2--3--4--9--10--11--12). In Atlantic City, a 4--5 is called a \"railroad nine\". The 4--5 nine is also known as \"Jesse James\" because the outlaw Jesse James was killed by a .45 caliber pistol. Other names for the nine include \"Nina from Pasadena\", \"Nina at the Marina\", and \"niner from Carolina\". Nine can also be referred to as \"Old Mike\", named after NBA Hall-of-Famer Michael Jordan, who wore No. 9 in his FIBA international career, when players could only wear numbers 4 to 15.
Ten (hard) --- \"Big Dick\", \"Big Dick from Boston\", \"Big Dick the Ladies\' Friend\", \"Dos Equis\", \"Puppy Paws\", \"Pair of Sunflowers\", \"Big John\"
: the hard way is \"a hard ten\", \"dos equis\" (Spanish, meaning \"two X\'s\", because the pip arrangement on both dice on this roll resembles \"XX\"), or \"Hard ten -- a woman\'s best friend\", an example of both rhyming slang and sexual double entendre. Ten as a pair of 5\'s may also be known as \"puppy paws\" or \"a pair of sunflowers\" or \"Big Dick\" or \"Big John.\" Another slang for a hard ten is \"moose head\", because it resembles a moose\'s antlers. This phrase came from players in the Pittsburgh area.
Eleven --- \"Yo\", \"Yo-leven\", \"Six Five No Jive\"
: called out as \"yo\" or \"yo-leven\" to prevent being misheard as \"seven\". An older term for eleven is \"six five, no jive\" because it is a winning roll. During the comeout, eleven is typically followed by \"front line winner\". After the point is established, \"good field and come\" is often added.
Twelve --- \"Boxcars\", \"Midnight\", \"Double-action Field Traction\", \"12 Craps 12\"
: known as \"boxcars\" because the spots on the two dice that show 6--6 look like schematic drawings of railroad boxcars; it is also called \"midnight\", referring to twelve o\'clock; and also as \"double-action field traction\", because of the (standard) 2-to-1 pay on Field bets for this roll and the fact that the arrangement of the pips on the two dice, when laid end-to-end, resemble tire tracks. On tables that pay triple the field on a twelve roll, the stickman will often loudly exclaim \"triple\" either alone or in combination with \"12 craps 12\" or \"come away triple\".
Rolls of 4, 6, 8, and 10 are called \"hard\" or \"gag\", when rolled as a double, or \"easy\", when rolled with two different numbers. For example, rolls will be called \"six the hard way\", \"easy eight\", \"hard ten\", etc., because of their significance in center table bets known as the \"hard ways\". Hard way rolls are so named because there is only one way to roll them (i.e., the value on each die is the same when the number is rolled). Consequently, it is more likely to roll the number in different-number combinations (easy) rather than as a double (hard).
## Bet odds and summary {#bet_odds_and_summary}
: Note: Individual casinos may pay some of these bets at different payout ratios than those listed below. Some bets are listed more than once below -- the most common payout in North American casinos is listed first, followed by other known variants.
```{=html}
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```
: Note: \"True Odds\" do not vary.
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Bet | Type | True Odds | Odds Paid | House Edge | Single or Multi Roll | Win | Lose | Notes |
+=====================================+==========+==============+=========================+======================================================+======================+=============================================================================+=============================================================================+====================================================================================================================================================================================================================================================================================================================================================================+
| Pass / Come | Line | 251:244 | 1:1 | 1.41% | Multi | Come out roll: 7, 11. | Come out roll: 2, 3, 12. | Considered a \"contract bet\": once the point is established, the bet is locked until it wins or loses. See Optimal betting. Come uses only the come-out roll criteria (7, 11 to win \"come\") for a single roll after the point is established. |
| | | | | | | | | |
| | | | | | | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | Once the point is established: 7 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Don\'t Pass / Don\'t Come\ | Line | 976:949 | 1:1 | 1.36% | Multi | Come out roll: 2 (or 12, depending on Bar), 3 | Come out roll: 7, 11. | Controlled by the player: can be decreased at any time, but see Optimal betting. In some casinos, Bar-3 (1--2) is applied in lieu of either Bar-12 or Bar-2; this increases the house edge to 4.39%. Don\'t come uses only the come-out roll criteria (2, 3, 12 to win or tie \"don\'t come\", depending on Bar) for a single roll after the point is established. |
| (Bar-12 or Bar-2) | | | | | | | | |
| | | | | | | Tie: 12 (or 2, depending on Bar) | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | |
| | | | | | | | | |
| | | | | | | Once the point is established: 7 | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Pass Odds / Come Odds | Line | Same as paid | 2:1 on 4,10; | 0% | Multi | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | Once the point is established: 7 | Controlled by the player: can be increased or decreased at any time |
| | | | | | | | | |
| | | | 3:2 on 5,9; | | | | | |
| | | | | | | | | |
| | | | 6:5 on 6,8 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Don\'t Pass Odds / Don\'t Come Odds | Line | Same as paid | 1:2 against 4,10; | 0% | Multi | Once the point is established: 7 | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | Controlled by the player: can be increased or decreased at any time |
| | | | | | | | | |
| | | | 2:3 against 5,9; | | | | | |
| | | | | | | | | |
| | | | 5:6 against 6,8 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Yo (11) | Prop | 17:1 | 15:1 | 11.11% | Single | 11 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| 3 | Prop | 17:1 | 15:1 | 11.11% | Single | 3 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| 2 | Prop | 35:1 | 30:1 | 13.89% | Single | 2 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| 12 | Prop | 35:1 | 30:1 | 13.89% | Single | 12 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Hi-Lo (2 or 12) | Prop | 17:1 | 15:1 | 11.11% | Single | 2 or 12 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Craps (2, 3, or 12) | Prop | 8:1 | 7:1 | 11.11% | Single | 2, 3, 12 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| C & E (the combined bet) | Prop | 5:1 | 3:1 on 2,3,12; | 11.11% | Single | 2, 3, 11, 12 | Any other number | |
| | | | | | | | | |
| | | | 7:1 on 11 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Any 7 | Prop | 5:1 | 4:1 | 16.67% | Single | 7 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Field | Prop | 5:4 | 1:1 on 3,4,9,10,11; | 5.56% (2.78% if 12 pays 3:1, 0% if 2 and 12 pay 3:1) | Single | 2,3,4,9,10,11,12 | Any other number | Most common payout schedule. Some casinos pay 2:1 for 2 and 3:1 for 12, reducing house edge to 2.78%. A few pay both 2 and 12 at 3:1, eliminating the house edge. |
| | | | | | | | | |
| | | | 2:1 on 2,12 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Horn (the combined bet) | Prop | 5:1 | 27:4 on 2,12; | 12.5% | Single | 2,3,11,12 | Any other number | |
| | | | | | | | | |
| | | | 3:1 on 3,11 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Whirl/World (the combined bet) | Prop | 2:1 | 26:5 on 2,12; | 13.33% | Single | 2,3,7,11,12 | Any other number | |
| | | | | | | | | |
| | | | 11:5 on 3,11; | | | | | |
| | | | | | | | | |
| | | | 0:1 (push) on 7 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Hard 4 / Hard 10 | Hard way | 8:1 | 7:1 | 11.11% | Multi | 4 as a pair (2-2) | 7 | In the UK and Australia, the payout is 7.5:1 lowering the house edge to 5.56%. |
| | | | | | | | | |
| | | | | | | 10 as a pair (5-5) | 4 as a non-pair (1--3) | |
| | | | | | | | | |
| | | | | | | | 10 as a non-pair (4--6) | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Hard 6 / Hard 8 | Hard way | 10:1 | 9:1 | 9.09% | Multi | 6 as a pair (3-3) | 7 | In the UK and Australia, the payout is 9.5:1 lowering the house edge to 4.55%. |
| | | | | | | | | |
| | | | | | | 8 as a pair (4-4) | 6 as a non-pair (1--5,2-4) | |
| | | | | | | | | |
| | | | | | | | 8 as a non-pair (2--6,3-5) | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Big 6 / Big 8 | Big 6/8 | 6:5 | 1:1 | 9.09% | Multi | 6/8 | 7 | Same true odds, better payout if the player places the 6/8 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Place 4 / Place 10 | Place | 2:1 | 9:5 | 6.67% | Multi | 4/10 | 7 | Same true odds, better payout if the player buys the 4/10 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Place 5 / Place 9 | Place | 3:2 | 7:5 | 4% | Multi | 5/9 | 7 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Place 6 / Place 8 | Place | 6:5 | 7:6 | 1.52% | Multi | 6/8 | 7 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Buy 4 / Buy 10 | Buy | 2:1 | 2:1 -5% of intended bet | 4.76% (1.67% if commission taken only on win) | Multi | 4/10 | 7 | Certain casinos such as Santa Ana Star Casino offer \"Free buy\" reducing house edge to 0% |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Buy 5 / Buy 9 | Buy | 3:2 | 3:2 -5% of intended bet | 4.76% (1.96% if commission taken only on win) | Multi | 5/9 | 7 | Same true odds, better payout if the player places the 5/9 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Buy 6 / Buy 8 | Buy | 6:5 | 6:5 -5% of intended bet | 4.76% (2.22% if commission taken only on win) | Multi | 6/8 | 7 | Same true odds, better payout if the player places the 6/8 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Lay 4 / Lay 10 | Lay | 1:2 | 1:2 -5% of intended win | 2.44% (1.67% if commission taken only on win) | Multi | 7 | 4/10 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Lay 5 / Lay 9 | Lay | 2:3 | 2:3 -5% of intended win | 3.23% (2% if commission taken only on win) | Multi | 7 | 5/9 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Lay 6 / Lay 8 | Lay | 5:6 | 5:6 -5% intended win | 4.00% (2.27% if commission taken only on win) | Multi | 7 | 6/8 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
: Summary of wagers, true odds, and typical payouts
The probability of dice combinations determine the odds of the payout. There are a total of 36 (6 × 6) possible combinations when rolling two dice. The following chart shows the dice combinations needed to roll each number. The two and twelve are the hardest to roll since only one combination of dice is possible. The game of craps is built around the dice roll of seven, since it is the most easily rolled dice combination.
thumb\|right\|upright=1.8\|Combinations of two dice, illustrated
Dice roll (sum) Possible dice combinations Probability
----------------- ---------------------------------------- ------------------------------
2 1--1
3 1--2, 2--1 =`{{frac|1|18}}`{=mediawiki}
4 1--3, 2--2, 3--1 =`{{frac|1|12}}`{=mediawiki}
5 1--4, 2--3, 3--2, 4--1 =`{{frac|1|9}}`{=mediawiki}
6 1--5, 2--4, 3--3, 4--2, 5--1
**7** **1--6, 2--5, 3--4, 4--3, 5--2, 6--1** =`{{frac|1|6}}`{=mediawiki}
8 2--6, 3--5, 4--4, 5--3, 6--2
9 3--6, 4--5, 5--4, 6--3 =`{{frac|1|9}}`{=mediawiki}
10 4--6, 5--5, 6--4 =`{{frac|1|12}}`{=mediawiki}
11 5--6, 6--5 =`{{frac|1|18}}`{=mediawiki}
12 6--6
: Combinations of two dice, with probability of occurrence
Viewed another way:
1 `{{die|1}}`{=mediawiki} 2 `{{die|2}}`{=mediawiki} 3 `{{die|3}}`{=mediawiki} 4 `{{die|4}}`{=mediawiki} 5 `{{die|5}}`{=mediawiki} 6 `{{die|6}}`{=mediawiki}
--------------------------- --------------------------- --------------------------- --------------------------- --------------------------- --------------------------- ---------------------------
1 `{{die|1}}`{=mediawiki} 2 3 4 5 6 **7**
2 `{{die|2}}`{=mediawiki} 3 4 5 6 **7** 8
3 `{{die|3}}`{=mediawiki} 4 5 6 **7** 8 9
4 `{{die|4}}`{=mediawiki} 5 6 **7** 8 9 10
5 `{{die|5}}`{=mediawiki} 6 **7** 8 9 10 11
6 `{{die|6}}`{=mediawiki} **7** 8 9 10 11 12
: Sum of two six-sided dice
The expected value of all bets is usually negative, such that the average player will always lose money. This is because the house always sets the paid odds to below the actual odds. The only exception is the \"odds\" bet that the player is allowed to make after a point is established on a pass/come Don\'t Pass/Don\'t Come bet (the odds portion of the bet has a long-term expected value of 0). However, this \"free odds\" bet cannot be made independently, so the expected value of the entire bet, including odds, is still negative. Since there is no correlation between die rolls, there is normally no possible long-term winning strategy in craps.
There are occasional promotional variants that provide either no house edge or even a player edge. One example is a field bet that pays 3:1 on 12 and 2:1 on either 3 or 11. Overall, given the 5:4 true odds of this bet, and the weighted average paid odds of approximately 7:5, the player has a 5% advantage on this bet. This is sometimes seen at casinos running limited-time incentives, in jurisdictions or gaming houses that require the game to be fair, or in layouts for use in informal settings using play money. No casino currently runs a craps table with a bet that yields a player edge full-time.
Maximizing the size of the odds bet in relation to the line bet will reduce, but never eliminate the house edge, and will increase variance. Most casinos have a limit on how large the odds bet can be in relation to the line bet, with single, double, and five times odds common. Some casinos offer 3--4--5 odds, referring to the maximum multiple of the line bet a player can place in odds for the points of 4 and 10, 5 and 9, and 6 and 8, respectively. During promotional periods, a casino may even offer 100× odds bets, which reduces the house edge to almost nothing, but dramatically increases variance, as the player will be betting in large betting units.
Since several of the multiple roll bets pay off in ratios of fractions on the dollar, it is important that the player bets in multiples that will allow a correct payoff in complete dollars. Normally, payoffs will be rounded down to the nearest dollar, resulting in a higher house advantage. These bets include all place bets, taking odds, and buying on numbers 6, 8, 5, and 9, as well as laying all numbers.
## Types of wagers {#types_of_wagers}
### Line bets {#line_bets}
The shooter is required to make either a Pass line bet or a Don\'t Pass bet if he wants to shoot. On the come out roll each player may only make one bet on the Pass or Don\'t Pass, but may bet both if desired. The Pass Line and Don\'t Pass bet is optional for any player not shooting. In rare cases, some casinos require all players to make a minimum Pass Line or Don\'t Pass bet (if they want to make any other bet), whether they are currently shooting or not.
\[\[<File:Craps> table diagram L.svg\|thumb\|right\|upright=2\|Left section of bank craps table, with spaces for common line and place bets. From top to bottom, these bets are:
- Don\'t Come (Bar-12) and Place 4 / 5 / 6 / 8 / 9 / 10
- Don\'t Pass (Bar-12) and Come
- Big 6, Big 8, and Field
- Don\'t Pass (Bar-12)
- Pass (wraps around to outside of diagram)
\]\]
#### Pass line {#pass_line}
The basic bet in craps is the Pass line bet, which is a bet for the shooter to win. This bet must be at least the table minimum and at most the table maximum.
- If the come-out roll is 7 or 11, the bet wins.
- If the come-out roll is 2, 3 or 12, the bet loses (known as \"crapping out\").
- If the roll is any other value, it establishes a point.
- If, with a point established, that point is rolled again before a 7, the bet wins.
- If, with a point established, a 7 is rolled before the point is rolled again (\"seven out\"), the bet loses.
The Pass line bet pays even money.
The Pass line bet is a contract bet. Once a Pass line bet is made, it is always working and cannot be turned \"Off\", taken down, or reduced until a decision is reached -- the point is made, or the shooter sevens out. A player may increase any corresponding odds (up to the table limit) behind the Pass line at any time after a point is established. Players may only bet the Pass line on the come out roll when no point has been established, unless the casino allows put betting where the player can bet Pass line or increase an existing Pass line bet whenever desired and may take odds immediately if the point is already on.
#### Don\'t Pass {#dont_pass}
A Don\'t Pass bet is a bet for the shooter to lose (\"seven out, line away\") and is almost the opposite of the Pass line bet. Like the Pass bet, this bet must be at least the table minimum and at most the table maximum.
- If the come-out roll is 3, the bet wins.
- If the come-out roll is 7 or 11, the bet loses.
- If the game is being played under \"Bar-12\" or \"Bar Sixes\":
- If the come-out roll is 2, the bet wins.
- If the come-out roll is 12, the bet is a push (neither won nor lost).
- Alternatively, if the game instead is played under \"Bar-2\" or \"Bar Aces\":
- If the come-out roll is 2, the bet is a push.
- If the come-out roll is 12, the bet wins.
- If the roll is any other value, it establishes a point.
- If, with a point established, a 7 is rolled before the point is rolled again (\"seven out\"), the bet wins.
- If, with a point established, that point is rolled again before a 7, the bet loses.
The Don\'t Pass bet pays even money.
The Don\'t Pass bet is a no-contract bet. After a point is established, a player may take down or reduce a Don\'t Pass bet and any corresponding odds at any time because odds of rolling a 7 before the point is in the player\'s favor. Once taken down or reduced, however, the Don\'t Pass bet may not be restored or increased. Because the shooter must have a line bet the shooter generally may not reduce a Don\'t Pass bet below the table minimum. In Las Vegas, a majority of casinos will allow the shooter to move the bet to the Pass line in lieu of taking it down; however, in other areas such as Pennsylvania and Atlantic City, this is not allowed. Even though players are allowed to remove the Don\'t Pass line bet after a point has been established, the bet cannot be turned \"Off\" without being removed. Players choosing to remove the Don\'t Pass line bet can no longer lay odds behind the Don\'t Pass line. The player can, however, still make standard lay bets on any of the point numbers (4, 5, 6, 8, 9, 10).
The casino chooses either Bar-2 or Bar-12, but not both. The push on 12 or 2 is mathematically necessary to maintain the house edge over the player. Other casinos allow the player to choose to either push on 2 (\"Bar Aces\") or push on 12 (\"Bar Sixes\") depending on where it is placed on the layout. Some older bank crap games used Bar-3 (\"Bar Ace-Deuce\"), which increases the house edge.
There are two different ways to calculate the odds and house edge of this bet. The summary table gives the numbers considering that the game ends in a push when a 12 is rolled, rather than being undetermined. Betting on Don\'t Pass is often called \"playing the dark side\", and it is considered by some players to be in poor taste, or even taboo, because it goes directly against conventional play, winning when most of the players lose.
#### Pass odds {#pass_odds}
If a 4, 5, 6, 8, 9, or 10 is thrown on the come-out roll (i.e., when a point is established), most casinos allow Pass line players to take odds by placing up to some predetermined multiple of the Pass line bet, behind the Pass line. This additional bet wins if the point is rolled again before a 7 is rolled (the point is made) and pays at the true odds:
- 2-to-1 if 4 or 10 is the point,
- 3-to-2 if 5 or 9 is the point, or
- 6-to-5 if 6 or 8 is the point.
Unlike the Pass line bet itself, the Pass line odds bet can be turned \"Off\" (not working), removed or reduced anytime before it loses. In Las Vegas, generally odds bets are required to be the table minimum. In Atlantic City and Pennsylvania, the combine odds and Pass bet must be table minimum so players can bet the minimum single unit on odds depending on the point. If the point is a 4 or 10, players can bet as little as \$1 on odds if the table minimum is low such as is \$5, \$10 or \$15. If the player requests the Pass odds be not working (\"Off\") and the shooter sevens-out or hits the point, the Pass line bet will be lost or doubled and the Pass odds returned.
Individual casinos (and sometimes tables within a casino) vary greatly in the maximum odds they offer, from single or double odds (one or two times the Pass line bet) up to 100× or even unlimited odds. A variation often seen is \"3-4-5× Odds\", where the maximum allowed odds bet depends on the point: three times if the point is 4 or 10; four times on points of 5 or 9; or five times on points of 6 or 8. This rule simplifies the calculation of winnings: a maximum Pass odds bet on a 3--4--5× table will always be paid at six times the Pass line bet regardless of the point.
As odds bets are paid at true odds, in contrast with the Pass line which is always even money, taking odds on a minimum Pass line bet lessens the house advantage compared with betting the same total amount on the Pass line only. A maximum odds bet on a minimum Pass line bet often gives the lowest house edge available in any game in the casino. However, the odds bet cannot be made independently, so the house retains an edge on the Pass line bet itself.
#### Don\'t Pass odds {#dont_pass_odds}
If a player is playing Don\'t Pass instead of pass, they also may lay odds by placing chips behind the Don\'t Pass line. If a 7 comes before the point is rolled, the Don\'t Pass odds pay at true odds:
- 1-to-2 if 4 or 10 is the point,
- 2-to-3 if 5 or 9 is the point, or
- 5-to-6 if 6 or 8 is the point.
Typically the maximum lay bet will be expressed such that a player may win up to an amount equal to the maximum odds multiple at the table. If a player lays maximum odds with a point of 4 or 10 on a table offering five-times odds, he would be able to lay a maximum of ten times the amount of his Don\'t Pass bet. At 5× odds table, the maximum amount the combined bet can win will always be 6× the amount of the Don\'t Pass bet. Players can bet table minimum odds if desired and win less than table minimum.
Like the Don\'t Pass bet the odds can be removed or reduced. Unlike the Don\'t Pass bet itself, the Don\'t Pass odds can be turned \"Off\" (not working). In Las Vegas generally odds bets are required to be the table minimum. In Atlantic City and Pennsylvania, the combine lay odds and Don\'t Pass bet must be table minimum so players may bet as little as the minimum two units on odds depending on the point. If the point is a 4 or 10 players can bet as little as \$2 if the table minimum is low such as \$5, \$10 or \$15 tables. If the player requests the Don\'t Pass odds to be not working (\"Off\") and the shooter hits the point or sevens-out, the Don\'t Pass bet will be lost or doubled and the Don\'t Pass odds returned. Unlike a standard lay bet on a point, lay odds behind the Don\'t Pass line does not charge commission (vig).
#### Come bet {#come_bet}
A player making a Come bet is wagering on the first number that \"comes\" from the shooter\'s next roll, regardless of the table\'s phase. In other words, a Come bet can be considered as starting an entirely new Pass line bet, unique to that player.
- If a 7 or 11 is rolled on the shooter\'s next roll, the Come bet wins.
- If a 2, 3, or 12 is rolled on the shooter\'s next roll, the Come bet loses.
- If a 4, 5, 6, 8, 9, or 10 is rolled on the shooter\'s next roll, the number becomes the \"come-bet point\".
- The Come bet will be moved by the base dealer onto a box representing the same \"come-bet point\" number the shooter threw.
- If, with the Come-bet point established, that number is rolled during this second phase, the Come bet wins.
- If, with the Come-bet point established, a 7 is rolled during this second phase, the Come bet loses.
- The player is allowed to take odds on the Come-bet point, just like a Pass line bet.
The Come bet pays off at even money, like the Pass line bet.
Come bets can only be made after a point has been established since, on the come-out roll, a Come bet would be the same as a Pass line bet. Like the Pass line bet, each player may only make one Come bet per roll; this does not exclude a player from betting odds on an already established come-bet point. The Come bet must be at least the table minimum and at most the table maximum. Players may bet both the Come and Don\'t Come on the same roll if desired.
Also like a Pass line bet, the come bet is a contract bet and is always working, and cannot be turned \"Off\", removed or reduced until it wins or loses. However, the odds taken behind a Come bet can be turned \"Off\" (not working), removed or reduced anytime before the bet loses. In Las Vegas generally odds bets are required to be the table minimum. In Atlantic City and Pennsylvania, the combine odds and Pass bet must be table minimum so players can bet the minimum single unit depending on the point. If the point is a 4 or 10, players can bet as little as \$1 if the table minimum is low such as \$5, \$10, or \$15 minimums. If the player requests the Come odds to be not working (\"Off\") and the shooter sevens-out or hits the Come bet point, the Come bet will be lost or doubled and the Come odds returned. If the casino allows put betting a player may increase a Come bet after a point has been established and bet larger odds behind if desired. Put betting also allows a player to bet on a Come and take odds immediately on a point number without a Come bet point being established.
The dealer will place the odds on top of the come bet, but slightly off center in order to differentiate between the original bet and the odds. The second round wins if the shooter rolls the come bet point again before a seven. Winning come bets are paid the same as winning Pass line bets: even money for the original bet and true odds for the odds bet. If, instead, the seven is rolled before the come-bet point, the come bet (and any odds bet) loses.
Because of the come bet, if the shooter makes their point, a player can find themselves in the situation where they still have a come bet (possibly with odds on it) and the next roll is a come-out roll. In this situation, odds bets on the come wagers are usually presumed to be not working for the come-out roll. That means that if the shooter rolls a 7 on the come-out roll, any players with active come bets waiting for a come-bet point lose their initial wager but will have their odds bets returned to them.
If the come-bet point is rolled on the come-out roll, the odds do not win but the come bet does and the odds bet is returned (along with the come bet and its payoff). The player can tell the dealer that they want their odds working, such that if the shooter rolls a number that matches the come point, the odds bet will win along with the come bet, and if a seven is rolled, both lose.
Many players will use a come bet as \"insurance\" against sevening out: if the shooter rolls a seven, the come bet pays 1:1, offsetting the loss of the Pass line bet. The risk in this strategy is the situation where the shooter does not hit a seven for several rolls, leading to multiple come bets that will be lost if the shooter eventually sevens out.
#### Don\'t Come bet {#dont_come_bet}
In the same way that a Come bet is similar to a Pass line bet, a Don\'t Come bet is similar to a Don\'t Pass bet. Like the Come, the Don\'t Come can only be bet after a point has already been established as it is the same as a Don\'t Pass line bet when no point is established. This bet must be at least the table minimum and at most the table maximum. A Don\'t Come bet is played in two phases, just like the Don\'t Pass line bet.
- If a 2 or 3 is rolled in the first phase, it wins.
- If a 7 or 11 is rolled, it loses.
- If a 12 is rolled, it is a push, assuming that Bar-12 is being followed; if Bar-2 is being followed, 2 instead is a push and 12 wins, in the same way as described above for the variants of the Don\'t Pass bet.
- If, instead, the roll is 4, 5, 6, 8, 9, or 10, this sets the Don\'t Come point.
- The base dealer will move the Don\'t Come bet onto a box representing the Don\'t Come point, i.e., the number the shooter threw.
- The second phase wins if the shooter rolls a seven before the Don\'t Come point.
Like the Don\'t Pass each player may only make one Don\'t Come bet per roll, this does not exclude a player from laying odds on an already established Don\'t Come points. Players may bet both the Don\'t Come and Come on the same roll if desired.
The player may lay odds on a Don\'t Come bet, just like a Don\'t Pass bet; in this case, the dealer (not the player) places the odds bet on top of the bet in the box, because of limited space, slightly offset to signify that it is an odds bet and not part of the original Don\'t Come bet. Lay odds behind a Don\'t Come are subject to the same rules as Don\'t Pass lay odds. Unlike a standard lay bet on a point, lay odds behind a Don\'t Come point does not charge commission (vig) and gives the player true odds. Like the Don\'t Pass line bet, Don\'t Come bets are no-contract, and can be removed or reduced after a Don\'t Come point has been established, but cannot be turned off (\"not working\") without being removed. A player may also call, \"No Action\" when a point is established, and the bet will not be moved to its point. This play is not to the player\'s advantage. If the bet is removed, the player can no longer lay odds behind the Don\'t Come point and cannot restore or increase the same Don\'t Come bet. Players must wait until next roll as long as a Pass line point has been established (players cannot bet Don\'t Come on come out rolls) before they can make a new Don\'t Come bet. Las Vegas casinos which allow put betting allows players to move the Don\'t Come directly to any Come point as a put; however, this is not allowed in Atlantic City or Pennsylvania. Unlike the Don\'t Come bet itself, the Don\'t Come odds can be turned \"Off\" (not working), removed, or reduced if desired. In Las Vegas, players generally must lay at least table minimum on odds if desired and win less than table minimum; in Atlantic City and Pennsylvania a player\'s combined bet must be at least table minimum, so depending on the point number players may lay as little as 2 minimum units (e.g. if the point is 4 or 10). If the player requests the Don\'t Come odds be not working (\"Off\") and the shooter hits the Don\'t Come point or sevens-out, the Don\'t Come bet will be lost or doubled and the Don\'t Come odds returned.
Winning Don\'t Come bets are paid the same as winning Don\'t Pass bets: even money for the original bet and true odds for the odds lay. Unlike come bets, the odds laid behind points established by Don\'t Come bets are always working including come out rolls unless the player specifies otherwise.
### Multi-roll bets {#multi_roll_bets}
These are bets that may not be settled on the first roll and may need one or more subsequent rolls before an outcome is determined.
Most multi-roll bets may fall into the situation where a point is made by the shooter before the outcome of the multi-roll bet is decided. These bets are often considered \"not working\" on the new come-out roll until the next point is established, unless the player calls the bet as \"working.\"
Casino rules vary on this; some of these bets may not be callable, while others may be considered \"working\" during the come-out. Dealers will usually announce if bets are working unless otherwise called off. If a non-working point number placed, bought or laid becomes the new point as the result of a come-out, the bet is usually refunded, or can be moved to another number for free.
#### Place
Players can bet any point number (4, 5, 6, 8, 9, 10) by placing their wager in the come area and telling the dealer how much and on what number(s), \"30 on the 6\", \"5 on the 5\", or \"25 on the 10\". These are typically \"Place Bets to Win\". These are bets that the number bet on will be rolled before a 7 is rolled, similar to the Pass odds bets. These bets are considered working bets, and will continue to be paid out each time a shooter rolls the number bet. On a come-out roll, a place bet is considered to be not in effect unless the player who made it specifies otherwise. This bet may be removed or reduced at any time until it loses; in the latter case, the player must abide by any table minimums.
Place bets to win pay out at slightly worse than the true odds: 9-to-5 on points 4 or 10, 7-to-5 on points 5 or 9, and 7-to-6 on points 6 or 8. The place bets on the outside numbers (4,5,9,10) should be made in units of \$5, (on a \$5 minimum table), in order to receive the correct exact payout of \$5 paying \$7 or \$5 paying \$9. The place bets on the 6 & 8 should be made in units of \$6, (on a \$5 minimum table), in order to receive the correct exact payout of \$6 paying \$7. For the 4 and 10, it is to the player\'s advantage to \'buy\' the bet (see below).
An alternative form, rarely offered by casinos, is the \"place bet to lose.\" This bet is the opposite of the place bet to win and pays off if a 7 is rolled before the specific point number. The place bet to lose typically carries a lower house edge than a place bet to win. Payouts are 4-to-5 on points 6 or 8, 5-to-8 on 5 or 9, and 5-to-11 on 4 or 10.
#### Buy
Players can also buy a bet which are paid at true odds, but a 5% commission is charged on the amount of the bet. Buy bets are placed with the shooter betting at a specific number will come out before a player sevens out. The buy bet must be at least table minimum excluding commission; however, some casinos require the minimum buy bet amount to be at least \$20 to match the \$1 charged on the 5% commission. Traditionally, the buy bet commission is paid no matter what, but in recent years a number of casinos have changed their policy to charge the commission only when the buy bet wins. Some casinos charge the commission as a one-time fee to buy the number; payouts are then always at true odds. Most casinos usually charge only \$1 for a \$25 green-chip bet (4% commission), or \$2 for \$50 (two green chips), reducing the house advantage a bit more. Players may remove or reduce this bet (bet must be at least table minimum excluding vig) anytime before it loses. Buy bets like place bets are not working when no point has been established unless the player specifies otherwise.
Where commission is charged only on wins, the commission is often deducted from the winning payoff---a winning \$25 buy bet on the 10 would pay \$49, for instance. The house edges stated in the table assume the commission is charged on all bets. They are reduced by at least a factor of two if commission is charged on winning bets only.
#### Lay
A lay bet is the opposite of a buy bet, where a player bets on a 7 to roll before the number that is laid. Players may only lay the 4, 5, 6, 8, 9, or 10 and may lay multiple numbers if desired. Just like the buy bet lay bets pay true odds, but because the lay bet is the opposite of the buy bet, the payout is reversed. Therefore, players get 1 to 2 for the numbers 4 and 10, 2 to 3 for the numbers 5 and 9, and 5 to 6 for the numbers 6 and 8. A 5% commission (vigorish, vig, juice) is charged up front on the possible winning amount. For example: A \$40 Lay Bet on the 4 would pay \$20 on a win. The 5% vig would be \$1 based on the \$20 win. (not \$2 based on the \$40 bet as the way buy bet commissions are figured.) Like the buy bet the commission is adjusted to suit the betting unit such that fraction of a dollar payouts are not needed. Casinos may charge the vig up front thereby requiring the player to pay a vig win or lose, other casinos may only take the vig if the bet wins. Taking vig only on wins lowers house edge. Players may removed or reduce this bet (bet must be at least table minimum) anytime before it loses. Some casinos in Las Vegas allow players to lay table minimum plus vig if desired and win less than table minimum. Lay bet maximums are equal to the table maximum win, so if a player wishes to lay the 4 or 10, he or she may bet twice at amount of the table maximum for the win to be table maximum. Other casinos require the minimum bet to win at \$20 even at the lowest minimum tables in order to match the \$1 vig, this requires a \$40 bet. Similar to buy betting, some casinos only take commission on win reducing house edge. Unlike place and buy bets, lay bets are always working even when no point has been established. The player must specify otherwise if he or she wishes to have the bet not working.
If a player is unsure of whether a bet is a single or multi-roll bet, it can be noted that all single-roll bets will be displayed on the playing surface in one color (usually red), while all multi-roll bets will be displayed in a different color (usually yellow).
#### Put
A put bet is a bet which allows players to increase or make a Pass line bet after a point has been established (after come-out roll). Players may make a put bet on the Pass line and take odds immediately or increase odds behind if a player decides to add money to an already existing Pass line bet. Put betting also allows players to increase an existing come bet for additional odds after a come point has been established or make a new come bet and take odds immediately behind if desired without a come bet point being established. If increased or added put bets on the Pass line and Come cannot be turned \"Off\", removed or reduced, but odds bet behind can be turned \"Off\", removed or reduced. The odds bet is generally required to be the table minimum. Player cannot put bet the Don\'t Pass or Don\'t Come. Put betting may give a larger house edge over place betting unless the casino offers high odds.
Put bets are generally allowed in Las Vegas, but not allowed in Atlantic City and Pennsylvania.
Put bets are better than place bets (to win) when betting more than 5-times odds over the flat bet portion of the put bet. For example, a player wants a \$30 bet on the six. Looking at two possible bets: 1) Place the six, or 2) Put the six with odds. A \$30 place bet on the six pays \$35 if it wins. A \$30 put bet would be a \$5 flat line bet plus \$25 (5-times) in odds, and also would pay \$35 if it wins. Now, with a \$60 bet on the six, the place bet wins \$70, where the put bet (\$5 + \$55 in odds) would pay \$71. The player needs to be at a table which not only allows put bets, but also high-times odds, to take this advantage.
#### Hard way {#hard_way}
\[\[<File:Craps> table diagram C.svg\|thumb\|right\|upright=1.8\|Center section of craps table, with typical service bets, which in this generic diagram include, from top to bottom and left to right:
- Any seven
- Hard Six and Hard Ten
- Hard Eight and Hard Four
- Ace-Deuce (3), Snake Eyes (2), and Boxcars (12)
- Yo-leven (11) and Yo-leven (11)
- Any Craps (2, 3, or 12)
The C&E / E&C bets stand for Craps and Eleven (2, 3, 11, or 12).\]\] This bet can only be placed on the numbers 4, 6, 8, and 10. In order for this bet to win, the chosen number must be rolled the \"hard way\" (as doubles) before a 7 or any other non-double combination (\"easy way\") totaling that number is rolled. For example, a player who bets a hard 6 can only win by seeing a 3--3 roll come up before any 7 or any easy roll totaling 6 (4--2 or 5--1); otherwise, the player loses.
In Las Vegas casinos, this bet is generally working, including when no point has been established, unless the player specifies otherwise. In other casinos such as those in Atlantic City, hard ways are not working when the point is off unless the player requests to have it working on the come out roll.
Like single-roll bets, hard way bets can be lower than the table minimum; however, the maximum bet allowed is also lower than the table maximum. The minimum hard way bet can be a minimum one unit. For example, lower stake table minimums of \$5 or \$10, generally allow minimum hard ways bets of \$1. The maximum bet is based on the maximum allowed win from a single roll.
Easy way is not a specific bet offered in standard casinos, but a term used to define any number combination which has two ways to roll. For example, (6--4, 4--6) would be a \"10 easy\". The 4, 6, 8 or 10 can be made both hard and easy ways. Betting point numbers (which pays off on easy or hard rolls of that number) or single-roll (\"hop\") bets (e.g., \"hop the 2--4\" is a bet for the next roll to be an easy six rolled as a two and four) are methods of betting easy ways.
#### Big 6 and Big 8 {#big_6_and_big_8}
A player can wager on either the 6 or 8 being rolled before the shooter throws a seven. These wagers are usually avoided by experienced craps players since they create a large house edge by paying even money (1:1) while the true odds are 6:5; experienced players realize the house edge would be reduced by instead making place bets on the 6 or the 8, since those pay more (7:6) and are closer to the true odds. Some casinos (especially all those in Atlantic City) do not even offer the Big 6 & 8. The bets are located in the corners behind the Pass line, and bets may be placed directly by players.
The only real advantage offered by the Big 6 & 8 is that they can be bet for the table minimum, whereas a place bet minimum may sometimes be greater than the table minimum (e.g. \$6 place bet on a \$3 minimum game.) In addition place bets are usually not working, except by agreement, when the shooter is \"coming out\" i.e. shooting for a point, and Big 6 and 8 bets always work. Some modern layouts no longer show the Big 6/Big 8 bet.
### Single-roll bets {#single_roll_bets}
Single-roll (proposition) bets are resolved in one dice roll by the shooter. Most of these are called \"service bets\", and they are located at the center of most craps tables. Only the stickman or a dealer can place a service bet. Single-roll bets can be lower than the table minimum, but the maximum bet allowed is also lower than the table maximum. The maximum bet is based on the maximum allowed win from a single roll. The lowest single-roll bet can be a minimum one unit bet. For example, tables with minimums of \$5 or \$10 generally allow minimum single-roll bets of \$1. Single bets are always working by default unless the player specifies otherwise. The bets include:
2 (snake eyes, or Aces): Wins if shooter rolls a 2.\
3 (ace-deuce): Wins if the shooter rolls a 3.\
Yo: Wins if the shooter rolls 11.\
12 (boxcars, midnight, or cornrows): Wins if shooter rolls a 12.\
2 or 12 (hi-lo): Wins if shooter rolls a 2 or 12. The stickman places this bet on the line dividing the 2 and 12 bets.\
Any Craps (Three-Way): Wins if the shooter rolls 2, 3 or 12.\
C & E: A combined bet, a player is betting half their bet on craps (2,3,12) and the other half on 11 (yo). The combine payout is 3:1 on craps and 7:1 on 11 (yo). Another method of calculating the payout is to divide the total bet in half. The player would receive 7:1 minus half the total bet payout on half the total bet for craps and 15:1 minus half the total bet payout on half the total bet for 11 (yo). For example, using this method if a player were to bet \$2 on C & E, \$1 would receive 7:1 payout on craps minus \$1 for the bet on 11 so the total profit would be \$6. If an 11 was rolled the player would receive 15:1 minus \$1 for the bet on craps so the player\'s total profit is \$14. Both methods of calculation yield the same result so either method can be used. If a player wishes to take the bet down after a win the player would receive the whole bet not half even though only one of the two bets can win per roll. The minimum bet on C & E is double the lowest unit bet allowed at the table. So if the minimum single roll bet is \$1 the lowest C & E bet allowed would be \$2. Players are, however, able to make odd number bets larger than \$2 if desired. One of the two bets will always lose, the other may win.\
Any seven: A single roll bet which wins if the shooter rolls a 7 with 4:1 payout. This bet is also nicknamed Big Red, since the 7 on its betting space on the layout is usually large and red, and it is considered bad luck and a breach of etiquette among gamblers to speak the word \"seven\" at the table.\
Horn: This is a bet that involves betting on 1 unit each for 2, 3, 11, and 12 at the same time for the next roll. The bet is actually four separate bets, and pays off depending on which number is actually rolled. The combined payout is 27:4 for 2, 12 and 3:1 for 3, 11. Each individual bet has the same payout as a single bet on the specific numbers, 30:1 for 2 and 12 minus the other three bets, 15:1 for 3 and 11 minus the other three bets. If a player wins the bet he can take down all four bets instead of a single bet even though only one bet can win per roll. Many players, in order to eliminate the confusion of tossing four chips to the center of the table or having change made while bets are being placed, will make a five-unit Horn High bet, which is a four-way bet with the extra unit going to one specific number. For example, if one tosses a \$5 chip into the center and says \"horn high yo\", they are placing four \$1 bets on each of the horn numbers and the extra dollar will go on the yo (11). Horn bets are generally required to be in multiples of 4 or 5 with the minimum bet being 4 times the minimum unit allowed. For example, if the single roll minimum at the table is \$1 the Horn bet must be \$4 or more.\
Whirl or World: A five-unit bet that is a combination of a horn and any-seven bet, with the idea that if a seven is rolled the bet is a push, because the money won on the seven is lost on the horn portions of the bet. The combine odds are 26:5 on the 2, 12, 11:5 on the 3, 11, and a push on the 7. Like the C & E and Horn bet, if a player wishes to take down the bet after a win he or she would receive all five units back. The minimum bet is five of the minimum units. For example, if the minimum single roll bet is \$1, the minimum World/Whirl bet is \$5.\
On the Hop: (also Hop, or Hopping) A single roll bet on any particular combination of the two dice on the next roll including combinations whose sum is 7 (e.g. 4 and 3). For example, if someone bets on \"5 and 1\" on the hop, they are betting that the next roll will have a 5 on one die and a 1 on the other die. The bet pays 15:1 on easy ways (same as a bet on 3 or 11). Hard ways hop pays 30:1 (e.g., 3 and 3 on the hop, same as a bet on 2 or 12). The true odds are 17:1 and 35:1, resulting in a house edge of 11.11% and 13.89% respectively. When presented, hop bets are located at the center of the craps layout with the other proposition bets. If hop bets are not on the craps layout, they still may be bet on by players but they become the responsibility of the boxman to book the bet. Sometimes players may request to hop a whole number. In this case the money on the bet different combinations. For example, if a player says \"hop the tens\" (6--4, 5--5, 4--6) the player must give the dealer an even number bet so it can be divided among the hard and easy ways. If the player gives \$10, \$5 would be placed on the easy ways 10 with 15:1 odds and \$5 would be placed on the hard way with 30:1 odds. If a player wishes to \"hop the sevens\" there would be three different combinations and six possible ways to roll a 7 (6--1, 5--2, 4--3, 3--4, 2--5, 1--6) therefore the player should bet in multiples of 3 so the bet can be divided among each combination with a 15:1 payout minus the other two bets, otherwise if players does not bet in multiples of 3, they would specific which combination has additional units.\
Field: This bet is a wager that one of the numbers 2, 3, 4, 9, 10, 11, or 12 will appear on the next roll of the dice. This bet typically pays more (2:1 or 3:1) if 2 or 12 is rolled, and 1:1 if 3, 4, 9, 10, or 11 is rolled. The Field bet is a \"Self-Service\" Bet. Unlike the other proposition bets which are handled by the dealers or stickman, the field bet is placed directly by the player. Players identify their Field bets by placing them in the Field area directly in front of them or as close to their position as possible. The initial bet and/or any payouts can \"ride\" through several rolls until they lose, and are assumed to be \"riding\" by dealers. It is thus the player\'s responsibility to collect their bet and/or winnings immediately upon payout, before the next dice roll, if they do not wish to let it ride.
### Player bets {#player_bets}
Fire Bet: Before the shooter begins, some casinos will allow a bet known as a fire bet to be placed. A fire bet is a bet of as little as \$1 and generally up to a maximum of \$5 to \$10 sometimes higher, depending on casino, made in the hope that the next shooter will have a hot streak of setting and getting many points of different values. As different individual points are made by the shooter, they will be marked on the craps layout with a fire symbol.
The first three points will not pay out on the fire bet, but the fourth, fifth, and sixth will pay out at increasing odds. The fourth point pays at 24-to-1, the fifth point pays at 249-to-1, and the 6th point pays at 999-to-1. (The points must all be different numbers for them to count toward the fire bet.) For example, a shooter who successfully hits a point of 10 twice will only garner credit for the first one on the fire bet. Players must hit the established point in order for it to count toward the fire bet. The payout is determine by the number of points which have been established and hit after the shooter sevens out.
Bonus Craps: Prior to the initial \"come out roll\", players may place an optional wager (usually a \$1 minimum to a maximum \$25) on one or more of the three Bonus Craps wagers, \"All Small\", \"All Tall\", or \"All or Nothing at All.\" For players to win the \"All Small\" wager, the shooter must hit all five small numbers (2, 3, 4, 5, 6) before a seven is rolled; similarly, \"All Tall\" wins if all five high numbers (8, 9, 10, 11, 12) are hit before a seven is rolled.
These bets pay 35-for-1, for a house advantage of 7.76%. \"All or Nothing at All\" wins if the shooter hits all 10 numbers before a seven is rolled. This pays 176-for-1, for a house edge of 7.46%. For all three wagers, the order in which the numbers are hit does not matter. Whenever a seven is hit, including on the come out roll, all bonus bets lose, the bonus board is reset, and new bonus bets may be placed.
### Multiple different bets {#multiple_different_bets}
A player may wish to make multiple different bets. For example, a player may be wish to bet \$1 on all hard ways and the horn. If one of the bets win the dealer may automatically replenish the losing bet with profits from the winning bet. In this example, if the shooter rolls a hard 8 (pays 9:1), the horn loses. The dealer may return \$5 to the player and place the other \$4 on the horn bet which lost. If the player does not want the bet replenished, he or she should request any or all bets be taken down.
### Working and not working bets {#working_and_not_working_bets}
A working bet is a live bet. Bets may also be on the board, but not in play and therefore not working. Pass line and come bets are always working meaning the chips are in play and the player is therefore wagering live money. Other bets may be working or not working depending whether a point has been established or player\'s choice. Place and buy bets are working by default when a point is established and not working when the point is off unless the player specifies otherwise. Lay bets are always working even if a point has not been established unless the player requests otherwise. At any time, a player may wish to take any bet or bets out of play. The dealer will put an \"Off\" button on the player\'s specific bet or bets; this allows the player to keep his chips on the board without a live wager. For example, if a player decides not to wager a place bet mid-roll but wishes to keep the chips on the number, he or she may request the bet be \"not working\" or \"Off\". The chips remain on the table, but the player cannot win from or lose chips which are not working.
The opposite is also allowed. By default place and buy bets are not working without an established point; a player may wish to wager chips before a point has been established. In this case, the player would request the bet be working in which the dealer will place an \"On\" button on the specified chips.
### Betting variants {#betting_variants}
These variants depend on the casino and the table, and sometimes a casino will have different tables that use or omit these variants and others.
- 11 is a point number instead of a natural. Rolling an 11 still pays \"Yo\" center-table bets, but the Pass line does not automatically win (and the Don\'t Pass line does not automatically lose) when 11 is rolled on the come-out. Making the point pays 3:1 on Pass/Come odds bets (1:3 on Don\'t Pass/Come odds); all line bets are still even money. This substantially reduces the odds of a natural (from 8/36 to 6/36) and of making the point in general (since a 3:1 dog is added to the mix). All other things equal, the house edge on the Pass Line and Come bets for this play variation jumps dramatically to 9.75%.
- 12 pays 3:1 on the field. This is generally seen in rooms that have two different table minimums, on the tables with the higher minimums. The lower minimum ones will then have 2:1 odds. For example, the Mirage casino in Las Vegas features 3:1 odds.
- 11 pays 2:1 on the field. This variant is normally used when 12 pays 3:1, and neutralizes the house edge on the field.
- Big 6/8 are unavailable. These bets are equivalent to placing or buying 6 or 8 as points, which have better payout for the same real odds, so Big 6/8 are rarely used and many casinos simply omit them from the layout. Casinos in Atlantic City are even prohibited by law from offering Big 6/8 bets.
## Optimal betting {#optimal_betting}
When craps is played in a casino, all bets have a house advantage. That is, it can be shown mathematically that a player will (with 100% probability) lose all his or her money to the casino in the long run, while in the short run the player is more likely to lose money than make money. There may be players who are lucky and get ahead for a period of time, but in the long run these winning streaks are eroded away. One can slow, but not eliminate, one\'s average losses by only placing bets with the smallest house advantage.
The Pass/Don\'t Pass line, Come/Don\'t Come line, place 6, place 8, buy 4 and buy 10 (only under the casino rules where commission is charged only on wins) have the lowest house edge in the casino, and all other bets will, on average, lose money between three and twelve times faster because of the difference in house edges.
The place bets and buy bets differ from the Pass line and come line, in that place bets and buy bets can be removed at any time, since, while they are multi-roll bets, their odds of winning do not change from roll to roll, whereas Pass line bets and come line bets are a combination of different odds on their first roll and subsequent rolls. The first roll of a Pass line bet is 2:1 advantage for the player (8 wins, 4 losses), but it is \"paid for\" by subsequent rolls that are at the same disadvantage to the player as the Don\'t Pass bets were at an advantage. As such, they cannot profitably let the player take down the bet after the first roll. Players can bet or lay odds behind an established point depending on whether it was a Pass/Come or Don\'t Pass/Don\'t Come to lower house edge by receiving true odds on the point. Casinos which allow put betting allows players to increase or make new pass/come bets after the come-out roll. This bet generally has a higher house edge than place betting, unless the casino offers high odds.
Conversely, a player can take back (pick up) a Don\'t Pass or Don\'t Come bet after the first roll, but this cannot be recommended, because they already endured the disadvantaged part of the combination -- the first roll. On that come-out roll, they win just 3 times (2 and 3), while losing 8 of them (7 and 11) and pushing one (12) out of the 36 possible rolls. On the other 24 rolls that become a point, their Don\'t Pass bet is now to their advantage by 6:3 (4 and 10), 6:4 (5 and 9) and 6:5 (6 and 8). If a player chooses to remove the initial Don\'t Come and/or Don\'t Pass line bet, he or she can no longer lay odds behind the bet and cannot re-bet the same Don\'t Pass and/or Don\'t Come number (players must make a new Don\'t Pass or come bets if desired). However, players can still make standard lay bets odds on any of the point numbers (4,5,6,8,9,10).
Among these, and the remaining numbers and possible bets, there are a myriad of systems and progressions that can be used with many combinations of numbers.
An important alternative metric is house advantage per roll (rather than per bet), which may be expressed in loss per hour. The typical pace of rolls varies depending on the number of players, but 102 rolls per hour is a cited rate for a nearly full table. This same reference states that only \"29.6% of total rolls are come out rolls, on average\", so for this alternative metric, needing extra rolls to resolve the Pass line bet, for example, is factored. This number then permits calculation of rate of loss per hour, and per the 4 day/5 hour per day gambling trip:
- \$10 Pass line bets 0.42% per roll, \$4.28 per hour, \$86 per trip
- \$10 Place 6,8 bets 0.46% per roll, \$4.69 per hour, \$94 per trip
- \$10 Place 5,9 bets 1.11% per roll, \$11.32 per hour, \$226 per trip
- \$10 Place 4,10 bets 1.19% per roll, \$12.14 per hour, \$243 per trip
- \$1 Single Hardways 2.78% per roll, \$2.84 per hour, \$56.71 per trip
- \$1 All hardways 2.78% per roll, \$11.34 per hour, \$227 per trip
- \$5 All hardways 2.78% per roll, \$56.71 per hour, \$1134 per trip
- \$1 Craps only on come out 3.29% per roll, \$3.35 per hour, \$67.09 per trip
- \$1 Eleven only on come out 3.29% per roll, \$3.35 per hour, \$67.09 per trip
## Table rules {#table_rules}
Besides the rules of the game itself, a number of formal and informal rules are commonly applied in the table form of Craps, especially when played in a casino.
To reduce the potential opportunity for switching dice by sleight-of-hand, players are not supposed to handle the dice with more than one hand (such as shaking them in cupped hands before rolling) nor take the dice past the edge of the table. If a player wishes to change shooting hands, they may set the dice on the table, let go, then take them with the other hand.
When throwing the dice, the player is expected to hit the farthest wall at the opposite end of the table (these walls are typically augmented with pyramidal structures to ensure highly unpredictable bouncing after impact). Casinos will sometimes allow a roll that does not hit the opposite wall as long as the dice are thrown past the middle of the table; a very short roll will be nullified as a \"no roll\". The dice may not be slid across the table and must be tossed. These rules are intended to prevent dexterous players from physically influencing the outcome of the roll.
Players are generally asked not to throw the dice above a certain height (such as the eye level of the dealers). This is both for the safety of those around the table, and to eliminate the potential use of such a throw as a distraction device in order to cheat.
Dice are still considered \"in play\" if they land on players\' bets on the table, the dealer\'s working stacks, on the marker puck, or with one die resting on top of the other. The roll is invalid if either or both dice land in the boxman\'s bank, the stickman\'s bowl (where the extra three dice are kept between rolls), or in the rails around the top of the table where players chips are kept. If one or both dice hits a player or dealer and rolls back onto the table, the roll counts as long as the person being hit did not intentionally interfere with either of the dice, though some casinos will rule \"no roll\" for this situation. If one or both leave the table, it is also a \"no roll\", and the dice may either be replaced or examined by the boxman and returned to play.
Shooters may wish to \"set\" the dice to a particular starting configuration before throwing (such as showing a particular number or combination, stacking the dice, or spacing them to be picked up between different fingers), but if they do, they are often asked to be quick about it so as not to delay the game. Some casinos disallow such rituals to speed up the pace of the game. Some may also discourage or disallow unsanitary practices such as kissing or spitting on the dice.
In most casinos, players are not allowed to hand anything directly to dealers, and vice versa. Items such as cash, checks, and chips are exchanged by laying them down on the table; for example, when \"buying in\" (paying cash for chips), players are expected to place the cash on the layout: the dealer will take it and then place the chips in front of the player. This rule is enforced in order to allow the casino to easily monitor and record all transfers via overhead surveillance cameras, and to reduce the opportunity for cheating via sleight-of-hand.
Most casinos prohibit \"call bets\", and may have a warning such as \"No Call Bets\" printed on the layout to make this clear. This means a player may not call out a bet without also placing the corresponding chips on the table. Such a rule reduces the potential for misunderstanding in loud environments, as well as disputes over the amount that the player intended to bet after the outcome has been decided. Some casinos choose to allow call bets once players have bought-in. When allowed, they are usually made when a player wishes to bet at the last second, immediately before the dice are thrown, to avoid the risk of obstructing the roll.
## Etiquette
Craps is among the most social and most superstitious of all gambling games, which leads to an enormous variety of informal rules of etiquette that players may be expected to follow. An exhaustive list of these is beyond the scope of this article, but the guidelines below are most commonly given.
### Tips
Tipping the dealers is universal and expected in Craps. As in most other casino games, a player may simply place (or toss) chips onto the table and say, \"For the dealers\", \"For the crew\", *etc.* In craps, it is also common to place a bet for the dealers. This is usually done one of three ways: by placing an ordinary bet and simply declaring it for the dealers, as a \"two-way\", or \"on top\". A \"Two-Way\" is a bet for both parties: for example, a player may toss in two chips and say \"Two Way Hard Eight\", which will be understood to mean one chip for the player and one chip for the dealers. Players may also place a stack of chips for a bet as usual, but leave the top chip off-center and announce \"on top for the dealers\". The dealer\'s portion is often called a \"toke\" bet, which comes from the practice of using \$1 slot machine tokens to place dealer bets in some casinos.
In some cases, players may also tip each other, for example as a show of gratitude to the thrower for a roll on which they win a substantial bet.
### Superstition
Craps players routinely practice a wide range of superstitious behaviors, and may expect or demand these from other players as well.
Most prominently, it is universally considered bad luck to say the word \"seven\" (after the \"come-out\", a roll of 7 is a loss for \"pass\" bets). Dealers themselves often make significant efforts to avoid calling out the number. When necessary, participants may refer to seven with a \"nickname\" such as \"Big Red\" (or just \"Red\"), \"the S-word\", etc.
## Dice setting or dice control {#dice_setting_or_dice_control}
An approach to achieving an advantage is to \"set\" the dice in a particular orientation, and then throw them in such a manner that they do not tumble randomly. The theory is that given exactly the same throw from exactly the same starting configuration, the dice will tumble in the same way and therefore show the same or similar values every time.
Casinos take steps to prevent this. The dice are usually required to hit the back wall of the table, which is normally faced with a jagged angular texture such as pyramids, making controlled spins more difficult. There has been no independent evidence that such methods can be successfully applied in a real casino.
## Variants
Bank craps is a variation of the original craps game and is sometimes known as Las Vegas Craps. This variant is quite popular in Nevada gambling houses, and its availability online has now made it a globally played game. Bank craps uses a special table layout and all bets must be made against the house. In Bank Craps, the dice are thrown over a wire or a string that is normally stretched a few inches from the table\'s surface. The lowest house edge (for the Pass/Don\'t Pass) in this variation is around 1.4%. Generally, if the word \"craps\" is used without any modifier, it can be inferred to mean this version of the game, to which most of this article refers.
Crapless craps, also known as bastard craps, is a simple version of the original craps game, and is normally played as an online private game. The biggest difference between crapless craps and original craps is that the shooter (person throwing the dice) is at a far greater disadvantage and has a house edge of 5.38%. Another difference is that this is one of the craps games in which a player can bet on rolling a 2, 3, 11 or 12 before a 7 is thrown. In crapless craps, 2 and 12 have odds of 11:2 and have a house edge of 7.143% while 3 and 11 have odds of 11:4 with a house edge of 6.25%.
New York Craps is one of the variations of craps played mostly in the Eastern coast of the US, true to its name. History states that this game was actually found and played in casinos in Yugoslavia, the UK and the Bahamas. In this craps variant, the house edge is greater than Las Vegas Craps or Bank craps. The table layout is also different, and is called a double-end-dealer table. This variation is different from the original craps game in several ways, but the primary difference is that New York craps does not allow Come or Don\'t Come bets. New York Craps Players bet on box numbers like 4, 5, 6, 8, 9, or 10. The overall house edge in New York craps is 5%.
## Card-based variations {#card_based_variations}
In order to get around Californian laws barring the payout of a game being directly related to the roll of dice, Indian reservations have adapted the game to substitute cards for dice.
### Cards replacing dice {#cards_replacing_dice}
To replicate the original dice odds exactly without dice or possibility of card-counting, one scheme uses two shuffle machines each with just one deck of Ace through 6 each. Each machine selects one of the 6 cards at random and this is the roll. The selected cards are replaced and the decks are reshuffled for the next roll.
In one variation, two shoes are used, each containing some number of regular card decks that have been stripped down to just the Aces and deuces through sixes. The boxman simply deals one card from each shoe and that is the roll on which bets are settled. Since a card-counting scheme is easily devised to make use of the information of cards that have already been dealt, a relatively small portion (less than 50%) of each shoe is usually dealt in order to protect the house.
In a similar variation, cards representing dice are dealt directly from a continuous shuffling machine (CSM). Typically, the CSM will hold approximately 264 cards, or 44 sets of 1 through 6 spot cards. Two cards are dealt from the CSM for each roll. The game is played exactly as regular craps, but the roll distribution of the remaining cards in the CSM is slightly skewed from the normal symmetric distribution of dice.
Even if the dealer were to shuffle each roll back into the CSM, the effect of buffering a number of cards in the chute of the CSM provides information about the skew of the next roll. Analysis shows this type of game is biased towards the Don\'t Pass and Don\'t Come bets. A player betting Don\'t Pass and Don\'t Come every roll and laying 10x odds receives a 2% profit on the initial Don\'t Pass / Don\'t Come bet each roll. Using a counting system allows the player to attain a similar return at lower variance.
### Cards mapping physical dice {#cards_mapping_physical_dice}
In this game variation, one red deck and one blue deck of six cards each (A through 6), and a red die and a blue die are used. Each deck is shuffled separately, usually by machine. Each card is then dealt onto the layout, into the 6 red and 6 blue numbered boxes. The shooter then shoots the dice. The red card in the red-numbered box corresponding to the red die, and the blue card in the blue-numbered box corresponding to the blue die are then turned over to form the roll on which bets are settled.
Another variation uses a red and a blue deck of 36 custom playing cards each. Each card has a picture of a two-die roll on it -- from 1--1 to 6--6. The shooter shoots what looks like a red and a blue die, called \"cubes\". They are numbered such that they can never throw a pair, and that the blue one will show a higher value than the red one exactly half the time. One such scheme could be 222555 on the red die and 333444 on the blue die.
One card is dealt from the red deck and one is dealt from the blue deck. The shooter throws the \"cubes\" and the color of the cube that is higher selects the color of the card to be used to settle bets. On one such table, an additional one-roll prop bet was offered: If the card that was turned over for the \"roll\" was either 1--1 or 6--6, the other card was also turned over. If the other card was the \"opposite\" (6--6 or 1--1, respectively) of the first card, the bet paid 500:1 for this 647:1 proposition.
And additional variation uses a single set of 6 cards, and regular dice. The roll of the dice maps to the card in that position, and if a pair is rolled, then the mapped card is used twice, as a pair.
## Rules of play against other players (\"Street Craps\") {#rules_of_play_against_other_players_street_craps}
Recreational or informal playing of craps outside of a casino is referred to as street craps or private craps. The most notable difference between playing street craps and bank craps is that there is no bank or house to cover bets in street craps. Players must bet against each other by covering or fading each other\'s bets for the game to be played. If money is used instead of chips and depending on the laws of where it is being played, street craps can be an illegal form of gambling.
There are many variations of street craps. The simplest way is to either agree on or roll a number as the point, then roll the point again before rolling a seven. Unlike more complex proposition bets offered by casinos, street craps has more simplified betting options. The shooter is required to make either a Pass or a Don\'t Pass bet if he wants to roll the dice. Another player must choose to cover the shooter to create a stake for the game to continue.
If there are several players, the rotation of the player who must cover the shooter may change with the shooter (comparable to a blind in poker). The person covering the shooter will always bet against the shooter. For example, if the shooter made a \"Pass\" bet, the person covering the shooter would make a \"Don\'t Pass\" bet to win. Once the shooter is covered, other players may make Pass/Don\'t Pass bets, or any other proposition bets, as long as there is another player willing to cover.
## In popular culture {#in_popular_culture}
Due to the random nature of the game, in popular culture a **\"crapshoot\"** is often used to describe an action with an unpredictable outcome.
The prayer or invocation \"Baby needs a new pair of shoes!\" is associated with shooting craps.
### Floating craps {#floating_craps}
**Floating craps** is an illegal operation of craps. The term *floating* refers to the practice of the game\'s operators using portable tables and equipment to quickly move the game from location to location to stay ahead of the law enforcement authorities. The term may have originated in the 1930s when Benny Binion (later known for founding the downtown Las Vegas hotel Binion\'s) set up an illegal craps game utilizing tables created from portable crates for the Texas Centennial Exposition.
The 1950 Broadway musical *Guys and Dolls* features a major plot point revolving around a floating craps game.
In the 1950s and 1960s The Sands Hotel in Las Vegas had a craps table that floated in the swimming pool, as a joke reference to the notoriety of the term.
### Records
A Golden Arm is a craps player who rolls the dice for longer than one hour without losing. Likely the first known Golden Arm was Oahu native Stanley Fujitake, who rolled 118 times without sevening out in 3 hours and 6 minutes at the California Hotel and Casino on May 28, 1989.
The current record for length of a \"hand\" (successive rounds won by the same shooter) is 154 rolls including 25 passes by Patricia DeMauro of New Jersey, lasting 4 hours and 18 minutes, at the Borgata in Atlantic City, New Jersey, on May 23--24, 2009. She bested by over an hour the record held for almost 20 years -- that of Fujitake.
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Common Lisp
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**Common Lisp** (**CL**) is a dialect of the Lisp programming language, published in American National Standards Institute (ANSI) standard document *ANSI INCITS 226-1994 (S2018)* (formerly *X3.226-1994 (R1999)*). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard.
The Common Lisp language was developed as a standardized and improved successor of Maclisp. By the early 1980s several groups were already at work on diverse successors to MacLisp: Lisp Machine Lisp (aka ZetaLisp), Spice Lisp, NIL and S-1 Lisp. Common Lisp sought to unify, standardise, and extend the features of these MacLisp dialects. Common Lisp is not an implementation, but rather a language specification. Several implementations of the Common Lisp standard are available, including free and open-source software and proprietary products. Common Lisp is a general-purpose, multi-paradigm programming language. It supports a combination of procedural, functional, and object-oriented programming paradigms. As a dynamic programming language, it facilitates evolutionary and incremental software development, with iterative compilation into efficient run-time programs. This incremental development is often done interactively without interrupting the running application.
It also supports optional type annotation and casting, which can be added as necessary at the later profiling and optimization stages, to permit the compiler to generate more efficient code. For instance, `fixnum` can hold an unboxed integer in a range supported by the hardware and implementation, permitting more efficient arithmetic than on big integers or arbitrary precision types. Similarly, the compiler can be told on a per-module or per-function basis which type of safety level is wanted, using *optimize* declarations.
Common Lisp includes CLOS, an object system that supports multimethods and method combinations. It is often implemented with a Metaobject Protocol.
Common Lisp is extensible through standard features such as *Lisp macros* (code transformations) and *reader macros* (input parsers for characters).
Common Lisp provides partial backwards compatibility with Maclisp and John McCarthy\'s original Lisp. This allows older Lisp software to be ported to Common Lisp.
## History
Work on Common Lisp started in 1981 after an initiative by ARPA manager Bob Engelmore to develop a single community standard Lisp dialect. Much of the initial language design was done via electronic mail. In 1982, Guy L. Steele Jr. gave the first overview of Common Lisp at the 1982 ACM Symposium on LISP and functional programming.
The first language documentation was published in 1984 as Common Lisp the Language (known as CLtL1), first edition. A second edition (known as CLtL2), published in 1990, incorporated many changes to the language, made during the ANSI Common Lisp standardization process: extended LOOP syntax, the Common Lisp Object System, the Condition System for error handling, an interface to the pretty printer and much more. But CLtL2 does not describe the final ANSI Common Lisp standard and thus is not a documentation of ANSI Common Lisp. The final ANSI Common Lisp standard then was published in 1994. Since then no update to the standard has been published. Various extensions and improvements to Common Lisp (examples are Unicode, Concurrency, CLOS-based IO) have been provided by implementations and libraries.
## Syntax
Common Lisp is a dialect of Lisp. It uses S-expressions to denote both code and data structure. Function calls, macro forms and special forms are written as lists, with the name of the operator first, as in these examples:
``` lisp
(+ 2 2) ; adds 2 and 2, yielding 4. The function's name is '+'. Lisp has no operators as such.
```
``` lisp
(defvar *x*) ; Ensures that a variable *x* exists,
; without giving it a value. The asterisks are part of
; the name, by convention denoting a special (global) variable.
; The symbol *x* is also hereby endowed with the property that
; subsequent bindings of it are dynamic, rather than lexical.
(setf *x* 42.1) ; Sets the variable *x* to the floating-point value 42.1
```
``` lisp
;; Define a function that squares a number:
(defun square (x)
(* x x))
```
``` lisp
;; Execute the function:
(square 3) ; Returns 9
```
``` lisp
;; The 'let' construct creates a scope for local variables. Here
;; the variable 'a' is bound to 6 and the variable 'b' is bound
;; to 4. Inside the 'let' is a 'body', where the last computed value is returned.
;; Here the result of adding a and b is returned from the 'let' expression.
;; The variables a and b have lexical scope, unless the symbols have been
;; marked as special variables (for instance by a prior DEFVAR).
(let ((a 6)
(b 4))
(+ a b)) ; returns 10
```
## Data types {#data_types}
Common Lisp has many data types.
### Scalar types {#scalar_types}
*Number* types include integers, ratios, floating-point numbers, and complex numbers. Common Lisp uses bignums to represent numerical values of arbitrary size and precision. The ratio type represents fractions exactly, a facility not available in many languages. Common Lisp automatically coerces numeric values among these types as appropriate.
The Common Lisp *character* type is not limited to ASCII characters. Most modern implementations allow Unicode characters.
The *symbol* type is common to Lisp languages, but largely unknown outside them. A symbol is a unique, named data object with several parts: name, value, function, property list, and package. Of these, *value cell* and *function cell* are the most important. Symbols in Lisp are often used similarly to identifiers in other languages: to hold the value of a variable; however there are many other uses. Normally, when a symbol is evaluated, its value is returned. Some symbols evaluate to themselves, for example, all symbols in the keyword package are self-evaluating. Boolean values in Common Lisp are represented by the self-evaluating symbols T and NIL. Common Lisp has namespaces for symbols, called \'packages\'.
A number of functions are available for rounding scalar numeric values in various ways. The function `round` rounds the argument to the nearest integer, with halfway cases rounded to the even integer. The functions `truncate`, `floor`, and `ceiling` round towards zero, down, or up respectively. All these functions return the discarded fractional part as a secondary value. For example, `(floor -2.5)` yields −3, 0.5; `(ceiling -2.5)` yields −2, −0.5; `(round 2.5)` yields 2, 0.5; and `(round 3.5)` yields 4, −0.5.
### Data structures {#data_structures}
*Sequence* types in Common Lisp include lists, vectors, bit-vectors, and strings. There are many operations that can work on any sequence type.
As in almost all other Lisp dialects, *lists* in Common Lisp are composed of *conses*, sometimes called *cons cells* or *pairs*. A cons is a data structure with two slots, called its *car* and *cdr*. A list is a linked chain of conses or the empty list. Each cons\'s car refers to a member of the list (possibly another list). Each cons\'s cdr refers to the next cons---except for the last cons in a list, whose cdr refers to the `nil` value. Conses can also easily be used to implement trees and other complex data structures; though it is usually advised to use structure or class instances instead. It is also possible to create circular data structures with conses.
Common Lisp supports multidimensional *arrays*, and can dynamically resize *adjustable* arrays if required. Multidimensional arrays can be used for matrix mathematics. A *vector* is a one-dimensional array. Arrays can carry any type as members (even mixed types in the same array) or can be specialized to contain a specific type of members, as in a vector of bits. Usually, only a few types are supported. Many implementations can optimize array functions when the array used is type-specialized. Two type-specialized array types are standard: a *string* is a vector of characters, while a *bit-vector* is a vector of bits.
*Hash tables* store associations between data objects. Any object may be used as key or value. Hash tables are automatically resized as needed.
*Packages* are collections of symbols, used chiefly to separate the parts of a program into namespaces. A package may *export* some symbols, marking them as part of a public interface. Packages can use other packages.
*Structures*, similar in use to C structs and Pascal records, represent arbitrary complex data structures with any number and type of fields (called *slots*). Structures allow single-inheritance.
*Classes* are similar to structures, but offer more dynamic features and multiple-inheritance. (See CLOS). Classes have been added late to Common Lisp and there is some conceptual overlap with structures. Objects created of classes are called *Instances*. A special case is Generic Functions. Generic Functions are both functions and instances.
### Functions
Common Lisp supports first-class functions. For instance, it is possible to write functions that take other functions as arguments or return functions as well. This makes it possible to describe very general operations.
The Common Lisp library relies heavily on such higher-order functions. For example, the `sort` function takes a relational operator as an argument and key function as an optional keyword argument. This can be used not only to sort any type of data, but also to sort data structures according to a key.
``` lisp
;; Sorts the list using the > and < function as the relational operator.
(sort (list 5 2 6 3 1 4) #'>) ; Returns (6 5 4 3 2 1)
(sort (list 5 2 6 3 1 4) #'<) ; Returns (1 2 3 4 5 6)
```
``` lisp
;; Sorts the list according to the first element of each sub-list.
(sort (list '(9 A) '(3 B) '(4 C)) #'< :key #'first) ; Returns ((3 B) (4 C) (9 A))
```
The evaluation model for functions is very simple. When the evaluator encounters a form `(f a1 a2...)` then it presumes that the symbol named f is one of the following:
1. A special operator (easily checked against a fixed list)
2. A macro operator (must have been defined previously)
3. The name of a function (default), which may either be a symbol, or a sub-form beginning with the symbol `lambda`.
If f is the name of a function, then the arguments a1, a2, \..., an are evaluated in left-to-right order, and the function is found and invoked with those values supplied as parameters.
#### Defining functions {#defining_functions}
The macro `defun` defines functions where a function definition gives the name of the function, the names of any arguments, and a function body:
``` lisp
(defun square (x)
(* x x))
```
Function definitions may include compiler directives, known as *declarations*, which provide hints to the compiler about optimization settings or the data types of arguments. They may also include *documentation strings* (docstrings), which the Lisp system may use to provide interactive documentation:
``` lisp
(defun square (x)
"Calculates the square of the single-float x."
(declare (single-float x) (optimize (speed 3) (debug 0) (safety 1)))
(the single-float (* x x)))
```
Anonymous functions (function literals) are defined using `lambda` expressions, e.g. `(lambda (x) (* x x))` for a function that squares its argument. Lisp programming style frequently uses higher-order functions for which it is useful to provide anonymous functions as arguments.
Local functions can be defined with `flet` and `labels`.
``` lisp
(flet ((square (x)
(* x x)))
(square 3))
```
There are several other operators related to the definition and manipulation of functions. For instance, a function may be compiled with the `compile` operator. (Some Lisp systems run functions using an interpreter by default unless instructed to compile; others compile every function).
#### Defining generic functions and methods {#defining_generic_functions_and_methods}
The macro `defgeneric` defines generic functions. Generic functions are a collection of methods. The macro `defmethod` defines methods.
Methods can specialize their parameters over CLOS *standard classes*, *system classes*, *structure classes* or individual objects. For many types, there are corresponding *system classes*.
When a generic function is called, multiple-dispatch will determine the effective method to use.
``` lisp
(defgeneric add (a b))
```
``` lisp
(defmethod add ((a number) (b number))
(+ a b))
```
``` lisp
(defmethod add ((a vector) (b number))
(map 'vector (lambda (n) (+ n b)) a))
```
``` lisp
(defmethod add ((a vector) (b vector))
(map 'vector #'+ a b))
```
``` lisp
(defmethod add ((a string) (b string))
(concatenate 'string a b))
```
``` lisp
(add 2 3) ; returns 5
(add #(1 2 3 4) 7) ; returns #(8 9 10 11)
(add #(1 2 3 4) #(4 3 2 1)) ; returns #(5 5 5 5)
(add "COMMON " "LISP") ; returns "COMMON LISP"
```
Generic Functions are also a first class data type. There are many more features to Generic Functions and Methods than described above.
#### The function namespace {#the_function_namespace}
The namespace for function names is separate from the namespace for data variables. This is a key difference between Common Lisp and Scheme. For Common Lisp, operators that define names in the function namespace include `defun`, `flet`, `labels`, `defmethod` and `defgeneric`.
To pass a function by name as an argument to another function, one must use the `function` special operator, commonly abbreviated as `#'`. The first `sort` example above refers to the function named by the symbol `>` in the function namespace, with the code `#'>`. Conversely, to call a function passed in such a way, one would use the `funcall` operator on the argument.
Scheme\'s evaluation model is simpler: there is only one namespace, and all positions in the form are evaluated (in any order) -- not just the arguments. Code written in one dialect is therefore sometimes confusing to programmers more experienced in the other. For instance, many Common Lisp programmers like to use descriptive variable names such as *list* or *string* which could cause problems in Scheme, as they would locally shadow function names.
Whether a separate namespace for functions is an advantage is a source of contention in the Lisp community. It is usually referred to as the *Lisp-1 vs. Lisp-2 debate*. Lisp-1 refers to Scheme\'s model and Lisp-2 refers to Common Lisp\'s model. These names were coined in a 1988 paper by Richard P. Gabriel and Kent Pitman, which extensively compares the two approaches.
#### Multiple return values {#multiple_return_values}
Common Lisp supports the concept of *multiple values*, where any expression always has a single *primary value*, but it might also have any number of *secondary values*, which might be received and inspected by interested callers. This concept is distinct from returning a list value, as the secondary values are fully optional, and passed via a dedicated side channel. This means that callers may remain entirely unaware of the secondary values being there if they have no need for them, and it makes it convenient to use the mechanism for communicating information that is sometimes useful, but not always necessary. For example,
- The `TRUNCATE` function rounds the given number to an integer towards zero. However, it also returns a remainder as a secondary value, making it very easy to determine what value was truncated. It also supports an optional divisor parameter, which can be used to perform Euclidean division trivially:
``` cl
(let ((x 1266778)
(y 458))
(multiple-value-bind (quotient remainder)
(truncate x y)
(format nil "~A divided by ~A is ~A remainder ~A" x y quotient remainder)))
;;;; => "1266778 divided by 458 is 2765 remainder 408"
```
- `GETHASH` returns the value of a key in an associative map, or the default value otherwise, and a secondary Boolean indicating whether the value was found. Thus code that does not care about whether the value was found or provided as the default can simply use it as-is, but when such distinction is important, it might inspect the secondary Boolean and react appropriately. Both use cases are supported by the same call and neither is unnecessarily burdened or constrained by the other. Having this feature at the language level removes the need to check for the existence of the key or compare it to null as would be done in other languages.
``` cl
(defun get-answer (library)
(gethash 'answer library 42))
(defun the-answer-1 (library)
(format nil "The answer is ~A" (get-answer library)))
;;;; Returns "The answer is 42" if ANSWER not present in LIBRARY
(defun the-answer-2 (library)
(multiple-value-bind (answer sure-p)
(get-answer library)
(if (not sure-p)
"I don't know"
(format nil "The answer is ~A" answer))))
;;;; Returns "I don't know" if ANSWER not present in LIBRARY
```
Multiple values are supported by a handful of standard forms, most common of which are the `MULTIPLE-VALUE-BIND` special form for accessing secondary values and `VALUES` for returning multiple values:
``` cl
(defun magic-eight-ball ()
"Return an outlook prediction, with the probability as a secondary value"
(values "Outlook good" (random 1.0)))
;;;; => "Outlook good"
;;;; => 0.3187
```
### Other types {#other_types}
Other data types in Common Lisp include:
- *Pathnames* represent files and directories in the filesystem. The Common Lisp pathname facility is more general than most operating systems\' file naming conventions, making Lisp programs\' access to files broadly portable across diverse systems.
- Input and output *streams* represent sources and sinks of binary or textual data, such as the terminal or open files.
- Common Lisp has a built-in pseudo-random number generator (PRNG). *Random state* objects represent reusable sources of pseudo-random numbers, allowing the user to seed the PRNG or cause it to replay a sequence.
- *Conditions* are a type used to represent errors, exceptions, and other \"interesting\" events to which a program may respond.
- *Classes* are first-class objects, and are themselves instances of classes called metaobject classes (metaclasses for short).
- *Readtables* are a type of object which control how Common Lisp\'s reader parses the text of source code. By controlling which readtable is in use when code is read in, the programmer can change or extend the language\'s syntax.
## Scope
Like programs in many other programming languages, Common Lisp programs make use of names to refer to variables, functions, and many other kinds of entities. Named references are subject to scope.
The association between a name and the entity which the name refers to is called a binding.
Scope refers to the set of circumstances in which a name is determined to have a particular binding.
### Determiners of scope {#determiners_of_scope}
The circumstances which determine scope in Common Lisp include:
- the location of a reference within an expression. If it\'s the leftmost position of a compound, it refers to a special operator or a macro or function binding, otherwise to a variable binding or something else.
- the kind of expression in which the reference takes place. For instance, `(go x)` means transfer control to label `x`, whereas `(print x)` refers to the variable `x`. Both scopes of `x` can be active in the same region of program text, since tagbody labels are in a separate namespace from variable names. A special form or macro form has complete control over the meanings of all symbols in its syntax. For instance, in `(defclass x (a b) ())`, a class definition, the `(a b)` is a list of base classes, so these names are looked up in the space of class names, and `x` isn\'t a reference to an existing binding, but the name of a new class being derived from `a` and `b`. These facts emerge purely from the semantics of `defclass`. The only generic fact about this expression is that `defclass` refers to a macro binding; everything else is up to `defclass`.
- the location of the reference within the program text. For instance, if a reference to variable `x` is enclosed in a binding construct such as a `let` which defines a binding for `x`, then the reference is in the scope created by that binding.
- for a variable reference, whether or not a variable symbol has been, locally or globally, declared special. This determines whether the reference is resolved within a lexical environment, or within a dynamic environment.
- the specific instance of the environment in which the reference is resolved. An environment is a run-time dictionary which maps symbols to bindings. Each kind of reference uses its own kind of environment. References to lexical variables are resolved in a lexical environment, et cetera. More than one environment can be associated with the same reference. For instance, thanks to recursion or the use of multiple threads, multiple activations of the same function can exist at the same time. These activations share the same program text, but each has its own lexical environment instance.
To understand what a symbol refers to, the Common Lisp programmer must know what kind of reference is being expressed, what kind of scope it uses if it is a variable reference (dynamic versus lexical scope), and also the run-time situation: in what environment is the reference resolved, where was the binding introduced into the environment, et cetera.
### Kinds of environment {#kinds_of_environment}
#### Global
Some environments in Lisp are globally pervasive. For instance, if a new type is defined, it is known everywhere thereafter. References to that type look it up in this global environment.
#### Dynamic
One type of environment in Common Lisp is the dynamic environment. Bindings established in this environment have dynamic extent, which means that a binding is established at the start of the execution of some construct, such as a `let` block, and disappears when that construct finishes executing: its lifetime is tied to the dynamic activation and deactivation of a block. However, a dynamic binding is not just visible within that block; it is also visible to all functions invoked from that block. This type of visibility is known as indefinite scope. Bindings which exhibit dynamic extent (lifetime tied to the activation and deactivation of a block) and indefinite scope (visible to all functions which are called from that block) are said to have dynamic scope.
Common Lisp has support for dynamically scoped variables, which are also called special variables. Certain other kinds of bindings are necessarily dynamically scoped also, such as restarts and catch tags. Function bindings cannot be dynamically scoped using `flet` (which only provides lexically scoped function bindings), but function objects (a first-level object in Common Lisp) can be assigned to dynamically scoped variables, bound using `let` in dynamic scope, then called using `funcall` or `APPLY`.
Dynamic scope is extremely useful because it adds referential clarity and discipline to global variables. Global variables are frowned upon in computer science as potential sources of error, because they can give rise to ad-hoc, covert channels of communication among modules that lead to unwanted, surprising interactions.
In Common Lisp, a special variable which has only a top-level binding behaves just like a global variable in other programming languages. A new value can be stored into it, and that value simply replaces what is in the top-level binding. Careless replacement of the value of a global variable is at the heart of bugs caused by the use of global variables. However, another way to work with a special variable is to give it a new, local binding within an expression. This is sometimes referred to as \"rebinding\" the variable. Binding a dynamically scoped variable temporarily creates a new memory location for that variable, and associates the name with that location. While that binding is in effect, all references to that variable refer to the new binding; the previous binding is hidden. When execution of the binding expression terminates, the temporary memory location is gone, and the old binding is revealed, with the original value intact. Of course, multiple dynamic bindings for the same variable can be nested.
In Common Lisp implementations which support multithreading, dynamic scopes are specific to each thread of execution. Thus special variables serve as an abstraction for thread local storage. If one thread rebinds a special variable, this rebinding has no effect on that variable in other threads. The value stored in a binding can only be retrieved by the thread which created that binding. If each thread binds some special variable `*x*`, then `*x*` behaves like thread-local storage. Among threads which do not rebind `*x*`, it behaves like an ordinary global: all of these threads refer to the same top-level binding of `*x*`.
Dynamic variables can be used to extend the execution context with additional context information which is implicitly passed from function to function without having to appear as an extra function parameter. This is especially useful when the control transfer has to pass through layers of unrelated code, which simply cannot be extended with extra parameters to pass the additional data. A situation like this usually calls for a global variable. That global variable must be saved and restored, so that the scheme doesn\'t break under recursion: dynamic variable rebinding takes care of this. And that variable must be made thread-local (or else a big mutex must be used) so the scheme doesn\'t break under threads: dynamic scope implementations can take care of this also.
In the Common Lisp library, there are many standard special variables. For instance, all standard I/O streams are stored in the top-level bindings of well-known special variables. The standard output stream is stored in \*standard-output\*.
Suppose a function foo writes to standard output:
``` lisp
(defun foo ()
(format t "Hello, world"))
```
To capture its output in a character string, \*standard-output\* can be bound to a string stream and called:
``` lisp
(with-output-to-string (*standard-output*)
(foo))
```
` -> "Hello, world" ; gathered output returned as a string`
#### Lexical
Common Lisp supports lexical environments. Formally, the bindings in a lexical environment have lexical scope and may have either an indefinite extent or dynamic extent, depending on the type of namespace. Lexical scope means that visibility is physically restricted to the block in which the binding is established. References which are not textually (i.e. lexically) embedded in that block simply do not see that binding.
The tags in a TAGBODY have lexical scope. The expression (GO X) is erroneous if it is not embedded in a TAGBODY which contains a label X. However, the label bindings disappear when the TAGBODY terminates its execution, because they have dynamic extent. If that block of code is re-entered by the invocation of a lexical closure, it is invalid for the body of that closure to try to transfer control to a tag via GO:
``` lisp
(defvar *stashed*) ;; will hold a function
(tagbody
(setf *stashed* (lambda () (go some-label)))
(go end-label) ;; skip the (print "Hello")
some-label
(print "Hello")
end-label)
-> NIL
```
When the TAGBODY is executed, it first evaluates the setf form which stores a function in the special variable \*stashed\*. Then the (go end-label) transfers control to end-label, skipping the code (print \"Hello\"). Since end-label is at the end of the tagbody, the tagbody terminates, yielding NIL. Suppose that the previously remembered function is now called:
``` lisp
(funcall *stashed*) ;; Error!
```
This situation is erroneous. One implementation\'s response is an error condition containing the message, \"GO: tagbody for tag SOME-LABEL has already been left\". The function tried to evaluate (go some-label), which is lexically embedded in the tagbody, and resolves to the label. However, the tagbody isn\'t executing (its extent has ended), and so the control transfer cannot take place.
Local function bindings in Lisp have lexical scope, and variable bindings also have lexical scope by default. By contrast with GO labels, both of these have indefinite extent. When a lexical function or variable binding is established, that binding continues to exist for as long as references to it are possible, even after the construct which established that binding has terminated. References to lexical variables and functions after the termination of their establishing construct are possible thanks to lexical closures.
Lexical binding is the default binding mode for Common Lisp variables. For an individual symbol, it can be switched to dynamic scope, either by a local declaration, by a global declaration. The latter may occur implicitly through the use of a construct like DEFVAR or DEFPARAMETER. It is an important convention in Common Lisp programming that special (i.e. dynamically scoped) variables have names which begin and end with an asterisk sigil `*` in what is called the \"earmuff convention\". If adhered to, this convention effectively creates a separate namespace for special variables, so that variables intended to be lexical are not accidentally made special.
Lexical scope is useful for several reasons.
Firstly, references to variables and functions can be compiled to efficient machine code, because the run-time environment structure is relatively simple. In many cases it can be optimized to stack storage, so opening and closing lexical scopes has minimal overhead. Even in cases where full closures must be generated, access to the closure\'s environment is still efficient; typically each variable becomes an offset into a vector of bindings, and so a variable reference becomes a simple load or store instruction with a base-plus-offset addressing mode.
Secondly, lexical scope (combined with indefinite extent) gives rise to the lexical closure, which in turn creates a whole paradigm of programming centered around the use of functions being first-class objects, which is at the root of functional programming.
Thirdly, perhaps most importantly, even if lexical closures are not exploited, the use of lexical scope isolates program modules from unwanted interactions. Due to their restricted visibility, lexical variables are private. If one module A binds a lexical variable X, and calls another module B, references to X in B will not accidentally resolve to the X bound in A. B simply has no access to X. For situations in which disciplined interactions through a variable are desirable, Common Lisp provides special variables. Special variables allow for a module A to set up a binding for a variable X which is visible to another module B, called from A. Being able to do this is an advantage, and being able to prevent it from happening is also an advantage; consequently, Common Lisp supports both lexical and dynamic scope.
## Macros
A *macro* in Lisp superficially resembles a function in usage. However, rather than representing an expression which is evaluated, it represents a transformation of the program source code. The macro gets the source it surrounds as arguments, binds them to its parameters and computes a new source form. This new form can also use a macro. The macro expansion is repeated until the new source form does not use a macro. The final computed form is the source code executed at runtime.
Typical uses of macros in Lisp:
- new control structures (example: looping constructs, branching constructs)
- scoping and binding constructs
- simplified syntax for complex and repeated source code
- top-level defining forms with compile-time side-effects
- data-driven programming
- embedded domain specific languages (examples: SQL, HTML, Prolog)
- implicit finalization forms
Various standard Common Lisp features also need to be implemented as macros, such as:
- the standard `setf` abstraction, to allow custom compile-time expansions of assignment/access operators
- `with-accessors`, `with-slots`, `with-open-file` and other similar `WITH` macros
- Depending on implementation, `if` or `cond` is a macro built on the other, the special operator; `when` and `unless` consist of macros
- The powerful `loop` domain-specific language
Macros are defined by the *defmacro* macro. The special operator *macrolet* allows the definition of local (lexically scoped) macros. It is also possible to define macros for symbols using *define-symbol-macro* and *symbol-macrolet*.
Paul Graham\'s book On Lisp describes the use of macros in Common Lisp in detail. Doug Hoyte\'s book Let Over Lambda extends the discussion on macros, claiming \"Macros are the single greatest advantage that lisp has as a programming language and the single greatest advantage of any programming language.\" Hoyte provides several examples of iterative development of macros.
### Example using a macro to define a new control structure {#example_using_a_macro_to_define_a_new_control_structure}
Macros allow Lisp programmers to create new syntactic forms in the language. One typical use is to create new control structures. The example macro provides an `until` looping construct. The syntax is:
``` text
(until test form*)
```
The macro definition for *until*:
``` lisp
(defmacro until (test &body body)
(let ((start-tag (gensym "START"))
(end-tag (gensym "END")))
`(tagbody ,start-tag
(when ,test (go ,end-tag))
(progn ,@body)
(go ,start-tag)
,end-tag)))
```
*tagbody* is a primitive Common Lisp special operator which provides the ability to name tags and use the *go* form to jump to those tags. The backquote *\`* provides a notation that provides code templates, where the value of forms preceded with a comma are filled in. Forms preceded with comma and at-sign are *spliced* in. The tagbody form tests the end condition. If the condition is true, it jumps to the end tag. Otherwise, the provided body code is executed and then it jumps to the start tag.
An example of using the above *until* macro:
``` lisp
(until (= (random 10) 0)
(write-line "Hello"))
```
The code can be expanded using the function *macroexpand-1*. The expansion for the above example looks like this:
``` lisp
(TAGBODY
#:START1136
(WHEN (ZEROP (RANDOM 10))
(GO #:END1137))
(PROGN (WRITE-LINE "hello"))
(GO #:START1136)
#:END1137)
```
During macro expansion the value of the variable *test* is *(= (random 10) 0)* and the value of the variable *body* is *((write-line \"Hello\"))*. The body is a list of forms.
Symbols are usually automatically upcased. The expansion uses the TAGBODY with two labels. The symbols for these labels are computed by GENSYM and are not interned in any package. Two *go* forms use these tags to jump to. Since *tagbody* is a primitive operator in Common Lisp (and not a macro), it will not be expanded into something else. The expanded form uses the *when* macro, which also will be expanded. Fully expanding a source form is called *code walking*.
In the fully expanded (*walked*) form, the *when* form is replaced by the primitive *if*:
``` lisp
(TAGBODY
#:START1136
(IF (ZEROP (RANDOM 10))
(PROGN (GO #:END1137))
NIL)
(PROGN (WRITE-LINE "hello"))
(GO #:START1136))
#:END1137)
```
All macros must be expanded before the source code containing them can be evaluated or compiled normally. Macros can be considered functions that accept and return S-expressions -- similar to abstract syntax trees, but not limited to those. These functions are invoked before the evaluator or compiler to produce the final source code. Macros are written in normal Common Lisp, and may use any Common Lisp (or third-party) operator available.
### Variable capture and shadowing {#variable_capture_and_shadowing}
Common Lisp macros are capable of what is commonly called *variable capture*, where symbols in the macro-expansion body coincide with those in the calling context, allowing the programmer to create macros wherein various symbols have special meaning. The term *variable capture* is somewhat misleading, because all namespaces are vulnerable to unwanted capture, including the operator and function namespace, the tagbody label namespace, catch tag, condition handler and restart namespaces.
*Variable capture* can introduce software defects. This happens in one of the following two ways:
- In the first way, a macro expansion can inadvertently make a symbolic reference which the macro writer assumed will resolve in a global namespace, but the code where the macro is expanded happens to provide a local, shadowing definition which steals that reference. Let this be referred to as type 1 capture.
- The second way, type 2 capture, is just the opposite: some of the arguments of the macro are pieces of code supplied by the macro caller, and those pieces of code are written such that they make references to surrounding bindings. However, the macro inserts these pieces of code into an expansion which defines its own bindings that accidentally captures some of these references.
The Scheme dialect of Lisp provides a macro-writing system which provides the referential transparency that eliminates both types of capture problem. This type of macro system is sometimes called \"hygienic\", in particular by its proponents (who regard macro systems which do not automatically solve this problem as unhygienic).
In Common Lisp, macro hygiene is ensured one of two different ways.
One approach is to use gensyms: guaranteed-unique symbols which can be used in a macro-expansion without threat of capture. The use of gensyms in a macro definition is a manual chore, but macros can be written which simplify the instantiation and use of gensyms. Gensyms solve type 2 capture easily, but they are not applicable to type 1 capture in the same way, because the macro expansion cannot rename the interfering symbols in the surrounding code which capture its references. Gensyms could be used to provide stable aliases for the global symbols which the macro expansion needs. The macro expansion would use these secret aliases rather than the well-known names, so redefinition of the well-known names would have no ill effect on the macro.
Another approach is to use packages. A macro defined in its own package can simply use internal symbols in that package in its expansion. The use of packages deals with type 1 and type 2 capture.
However, packages don\'t solve the type 1 capture of references to standard Common Lisp functions and operators. The reason is that the use of packages to solve capture problems revolves around the use of private symbols (symbols in one package, which are not imported into, or otherwise made visible in other packages). Whereas the Common Lisp library symbols are external, and frequently imported into or made visible in user-defined packages.
The following is an example of unwanted capture in the operator namespace, occurring in the expansion of a macro:
``` lisp
;; expansion of UNTIL makes liberal use of DO
(defmacro until (expression &body body)
`(do () (,expression) ,@body))
;; macrolet establishes lexical operator binding for DO
(macrolet ((do (...) ... something else ...))
(until (= (random 10) 0) (write-line "Hello")))
```
The `until` macro will expand into a form which calls `do` which is intended to refer to the standard Common Lisp macro `do`. However, in this context, `do` may have a completely different meaning, so `until` may not work properly.
Common Lisp solves the problem of the shadowing of standard operators and functions by forbidding their redefinition. Because it redefines the standard operator `do`, the preceding is actually a fragment of non-conforming Common Lisp, which allows implementations to diagnose and reject it.
## Condition system {#condition_system}
The *condition system* is responsible for exception handling in Common Lisp. It provides *conditions*, *handler*s and *restart*s. *Condition*s are objects describing an exceptional situation (for example an error). If a *condition* is signaled, the Common Lisp system searches for a *handler* for this condition type and calls the handler. The *handler* can now search for restarts and use one of these restarts to automatically repair the current problem, using information such as the condition type and any relevant information provided as part of the condition object, and call the appropriate restart function.
These restarts, if unhandled by code, can be presented to users (as part of a user interface, that of a debugger for example), so that the user can select and invoke one of the available restarts. Since the condition handler is called in the context of the error (without unwinding the stack), full error recovery is possible in many cases, where other exception handling systems would have already terminated the current routine. The debugger itself can also be customized or replaced using the `*debugger-hook*` dynamic variable. Code found within *unwind-protect* forms such as finalizers will also be executed as appropriate despite the exception.
In the following example (using Symbolics Genera) the user tries to open a file in a Lisp function *test* called from the Read-Eval-Print-LOOP (REPL), when the file does not exist. The Lisp system presents four restarts. The user selects the *Retry OPEN using a different pathname* restart and enters a different pathname (lispm-init.lisp instead of lispm-int.lisp). The user code does not contain any error handling code. The whole error handling and restart code is provided by the Lisp system, which can handle and repair the error without terminating the user code.
``` text
Command: (test ">zippy>lispm-int.lisp")
Error: The file was not found.
For lispm:>zippy>lispm-int.lisp.newest
LMFS:OPEN-LOCAL-LMFS-1
Arg 0: #P"lispm:>zippy>lispm-int.lisp.newest"
s-A, <Resume>: Retry OPEN of lispm:>zippy>lispm-int.lisp.newest
s-B: Retry OPEN using a different pathname
s-C, <Abort>: Return to Lisp Top Level in a TELNET server
s-D: Restart process TELNET terminal
-> Retry OPEN using a different pathname
Use what pathname instead [default lispm:>zippy>lispm-int.lisp.newest]:
lispm:>zippy>lispm-init.lisp.newest
...the program continues
```
## Common Lisp Object System (CLOS) {#common_lisp_object_system_clos}
Common Lisp includes a toolkit for object-oriented programming, the Common Lisp Object System or CLOS. Peter Norvig explains how many Design Patterns are simpler to implement in a dynamic language with the features of CLOS (Multiple Inheritance, Mixins, Multimethods, Metaclasses, Method combinations, etc.). Several extensions to Common Lisp for object-oriented programming have been proposed to be included into the ANSI Common Lisp standard, but eventually CLOS was adopted as the standard object-system for Common Lisp. CLOS is a dynamic object system with multiple dispatch and multiple inheritance, and differs radically from the OOP facilities found in static languages such as C++ or Java. As a dynamic object system, CLOS allows changes at runtime to generic functions and classes. Methods can be added and removed, classes can be added and redefined, objects can be updated for class changes and the class of objects can be changed.
CLOS has been integrated into ANSI Common Lisp. Generic functions can be used like normal functions and are a first-class data type. Every CLOS class is integrated into the Common Lisp type system. Many Common Lisp types have a corresponding class. There is more potential use of CLOS for Common Lisp. The specification does not say whether conditions are implemented with CLOS. Pathnames and streams could be implemented with CLOS. These further usage possibilities of CLOS for ANSI Common Lisp are not part of the standard. Actual Common Lisp implementations use CLOS for pathnames, streams, input--output, conditions, the implementation of CLOS itself and more.
## Compiler and interpreter {#compiler_and_interpreter}
A Lisp interpreter directly executes Lisp source code provided as Lisp objects (lists, symbols, numbers, \...) read from s-expressions. A Lisp compiler generates bytecode or machine code from Lisp source code. Common Lisp allows both individual Lisp functions to be compiled in memory and the compilation of whole files to externally stored compiled code (*fasl* files).
Several implementations of earlier Lisp dialects provided both an interpreter and a compiler. Unfortunately often the semantics were different. These earlier Lisps implemented lexical scoping in the compiler and dynamic scoping in the interpreter. Common Lisp requires that both the interpreter and compiler use lexical scoping by default. The Common Lisp standard describes both the semantics of the interpreter and a compiler. The compiler can be called using the function *compile* for individual functions and using the function *compile-file* for files. Common Lisp allows type declarations and provides ways to influence the compiler code generation policy. For the latter various optimization qualities can be given values between 0 (not important) and 3 (most important): *speed*, *space*, *safety*, *debug* and *compilation-speed*.
There is also a function to evaluate Lisp code: `eval`. `eval` takes code as pre-parsed s-expressions and not, like in some other languages, as text strings. This way code can be constructed with the usual Lisp functions for constructing lists and symbols and then this code can be evaluated with the function `eval`. Several Common Lisp implementations (like Clozure CL and SBCL) are implementing `eval` using their compiler. This way code is compiled, even though it is evaluated using the function `eval`.
The file compiler is invoked using the function *compile-file*. The generated file with compiled code is called a *fasl* (from *fast load*) file. These *fasl* files and also source code files can be loaded with the function *load* into a running Common Lisp system. Depending on the implementation, the file compiler generates byte-code (for example for the Java Virtual Machine), C language code (which then is compiled with a C compiler) or, directly, native code.
Common Lisp implementations can be used interactively, even though the code gets fully compiled. The idea of an Interpreted language thus does not apply for interactive Common Lisp.
The language makes a distinction between read-time, compile-time, load-time, and run-time, and allows user code to also make this distinction to perform the wanted type of processing at the wanted step.
Some special operators are provided to especially suit interactive development; for instance, `defvar` will only assign a value to its provided variable if it wasn\'t already bound, while `defparameter` will always perform the assignment. This distinction is useful when interactively evaluating, compiling and loading code in a live image.
Some features are also provided to help writing compilers and interpreters. Symbols consist of first-level objects and are directly manipulable by user code. The `progv` special operator allows to create lexical bindings programmatically, while packages are also manipulable. The Lisp compiler is available at runtime to compile files or individual functions. These make it easy to use Lisp as an intermediate compiler or interpreter for another language.
## Code examples {#code_examples}
### Birthday paradox {#birthday_paradox}
The following program calculates the smallest number of people in a room for whom the probability of unique birthdays is less than 50% (the birthday paradox, where for 1 person the probability is obviously 100%, for 2 it is 364/365, etc.). The answer is 23.
In Common Lisp, by convention, constants are enclosed with + characters.
``` lisp
(defconstant +year-size+ 365)
(defun birthday-paradox (probability number-of-people)
(let ((new-probability (* (/ (- +year-size+ number-of-people)
+year-size+)
probability)))
(if (< new-probability 0.5)
(1+ number-of-people)
(birthday-paradox new-probability (1+ number-of-people)))))
```
Calling the example function using the REPL (Read Eval Print Loop):
``` text
CL-USER > (birthday-paradox 1.0 1)
23
```
### Sorting a list of person objects {#sorting_a_list_of_person_objects}
We define a class `person` and a method for displaying the name and age of a person. Next we define a group of persons as a list of `person` objects. Then we iterate over the sorted list.
``` lisp
(defclass person ()
((name :initarg :name :accessor person-name)
(age :initarg :age :accessor person-age))
(:documentation "The class PERSON with slots NAME and AGE."))
(defmethod display ((object person) stream)
"Displaying a PERSON object to an output stream."
(with-slots (name age) object
(format stream "~a (~a)" name age)))
(defparameter *group*
(list (make-instance 'person :name "Bob" :age 33)
(make-instance 'person :name "Chris" :age 16)
(make-instance 'person :name "Ash" :age 23))
"A list of PERSON objects.")
(dolist (person (sort (copy-list *group*)
#'>
:key #'person-age))
(display person *standard-output*)
(terpri))
```
It prints the three names with descending age.
``` text
Bob (33)
Ash (23)
Chris (16)
```
### Exponentiating by squaring {#exponentiating_by_squaring}
Use of the LOOP macro is demonstrated:
``` lisp
(defun power (x n)
(loop with result = 1
while (plusp n)
when (oddp n) do (setf result (* result x))
do (setf x (* x x)
n (truncate n 2))
finally (return result)))
```
Example use:
``` lisp
CL-USER > (power 2 200)
1606938044258990275541962092341162602522202993782792835301376
```
Compare with the built in exponentiation:
``` lisp
CL-USER > (= (expt 2 200) (power 2 200))
T
```
### Find the list of available shells {#find_the_list_of_available_shells}
WITH-OPEN-FILE is a macro that opens a file and provides a stream. When the form is returning, the file is automatically closed. FUNCALL calls a function object. The LOOP collects all lines that match the predicate.
``` lisp
(defun list-matching-lines (file predicate)
"Returns a list of lines in file, for which the predicate applied to
the line returns T."
(with-open-file (stream file)
(loop for line = (read-line stream nil nil)
while line
when (funcall predicate line)
collect it)))
```
The function AVAILABLE-SHELLS calls the above function LIST-MATCHING-LINES with a pathname and an anonymous function as the predicate. The predicate returns the pathname of a shell or NIL (if the string is not the filename of a shell).
``` lisp
(defun available-shells (&optional (file #p"/etc/shells"))
(list-matching-lines
file
(lambda (line)
(and (plusp (length line))
(char= (char line 0) #\/)
(pathname
(string-right-trim '(#\space #\tab) line))))))
```
Example results (on Mac OS X 10.6):
``` lisp
CL-USER > (available-shells)
(#P"/bin/bash" #P"/bin/csh" #P"/bin/ksh" #P"/bin/sh" #P"/bin/tcsh" #P"/bin/zsh")
```
## Comparison with other Lisps {#comparison_with_other_lisps}
Common Lisp is most frequently compared with, and contrasted to, Scheme---if only because they are the two most popular Lisp dialects. Scheme predates CL, and comes not only from the same Lisp tradition but from some of the same engineers---Guy Steele, with whom Gerald Jay Sussman designed Scheme, chaired the standards committee for Common Lisp.
Common Lisp is a general-purpose programming language, in contrast to Lisp variants such as Emacs Lisp and AutoLISP which are extension languages embedded in particular products (GNU Emacs and AutoCAD, respectively). Unlike many earlier Lisps, Common Lisp (like Scheme) uses lexical variable scope by default for both interpreted and compiled code.
Most of the Lisp systems whose designs contributed to Common Lisp---such as ZetaLisp and Franz Lisp---used dynamically scoped variables in their interpreters and lexically scoped variables in their compilers. Scheme introduced the sole use of lexically scoped variables to Lisp; an inspiration from ALGOL 68. CL supports dynamically scoped variables as well, but they must be explicitly declared as \"special\". There are no differences in scoping between ANSI CL interpreters and compilers.
Common Lisp is sometimes termed a *Lisp-2* and Scheme a *Lisp-1*, referring to CL\'s use of separate namespaces for functions and variables. (In fact, CL has *many* namespaces, such as those for go tags, block names, and `loop` keywords). There is a long-standing controversy between CL and Scheme advocates over the tradeoffs involved in multiple namespaces. In Scheme, it is (broadly) necessary to avoid giving variables names that clash with functions; Scheme functions frequently have arguments named `lis`, `lst`, or `lyst` so as not to conflict with the system function `list`. However, in CL it is necessary to explicitly refer to the function namespace when passing a function as an argument---which is also a common occurrence, as in the `sort` example above.
CL also differs from Scheme in its handling of Boolean values. Scheme uses the special values #t and #f to represent truth and falsity. CL follows the older Lisp convention of using the symbols T and NIL, with NIL standing also for the empty list. In CL, *any* non-NIL value is treated as true by conditionals, such as `if`, whereas in Scheme all non-#f values are treated as true. These conventions allow some operators in both languages to serve both as predicates (answering a Boolean-valued question) and as returning a useful value for further computation, but in Scheme the value \'() which is equivalent to NIL in Common Lisp evaluates to true in a Boolean expression.
Lastly, the Scheme standards documents require tail-call optimization, which the CL standard does not. Most CL implementations do offer tail-call optimization, although often only when the programmer uses an optimization directive. Nonetheless, common CL coding style does not favor the ubiquitous use of recursion that Scheme style prefers---what a Scheme programmer would express with tail recursion, a CL user would usually express with an iterative expression in `do`, `dolist`, `loop`, or (more recently) with the `iterate` package.
## Implementations
See the Category Common Lisp implementations.
Common Lisp is defined by a specification (like Ada and C) rather than by one implementation (like Perl). There are many implementations, and the standard details areas in which they may validly differ.
In addition, implementations tend to come with extensions, which provide functionality not covered in the standard:
- Interactive Top-Level (REPL)
- Garbage Collection
- Debugger, Stepper and Inspector
- Weak data structures (hash tables)
- Extensible sequences
- Extensible LOOP
- Environment access
- CLOS Meta-object Protocol
- CLOS based extensible streams
- CLOS based Condition System
- Network streams
- Persistent CLOS
- Unicode support
- Foreign-Language Interface (often to C)
- Operating System interface
- Java Interface
- Threads and Multiprocessing
- Application delivery (applications, dynamic libraries)
- Saving of images
Free and open-source software libraries have been created to support extensions to Common Lisp in a portable way, and are most notably found in the repositories of the Common-Lisp.net and CLOCC (Common Lisp Open Code Collection) projects.
Common Lisp implementations may use any mix of native code compilation, byte code compilation or interpretation. Common Lisp has been designed to support incremental compilers, file compilers and block compilers. Standard declarations to optimize compilation (such as function inlining or type specialization) are proposed in the language specification. Most Common Lisp implementations compile source code to native machine code. Some implementations can create (optimized) stand-alone applications. Others compile to interpreted bytecode, which is less efficient than native code, but eases binary-code portability. Some compilers compile Common Lisp code to C code. The misconception that Lisp is a purely interpreted language is most likely because Lisp environments provide an interactive prompt and that code is compiled one-by-one, in an incremental way. With Common Lisp incremental compilation is widely used.
Some Unix-based implementations (CLISP, SBCL) can be used as a scripting language; that is, invoked by the system transparently in the way that a Perl or Unix shell interpreter is.
### List of implementations {#list_of_implementations}
#### Commercial implementations {#commercial_implementations}
Allegro Common Lisp: for Microsoft Windows, FreeBSD, Linux, Apple macOS and various UNIX variants. Allegro CL provides an Integrated Development Environment (IDE) (for Windows and Linux) and extensive capabilities for application delivery.\
Liquid Common Lisp: formerly called Lucid Common Lisp. Only maintenance, no new releases.\
LispWorks: for Microsoft Windows, FreeBSD, Linux, Apple macOS, iOS, Android and various UNIX variants. LispWorks provides an Integrated Development Environment (IDE) (available for most platforms, but not for iOS and Android) and extensive capabilities for application delivery.\
mocl: for iOS, Android and macOS.\
Open Genera: for DEC Alpha.\
Scieneer Common Lisp: which is designed for high-performance scientific computing.
#### Freely redistributable implementations {#freely_redistributable_implementations}
Armed Bear Common Lisp (ABCL): A CL implementation that runs on the Java Virtual Machine. It includes a compiler to Java byte code, and allows access to Java libraries from CL. It was formerly just a component of the Armed Bear J Editor.\
Clasp: A LLVM based implementation that seamlessly interoperates with C++ libraries. Runs on several Unix and Unix-like systems (including macOS).\
CLISP: A bytecode-compiling implementation, portable and runs on several Unix and Unix-like systems (including macOS), as well as Microsoft Windows and several other systems.\
Clozure CL (CCL): Originally a free and open-source fork of Macintosh Common Lisp. As that history implies, CCL was written for the Macintosh, but Clozure CL now runs on macOS, FreeBSD, Linux, Solaris and Windows. 32 and 64 bit x86 ports are supported on each platform. Additionally there are Power PC ports for Mac OS and Linux. CCL was previously known as OpenMCL, but that name is no longer used, to avoid confusion with the open source version of Macintosh Common Lisp.\
CMUCL: Originally from Carnegie Mellon University, now maintained as free and open-source software by a group of volunteers. CMUCL uses a fast native-code compiler. It is available on Linux and BSD for Intel x86; Linux for Alpha; macOS for Intel x86 and PowerPC; and Solaris, IRIX, and HP-UX on their native platforms.\
Corman Common Lisp: for Microsoft Windows. In January 2015 Corman Lisp has been published under MIT license.\
Embeddable Common Lisp (ECL): ECL includes a bytecode interpreter and compiler. It can also compile Lisp code to machine code via a C compiler. ECL then compiles Lisp code to C, compiles the C code with a C compiler and can then load the resulting machine code. It is also possible to embed ECL in C programs, and C code into Common Lisp programs.\
GNU Common Lisp (GCL): The GNU Project\'s Lisp compiler. Not yet fully ANSI-compliant, GCL is however the implementation of choice for several large projects including the mathematical tools Maxima, AXIOM and (historically) ACL2. GCL runs on Linux under eleven different architectures, and also under Windows, Solaris, and FreeBSD.\
Macintosh Common Lisp (MCL): Version 5.2 for Apple Macintosh computers with a PowerPC processor running Mac OS X is open source. RMCL (based on MCL 5.2) runs on Intel-based Apple Macintosh computers using the Rosetta binary translator from Apple.\
ManKai Common Lisp (MKCL): A branch of ECL. MKCL emphasises reliability, stability and overall code quality through a heavily reworked, natively multi-threaded, runtime system. On Linux, MKCL features a fully POSIX compliant runtime system.\
Movitz: Implements a Lisp environment for x86 computers without relying on any underlying OS.\
Poplog: Poplog implements a version of CL, with POP-11, and optionally Prolog, and Standard ML (SML), allowing mixed language programming. For all, the implementation language is POP-11, which is compiled incrementally. It also has an integrated Emacs-like editor that communicates with the compiler.\
Steel Bank Common Lisp (SBCL): A branch from CMUCL. \"Broadly speaking, SBCL is distinguished from CMU CL by a greater emphasis on maintainability.\"{{cite web
`|url=`[`http://sbcl.sourceforge.net/history.html`](http://sbcl.sourceforge.net/history.html)\
`|title=History and Copyright |work=Steel Bank Common Lisp`
}}
SBCL runs on the platforms CMUCL does, except HP/UX; in addition, it runs on Linux for AMD64, PowerPC, SPARC, MIPS, Windows x86 and AMD64. SBCL does not use an interpreter by default; all expressions are compiled to native code unless the user switches the interpreter on. The SBCL compiler generates fast native code according to a previous version of The Computer Language Benchmarks Game.
Ufasoft Common Lisp: port of CLISP for windows platform with core written in C++.
#### Other implementations {#other_implementations}
Austin Kyoto Common Lisp: an evolution of Kyoto Common Lisp by Bill Schelter\
Butterfly Common Lisp: an implementation written in Scheme for the BBN Butterfly multi-processor computer\
CLICC: a Common Lisp to C compiler\
CLOE: Common Lisp for PCs by Symbolics\
Codemist Common Lisp: used for the commercial version of the computer algebra system Axiom\
ExperCommon Lisp: an early implementation for the Apple Macintosh by ExperTelligence\
Golden Common Lisp: an implementation for the PC by GoldHill Inc.\
Ibuki Common Lisp: a commercialized version of Kyoto Common Lisp\
Kyoto Common Lisp: the first Common Lisp compiler that used C as a target language. GCL, ECL and MKCL originate from this Common Lisp implementation.\
L: a small version of Common Lisp for embedded systems developed by IS Robotics, now iRobot\
Lisp Machines (from Symbolics, TI and Xerox): provided implementations of Common Lisp in addition to their native Lisp dialect (Lisp Machine Lisp or Interlisp). CLOS was also available. Symbolics provides an enhanced version Common Lisp.\
Procyon Common Lisp: an implementation for Windows and Mac OS, used by Franz for their Windows port of Allegro CL\
Star Sapphire Common LISP: an implementation for the PC\
SubL: a variant of Common Lisp used for the implementation of the Cyc knowledge-based system\
Top Level Common Lisp: an early implementation for concurrent execution\
WCL: a shared library implementation\
VAX Common Lisp: Digital Equipment Corporation\'s implementation that ran on VAX systems running VMS or ULTRIX\
XLISP: an implementation written by David Betz
## Applications
Common Lisp is used to develop research applications (often in Artificial Intelligence), for rapid development of prototypes or for deployed applications.
Common Lisp is used in many commercial applications, including the Yahoo! Store web-commerce site, which originally involved Paul Graham and was later rewritten in C++ and Perl. Other notable examples include:
- ACT-R, a cognitive architecture used in a large number of research projects.
- Authorizer\'s Assistant, a large rule-based system used by American Express, analyzing credit requests.
- Cyc, a long running project to create a knowledge-based system that provides a huge amount of common sense knowledge.
- Gensym G2, a real-time expert system and business rules engine
- Genworks GDL, based on the open-source Gendl kernel.
- The development environment for the *Jak and Daxter* video game series, developed by Naughty Dog.
- ITA Software\'s low fare search engine, used by travel websites such as Orbitz and Kayak.com and airlines such as American Airlines, Continental Airlines and US Airways.
- Mirai, a 3D graphics suite.
- Opusmodus is a music composition system based on Common Lisp, used in Computer assisted composition.
- Prototype Verification System (PVS), a mechanized environment for formal specification and verification.
- PWGL is a sophisticated visual programming environment based on Common Lisp, used in Computer assisted composition and sound synthesis.
- Piano, a complete aircraft analysis suite, written in Common Lisp, used by companies like Boeing, Airbus, and Northrop Grumman.
- Grammarly, an English-language writing-enhancement platform, has its core grammar engine written in Common Lisp.
- The Dynamic Analysis and Replanning Tool (DART), which is said to alone have paid back during the years from 1991 to 1995 for all thirty years of DARPA investments in AI research.
- NASA\'s Jet Propulsion Lab\'s \"Deep Space 1\", an award-winning Common Lisp program for autopiloting the Deep Space One spaceship.
- SigLab, a Common Lisp platform for signal processing used in missile defense, built by Raytheon.
- NASA\'s Mars Pathfinder Mission Planning System.
- SPIKE, a scheduling system for Earth or space based observatories and satellites, notably the Hubble Space Telescope, written in Common Lisp.
- Common Lisp has been used for prototyping the garbage collector of Microsoft\'s .NET Common Language Runtime.
- The original version of Reddit, though the developers later switched to Python due to the lack of libraries for Common Lisp, according to an official blog post by Reddit co-founder Steve Huffman. The reddit v1 source code has been open-sourced and modernized.
There also exist open-source applications written in Common Lisp, such as:
- ACL2, a full-featured automated theorem prover for an applicative variant of Common Lisp.
- Axiom, a sophisticated computer algebra system.
- Maxima, a sophisticated computer algebra system, based on Macsyma.
- OpenMusic, an object-oriented visual programming environment based on Common Lisp, used in computer assisted composition.
- Pgloader, a data loader for PostgreSQL, which was re-written from Python to Common Lisp.
- Stumpwm, a tiling, keyboard driven X11 Window Manager written entirely in Common Lisp.
| 2025-06-20T00:00:00 |
6,069 |
Color code
|
A **color code** is a system for encoding and representing non-color information with colors to facilitate communication. This information tends to be categorical (representing unordered/qualitative categories) though may also be sequential (representing an ordered/quantitative variable).
## History
The earliest examples of color codes in use are for long-distance communication by use of flags, as in semaphore communication. The United Kingdom adopted a color code scheme for such communication wherein red signified danger and white signified safety, with other colors having similar assignments of meaning.
As chemistry and other technologies advanced, it became expedient to use coloration as a signal for telling apart things that would otherwise be confusingly similar, such as wiring in electrical and electronic devices, and pharmaceutical pills.
## Encoded Variable {#encoded_variable}
A color code encodes a variable, which may have different representations, where the color code type should match the variable type:
- Categorical variable -- the variable may represent discrete values of unordered qualitative data (e.g. blood type)
- Binary variables are typically treated as a categorical variable (e.g. sex)
- Quantitative variable -- the variable represents ordered, quantitative data (e.g. age)
- Discrete quantitative data (e.g. the 6 sides of a die: 1,2,3,4,5,6) are sometimes treated as a categorical variable, despite the ordered nature.
## Types
The types of color code are:
- **Categorical** -- the colors are unordered, but are chosen to maximize saliency of the colors, by maximizing color difference between all color pair permutations.
- **Continuous** -- the colors are ordered and form a smooth color gradient.
- **Discrete** -- only a subset of a continuous color code are used (still ordered), where each is distinguishable from the others.
### Categorical
When color is the only varied attribute, the color code is *unidimensional*. When other attributes are varied (e.g. shape, size), the code is *multidimensional*, where the dimensions can be *independent* (each encoding separate variables) or *redundant* (encoding the same variable). Partial redundancy sees one variable as a subset of another. For example, playing card suits are multidimensional with color (black, red) and shape (club, diamond, heart, spade), which are partially redundant since clubs and spades are always black and diamonds and hearts are always red. Tasks using categorical color codes can be classified as identification tasks, where a single stimulus is shown and must be identified (connotatively or denotatively), versus search tasks, where a color stimulus must be found within a field of heterogenous stimuli. Performance in these tasks is measured by speed and/or accuracy.
The ideal color scheme for a categorical color code depends on whether speed or accuracy is more important. Despite humans being able to distinguish 150 distinct colors along the hue dimension during comparative task, evidence supports that color schemes where colors differ only by hue (equal luminosity and colorfulness) should have a maximum of eight categories with optimized stimulus spacing along the hue dimension, though this would not be color blind accessible. The IALA recommends categorical color codes in seven colors: red, orange, yellow, green, blue, white and black. Adding redundant coding of luminosity and colorfulness adds information and increases speed and accuracy of color decoding tasks. Color codes are superior to others (encoding to letters, shape, size, etc.) in certain types of tasks. Adding color as a redundant attribute to a numeral or letter encoding in search tasks decreased time by 50--75%,`{{r|CHRIST75|at=Fig9}}`{=mediawiki} but in unidimensional identification tasks, using alphanumeric or line inclination codes caused less errors than color codes.`{{r|1=JONES62|2=CHRIST75|p2=19}}`{=mediawiki}
Several studies demonstrate a subjective preference for color codes over achromatic codes (e.g. shapes), even in studies where color coding did not increase performance over achromatic coding.`{{r|CHRIST75|p=18}}`{=mediawiki} Subjects reported the tasks as less monotonous and less inducing of eye strain and fatigue.`{{r|CHRIST75|p=18}}`{=mediawiki}
The ability to discriminate color differences decreases rapidly as the visual angle subtends less than 12\' (0.2° or \~2 mm at a viewing distance of 50 cm), so color stimulus of at least 3 mm in diameter or thickness is recommended when the color is on paper or on a screen. Under normal conditions, colored backgrounds do not affect the interpretation of color codes, but chromatic (and/or low) illumination of surface color code can degrade performance.
## Criticism
Color codes present some potential problems. On forms and signage, the use of color can distract from black and white text.
Color codes are often designed without consideration for accessibility to color blind and blind people, and may even be inaccessible for those with normal color vision, since use of many colors to code many variables can lead to use of confusingly similar colors. Only 15--40% of the colorblind can correctly name surface color codes with 8--10 color categories, most of which test as mildly colorblind. This finding uses ideal illumination; when dimmer illumination is used, performance drops sharply.
## Examples
Systems incorporating color-coding include:
- In electricity:
- 25-pair color code -- telecommunications wiring
- ANSI Z535.1 Color Safety Code Standards
- Audio and video interfaces and connectors § Color codes
- Optical fibers § Color codes
- Electrical wiring -- AC power phase, neutral, and grounding wires
- Electronic color code AKA resistor or EIA color code (today -- IEC 60062:2016)
- Ethernet twisted-pair wiring -- local area networks
- Jumper cables used to jump-start a vehicle
- PC99 connectors and ports
- Surround sound ports and cables
- Three-phase electric power § Color codes (electrical wiring)
- In video games
- Health and magic points
- To distinguish friend from foe, for instance in *StarCraft*, *Halo*, or *League of Legends*
- To distinguish rarity or quality of items in adventure and role-playing games
- In navigation:
- Characteristic light
- Navigation light
- Sea mark
- Traffic lights
- Other technology:
- At point of sale (especially for packaging within a huge range of products: to quickly differentiate variants, brands, categories)
- ANSI Standardized Safety Colors ANSI Z535
- Bottled gases
- Fire extinguishers
- Kerbside collection
- Pipe marking
- Queen bee birth year code
- Underground utility location
- Hospital emergency codes often incorporate colors (such as the widely used \"Code Blue\" indicating a cardiac arrest),
- In military use:
- Homeland Security Advisory System
- Artillery shells and other munitions, which are color-coded according to their pyrotechnic contents
- List of Rainbow Codes
- NATO Military Symbols for Land Based Systems
- Rainbow Herbicides
- In social functions:
- Black hat hacking, white hat, grey hat
- Blue-collar worker, white-collar worker, pink-collar worker, grey-collar, green-collar worker
- Handkerchief code
- ISO 22324, Guidelines for color-coded alerts in public warning
- Cooper\'s Color Code of the combat mindset
- Rank in judo
- Ribbon colors *see:* :Category:Ribbon symbolism
- In religion:
- Clerical vestments, frontals and altar hangings in Christian churches
| 2025-06-20T00:00:00 |
6,091 |
Charles Robert Malden
|
**Charles Robert Malden** (9 August 1797 -- 23 May 1855) was a nineteenth-century British naval officer, surveyor and educator. He is the discoverer of Malden Island in the central Pacific, which is named in his honour. He also founded Windlesham House School at Brighton, England.
## Biography
Malden was born in Putney, Surrey, son of Jonas Malden, a surgeon. He entered British naval service at the age of 11 on 22 June 1809. He served nine years as a volunteer 1st class, midshipman, and shipmate, including one year in the English Channel and Bay of Biscay (1809), four years at the Cape of Good Hope and in the East Indies (1809--14), two and a half years on the North American and West Indian stations (1814--16), and a year and a half in the Mediterranean (1817--18). He was present at the capture of Mauritius and Java, and at the battles of Baltimore and New Orleans.
He passed the examination in the elements of mathematics and the theory of navigation at the Royal Naval Academy on 2--4 September 1816, and became a 1st Lieutenant on 1 September 1818. In eight years of active service as an officer, he served two and a half years in a surveying ship in the Mediterranean (1818--21), one and a half years in a surveying sloop in the English Channel and off the coast of Ireland (1823--24), and one and a half years as Surveyor of the frigate `{{HMS|Blonde|1819|6}}`{=mediawiki} during a voyage (1824--26) to and from the Hawaiian Islands (then known as the \"Sandwich islands\"). In Hawaii he surveyed harbours which, he noted, were \"said not to exist by Captains Cook and Vancouver.\" On the return voyage he discovered and explored uninhabited Malden Island in the central Pacific on 30 July 1825. After his return he left active service but remained at half pay. He served for several years as hydrographer to King William IV.
He married Frances Cole, daughter of Rev. William Hodgson Cole, rector of West Clandon and Vicar of Wonersh, near Guildford, Surrey, on 8 April 1828. Malden became the father of seven sons and a daughter.
From 1830 to 1836 he took pupils for the Royal Navy at Ryde, Isle of Wight. He purchased the school of Henry Worsley at Newport, Isle of Wight, in December 1836, reopened it as a preparatory school on 20 February 1837, and moved it to Montpelier Road in Brighton in December 1837. He built the Windlesham House School at Brighton in 1844, and conducted the school until his death there in 1855. He was succeeded as headmaster by his son Henry Charles Malden.
| 2025-06-20T00:00:00 |
6,097 |
Canonization
|
`{{Use dmy dates|date=October 2020}}`{=mediawiki} `{{Use American English|date=February 2016}}`{=mediawiki}
**Canonization** is the declaration of a deceased person as an officially recognized saint, specifically, the official act of a Christian communion declaring a person worthy of public veneration and entering their name in the canon catalogue of saints, or authorized list of that communion\'s recognized saints.
## Catholic Church {#catholic_church}
`{{Catholic canon law}}`{=mediawiki} Canonization is a papal declaration that the Catholic faithful may venerate a particular deceased member of the church. Popes began making such decrees in the tenth century. Up to that point, the local bishops governed the veneration of holy men and women within their own dioceses; and there may have been, for any particular saint, no formal decree at all. In subsequent centuries, the procedures became increasingly regularized and the Popes began restricting to themselves the right to declare someone a Catholic saint. In contemporary usage, the term is understood to refer to the act by which any Christian church declares that a person who has died is a saint, upon which declaration the person is included in the list of recognized saints, called the \"canon\".
### Biblical roots {#biblical_roots}
In the Roman Martyrology, the following entry is given for the Penitent Thief: \"At Jerusalem, the commemoration of the good Thief, who confessed Christ on the cross, and deserved to hear from Him these words: \'This day thou shalt be with Me in paradise.\'
### Historical development {#historical_development}
The Roman Canon, the historical Eucharistic Prayer or Anaphora of Canon of the Roman Rite contains only the names of apostles and martyrs, along with that of the Blessed Virgin Mary and, since 1962, that of Saint Joseph her spouse.
By the fourth century, however, \"confessors\"---people who had confessed their faith not by dying but by word and life---began to be venerated publicly. Examples of such people are Saint Hilarion and Saint Ephrem the Syrian in the East, and Saint Martin of Tours and Saint Hilary of Poitiers in the West. Their names were inserted in the diptychs, the lists of saints explicitly venerated in the liturgy, and their tombs were honoured in like manner as those of the martyrs. Since the witness of their lives was not as unequivocal as that of the martyrs, they were venerated publicly only with the approval by the local bishop. This process is often referred to as \"local canonization\".
This approval was required even for veneration of a reputed martyr. In his history of the Donatist heresy, Saint Optatus recounts that at Carthage a Catholic matron, named Lucilla, incurred the censures of the Church for having kissed the relics of a reputed martyr whose claims to martyrdom had not been juridically proved. And Saint Cyprian (died 258) recommended that the utmost diligence be observed in investigating the claims of those who were said to have died for the faith. All the circumstances accompanying the martyrdom were to be inquired into; the faith of those who suffered, and the motives that animated them were to be rigorously examined, in order to prevent the recognition of undeserving persons. Evidence was sought from the court records of the trials or from people who had been present at the trials.
Augustine of Hippo (died 430) tells of the procedure which was followed in his day for the recognition of a martyr. The bishop of the diocese in which the martyrdom took place set up a canonical process for conducting the inquiry with the utmost severity. The acts of the process were sent either to the metropolitan or primate, who carefully examined the cause, and, after consultation with the suffragan bishops, declared whether the deceased was worthy of the name of \"martyr\" and public veneration.
Though not \"canonizations\" in the narrow sense, acts of formal recognition, such as the erection of an altar over the saint\'s tomb or transferring the saint\'s relics to a church, were preceded by formal inquiries into the sanctity of the person\'s life and the miracles attributed to that person\'s intercession.
Such acts of recognition of a saint were authoritative, in the strict sense, only for the diocese or ecclesiastical province for which they were issued, but with the spread of the fame of a saint, were often accepted elsewhere also.
### Nature
In the Catholic Church, both in the Latin and the constituent Eastern churches, the act of canonization is reserved to the Apostolic See and occurs at the conclusion of a long process requiring extensive proof that the candidate for canonization lived and died in such an exemplary and holy way that they are worthy to be recognized as a saint. The Church\'s official recognition of sanctity implies that the person is now in Heaven and that they may be publicly invoked and mentioned officially in the liturgy of the Church, including in the Litany of the Saints.
In the Catholic Church, canonization is a decree that allows universal veneration of the saint. For permission to venerate merely locally, only beatification is needed.
### Procedure prior to reservation to the Apostolic See {#procedure_prior_to_reservation_to_the_apostolic_see}
For several centuries the bishops, or in some places only the primates and patriarchs, could grant martyrs and confessors public ecclesiastical honor; such honor, however, was always decreed only for the local territory of which the grantors had jurisdiction. Only acceptance of the *cultus* by the Pope made the *cultus* universal, because he alone can rule the universal Catholic Church. Abuses, however, crept into this discipline, due as well to indiscretions of popular fervor as to the negligence of some bishops in inquiring into the lives of those whom they permitted to be honoured as saints.
In the Medieval West, the Apostolic See was asked to intervene in the question of canonizations so as to ensure more authoritative decisions. The canonization of Saint Udalric, Bishop of Augsburg by Pope John XV in 993 was the first undoubted example of papal canonization of a saint from outside of Rome being declared worthy of liturgical veneration for the entire church.
Thereafter, recourse to the judgment of the Pope occurred more frequently. Toward the end of the 11th century, the Popes began asserting their exclusive right to authorize the veneration of a saint against the older rights of bishops to do so for their dioceses and regions. Popes therefore decreed that the virtues and miracles of persons proposed for public veneration should be examined in councils, more specifically in general councils. Pope Urban II, Pope Calixtus II, and Pope Eugene III conformed to this discipline.
### Exclusive reservation to the Apostolic See {#exclusive_reservation_to_the_apostolic_see}
Hugh de Boves, Archbishop of Rouen, canonized Walter of Pontoise, or St. Gaultier, in 1153, the final saint in Western Europe to be canonized by an authority other than the Pope: \"The last case of canonization by a metropolitan is said to have been that of St. Gaultier, or Gaucher, \[A\]bbot of Pontoise, by the Archbishop of Rouen. A decree of Pope Alexander III \[in\] 1170 gave the prerogative to the \[P\]ope thenceforth, so far as the Western Church was concerned.\" In a decretal of 1173, Pope Alexander III reprimanded some bishops for permitting veneration of a man who was merely killed while intoxicated, prohibited veneration of the man, and most significantly decreed that \"you shall not therefore presume to honor him in the future; for, even if miracles were worked through him, it is not lawful for you to venerate him as a saint without the authority of the Catholic Church.\" Theologians disagree as to the full import of the decretal of Pope Alexander III: either a new law was instituted, in which case the Pope then for the first time reserved the right of beatification to himself, or an existing law was confirmed.
However, the procedure initiated by the decretal of Pope Alexander III was confirmed by a bull of Pope Innocent III issued on the occasion of the canonization of Cunigunde of Luxembourg in 1200. The bull of Pope Innocent III resulted in increasingly elaborate inquiries to the Apostolic See concerning canonizations. Because the decretal of Pope Alexander III did not end all controversy and some bishops did not obey it in so far as it regarded beatification, the right of which they had certainly possessed hitherto, Pope Urban VIII issued the Apostolic letter *Caelestis Hierusalem cives* of 5 July 1634 that exclusively reserved to the Apostolic See both its immemorial right of canonization and that of beatification. He further regulated both of these acts by issuing his *Decreta servanda in beatificatione et canonizatione Sanctorum* on 12 March 1642.
### Procedure from 1734 to 1738 to 1983 {#procedure_from_1734_to_1738_to_1983}
In his *De Servorum Dei beatificatione et de Beatorum canonizatione* of five volumes the eminent canonist Prospero Lambertini (1675--1758), who later became Pope Benedict XIV, elaborated on the procedural norms of Pope Urban VIII\'s Apostolic letter *Caelestis Hierusalem cives* of 1634 and *Decreta servanda in beatificatione et canonizatione Sanctorum* of 1642, and on the conventional practice of the time. His work published from 1734 to 1738 governed the proceedings until 1917. The article \"Beatification and canonization process in 1914\" describes the procedures followed until the promulgation of the *Codex* of 1917. The substance of *De Servorum Dei beatifιcatione et de Beatorum canonizatione* was incorporated into the *Codex Iuris Canonici* (*Code of Canon Law*) of 1917, which governed until the promulgation of the revised *Codex Iuris Canonici* in 1983 by Pope John Paul II. Prior to promulgation of the revised *Codex* in 1983, Pope Paul VI initiated a simplification of the procedures.
### Since 1983 {#since_1983}
The Apostolic constitution *Divinus Perfectionis Magister* of Pope John Paul II of 25 January 1983 and the norms issued by the Congregation for the Causes of Saints on 7 February 1983 to implement the constitution in dioceses, continued the simplification of the process initiated by Pope Paul VI. Contrary to popular belief, the reforms did not eliminate the office of the Promoter of the Faith (Latin: *Promotor Fidei*), popularly known as the Devil\'s advocate, whose office is to question the material presented in favor of canonization. The reforms were intended to reduce the adversarial nature of the process. In November 2012 Pope Benedict XVI appointed Monsignor Carmello Pellegrino as Promoter of the Faith.
Candidates for canonization undergo the following process: `{{ordered list
| [[Servant of God]] (''Servus Dei''): The process of canonization commences at the diocesan level. A [[bishop]] with jurisdiction, usually the bishop of the place where the candidate died or is buried, although another ordinary can be given this authority, gives permission to open an investigation into the virtues of the individual in response to a petition of members of the faithful, either actually or ''[[pro forma]]''.<ref>Pope John Paul II, [https://www.vatican.va/holy_father/john_paul_ii/apost_constitutions/documents/hf_jp-ii_apc_25011983_divinus-perfectionis-magister_en.html ''Divinus Perfectionis Magister''] (25 January 1983), Art. 1, Sec. 1.</ref> This investigation usually commences no sooner than five years after the death of the person being investigated.<ref>Pietro Cardinal Palazzini, [https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_07021983_norme_en.html ''Norms to be observed in inquiries made by bishops in the causes of saints''], 1983 {{webarchive |url=https://web.archive.org/web/20061022065149/https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_07021983_norme_en.html |date=22 October 2006 }}, §9(a).</ref> The [[Pope]], ''qua'' Bishop of Rome, may also open a process and has the authority to waive the waiting period of five years, e.g., as was done for [[St. Teresa of Calcutta]] by [[Pope John Paul II]],<ref>[https://www.vatican.va/news_services/liturgy/saints/ns_lit_doc_20031019_madre-teresa_en.html ''Mother Teresa of Calcutta (1910–1997), Biography''], Office of Papal Liturgical Celebrations, Internet Office of the Holy See</ref> and for [[Lúcia Santos]] and for [[Pope John Paul II]] himself by [[Pope Benedict XVI]].<ref>{{cite web|url=http://www.zenit.org/article-21764?l=english|title=Sister Lucia's Beatification Process to Begin|work=ZENIT – The World Seen from Rome|access-date=4 October 2014|url-status=dead|archive-url=https://web.archive.org/web/20120927020314/http://www.zenit.org/article-21764?l=english|archive-date=27 September 2012}}</ref><ref>[[Cardinal (Catholicism)|Cardinal]] [[José Saraiva Martins]], [[Claretians|CMF]], [https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_20050509_rescritto-gpii_en.html ''Response of His Holiness Benedict XVI for the Examination of the Cause for Beatification and Canonization of the Servant of God John Paul II''], 2005 {{webarchive |url=https://web.archive.org/web/20090105024819/https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_20050509_rescritto-gpii_en.html |date=5 January 2009 }}</ref> Normally, an association to promote the cause of the candidate is instituted, an exhaustive search of the candidate's writings, speeches, and sermons is undertaken, a detailed biography is written, and eyewitness accounts are collected. When sufficient evidence has been collected, the local bishop presents the investigation of the candidate, who is titled "Servant of God" ([[Latin]]: ''Servus Dei''), to the [[Congregation for the Causes of the Saints]] of the [[Roman Curia]], where the cause is assigned a [[postulator]], whose office is to collect further evidence of the life of the Servant of God. Religious orders that regularly deal with the Congregation often designate their own Postulator General. At some time, permission is then granted for the body of the Servant of God to be exhumed and examined. A certification ''non-cultus'' is made that no superstitious or heretical worship, or improper cult of the Servant of God or her/his tomb has emerged, and relics are taken and preserved.
| [[Venerable]] (''Venerabilis''; abbreviated "Ven.") or "Heroic in Virtue": When sufficient evidence has been collected, the Congregation recommends to the [[Pope]] that he proclaim the [[heroic virtue]] of the Servant of God; that is, that the Servant of God exercised "to a heroic degree" the [[theological virtues]] of faith, hope, and charity and the [[cardinal virtues]] of prudence, justice, fortitude, and temperance. From this time the one said to be "heroic in virtue" is entitled "[[Venerable]]" ([[Latin]]: ''Venerabilis''). A Venerable does not yet have a [[feast day]], permission to erect churches in their honor has not yet been granted, and the Church does not yet issue a statement on their probable or certain presence in [[Heaven]], but [[prayer card]]s and other materials may be printed to encourage the faithful to pray for a [[miracle]] wrought by their intercession as a sign of God's will that the person be canonized.
| [[Beatification|Blessed]] (''Beatus'' or ''Beata''; abbreviated "Bl."): Beatification is a statement of the Church that it is "worthy of belief" that the Venerable is in [[Heaven]] and saved. Attaining this grade depends on whether the Venerable is a [[martyr]]:{{bulleted list
| For a martyr, the [[Pope]] has only to make a declaration of martyrdom, which is a certification that the Venerable gave their life voluntarily as a witness of the Faith or in an [[act of heroic charity]] for others.
| For a non-martyr, all of them being denominated "confessors" because they "confessed", i.e., bore witness to the Faith by how they lived, proof is required of the occurrence of a [[miracle]] through the intercession of the Venerable; that is, that God granted a sign that the person is enjoying the [[beatific vision]] by performing a miracle for which the Venerable interceded. Presently, these miracles are almost always miraculous cures of infirmity, because these are the easiest to judge given the Church's evidentiary requirements for miracles; e.g., a patient was sick with an illness for which no cure was known; prayers were directed to the Venerable; the patient was cured; the cure was spontaneous, instantaneous, complete, and enduring; and physicians cannot discover any natural explanation for the cure.
}}
The satisfaction of the applicable conditions permits [[beatification]], which then bestows on the Venerable the title of "Blessed" ([[Latin]]: ''Beatus'' or ''Beata''). A [[feast day]] will be designated, but its observance is ordinarily only permitted for the Blessed's home [[diocese]], to specific locations associated with them, or to the churches or houses of the Blessed's religious order if they belonged to one. Parishes may not normally be named in honor of ''beati''.
| [[Saint]] (''Sanctus'' or ''Sancta''; abbreviated "St." or "S."): To be canonized as a saint, ordinarily at least two miracles must have been performed through the intercession of the Blessed after their death, but for ''beati'' confessors, i.e., ''beati'' who were not declared martyrs, only one miracle is required, ordinarily being additional to that upon which beatification was premised. Very rarely, a Pope may waive the requirement for a second miracle after beatification if he, the [[College of Cardinals|Sacred College of Cardinals]], and the [[Congregation for the Causes of Saints]] all agree that the Blessed lived a life of great merit proven by certain actions. This extraordinary procedure was used in [[Pope Francis]]' canonization of [[Pope John XXIII]], who convoked the first part of the [[Second Vatican Council]].
}}`{=mediawiki}
Canonization is a statement of the Church that the person certainly enjoys the beatific vision of Heaven. The title of \"Saint\" (Latin: *Sanctus* or *Sancta*) is then proper, reflecting that the saint is a refulgence of the holiness (*sanctitas*) of God himself, which alone comes from God\'s gift. The saint is assigned a feast day which may be celebrated anywhere in the universal Church, although it is not necessarily added to the General Roman Calendar or local calendars as an \"obligatory\" feast; parish churches may be erected in their honor; and the faithful may freely celebrate and honor the saint.
Although recognition of sainthood by the Pope does not directly concern a fact of Divine revelation, nonetheless it must be \"definitively held\" by the faithful as *infallible* pursuant to, at the least, the Universal Magisterium of the Church, because it is a truth related to revelation by historical necessity.
### Equipollent canonization {#equipollent_canonization}
Popes have several times permitted to the universal Church, without executing the ordinary judicial process of canonization described above, the veneration as a saint, the \"*cultus*\" of one long venerated as such locally. This act of a Pope is denominated \"equipollent\" or \"equivalent canonization\" and \"confirmation of *cultus*\". In such cases, there is no need to have a miracle attributed to the saint to allow their canonization. According to the rules Pope Benedict XIV (*regnat* 17 August 1740 -- 3 May 1758) instituted, there are three conditions for an equipollent canonization: (1) existence of an ancient *cultus* of the person, (2) a general and constant attestation to the virtues or martyrdom of the person by credible historians, and (3) uninterrupted fame of the person as a worker of miracles.
## Protestant denominations {#protestant_denominations}
The majority of Protestant denominations do not formally recognize saints because the Bible uses the term in a way that suggests all Christians are saints. However, some denominations do, as shown below.
### Anglican Communion {#anglican_communion}
The Church of England, the Mother Church of the Anglican Communion, canonized Charles I as a saint, in the Convocations of Canterbury and York of 1660.
### United Methodist Church {#united_methodist_church}
The General Conference of the United Methodist Church has formally declared individuals *martyrs*, including Dietrich Bonhoeffer (in 2008) and Martin Luther King Jr. (in 2012).
## Eastern Orthodox Church {#eastern_orthodox_church}
Various terms are used for canonization by the autocephalous Eastern Orthodox Churches: канонизация (\"canonization\") or прославление (\"glorification\", in the Russian Orthodox Church), კანონიზაცია (*kanonizats'ia*, Georgian Orthodox Church), канонизација (Serbian Orthodox Church), *canonizare* (Romanian Orthodox Church), and Канонизация (Bulgarian Orthodox Church). Additional terms are used for canonization by other autocephalous Eastern Orthodox Churches: *αγιοκατάταξη* (Katharevousa: *ἁγιοκατάταξις*) *agiokatataxi/agiokatataxis*, \"ranking among saints\" (Ecumenical Patriarchate of Constantinople, Church of Cyprus, Church of Greece), *kanonizim* (Albanian Orthodox Church), *kanonizacja* (Polish Orthodox Church), and *kanonizace/kanonizácia* (Czech and Slovak Orthodox Church).
The Orthodox Church in America, an Eastern Orthodox Church partly recognized as autocephalous, uses the term \"glorification\" for the official recognition of a person as a saint.
## Oriental Orthodox Church {#oriental_orthodox_church}
Within the Armenian Apostolic Church, part of Oriental Orthodoxy, there had been discussions since the 1980s about canonizing the victims of the Armenian genocide. On 23 April 2015, all of the victims of the genocide were canonized.
| 2025-06-20T00:00:00 |
6,099 |
Carboxylic acid
|
In organic chemistry, a **carboxylic acid** is an organic acid that contains a **carboxyl group** (`{{chem2|\sC(\dO)\sOH}}`{=mediawiki}) attached to an R-group. The general formula of a carboxylic acid is often written as **`{{chem2|R\sCOOH}}`{=mediawiki}** or **`{{chem2|R\sCO2H}}`{=mediawiki}**, sometimes as `{{chem2|R\sC(O)OH}}`{=mediawiki} with R referring to an organyl group (e.g., alkyl, alkenyl, aryl), or hydrogen, or other groups. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion.
## Examples and nomenclature {#examples_and_nomenclature}
Carboxylic acids are commonly identified by their trivial names. They often have the suffix *-ic acid*. `{{anchor|-oic}}`{=mediawiki}IUPAC-recommended names also exist; in this system, carboxylic acids have an *-oic acid* suffix. For example, butyric acid (`{{chem2|CH3CH2CH2CO2H}}`{=mediawiki}) is butanoic acid by IUPAC guidelines. For nomenclature of complex molecules containing a carboxylic acid, the carboxyl can be considered position one of the parent chain even if there are other substituents, such as 3-chloropropanoic acid. Alternately, it can be named as a \"carboxy\" or \"carboxylic acid\" substituent on another parent structure, such as 2-carboxyfuran.
The carboxylate anion (`{{chem2|R\sCOO−}}`{=mediawiki} or `{{chem2|R\sCO2−}}`{=mediawiki}) of a carboxylic acid is usually named with the suffix *-ate*, in keeping with the general pattern of *-ic acid* and *-ate* for a conjugate acid and its conjugate base, respectively. For example, the conjugate base of acetic acid is acetate.
Carbonic acid, which occurs in bicarbonate buffer systems in nature, is not generally classed as one of the carboxylic acids, despite it having a moiety that looks like a COOH group.
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| Carbon\ | Common name | IUPAC name | Chemical formula | Common location or use |
| atoms | | | | |
+=========+===================+====================+==================+==================================================================+
| 1 | Formic acid | Methanoic acid | HCOOH | Insect stings |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 2 | Acetic acid | Ethanoic acid | | Vinegar |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 3 | Propionic acid | Propanoic acid | | Preservative for stored grains, body odour, milk, butter, cheese |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 4 | Butyric acid | Butanoic acid | | Butter |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 5 | Valeric acid | Pentanoic acid | | Valerian plant |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 6 | Caproic acid | Hexanoic acid | | Goat fat |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 7 | Enanthic acid | Heptanoic acid | | Fragrance |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 8 | Caprylic acid | Octanoic acid | | Coconuts |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 9 | Pelargonic acid | Nonanoic acid | | Pelargonium plant |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 10 | Capric acid | Decanoic acid | | Coconut and Palm kernel oil |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 11 | Undecylic acid | Undecanoic acid | | Anti-fungal agent |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 12 | Lauric acid | Dodecanoic acid | | Coconut oil and hand wash soaps |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 13 | Tridecylic acid | Tridecanoic acid | | Plant metabolite |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 14 | Myristic acid | Tetradecanoic acid | | Nutmeg |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 15 | Pentadecylic acid | Pentadecanoic acid | | Milk fat |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 16 | Palmitic acid | Hexadecanoic acid | | Palm oil |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 17 | Margaric acid | Heptadecanoic acid | | Pheromone in various animals |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 18 | Stearic acid | Octadecanoic acid | | Chocolate, waxes, soaps, and oils |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 19 | Nonadecylic acid | Nonadecanoic acid | | Fats, vegetable oils, pheromone |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 20 | Arachidic acid | Icosanoic acid | | Peanut oil |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
: Straight-chain, saturated carboxylic acids (alkanoic acids)
Compound class Members
---------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
unsaturated monocarboxylic acids acrylic acid (2-propenoic acid) -- `{{chem2|CH2\dCH\sCOOH}}`{=mediawiki}, used in polymer synthesis
Fatty acids medium to long-chain saturated and unsaturated monocarboxylic acids, with even number of carbons; examples: docosahexaenoic acid and eicosapentaenoic acid (nutritional supplements)
Amino acids the building-blocks of proteins
Keto acids acids of biochemical significance that contain a ketone group; examples: acetoacetic acid and pyruvic acid
Aromatic carboxylic acids containing at least one aromatic ring; examples: benzoic acid -- the sodium salt of benzoic acid is used as a food preservative; salicylic acid -- a beta-hydroxy type found in many skin-care products; phenyl alkanoic acids -- the class of compounds where a phenyl group is attached to a carboxylic acid
Dicarboxylic acids containing two carboxyl groups; examples: adipic acid the monomer used to produce nylon and aldaric acid -- a family of sugar acids
Tricarboxylic acids containing three carboxyl groups; examples: citric acid -- found in citrus fruits and isocitric acid
Alpha hydroxy acids containing a hydroxy group in the first position; examples: glyceric acid, glycolic acid and lactic acid (2-hydroxypropanoic acid) -- found in sour milk, tartaric acid -- found in wine
Beta hydroxy acids containing a hydroxy group in the second position
Omega hydroxy acids containing a hydroxy group beyond the first or second position
Divinylether fatty acids containing a doubly unsaturated carbon chain attached via an ether bond to a fatty acid, found in some plants
: Other carboxylic acids
## Physical properties {#physical_properties}
### Solubility
Carboxylic acids are polar. Because they are both hydrogen-bond acceptors (the carbonyl `{{chem2|\sC(\dO)\s}}`{=mediawiki}) and hydrogen-bond donors (the hydroxyl `{{chem2|\sOH}}`{=mediawiki}), they also participate in hydrogen bonding. Together, the hydroxyl and carbonyl group form the functional group carboxyl. Carboxylic acids usually exist as dimers in nonpolar media due to their tendency to \"self-associate\". Smaller carboxylic acids (1 to 5 carbons) are soluble in water, whereas bigger carboxylic acids have limited solubility due to the increasing hydrophobic nature of the alkyl chain. These longer chain acids tend to be soluble in less-polar solvents such as ethers and alcohols. Aqueous sodium hydroxide and carboxylic acids, even hydrophobic ones, react to yield water-soluble sodium salts. For example, enanthic acid has a low solubility in water (0.2 g/L), but its sodium salt is very soluble in water.
:
### Boiling points {#boiling_points}
Carboxylic acids tend to have higher boiling points than water, because of their greater surface areas and their tendency to form stabilized dimers through hydrogen bonds. For boiling to occur, either the dimer bonds must be broken or the entire dimer arrangement must be vaporized, increasing the enthalpy of vaporization requirements significantly.
:
### Acidity
Carboxylic acids are Brønsted--Lowry acids because they are proton (H^+^) donors. They are the most common type of organic acid.
Carboxylic acids are typically weak acids, meaning that they only partially dissociate into `{{chem2|[H3O]+}}`{=mediawiki} cations and `{{chem2|R\sCO2−}}`{=mediawiki} anions in neutral aqueous solution. For example, at room temperature, in a 1-molar solution of acetic acid, only 0.001% of the acid are dissociated (i.e. 10^−5^ moles out of 1 mol). Electron-withdrawing substituents such as trifluoromethyl (`{{chem2|\sCF3}}`{=mediawiki}) give stronger acids (the p*K*~a~ of acetic acid is 4.76 whereas trifluoroacetic acid, with a trifluoromethyl substituent, has a p*K*~a~ of 0.23). Electron-donating substituents give weaker acids (the p*K*~a~ of formic acid is 3.75 whereas acetic acid, with a methyl substituent, has a p*K*~a~ of 4.76)
Carboxylic acid p*K*~a~
-------------------------------------------------------------------------------------------------- ---------
Formic acid (`{{chem2|HCO2H}}`{=mediawiki}) 3.75
Chloroformic acid (`{{chem2|ClCO2H}}`{=mediawiki}) 0.27
Acetic acid (`{{chem2|CH3CO2H}}`{=mediawiki}) 4.76
Glycine (`{{chem2|NH2CH2CO2H}}`{=mediawiki}) 2.34
Fluoroacetic acid (`{{chem2|FCH2CO2H}}`{=mediawiki}) 2.586
Difluoroacetic acid (`{{chem2|F2CHCO2H}}`{=mediawiki}) 1.33
Trifluoroacetic acid (`{{chem2|CF3CO2H}}`{=mediawiki}) 0.23
Chloroacetic acid (`{{chem2|ClCH2CO2H}}`{=mediawiki}) 2.86
Dichloroacetic acid (`{{chem2|Cl2CHCO2H}}`{=mediawiki}) 1.29
Trichloroacetic acid (`{{chem2|CCl3CO2H}}`{=mediawiki}) 0.65
Benzoic acid (`{{chem2|C6H5\sCO2H}}`{=mediawiki}) 4.2
2-Nitrobenzoic acid (*ortho*-`{{chem2|C6H4(NO2)CO2H}}`{=mediawiki}) 2.16
Oxalic acid (`{{chem2|HO\sC(\dO)\sC(\dO)\sOH}}`{=mediawiki}) (first dissociation) 1.27
Hydrogen oxalate (`{{chem2|HO\sC(\dO)\sCO2−}}`{=mediawiki}) (second dissociation of oxalic acid) 4.14
Deprotonation of carboxylic acids gives carboxylate anions; these are resonance stabilized, because the negative charge is delocalized over the two oxygen atoms, increasing the stability of the anion. Each of the carbon--oxygen bonds in the carboxylate anion has a partial double-bond character. The carbonyl carbon\'s partial positive charge is also weakened by the −^1^/~2~ negative charges on the 2 oxygen atoms.
### Odour
Carboxylic acids often have strong sour odours. Esters of carboxylic acids tend to have fruity, pleasant odours, and many are used in perfume.
### Characterization
Carboxylic acids are readily identified as such by infrared spectroscopy. They exhibit a sharp band associated with vibration of the C=O carbonyl bond (*ν*~C=O~) between 1680 and 1725 cm^−1^. A characteristic *ν*~O--H~ band appears as a broad peak in the 2500 to 3000 cm^−1^ region. By ^1^H NMR spectrometry, the hydroxyl hydrogen appears in the 10--13 ppm region, although it is often either broadened or not observed owing to exchange with traces of water.
## Occurrence and applications {#occurrence_and_applications}
Many carboxylic acids are produced industrially on a large scale. They are also frequently found in nature. Esters of fatty acids are the main components of lipids and polyamides of aminocarboxylic acids are the main components of proteins.
Carboxylic acids are used in the production of polymers, pharmaceuticals, solvents, and food additives. Industrially important carboxylic acids include acetic acid (component of vinegar, precursor to solvents and coatings), acrylic and methacrylic acids (precursors to polymers, adhesives), adipic acid (polymers), citric acid (a flavor and preservative in food and beverages), ethylenediaminetetraacetic acid (chelating agent), fatty acids (coatings), maleic acid (polymers), propionic acid (food preservative), terephthalic acid (polymers). Important carboxylate salts are soaps.
## Synthesis
### Industrial routes {#industrial_routes}
In general, industrial routes to carboxylic acids differ from those used on a smaller scale because they require specialized equipment.
- Carbonylation of alcohols as illustrated by the Cativa process for the production of acetic acid. Formic acid is prepared by a different carbonylation pathway, also starting from methanol.
- Oxidation of aldehydes with air using cobalt and manganese catalysts. The required aldehydes are readily obtained from alkenes by hydroformylation.
- Oxidation of hydrocarbons using air. For simple alkanes, this method is inexpensive but not selective enough to be useful. Allylic and benzylic compounds undergo more selective oxidations. Alkyl groups on a benzene ring are oxidized to the carboxylic acid, regardless of its chain length. Benzoic acid from toluene, terephthalic acid from *para*-xylene, and phthalic acid from *ortho*-xylene are illustrative large-scale conversions. Acrylic acid is generated from propene.
- Oxidation of ethene using silicotungstic acid catalyst.
- Base-catalyzed dehydrogenation of alcohols.
- Carbonylation coupled to the addition of water. This method is effective and versatile for alkenes that generate secondary and tertiary carbocations, e.g. isobutylene to pivalic acid. In the Koch reaction, the addition of water and carbon monoxide to alkenes or alkynes is catalyzed by strong acids. Hydrocarboxylations involve the simultaneous addition of water and CO. Such reactions are sometimes called \"Reppe chemistry.\"
:
- Hydrolysis of triglycerides obtained from plant or animal oils. These methods of synthesizing some long-chain carboxylic acids are related to soap making.
- Fermentation of ethanol. This method is used in the production of vinegar.
- The Kolbe--Schmitt reaction provides a route to salicylic acid, precursor to aspirin.
### Laboratory methods {#laboratory_methods}
Preparative methods for small scale reactions for research or for production of fine chemicals often employ expensive consumable reagents.
- Oxidation of primary alcohols or aldehydes with strong oxidants such as potassium dichromate, Jones reagent, potassium permanganate, or sodium chlorite. The method is more suitable for laboratory conditions than the industrial use of air, which is \"greener\" because it yields less inorganic side products such as chromium or manganese oxides.
- Oxidative cleavage of olefins by ozonolysis, potassium permanganate, or potassium dichromate.
- Hydrolysis of nitriles, esters, or amides, usually with acid- or base-catalysis.
- Carbonation of a Grignard reagent and organolithium reagents:
:
:
- Halogenation followed by hydrolysis of methyl ketones in the haloform reaction
- Base-catalyzed cleavage of non-enolizable ketones, especially aryl ketones:
:
### Less-common reactions {#less_common_reactions}
Many reactions produce carboxylic acids but are used only in specific cases or are mainly of academic interest.
- Disproportionation of an aldehyde in the Cannizzaro reaction
- Rearrangement of diketones in the benzilic acid rearrangement
- Involving the generation of benzoic acids are the von Richter reaction from nitrobenzenes and the Kolbe--Schmitt reaction from phenols.
## Reactions
### Acid-base reactions {#acid_base_reactions}
Carboxylic acids react with bases to form carboxylate salts, in which the hydrogen of the hydroxyl (--OH) group is replaced with a metal cation. For example, acetic acid found in vinegar reacts with sodium bicarbonate (baking soda) to form sodium acetate, carbon dioxide, and water:
:
### Conversion to esters, amides, anhydrides {#conversion_to_esters_amides_anhydrides}
Widely practiced reactions convert carboxylic acids into esters, amides, carboxylate salts, acid chlorides, and alcohols. Their conversion to esters is widely used, e.g. in the production of polyesters. Likewise, carboxylic acids are converted into amides, but this conversion typically does not occur by direct reaction of the carboxylic acid and the amine. Instead esters are typical precursors to amides. The conversion of amino acids into peptides is a significant biochemical process that requires ATP.
Converting a carboxylic acid to an amide is possible, but not straightforward. Instead of acting as a nucleophile, an amine will react as a base in the presence of a carboxylic acid to give the ammonium carboxylate salt. Heating the salt to above 100 °C will drive off water and lead to the formation of the amide. This method of synthesizing amides is industrially important, and has laboratory applications as well. In the presence of a strong acid catalyst, carboxylic acids can condense to form acid anhydrides. The condensation produces water, however, which can hydrolyze the anhydride back to the starting carboxylic acids. Thus, the formation of the anhydride via condensation is an equilibrium process.
Under acid-catalyzed conditions, carboxylic acids will react with alcohols to form esters via the Fischer esterification reaction, which is also an equilibrium process. Alternatively, diazomethane can be used to convert an acid to an ester. While esterification reactions with diazomethane often give quantitative yields, diazomethane is only useful for forming methyl esters.
### Reduction
Like esters, most carboxylic acids can be reduced to alcohols by hydrogenation, or using hydride transferring agents such as lithium aluminium hydride. Strong alkyl transferring agents, such as organolithium compounds but not Grignard reagents, will reduce carboxylic acids to ketones along with transfer of the alkyl group.
The Vilsmaier reagent (*N*,*N*-Dimethyl(chloromethylene)ammonium chloride; `{{chem2|[ClHC\dN+(CH3)2]Cl−}}`{=mediawiki}) is a highly chemoselective agent for carboxylic acid reduction. It selectively activates the carboxylic acid to give the carboxymethyleneammonium salt, which can be reduced by a mild reductant like lithium tris(*t*-butoxy)aluminum hydride to afford an aldehyde in a one pot procedure. This procedure is known to tolerate reactive carbonyl functionalities such as ketone as well as moderately reactive ester, olefin, nitrile, and halide moieties.
### Conversion to acyl halides {#conversion_to_acyl_halides}
The hydroxyl group on carboxylic acids may be replaced with a chlorine atom using thionyl chloride to give acyl chlorides. In nature, carboxylic acids are converted to thioesters. Thionyl chloride can be used to convert carboxylic acids to their corresponding acyl chlorides. First, carboxylic acid **1** attacks thionyl chloride, and chloride ion leaves. The resulting oxonium ion **2** is activated towards nucleophilic attack and has a good leaving group, setting it apart from a normal carboxylic acid. In the next step, **2** is attacked by chloride ion to give tetrahedral intermediate **3**, a chlorosulfite. The tetrahedral intermediate collapses with the loss of sulfur dioxide and chloride ion, giving protonated acyl chloride **4**. Chloride ion can remove the proton on the carbonyl group, giving the acyl chloride **5** with a loss of HCl.
Phosphorus(III) chloride (PCl~3~) and phosphorus(V) chloride (PCl~5~) will also convert carboxylic acids to acid chlorides, by a similar mechanism. One equivalent of PCl~3~ can react with three equivalents of acid, producing one equivalent of H~3~PO~3~, or phosphorus acid, in addition to the desired acid chloride. PCl~5~ reacts with carboxylic acids in a 1:1 ratio, and produces phosphorus(V) oxychloride (POCl~3~) and hydrogen chloride (HCl) as byproducts.
### Reactions with carbanion equivalents {#reactions_with_carbanion_equivalents}
Carboxylic acids react with Grignard reagents and organolithiums to form ketones. The first equivalent of nucleophile acts as a base and deprotonates the acid. A second equivalent will attack the carbonyl group to create a geminal alkoxide dianion, which is protonated upon workup to give the hydrate of a ketone. Because most ketone hydrates are unstable relative to their corresponding ketones, the equilibrium between the two is shifted heavily in favor of the ketone. For example, the equilibrium constant for the formation of acetone hydrate from acetone is only 0.002. The carboxylic group is the most acidic in organic compounds.
### Specialized reactions {#specialized_reactions}
- As with all carbonyl compounds, the protons on the α-carbon are labile due to keto--enol tautomerization. Thus, the α-carbon is easily halogenated in the Hell--Volhard--Zelinsky halogenation.
- The Schmidt reaction converts carboxylic acids to amines.
- Carboxylic acids are decarboxylated in the Hunsdiecker reaction.
- The Dakin--West reaction converts an amino acid to the corresponding amino ketone.
- In the Barbier--Wieland degradation, a carboxylic acid on an aliphatic chain having a simple methylene bridge at the alpha position can have the chain shortened by one carbon. The inverse procedure is the Arndt--Eistert synthesis, where an acid is converted into acyl halide, which is then reacted with diazomethane to give one additional methylene in the aliphatic chain.
- Many acids undergo oxidative decarboxylation. Enzymes that catalyze these reactions are known as carboxylases (EC 6.4.1) and decarboxylases (EC 4.1.1).
- Carboxylic acids are reduced to aldehydes via the ester and DIBAL, via the acid chloride in the Rosenmund reduction and via the thioester in the Fukuyama reduction.
- In ketonic decarboxylation carboxylic acids are converted to ketones.
- Organolithium reagents (\>2 equiv) react with carboxylic acids to give a dilithium 1,1-diolate, a stable tetrahedral intermediate which decomposes to give a ketone upon acidic workup.
- The Kolbe electrolysis is an electrolytic, decarboxylative dimerization reaction. It gets rid of the carboxyl groups of two acid molecules, and joins the remaining fragments together.
## Carboxyl radical {#carboxyl_radical}
The carboxyl radical, •COOH, only exists briefly. The acid dissociation constant of •COOH has been measured using electron paramagnetic resonance spectroscopy. The carboxyl group tends to dimerise to form oxalic acid.
| 2025-06-20T00:00:00 |
6,100 |
Chernobyl
|
**Chernobyl**, officially called **Chornobyl**, is a partially abandoned city in Vyshhorod Raion, Kyiv Oblast, Ukraine. It is located within the Chernobyl Exclusion Zone, 90 km to the north of Kyiv and 160 km to the southwest of Gomel in neighbouring Belarus. Prior to being evacuated in the aftermath of the Chernobyl disaster in 1986, it was home to approximately 14,000 residents---considerably less than adjacent Pripyat, which was completely abandoned following the incident. Since then, although living anywhere within the Chernobyl Exclusion Zone is technically illegal, Ukrainian authorities have tolerated those who have taken up living in some of the city\'s less irradiated areas; Chernobyl\'s 2020 population estimate was 150 people.
First mentioned as a ducal hunting lodge in Kievan Rus\' in 1193, the city has changed hands multiple times over the course of its history. In the 16th century, Jews began moving into Chernobyl, and at the end of the 18th century, it had become a major centre of Hasidic Judaism under the Twersky dynasty. During the early 20th century, pogroms and associated emigration caused the local Jewish community to dwindle significantly. By World War II, all remaining Jews in the city were murdered by Nazi Germany as part of the Holocaust.
In 1972, Chernobyl rose to prominence in the Soviet Union when it was selected as the site of the Chernobyl Nuclear Power Plant; Pripyat was constructed nearby to house the facility\'s workers. Located 15 km to the north of Chernobyl proper, it opened in 1977. On 5 May 1986, nine days after Reactor No. 4 at the Chernobyl Nuclear Power Plant exploded, the Soviet government began evacuating the residents of both Chernobyl and Pripyat in preparation for the liquidators\' management of the disaster. Following their subsequent settlement in the newly purpose-built city of Slavutych, most of the evacuees never returned. From 1923 onwards, Chernobyl had been the administrative centre of Chernobyl Raion, which was dissolved and merged with Ivankiv Raion in 1988, owing to widespread radioactive contamination in the region. Ivankiv Raion, in turn, was dissolved and merged with Vyshhorod Raion during Ukraine\'s 2020 administrative reform.
Workers on watch and administrative personnel of the Chernobyl Exclusion Zone are stationed in the city, which has two general stores and a hotel. Though the city\'s atmosphere remained calm after the disaster was contained, the beginning of the Russian invasion of Ukraine in February 2022 sparked international concern about the stability of Ukrainian nuclear facilities, especially pursuant to reports that Russia\'s occupation of the Chernobyl Exclusion Zone until April 2022 had caused a spike in radiation levels.
## Etymology
The city\'s name is the same as one of the Ukrainian names for *Artemisia vulgaris*, mugwort or common wormwood: *label=none* (or more commonly *полин звичайний* `{{transliteration|uk|polýn zvycháynyy}}`{=mediawiki}, \'common artemisia\'). The name is inherited from `{{proto|slavic|čьrnobylъ}}`{=mediawiki} or `{{proto|slavic|čьrnobyl}}`{=mediawiki}, a compound of `{{proto|slavic|čьrnъ|black}}`{=mediawiki} + `{{proto|slavic|bylь|grass}}`{=mediawiki}, the parts related to *links=no* and *било* `{{transliteration|uk|byló}}`{=mediawiki}, \'stalk\', so named in distinction to the lighter-stemmed wormwood *A. absinthium*.
The name in languages used nearby is:
- , `{{IPA|uk|tʃorˈnɔbɪlʲ|pron|uk-чорнобиль.ogg}}`{=mediawiki}
- , `{{IPA|be|t͡ʂarˈnɔbɨlʲ|pron}}`{=mediawiki}
- , `{{IPA|ru|tɕɪrˈnobɨlʲ|pron}}`{=mediawiki}.
The name in languages formerly used in the area is:
- , `{{IPA|pl|tʂarˈnɔbɨl|pron}}`{=mediawiki}
- , `{{IPA|yi|tʃɛrˈnɔbl̩|pron}}`{=mediawiki}.
In English, the Russian-derived spelling *Chernobyl* has been commonly used, but some style guides recommend the spelling *Chornobyl*, or the use of romanized Ukrainian names for Ukrainian places generally.
## History
The Polish Geographical Dictionary of the Kingdom of Poland of 1880--1902 states that the time the city was founded is not known.
### Identity of Ptolemy\'s \"Azagarium\" {#identity_of_ptolemys_azagarium}
Some older geographical dictionaries and descriptions of modern Eastern Europe mention \"Czernobol\" (Chernobyl) with reference to Ptolemy\'s world map (2nd century AD). Czernobol is identified as Azagarium \"oppidium Sarmatiae\" (Lat., \"a city in Sarmatia\"), by the 1605 *Lexicon geographicum* of Filippo Ferrari and the 1677 *Lexicon Universale* of Johann Jakob Hofmann. According to the *Dictionary of Ancient Geography* of Alexander Macbean (London, 1773), Azagarium is \"a town of Sarmatia Europaea, on the Borysthenes\" (Dnieper), 36° East longitude and 50°40\' latitude. The city is \"now supposed to be *Czernobol*, a town of Poland, in Red Russia \[Red Ruthenia\], in the Palatinate of Kiow \[Kiev Voivodeship\], not far from the Borysthenes.\"
Whether Azagarium is indeed Czernobol is debatable. The question of Azagarium\'s correct location was raised in 1842 by Habsburg-Slovak historian, Pavel Jozef Šafárik, who published a book titled \"Slavic Ancient History\" (\"Sławiańskie starożytności\"), where he claimed Azagarium to be the hill of Zaguryna, which he found on an old Russian map \"Bolzoj czertez\" (Big drawing)`{{dubious|Azagarium|reason=What is this "Big drawing"? The name of the map, or what?|date=September 2020}}`{=mediawiki} near the city of Pereiaslav, now in central Ukraine.
In 2019, Ukrainian architect Boris Yerofalov-Pylypchak published a book, *Roman Kyiv or Castrum Azagarium at Kyiv-Podil*.
### Kievan Rus\' and post-medieval era (880--1793) {#kievan_rus_and_post_medieval_era_8801793}
The archaeological excavations that were conducted in 2005--2008 found a cultural layer from the 10--12th centuries AD, which predates the first documentary mention of Chernobyl.
Around the 12th century Chernobyl was part of the land of Kievan Rus′. The first known mention of the settlement as Chernobyl is from an 1193 charter, which describes it as a hunting lodge of Knyaz Rurik Rostislavich. In 1362 it was a crown village of the Grand Duchy of Lithuania. Around that time the town had own castle which was ruined at least on two occasions in 1473 and 1482. The Chernobyl castle was rebuilt in the first quarter of the 16th century being located nearby the settlement in a hard to reach area. With revival of the castle, Chernobyl became a county seat. In 1552 it accounted for 196 buildings with 1,372 residents, out of which over 1,160 were considered city dwellers. In the city were developing various crafts professions such as blacksmith, cooper among others. Near Chernobyl has been excavated bog iron, out of which was produced iron. The village was granted to Filon Kmita, a captain of the royal cavalry, as a fiefdom in 1566. Following the Union of Lublin, the province where Chernobyl is located was transferred to the Crown of the Kingdom of Poland in 1569. Under the Polish Crown, Chernobyl became a seat of eldership (starostwo). During that period Chernobyl was inhabited by Ukrainian peasants, some Polish people and a relatively large number of Jews. Jews were brought to Chernobyl by Filon Kmita, during the Polish campaign of colonization. The first mentioning of Jewish community in Chernobyl is in the 17th century. In 1600 the first Roman Catholic church was built in the town. Local population was persecuted for holding Eastern Orthodox rite services. The traditionally Eastern Orthodox Ukrainian peasantry around the town were forcibly converted, by Poland, to the Ruthenian Uniate Church. In 1626, during the Counter-Reformation, a Dominican church and monastery were founded by Lukasz Sapieha. A group of Old Catholics opposed the decrees of the Council of Trent.`{{clarify|date=June 2017}}`{=mediawiki} The Chernobyl residents actively supported the Khmelnytsky Uprising (1648--1657).
With the signing of the Truce of Andrusovo in 1667, Chernobyl was secured after`{{dubious|What is the meaning of "was secured after the Sapieha family" in proper English?|date=September 2020}}`{=mediawiki} the Sapieha family. Sometime in the 18th century, the place was passed on to the Chodkiewicz family. In the mid-18th century the area around Chernobyl was engulfed in a number of peasant riots, which caused Prince Riepnin to write from Warsaw to Major General Krechetnikov, requesting hussars to be sent from Kharkiv to deal with the uprising near Chernobyl in 1768. The 8th Lithuanian Infantry Regiment was stationed in the town in 1791. By the end of the 18th century, the town accounted for 2,865 residents and had 642 buildings.
### Imperial Russian era (1793--1917) {#imperial_russian_era_17931917}
Following the Second Partition of Poland, in 1793 Chernobyl was annexed by the Russian Empire and became part of Radomyshl county (*uezd*) as a supernumerary town (\"zashtatny gorod\"). Many of the Uniate Church converts returned to Eastern Orthodoxy.
In 1832, following the failed Polish November Uprising, the Dominican monastery was sequestrated. The church of the Old Catholics was disbanded in 1852.
Until the end of the 19th century, Chernobyl was a privately owned city that belonged to the Chodkiewicz family. In 1896 they sold the city to the state, but until 1910 they owned a castle and a house in the city.
#### Hasidic Jewish dynasty of Chernobyl {#hasidic_jewish_dynasty_of_chernobyl}
In the second half of the 18th century, Chernobyl became a major centre of Hasidic Judaism. The Chernobyl Hasidic dynasty had been founded by Rabbi Menachem Nachum Twersky. The Jewish population suffered greatly from pogroms in October 1905 and in March--April 1919; many Jews were killed or robbed at the instigation of the Russian nationalist Black Hundreds. When the Twersky Dynasty left Chernobyl in 1920, it ceased to exist as a center of Hasidism.
Chernobyl had a population of 10,800 in 1898, including 7,200 Jews. In the beginning of March 1918 Chernobyl was occupied in World War I by German forces in accordance with the Treaty of Brest-Litovsk
### Soviet era (1920--1991) {#soviet_era_19201991}
Ukrainians and Bolsheviks fought over the city in the ensuing Civil War. In the Polish--Soviet War of 1919--20, Chernobyl was taken first by the Polish Army and then by the cavalry of the Red Army. From 1921 onwards, it was officially incorporated into the Ukrainian SSR.
#### Holodomor
Between 1929 and 1933, Chernobyl suffered from killings during Stalin\'s collectivization campaign. It was also affected by the famine that resulted from Stalin\'s policies. The Polish and German community of Chernobyl was deported to Kazakhstan in 1936, during the Frontier Clearances.
#### World War II and the Holocaust {#world_war_ii_and_the_holocaust}
During World War II, Chernobyl was occupied by the German Army from 25 August 1941 to 17 November 1943. When the Germans arrived, only 400 Jews remained in Chernobyl; they were murdered during the Holocaust.
#### Chernobyl Nuclear Power Plant {#chernobyl_nuclear_power_plant}
In 1972, the Duga-1 radio receiver, part of the larger Duga over-the-horizon radar array, began construction 11 km west-northwest of Chernobyl. It was the origin of the Russian Woodpecker and was designed as part of an anti-ballistic missile early-warning radar network.
On 15 August 1972, the Chernobyl Nuclear Power Plant (officially the Vladimir Ilyich Lenin Nuclear Power Plant) began construction about 15 km northwest of Chernobyl. The plant was built alongside Pripyat, an \"atomograd\" city founded on 4 February 1970 that was intended to serve the nuclear power plant. The decision to build the power plant was adopted by the Central Committee of the Communist Party of the Soviet Union and the Council of Ministers of the Soviet Union on recommendations of the State Planning Committee that the Ukrainian SSR be its location. It was the first nuclear power plant to be built in Ukraine.
#### 26 April 1986: Chernobyl disaster {#april_1986_chernobyl_disaster}
After the nuclear disaster at the Chernobyl Nuclear Power Plant; the worst nuclear disaster in history, the city of Chernobyl was evacuated on 5 May 1986. Along with the residents of the nearby city of Pripyat, built as a home for the plant\'s workers, the population was relocated to the newly built city of Slavutych. While Pripyat remains completely abandoned with no remaining inhabitants, Chernobyl has since hosted a small population.
### Independent Ukrainian era (1991--present) {#independent_ukrainian_era_1991present}
With the dissolution of the Soviet Union in 1991, Chernobyl remained part of Ukraine within the Chernobyl Exclusion Zone which Ukraine inherited from the Soviet Union.
#### 2022 Russian occupation of Chernobyl {#russian_occupation_of_chernobyl}
During the Russian invasion of Ukraine, Russian forces captured the city on 24 February. Following the capture of Chernobyl, the Russian army used the city as a staging point for attacks on Kyiv. Ukrainian officials reported that the radiation levels in the city had started to rise due to recent military activity causing radioactive dust to ascend into the air. Hundreds of Russian soldiers were suffering from radiation poisoning after digging trenches in a contaminated area, and one died. On 31 March it was reported that Russian forces had left the exclusion zone. Ukrainian authorities reasserted control over the area on 2 April.
## Geography
Chernobyl is located about 90 km north of Kyiv, and 160 km southwest of the Belarusian city of Gomel.
### Climate
Chernobyl has a humid continental climate (Dfb) with very warm, wet summers with cool nights and long, cold, and snowy winters.`{{Weather box
|location = Chernobyl, 127 m asl (1981–2010 normals, extremes 1955–present)
|collapsed =
|metric first = Yes
|single line = Yes
|Jan record high C = 11.5
|Feb record high C = 17.0
|Mar record high C = 22.6
|Apr record high C = 26.6
|May record high C = 32.9
|Jun record high C = 34.0
|Jul record high C = 35.2
|Aug record high C = 36.3
|Sep record high C = 35.9
|Oct record high C = 26.3
|Nov record high C = 19.6
|Dec record high C = 11.3
|year record high C = 36.3
|Jan high C = -0.8
|Feb high C = 0.1
|Mar high C = 6.0
|Apr high C = 14.5
|May high C = 21.0
|Jun high C = 23.7
|Jul high C = 25.7
|Aug high C = 25.0
|Sep high C = 18.9
|Oct high C = 12.4
|Nov high C = 4.2
|Dec high C = -0.3
|year high C = 12.5
|Jan mean C = -3.5
|Feb mean C = -3.4
|Mar mean C = 1.5
|Apr mean C = 8.9
|May mean C = 14.9
|Jun mean C = 17.9
|Jul mean C = 19.9
|Aug mean C = 18.8
|Sep mean C = 13.4
|Oct mean C = 7.7
|Nov mean C = 1.4
|Dec mean C = -2.8
|year mean C = 7.9
|Jan low C = -6.1
|Feb low C = -6.7
|Mar low C = -2.3
|Apr low C = 3.9
|May low C = 9.1
|Jun low C = 12.3
|Jul low C = 14.5
|Aug low C = 13.3
|Sep low C = 8.7
|Oct low C = 3.8
|Nov low C = -1.1
|Dec low C = -5.2
|year low C = 3.7
|Jan record low C = -29.7
|Feb record low C = -32.8
|Mar record low C = -20.0
|Apr record low C = -9.0
|May record low C = -6.0
|Jun record low C = 2.2
|Jul record low C = 6.2
|Aug record low C = 0.0
|Sep record low C = -1.6
|Oct record low C = -10.5
|Nov record low C = -20.0
|Dec record low C = -30.8
|year record low C = -32.8
|precipitation colour = green
|Jan precipitation mm = 34.0
|Feb precipitation mm = 36.8
|Mar precipitation mm = 35.6
|Apr precipitation mm = 40.0
|May precipitation mm = 60.8
|Jun precipitation mm = 73.2
|Jul precipitation mm = 79.5
|Aug precipitation mm = 55.3
|Sep precipitation mm = 56.3
|Oct precipitation mm = 42.2
|Nov precipitation mm = 47.7
|Dec precipitation mm = 42.6
|year precipitation mm = 604.0
|unit precipitation days = 1.0 mm
|Jan precipitation days = 8.1
|Feb precipitation days = 8.9
|Mar precipitation days = 8.1
|Apr precipitation days = 7.5
|May precipitation days = 8.7
|Jun precipitation days = 10.2
|Jul precipitation days = 9.2
|Aug precipitation days = 7.1
|Sep precipitation days = 8.7
|Oct precipitation days = 7.4
|Nov precipitation days = 8.7
|Dec precipitation days = 9.1
|year precipitation days = 101.7
|Jan humidity = 83.5
|Feb humidity = 79.8
|Mar humidity = 74.7
|Apr humidity = 66.7
|May humidity = 66.0
|Jun humidity = 70.4
|Jul humidity = 72.8
|Aug humidity = 72.3
|Sep humidity = 77.8
|Oct humidity = 80.8
|Nov humidity = 85.3
|Dec humidity = 85.9
|year humidity = 76.3
|source 1 = [[NOAA]]<ref name=WMOCLINO>{{cite web
| archive-url = https://web.archive.org/web/20210717143555/https://www.ncei.noaa.gov/pub/data/normals/WMO/1981-2010/RA-VI/Ukraine/12.6.%20WMO_Normals_Excel_Template%20%282%29.xls
| archive-date = 17 July 2021
| url = https://www.ncei.noaa.gov/pub/data/normals/WMO/1981-2010/RA-VI/Ukraine/12.6.%20WMO_Normals_Excel_Template%20(2).xls
| format = XLS
| title = World Meteorological Organization Climate Normals for 1981–2010
| publisher = [[NCEI|National Centers for Environmental Information]]
| access-date = 17 July 2021}}</ref>
|source 2 = Météo Climat (extremes)<ref>{{cite web|url=http://meteo-climat-bzh.dyndns.org/station-1986.php|title=Weather extremes for Tchernobyl|publisher=Météo Climat|language=fr|access-date=17 July 2021|archive-date=13 October 2020|archive-url=https://web.archive.org/web/20201013210112/http://meteo-climat-bzh.dyndns.org/station-1986.php|url-status=live}}</ref>
}}`{=mediawiki}
## Aftermath of the Chernobyl disaster and evacuation {#aftermath_of_the_chernobyl_disaster_and_evacuation}
*Main article: Chernobyl disaster, Effects of the Chernobyl disaster*
On 26 April 1986, one of the reactors at the Chernobyl Nuclear Power Plant exploded after a scheduled test on the reactor was carried out improperly by plant operators. The resulting loss of control was due to design flaws of the RBMK reactor, which made it unstable when operated at low power, and prone to thermal runaway where increases in temperature increase reactor power output.
Chernobyl city was evacuated nine days after the disaster. The level of contamination with caesium-137 was around 555 kBq/m^2^ (surface ground deposition in 1986).
Later analyses concluded that, even with very conservative estimates, relocation of the city (or of any area below 1500 kBq/m^2^) could not be justified on the grounds of radiological health. This however does not account for the uncertainty in the first few days of the accident about further depositions and weather patterns. Moreover, an earlier short-term evacuation could have averted more significant doses from short-lived isotope radiation (specifically iodine-131, which has a half-life of eight days). The long-term health effects of the Chernobyl disaster are a subject of some controversy.
In 1998, average caesium-137 doses from the accident (estimated at 1--2 mSv per year) did not exceed those from other sources of exposure. Current effective caesium-137 dose rates as of 2019 are 200--250 nSv/h, or roughly 1.7--2.2 mSv per year, which is comparable to the worldwide average background radiation from natural sources.
The base of operations for the administration and monitoring of the Chernobyl Exclusion Zone was moved from Pripyat to Chernobyl. Chernobyl currently contains offices for the State Agency of Ukraine on the Exclusion Zone Management and accommodations for visitors. Apartment blocks have been repurposed as accommodations for employees of the State Agency. The length of time that workers may spend within the Chernobyl Exclusion Zone is restricted by regulations that have been implemented to limit radiation exposure. Today, visits are allowed to Chernobyl but limited by strict rules.
In 2003, the United Nations Development Programme launched a project, called the Chernobyl Recovery and Development Programme (CRDP), for the recovery of the affected areas. The main goal of the CRDP\'s activities is supporting the efforts of the Government of Ukraine to mitigate the long-term social, economic, and ecological consequences of the Chernobyl disaster.
The city has become overgrown and many types of animals live there. According to census information collected over an extended period of time, it is estimated that more mammals live there now than before the disaster.
Notably, Mikhail Gorbachev, the final leader of the Soviet Union, stated in respect to the Chernobyl disaster that, \"More than anything else, (Chernobyl) opened the possibility of much greater freedom of expression, to the point that the (Soviet) system as we knew it could no longer continue.\"
## Notable people {#notable_people}
- Aaron Twersky of Chernobyl (1784--1871), rabbi
- Aleksander Franciszek Chodkiewicz (1776--1838), Polish politician and lithographer
- Alexander Krasnoshchyokov (1880--1937), politician
- Andriy Smalko (1981--), football player
- Arnold Lakhovsky (1880--1937), artist
- Jan Mikołaj Chodkiewicz (1738--1781), Polish nobleman, father of Rozalia Lubomirska
- Ekaterina Scherbachenko (1977--), opera singer
- Grigory Irmovich Novak (1919--1980), Jewish Soviet weightlifter
- Joshua ben Aaron Zeitlin (1823--1888), scholar and philanthropist
- Markiyan Kamysh (1988--), novelist and son of a liquidator
- Rozalia Lubomirska (1768--1794), Polish noblewoman guillotined during the French Revolution
- Volodymyr Pravyk (1962--1986), firefighter and liquidator
| 2025-06-20T00:00:00 |
6,113 |
Chain rule
|
In calculus, the **chain rule** is a formula that expresses the derivative of the composition of two differentiable functions `{{mvar|f}}`{=mediawiki} and `{{mvar|g}}`{=mediawiki} in terms of the derivatives of `{{mvar|f}}`{=mediawiki} and `{{mvar|g}}`{=mediawiki}. More precisely, if $h=f\circ g$ is the function such that $h(x)=f(g(x))$ for every `{{mvar|x}}`{=mediawiki}, then the chain rule is, in Lagrange\'s notation, $h'(x) = f'(g(x)) g'(x).$ or, equivalently, $h'=(f\circ g)'=(f'\circ g)\cdot g'.$
The chain rule may also be expressed in Leibniz\'s notation. If a variable `{{mvar|z}}`{=mediawiki} depends on the variable `{{mvar|y}}`{=mediawiki}, which itself depends on the variable `{{mvar|x}}`{=mediawiki} (that is, `{{mvar|y}}`{=mediawiki} and `{{mvar|z}}`{=mediawiki} are dependent variables), then `{{mvar|z}}`{=mediawiki} depends on `{{mvar|x}}`{=mediawiki} as well, via the intermediate variable `{{mvar|y}}`{=mediawiki}. In this case, the chain rule is expressed as $\frac{dz}{dx} = \frac{dz}{dy} \cdot \frac{dy}{dx},$ and $\left.\frac{dz}{dx}\right|_{x} = \left.\frac{dz}{dy}\right|_{y(x)}
\cdot \left. \frac{dy}{dx}\right|_{x} ,$ for indicating at which points the derivatives have to be evaluated.
In integration, the counterpart to the chain rule is the substitution rule.
## Intuitive explanation {#intuitive_explanation}
Intuitively, the chain rule states that knowing the instantaneous rate of change of `{{math|''z''}}`{=mediawiki} relative to `{{math|''y''}}`{=mediawiki} and that of `{{math|''y''}}`{=mediawiki} relative to `{{math|''x''}}`{=mediawiki} allows one to calculate the instantaneous rate of change of `{{math|''z''}}`{=mediawiki} relative to `{{math|''x''}}`{=mediawiki} as the product of the two rates of change.
As put by George F. Simmons: \"If a car travels twice as fast as a bicycle and the bicycle is four times as fast as a walking man, then the car travels 2 × 4 = 8 times as fast as the man.\"
The relationship between this example and the chain rule is as follows. Let `{{mvar|z}}`{=mediawiki}, `{{mvar|y}}`{=mediawiki} and `{{mvar|x}}`{=mediawiki} be the (variable) positions of the car, the bicycle, and the walking man, respectively. The rate of change of relative positions of the car and the bicycle is $\frac {dz}{dy}=2.$ Similarly, $\frac {dy}{dx}=4.$ So, the rate of change of the relative positions of the car and the walking man is $\frac{dz}{dx}=\frac{dz}{dy}\cdot\frac{dy}{dx}=2\cdot 4=8.$
The rate of change of positions is the ratio of the speeds, and the speed is the derivative of the position with respect to the time; that is, $\frac{dz}{dx}=\frac \frac{dz}{dt}\frac{dx}{dt},$ or, equivalently, $\frac{dz}{dt}=\frac{dz}{dx}\cdot \frac{dx}{dt},$ which is also an application of the chain rule.
## History
The chain rule seems to have first been used by Gottfried Wilhelm Leibniz. He used it to calculate the derivative of $\sqrt{a + bz + cz^2}$ as the composite of the square root function and the function $a + bz + cz^2\!$. He first mentioned it in a 1676 memoir (with a sign error in the calculation). The common notation of the chain rule is due to Leibniz. Guillaume de l\'Hôpital used the chain rule implicitly in his *Analyse des infiniment petits*. The chain rule does not appear in any of Leonhard Euler\'s analysis books, even though they were written over a hundred years after Leibniz\'s discovery.. It is believed that the first \"modern\" version of the chain rule appears in Lagrange\'s 1797 *Théorie des fonctions analytiques*; it also appears in Cauchy\'s 1823 *Résumé des Leçons données a L'École Royale Polytechnique sur Le Calcul Infinitesimal*.
## Statement
The simplest form of the chain rule is for real-valued functions of one real variable. It states that if *`{{mvar|g}}`{=mediawiki}* is a function that is differentiable at a point *`{{mvar|c}}`{=mediawiki}* (i.e. the derivative `{{math|''g''′(''c'')}}`{=mediawiki} exists) and *`{{mvar|f}}`{=mediawiki}* is a function that is differentiable at `{{math|''g''(''c'')}}`{=mediawiki}, then the composite function $f \circ g$ is differentiable at *`{{mvar|c}}`{=mediawiki}*, and the derivative is $(f\circ g)'(c) = f'(g(c))\cdot g'(c).$ The rule is sometimes abbreviated as $(f\circ g)' = (f'\circ g) \cdot g'.$
If `{{math|1=''y'' = ''f''(''u'')}}`{=mediawiki} and `{{math|1=''u'' = ''g''(''x'')}}`{=mediawiki}, then this abbreviated form is written in Leibniz notation as: $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}.$
The points where the derivatives are evaluated may also be stated explicitly: $\left.\frac{dy}{dx}\right|_{x=c} = \left.\frac{dy}{du}\right|_{u = g(c)} \cdot \left.\frac{du}{dx}\right|_{x=c}.$
Carrying the same reasoning further, given *`{{mvar|n}}`{=mediawiki}* functions $f_1, \ldots, f_n\!$ with the composite function $f_1 \circ ( f_2 \circ \cdots (f_{n-1} \circ f_n) )\!$, if each function $f_i\!$ is differentiable at its immediate input, then the composite function is also differentiable by the repeated application of Chain Rule, where the derivative is (in Leibniz\'s notation): $\frac{df_1}{dx} = \frac{df_1}{df_2}\frac{df_2}{df_3}\cdots\frac{df_n}{dx}.$
## Applications
thumb\|upright=1.6\|The chain rule in case of composites of more than two functions
### Composites of more than two functions {#composites_of_more_than_two_functions}
The chain rule can be applied to composites of more than two functions. To take the derivative of a composite of more than two functions, notice that the composite of `{{mvar|f}}`{=mediawiki}, `{{mvar|g}}`{=mediawiki}, and *`{{mvar|h}}`{=mediawiki}* (in that order) is the composite of `{{mvar|f}}`{=mediawiki} with `{{math|''g'' ∘ ''h''}}`{=mediawiki}. The chain rule states that to compute the derivative of `{{math|''f'' ∘ ''g'' ∘ ''h''}}`{=mediawiki}, it is sufficient to compute the derivative of *`{{mvar|f}}`{=mediawiki}* and the derivative of `{{math|''g'' ∘ ''h''}}`{=mediawiki}. The derivative of `{{mvar|f}}`{=mediawiki} can be calculated directly, and the derivative of `{{math|''g'' ∘ ''h''}}`{=mediawiki} can be calculated by applying the chain rule again.
For concreteness, consider the function $y = e^{\sin (x^2)}.$ This can be decomposed as the composite of three functions: $\begin{align}
y &= f(u) = e^u, \\
u &= g(v) = \sin v, \\
v &= h(x) = x^2.
\end{align}$ So that $y = f(g(h(x)))$.
Their derivatives are: $\begin{align}
\frac{dy}{du} &= f'(u) = e^u, \\
\frac{du}{dv} &= g'(v) = \cos v, \\
\frac{dv}{dx} &= h'(x) = 2x.
\end{align}$
The chain rule states that the derivative of their composite at the point `{{math|1=''x'' = ''a''}}`{=mediawiki} is: $\begin{align}
(f \circ g \circ h)'(a) & = f'((g \circ h)(a)) \cdot (g \circ h)'(a) \\
& = f'((g \circ h)(a)) \cdot g'(h(a)) \cdot h'(a) \\
& = (f' \circ g \circ h)(a) \cdot (g' \circ h)(a) \cdot h'(a).
\end{align}$
In Leibniz\'s notation, this is: $\frac{dy}{dx} = \left.\frac{dy}{du}\right|_{u=g(h(a))}\cdot\left.\frac{du}{dv}\right|_{v=h(a)}\cdot\left.\frac{dv}{dx}\right|_{x=a},$ or for short, $\frac{dy}{dx} = \frac{dy}{du}\cdot\frac{du}{dv}\cdot\frac{dv}{dx}.$ The derivative function is therefore: $\frac{dy}{dx} = e^{\sin(x^2)}\cdot\cos(x^2)\cdot 2x.$
Another way of computing this derivative is to view the composite function `{{math|''f'' ∘ ''g'' ∘ ''h''}}`{=mediawiki} as the composite of `{{math|''f'' ∘ ''g''}}`{=mediawiki} and *h*. Applying the chain rule in this manner would yield: $\begin{align}
(f \circ g \circ h)'(a) &= (f \circ g)'(h(a)) \cdot h'(a) \\
&= f'(g(h(a))) \cdot g'(h(a)) \cdot h'(a).
\end{align}$
This is the same as what was computed above. This should be expected because `{{math|1=(''f'' ∘ ''g'') ∘ ''h'' = ''f'' ∘ (''g'' ∘ ''h'')}}`{=mediawiki}.
Sometimes, it is necessary to differentiate an arbitrarily long composition of the form $f_1 \circ f_2 \circ \cdots \circ f_{n-1} \circ f_n\!$. In this case, define $f_{a\,.\,.\,b} = f_{a} \circ f_{a+1} \circ \cdots \circ f_{b-1} \circ f_{b}$ where $f_{a\,.\,.\,a} = f_a$ and $f_{a\,.\,.\,b}(x) = x$ when $b < a$. Then the chain rule takes the form $\begin{align}
Df_{1\,.\,.\,n}
&= (Df_1 \circ f_{2\,.\,.\,n}) (Df_2 \circ f_{3\,.\,.\,n}) \cdots (Df_{n-1} \circ f_{n\,.\,.\,n}) Df_n \\
&= \prod_{k=1}^n \left[Df_k \circ f_{(k+1)\,.\,.\,n}\right]
\end{align}$ or, in the Lagrange notation, $\begin{align}
f_{1\,.\,.\,n}'(x)
&= f_1' \left( f_{2\,.\,.\,n}(x) \right) \; f_2' \left( f_{3\,.\,.\,n}(x) \right) \cdots f_{n-1}' \left(f_{n\,.\,.\,n}(x)\right) \; f_n'(x) \\[1ex]
&= \prod_{k=1}^{n} f_k' \left(f_{(k+1\,.\,.\,n)}(x) \right)
\end{align}$
### Quotient rule {#quotient_rule}
The chain rule can be used to derive some well-known differentiation rules. For example, the quotient rule is a consequence of the chain rule and the product rule. To see this, write the function `{{math|''f''(''x'')/''g''(''x'')}}`{=mediawiki} as the product `{{math|''f''(''x'') · 1/''g''(''x'')}}`{=mediawiki}. First apply the product rule: $\begin{align}
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)
&= \frac{d}{dx}\left(f(x)\cdot\frac{1}{g(x)}\right) \\
&= f'(x)\cdot\frac{1}{g(x)} + f(x)\cdot\frac{d}{dx}\left(\frac{1}{g(x)}\right).
\end{align}$
To compute the derivative of `{{math|1/''g''(''x'')}}`{=mediawiki}, notice that it is the composite of `{{mvar|g}}`{=mediawiki} with the reciprocal function, that is, the function that sends `{{mvar|x}}`{=mediawiki} to `{{math|1/''x''}}`{=mediawiki}. The derivative of the reciprocal function is $-1/x^2\!$. By applying the chain rule, the last expression becomes: $f'(x)\cdot\frac{1}{g(x)} + f(x)\cdot\left(-\frac{1}{g(x)^2}\cdot g'(x)\right)
= \frac{f'(x) g(x) - f(x) g'(x)}{g(x)^2},$ which is the usual formula for the quotient rule.
### Derivatives of inverse functions {#derivatives_of_inverse_functions}
Suppose that `{{math|1=''y'' = ''g''(''x'')}}`{=mediawiki} has an inverse function. Call its inverse function `{{mvar|f}}`{=mediawiki} so that we have `{{math|1=''x'' = ''f''(''y'')}}`{=mediawiki}. There is a formula for the derivative of `{{mvar|f}}`{=mediawiki} in terms of the derivative of `{{mvar|g}}`{=mediawiki}. To see this, note that `{{mvar|f}}`{=mediawiki} and `{{mvar|g}}`{=mediawiki} satisfy the formula $f(g(x)) = x.$
And because the functions $f(g(x))$ and `{{mvar|x}}`{=mediawiki} are equal, their derivatives must be equal. The derivative of `{{mvar|x}}`{=mediawiki} is the constant function with value 1, and the derivative of $f(g(x))$ is determined by the chain rule. Therefore, we have that: $f'(g(x)) g'(x) = 1.$
To express `{{mvar|f'}}`{=mediawiki} as a function of an independent variable `{{mvar|y}}`{=mediawiki}, we substitute $f(y)$ for `{{mvar|x}}`{=mediawiki} wherever it appears. Then we can solve for `{{mvar|f'}}`{=mediawiki}. $\begin{align}
f'(g(f(y))) g'(f(y)) &= 1 \\
f'(y) g'(f(y)) &= 1 \\
f'(y) = \frac{1}{g'(f(y))}.
\end{align}$
For example, consider the function `{{math|1=''g''(''x'') = ''e''<sup>''x''</sup>}}`{=mediawiki}. It has an inverse `{{math|1=''f''(''y'') = ln ''y''}}`{=mediawiki}. Because `{{math|1=''g''′(''x'') = ''e''<sup>''x''</sup>}}`{=mediawiki}, the above formula says that $\frac{d}{dy}\ln y = \frac{1}{e^{\ln y}} = \frac{1}{y}.$
This formula is true whenever `{{mvar|g}}`{=mediawiki} is differentiable and its inverse `{{mvar|f}}`{=mediawiki} is also differentiable. This formula can fail when one of these conditions is not true. For example, consider `{{math|1=''g''(''x'') = ''x''<sup>3</sup>}}`{=mediawiki}. Its inverse is `{{math|1=''f''(''y'') = ''y''<sup>1/3</sup>}}`{=mediawiki}, which is not differentiable at zero. If we attempt to use the above formula to compute the derivative of `{{mvar|f}}`{=mediawiki} at zero, then we must evaluate `{{math|1=1/''g''′(''f''(0))}}`{=mediawiki}. Since `{{math|1=''f''(0) = 0}}`{=mediawiki} and `{{math|1=''g''′(0) = 0}}`{=mediawiki}, we must evaluate 1/0, which is undefined. Therefore, the formula fails in this case. This is not surprising because `{{mvar|f}}`{=mediawiki} is not differentiable at zero.
### Back propagation {#back_propagation}
The chain rule forms the basis of the back propagation algorithm, which is used in gradient descent of neural networks in deep learning (artificial intelligence).
## Higher derivatives {#higher_derivatives}
Faà di Bruno\'s formula generalizes the chain rule to higher derivatives. Assuming that `{{math|''y'' {{=}}`{=mediawiki} *f*(*u*)}} and `{{math|''u'' {{=}}`{=mediawiki} *g*(*x*)}}, then the first few derivatives are: $\begin{align}
\frac{dy}{dx} & = \frac{dy}{du} \frac{du}{dx} \\
\frac{d^2 y }{d x^2} & =
\frac{d^2 y}{d u^2} \left(\frac{du}{dx}\right)^2
+ \frac{dy}{du} \frac{d^2 u}{dx^2} \\
\frac{d^3 y }{d x^3} & =
\frac{d^3 y}{d u^3} \left(\frac{du}{dx}\right)^3
+ 3 \, \frac{d^2 y}{d u^2} \frac{du}{dx} \frac{d^2 u}{d x^2}
+ \frac{dy}{du} \frac{d^3 u}{d x^3} \\
\frac{d^4 y}{d x^4} & =
\frac{d^4 y}{du^4} \left(\frac{du}{dx}\right)^4
+ 6 \, \frac{d^3 y}{d u^3} \left(\frac{du}{dx}\right)^2 \frac{d^2 u}{d x^2}
+ \frac{d^2 y}{d u^2} \left( 4 \, \frac{du}{dx} \frac{d^3 u}{dx^3}
+ 3 \, \left(\frac{d^2 u}{dx^2}\right)^2\right)
+ \frac{dy}{du} \frac{d^4 u}{dx^4}.
\end{align}$
## Proofs
### First proof {#first_proof}
One proof of the chain rule begins by defining the derivative of the composite function `{{math|''f'' ∘ ''g''}}`{=mediawiki}, where we take the limit of the difference quotient for `{{math|''f'' ∘ ''g''}}`{=mediawiki} as `{{mvar|x}}`{=mediawiki} approaches `{{mvar|a}}`{=mediawiki}: $(f \circ g)'(a) = \lim_{x \to a} \frac{f(g(x)) - f(g(a))}{x - a}.$
Assume for the moment that $g(x)\!$ does not equal $g(a)$ for any $x$ near $a$. Then the previous expression is equal to the product of two factors: $\lim_{x \to a} \frac{f(g(x)) - f(g(a))}{g(x) - g(a)} \cdot \frac{g(x) - g(a)}{x - a}.$
If $g$ oscillates near `{{mvar|a}}`{=mediawiki}, then it might happen that no matter how close one gets to `{{mvar|a}}`{=mediawiki}, there is always an even closer `{{mvar|x}}`{=mediawiki} such that `{{math|1=''g''(''x'') = ''g''(''a'')}}`{=mediawiki}. For example, this happens near `{{math|1=''a'' = 0}}`{=mediawiki} for the continuous function `{{mvar|g}}`{=mediawiki} defined by `{{math|1=''g''(''x'') = 0}}`{=mediawiki} for `{{math|1=''x'' = 0}}`{=mediawiki} and `{{math|1=''g''(''x'') = ''x''<sup>2</sup> sin(1/''x'')}}`{=mediawiki} otherwise. Whenever this happens, the above expression is undefined because it involves division by zero. To work around this, introduce a function $Q$ as follows: $Q(y) = \begin{cases}
\displaystyle\frac{f(y) - f(g(a))}{y - g(a)}, & y \neq g(a), \\
f'(g(a)), & y = g(a).
\end{cases}$ We will show that the difference quotient for `{{math|''f'' ∘ ''g''}}`{=mediawiki} is always equal to: $Q(g(x)) \cdot \frac{g(x) - g(a)}{x - a}.$
Whenever `{{math|''g''(''x'')}}`{=mediawiki} is not equal to `{{math|''g''(''a'')}}`{=mediawiki}, this is clear because the factors of `{{math|''g''(''x'') − ''g''(''a'')}}`{=mediawiki} cancel. When `{{math|''g''(''x'')}}`{=mediawiki} equals `{{math|''g''(''a'')}}`{=mediawiki}, then the difference quotient for `{{math|''f'' ∘ ''g''}}`{=mediawiki} is zero because `{{math|''f''(''g''(''x''))}}`{=mediawiki} equals `{{math|''f''(''g''(''a''))}}`{=mediawiki}, and the above product is zero because it equals `{{math|''f''′(''g''(''a''))}}`{=mediawiki} times zero. So the above product is always equal to the difference quotient, and to show that the derivative of `{{math|''f'' ∘ ''g''}}`{=mediawiki} at `{{math|''a''}}`{=mediawiki} exists and to determine its value, we need only show that the limit as `{{math|''x''}}`{=mediawiki} goes to `{{math|''a''}}`{=mediawiki} of the above product exists and determine its value.
To do this, recall that the limit of a product exists if the limits of its factors exist. When this happens, the limit of the product of these two factors will equal the product of the limits of the factors. The two factors are `{{math|''Q''(''g''(''x''))}}`{=mediawiki} and `{{math|(''g''(''x'') − ''g''(''a'')) / (''x'' − ''a'')}}`{=mediawiki}. The latter is the difference quotient for `{{mvar|g}}`{=mediawiki} at `{{mvar|a}}`{=mediawiki}, and because `{{mvar|g}}`{=mediawiki} is differentiable at `{{mvar|a}}`{=mediawiki} by assumption, its limit as `{{mvar|x}}`{=mediawiki} tends to `{{mvar|a}}`{=mediawiki} exists and equals `{{math|''g''′(''a'')}}`{=mediawiki}.
As for `{{math|''Q''(''g''(''x''))}}`{=mediawiki}, notice that `{{math|''Q''}}`{=mediawiki} is defined wherever *`{{mvar|f}}`{=mediawiki}* is. Furthermore, *`{{mvar|f}}`{=mediawiki}* is differentiable at `{{math|''g''(''a'')}}`{=mediawiki} by assumption, so `{{math|''Q''}}`{=mediawiki} is continuous at `{{math|''g''(''a'')}}`{=mediawiki}, by definition of the derivative. The function `{{mvar|g}}`{=mediawiki} is continuous at `{{mvar|a}}`{=mediawiki} because it is differentiable at `{{mvar|a}}`{=mediawiki}, and therefore `{{math|''Q'' ∘ ''g''}}`{=mediawiki} is continuous at `{{mvar|a}}`{=mediawiki}. So its limit as *`{{mvar|x}}`{=mediawiki}* goes to *`{{mvar|a}}`{=mediawiki}* exists and equals `{{math|''Q''(''g''(''a''))}}`{=mediawiki}, which is `{{math|''f''′(''g''(''a''))}}`{=mediawiki}.
This shows that the limits of both factors exist and that they equal `{{math|''f''′(''g''(''a''))}}`{=mediawiki} and `{{math|''g''′(''a'')}}`{=mediawiki}, respectively. Therefore, the derivative of `{{math|''f'' ∘ ''g''}}`{=mediawiki} at *a* exists and equals `{{math|''f''′(''g''(''a''))}}`{=mediawiki}`{{math|''g''′(''a'')}}`{=mediawiki}.
### Second proof {#second_proof}
Another way of proving the chain rule is to measure the error in the linear approximation determined by the derivative. This proof has the advantage that it generalizes to several variables. It relies on the following equivalent definition of differentiability at a point: A function *g* is differentiable at *a* if there exists a real number *g*′(*a*) and a function *ε*(*h*) that tends to zero as *h* tends to zero, and furthermore $g(a + h) - g(a) = g'(a) h + \varepsilon(h) h.$ Here the left-hand side represents the true difference between the value of *g* at *a* and at `{{math|''a'' + ''h''}}`{=mediawiki}, whereas the right-hand side represents the approximation determined by the derivative plus an error term.
In the situation of the chain rule, such a function *ε* exists because *g* is assumed to be differentiable at *a*. Again by assumption, a similar function also exists for *f* at *g*(*a*). Calling this function *η*, we have $f(g(a) + k) - f(g(a)) = f'(g(a)) k + \eta(k) k.$ The above definition imposes no constraints on *η*(0), even though it is assumed that *η*(*k*) tends to zero as *k* tends to zero. If we set `{{math|1=''η''(0) = 0}}`{=mediawiki}, then *η* is continuous at 0.
Proving the theorem requires studying the difference `{{math|''f''(''g''(''a'' + ''h'')) − ''f''(''g''(''a''))}}`{=mediawiki} as *h* tends to zero. The first step is to substitute for `{{math|''g''(''a'' + ''h'')}}`{=mediawiki} using the definition of differentiability of *g* at *a*: $f(g(a + h)) - f(g(a)) = f(g(a) + g'(a) h + \varepsilon(h) h) - f(g(a)).$ The next step is to use the definition of differentiability of *f* at *g*(*a*). This requires a term of the form `{{math|''f''(''g''(''a'') + ''k'')}}`{=mediawiki} for some *k*. In the above equation, the correct *k* varies with *h*. Set `{{math|1=''k''<sub>''h''</sub> = ''g''′(''a'') ''h'' + ''ε''(''h'') ''h''}}`{=mediawiki} and the right hand side becomes `{{math|''f''(''g''(''a'') + ''k''<sub>''h''</sub>) − ''f''(''g''(''a''))}}`{=mediawiki}. Applying the definition of the derivative gives: $f(g(a) + k_h) - f(g(a)) = f'(g(a)) k_h + \eta(k_h) k_h.$ To study the behavior of this expression as *h* tends to zero, expand *k*~*h*~. After regrouping the terms, the right-hand side becomes: $f'(g(a)) g'(a)h + [f'(g(a)) \varepsilon(h) + \eta(k_h) g'(a) + \eta(k_h) \varepsilon(h)] h.$ Because *ε*(*h*) and *η*(*k*~*h*~) tend to zero as *h* tends to zero, the first two bracketed terms tend to zero as *h* tends to zero. Applying the same theorem on products of limits as in the first proof, the third bracketed term also tends zero. Because the above expression is equal to the difference `{{math|''f''(''g''(''a'' + ''h'')) − ''f''(''g''(''a''))}}`{=mediawiki}, by the definition of the derivative `{{math|''f'' ∘ ''g''}}`{=mediawiki} is differentiable at *a* and its derivative is `{{math|''f''′(''g''(''a'')) ''g''′(''a'').}}`{=mediawiki}
The role of *Q* in the first proof is played by *η* in this proof. They are related by the equation: $Q(y) = f'(g(a)) + \eta(y - g(a)).$ The need to define *Q* at *g*(*a*) is analogous to the need to define *η* at zero.
### Third proof {#third_proof}
Constantin Carathéodory\'s alternative definition of the differentiability of a function can be used to give an elegant proof of the chain rule.
Under this definition, a function `{{mvar|f}}`{=mediawiki} is differentiable at a point `{{mvar|a}}`{=mediawiki} if and only if there is a function `{{mvar|q}}`{=mediawiki}, continuous at `{{mvar|a}}`{=mediawiki} and such that `{{math|1=''f''(''x'') − ''f''(''a'') = ''q''(''x'')(''x'' − ''a'')}}`{=mediawiki}. There is at most one such function, and if `{{mvar|f}}`{=mediawiki} is differentiable at `{{mvar|a}}`{=mediawiki} then `{{math|1=''f'' ′(''a'') = ''q''(''a'')}}`{=mediawiki}.
Given the assumptions of the chain rule and the fact that differentiable functions and compositions of continuous functions are continuous, we have that there exist functions `{{mvar|q}}`{=mediawiki}, continuous at `{{math|''g''(''a'')}}`{=mediawiki}, and `{{mvar|r}}`{=mediawiki}, continuous at `{{mvar|a}}`{=mediawiki}, and such that, $f(g(x))-f(g(a))=q(g(x))(g(x)-g(a))$ and $g(x)-g(a)=r(x)(x-a).$ Therefore, $f(g(x))-f(g(a))=q(g(x))r(x)(x-a),$ but the function given by `{{math|1=''h''(''x'') = ''q''(''g''(''x''))''r''(''x'')}}`{=mediawiki} is continuous at `{{mvar|a}}`{=mediawiki}, and we get, for this `{{mvar|a}}`{=mediawiki} $(f(g(a)))'=q(g(a))r(a)=f'(g(a))g'(a).$ A similar approach works for continuously differentiable (vector-)functions of many variables. This method of factoring also allows a unified approach to stronger forms of differentiability, when the derivative is required to be Lipschitz continuous, Hölder continuous, etc. Differentiation itself can be viewed as the polynomial remainder theorem (the little Bézout theorem, or factor theorem), generalized to an appropriate class of functions.{{ citation needed\|date=February 2016}}
### Proof via infinitesimals {#proof_via_infinitesimals}
If $y=f(x)$ and $x=g(t)$ then choosing infinitesimal $\Delta t\not=0$ we compute the corresponding $\Delta x=g(t+\Delta t)-g(t)$ and then the corresponding $\Delta y=f(x+\Delta x)-f(x)$, so that $\frac{\Delta y}{\Delta t} = \frac{\Delta y}{\Delta x} \frac{\Delta x}{\Delta t}$ and applying the standard part we obtain $\frac{d y}{d t}=\frac{d y}{d x} \frac{dx}{dt}$ which is the chain rule.
## Multivariable case {#multivariable_case}
The full generalization of the chain rule to multi-variable functions (such as $f : \mathbb{R}^m \to \mathbb{R}^n$) is rather technical. However, it is simpler to write in the case of functions of the form $f(g_1(x), \dots, g_k(x)),$ where $f : \reals^k \to \reals$, and $g_i : \mathbb{R} \to \mathbb{R}$ for each $i = 1, 2, \dots, k.$
As this case occurs often in the study of functions of a single variable, it is worth describing it separately.
### Case of scalar-valued functions with multiple inputs {#case_of_scalar_valued_functions_with_multiple_inputs}
Let $f : \reals^k \to \reals$, and $g_i : \mathbb{R} \to \mathbb{R}$ for each $i = 1, 2, \dots, k.$ To write the chain rule for the composition of functions $x \mapsto f(g_1(x), \dots , g_k(x)),$ one needs the partial derivatives of `{{mvar|f}}`{=mediawiki} with respect to its `{{mvar|k}}`{=mediawiki} arguments. The usual notations for partial derivatives involve names for the arguments of the function. As these arguments are not named in the above formula, it is simpler and clearer to use *D*-Notation, and to denote by $D_i f$ the partial derivative of `{{mvar|f}}`{=mediawiki} with respect to its `{{mvar|i}}`{=mediawiki}th argument, and by $D_i f(z)$ the value of this derivative at `{{mvar|z}}`{=mediawiki}.
With this notation, the chain rule is $\frac{d}{dx}f(g_1(x), \dots, g_k (x))=\sum_{i=1}^k \left(\frac{d}{dx}{g_i}(x)\right) D_i f(g_1(x), \dots, g_k (x)).$
#### Example: arithmetic operations {#example_arithmetic_operations}
If the function `{{mvar|f}}`{=mediawiki} is addition, that is, if $f(u,v)=u+v,$ then $D_1 f = \frac{\partial f}{\partial u} = 1$ and $D_2 f = \frac{\partial f}{\partial v} = 1$. Thus, the chain rule gives $\frac{d}{dx}(g(x)+h(x)) = \left( \frac{d}{dx}g(x) \right) D_1 f+\left( \frac{d}{dx}h(x)\right) D_2 f=\frac{d}{dx}g(x) +\frac{d}{dx}h(x).$
For multiplication $f(u,v)=uv,$ the partials are $D_1 f = v$ and $D_2 f = u$. Thus, $\frac{d}{dx}(g(x)h(x)) = h(x) \frac{d}{dx} g(x) + g(x) \frac{d}{dx} h(x).$
The case of exponentiation $f(u,v)=u^v$ is slightly more complicated, as $D_1 f = vu^{v-1},$ and, as $u^v=e^{v\ln u},$ $D_2 f = u^v\ln u.$ It follows that $\frac{d}{dx}\left(g(x)^{h(x)}\right) = h(x)g(x)^{h(x)-1} \frac{d}{dx}g(x) + g(x)^{h(x)} \ln g(x) \,\frac{d}{dx}h(x).$
### General rule: Vector-valued functions with multiple inputs {#general_rule_vector_valued_functions_with_multiple_inputs}
The simplest way for writing the chain rule in the general case is to use the total derivative, which is a linear transformation that captures all directional derivatives in a single formula. Consider differentiable functions `{{math|''f'' : '''R'''<sup>''m''</sup> → '''R'''<sup>''k''</sup>}}`{=mediawiki} and `{{math|''g'' : '''R'''<sup>''n''</sup> → '''R'''<sup>''m''</sup>}}`{=mediawiki}, and a point `{{math|'''a'''}}`{=mediawiki} in `{{math|'''R'''<sup>''n''</sup>}}`{=mediawiki}. Let `{{math|''D''<sub>'''a'''</sub> ''g''}}`{=mediawiki} denote the total derivative of `{{math|''g''}}`{=mediawiki} at `{{math|'''a'''}}`{=mediawiki} and `{{math|''D''<sub>''g''('''a''')</sub> ''f''}}`{=mediawiki} denote the total derivative of `{{math|''f''}}`{=mediawiki} at `{{math|''g''('''a''')}}`{=mediawiki}. These two derivatives are linear transformations `{{math|'''R'''<sup>''n''</sup> → '''R'''<sup>''m''</sup>}}`{=mediawiki} and `{{math|'''R'''<sup>''m''</sup> → '''R'''<sup>''k''</sup>}}`{=mediawiki}, respectively, so they can be composed. The chain rule for total derivatives is that their composite is the total derivative of `{{math|''f'' ∘ ''g''}}`{=mediawiki} at `{{math|'''a'''}}`{=mediawiki}: $D_{\mathbf{a}}(f \circ g) = D_{g(\mathbf{a})}f \circ D_{\mathbf{a}}g,$ or for short, $D(f \circ g) = Df \circ Dg.$ The higher-dimensional chain rule can be proved using a technique similar to the second proof given above.
Because the total derivative is a linear transformation, the functions appearing in the formula can be rewritten as matrices. The matrix corresponding to a total derivative is called a Jacobian matrix, and the composite of two derivatives corresponds to the product of their Jacobian matrices. From this perspective the chain rule therefore says: $J_{f \circ g}(\mathbf{a}) = J_{f}(g(\mathbf{a})) J_{g}(\mathbf{a}),$ or for short, $J_{f \circ g} = (J_f \circ g)J_g.$
That is, the Jacobian of a composite function is the product of the Jacobians of the composed functions (evaluated at the appropriate points).
The higher-dimensional chain rule is a generalization of the one-dimensional chain rule. If `{{mvar|k}}`{=mediawiki}, `{{mvar|m}}`{=mediawiki}, and `{{mvar|n}}`{=mediawiki} are 1, so that `{{math|''f'' : '''R''' → '''R'''}}`{=mediawiki} and `{{math|''g'' : '''R''' → '''R'''}}`{=mediawiki}, then the Jacobian matrices of `{{math|''f''}}`{=mediawiki} and `{{math|''g''}}`{=mediawiki} are `{{math|1 × 1}}`{=mediawiki}. Specifically, they are: $\begin{align}
J_g(a) &= \begin{pmatrix} g'(a) \end{pmatrix}, \\
J_{f}(g(a)) &= \begin{pmatrix} f'(g(a)) \end{pmatrix}.
\end{align}$ The Jacobian of `{{math|''f'' ∘ ''g''}}`{=mediawiki} is the product of these `{{math|1 × 1}}`{=mediawiki} matrices, so it is `{{math|''f''′(''g''(''a''))⋅''g''′(''a'')}}`{=mediawiki}, as expected from the one-dimensional chain rule. In the language of linear transformations, `{{math|''D''<sub>''a''</sub>(''g'')}}`{=mediawiki} is the function which scales a vector by a factor of `{{math|''g''′(''a'')}}`{=mediawiki} and `{{math|''D''<sub>''g''(''a'')</sub>(''f'')}}`{=mediawiki} is the function which scales a vector by a factor of `{{math|''f''′(''g''(''a''))}}`{=mediawiki}. The chain rule says that the composite of these two linear transformations is the linear transformation `{{math|''D''<sub>''a''</sub>(''f'' ∘ ''g'')}}`{=mediawiki}, and therefore it is the function that scales a vector by `{{math|''f''′(''g''(''a''))⋅''g''′(''a'')}}`{=mediawiki}.
Another way of writing the chain rule is used when *f* and *g* are expressed in terms of their components as `{{math|1='''y''' = ''f''('''u''') = (''f''<sub>1</sub>('''u'''), …, ''f''<sub>''k''</sub>('''u'''))}}`{=mediawiki} and `{{math|1='''u''' = ''g''('''x''') = (''g''<sub>1</sub>('''x'''), …, ''g''<sub>''m''</sub>('''x'''))}}`{=mediawiki}. In this case, the above rule for Jacobian matrices is usually written as: $\frac{\partial(y_1, \ldots, y_k)}{\partial(x_1, \ldots, x_n)} = \frac{\partial(y_1, \ldots, y_k)}{\partial(u_1, \ldots, u_m)} \frac{\partial(u_1, \ldots, u_m)}{\partial(x_1, \ldots, x_n)}.$
The chain rule for total derivatives implies a chain rule for partial derivatives. Recall that when the total derivative exists, the partial derivative in the `{{mvar|i}}`{=mediawiki}-th coordinate direction is found by multiplying the Jacobian matrix by the `{{mvar|i}}`{=mediawiki}-th basis vector. By doing this to the formula above, we find: $\frac{\partial(y_1, \ldots, y_k)}{\partial x_i} = \frac{\partial(y_1, \ldots, y_k)}{\partial(u_1, \ldots, u_m)} \frac{\partial(u_1, \ldots, u_m)}{\partial x_i}.$ Since the entries of the Jacobian matrix are partial derivatives, we may simplify the above formula to get: $\frac{\partial(y_1, \ldots, y_k)}{\partial x_i} = \sum_{\ell = 1}^m \frac{\partial(y_1, \ldots, y_k)}{\partial u_\ell} \frac{\partial u_\ell}{\partial x_i}.$ More conceptually, this rule expresses the fact that a change in the `{{math|''x''<sub>''i''</sub>}}`{=mediawiki} direction may change all of `{{math|''g''<sub>1</sub>}}`{=mediawiki} through `{{math|''g<sub>m</sub>''}}`{=mediawiki}, and any of these changes may affect `{{math|''f''}}`{=mediawiki}.
In the special case where `{{math|1=''k'' = 1}}`{=mediawiki}, so that `{{math|''f''}}`{=mediawiki} is a real-valued function, then this formula simplifies even further: $\frac{\partial y}{\partial x_i} = \sum_{\ell = 1}^m \frac{\partial y}{\partial u_\ell} \frac{\partial u_\ell}{\partial x_i}.$ This can be rewritten as a dot product. Recalling that `{{math|'''u''' {{=}}`{=mediawiki} (*g*~1~, ..., *g*~*m*~)}}, the partial derivative `{{math|∂'''u''' / ∂''x''<sub>''i''</sub>}}`{=mediawiki} is also a vector, and the chain rule says that: $\frac{\partial y}{\partial x_i} = \nabla y \cdot \frac{\partial \mathbf{u}}{\partial x_i}.$
#### Example
Given `{{math|1=''u''(''x'', ''y'') = ''x''<sup>2</sup> + 2''y''}}`{=mediawiki} where `{{math|1=''x''(''r'', ''t'') = ''r'' sin(''t'')}}`{=mediawiki} and `{{math|1=''y''(''r'',''t'') = sin<sup>2</sup>(''t'')}}`{=mediawiki}, determine the value of `{{math|∂''u'' / ∂''r''}}`{=mediawiki} and `{{math|∂''u'' / ∂''t''}}`{=mediawiki} using the chain rule. $\frac{\partial u}{\partial r}=\frac{\partial u}{\partial x} \frac{\partial x}{\partial r}+\frac{\partial u}{\partial y} \frac{\partial y}{\partial r} = (2x)(\sin(t)) + (2)(0) = 2r \sin^2(t),$ and $\begin{align}
\frac{\partial u}{\partial t}
&= \frac{\partial u}{\partial x} \frac{\partial x}{\partial t}+\frac{\partial u}{\partial y} \frac{\partial y}{\partial t} \\
&= (2x)(r\cos(t)) + (2)(2\sin(t)\cos(t)) \\
&= (2r\sin(t))(r\cos(t)) + 4\sin(t)\cos(t) \\
&= 2(r^2 + 2) \sin(t)\cos(t) \\
&= (r^2 + 2) \sin(2t).
\end{align}$
#### Higher derivatives of multivariable functions {#higher_derivatives_of_multivariable_functions}
Faà di Bruno\'s formula for higher-order derivatives of single-variable functions generalizes to the multivariable case. If `{{math|1=''y'' = ''f''('''u''')}}`{=mediawiki} is a function of `{{math|1='''u''' = ''g''('''x''')}}`{=mediawiki} as above, then the second derivative of `{{math|''f'' ∘ ''g''}}`{=mediawiki} is: $\frac{\partial^2 y}{\partial x_i \partial x_j} = \sum_k \left(\frac{\partial y}{\partial u_k}\frac{\partial^2 u_k}{\partial x_i \partial x_j}\right) + \sum_{k, \ell} \left(\frac{\partial^2 y}{\partial u_k \partial u_\ell}\frac{\partial u_k}{\partial x_i}\frac{\partial u_\ell}{\partial x_j}\right).$
## Further generalizations {#further_generalizations}
All extensions of calculus have a chain rule. In most of these, the formula remains the same, though the meaning of that formula may be vastly different.
One generalization is to manifolds. In this situation, the chain rule represents the fact that the derivative of `{{math|''f'' ∘ ''g''}}`{=mediawiki} is the composite of the derivative of `{{math|''f''}}`{=mediawiki} and the derivative of `{{math|''g''}}`{=mediawiki}. This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula.
The chain rule is also valid for Fréchet derivatives in Banach spaces. The same formula holds as before. This case and the previous one admit a simultaneous generalization to Banach manifolds.
In differential algebra, the derivative is interpreted as a morphism of modules of Kähler differentials. A ring homomorphism of commutative rings `{{math|''f'' : ''R'' → ''S''}}`{=mediawiki} determines a morphism of Kähler differentials `{{math|''Df'' : Ω<sub>''R''</sub> → Ω<sub>''S''</sub>}}`{=mediawiki} which sends an element `{{math|''dr''}}`{=mediawiki} to `{{math|''d''(''f''(''r''))}}`{=mediawiki}, the exterior differential of `{{math|''f''(''r'')}}`{=mediawiki}. The formula `{{math|1=''D''(''f'' ∘ ''g'') = ''Df'' ∘ ''Dg''}}`{=mediawiki} holds in this context as well.
The common feature of these examples is that they are expressions of the idea that the derivative is part of a functor. A functor is an operation on spaces and functions between them. It associates to each space a new space and to each function between two spaces a new function between the corresponding new spaces. In each of the above cases, the functor sends each space to its tangent bundle and it sends each function to its derivative. For example, in the manifold case, the derivative sends a `{{math|''C''<sup>''r''</sup>}}`{=mediawiki}-manifold to a `{{math|''C''<sup>''r''−1</sup>}}`{=mediawiki}-manifold (its tangent bundle) and a `{{math|''C''<sup>''r''</sup>}}`{=mediawiki}-function to its total derivative. There is one requirement for this to be a functor, namely that the derivative of a composite must be the composite of the derivatives. This is exactly the formula `{{math|1=''D''(''f'' ∘ ''g'') = ''Df'' ∘ ''Dg''}}`{=mediawiki}.
There are also chain rules in stochastic calculus. One of these, Itō\'s lemma, expresses the composite of an Itō process (or more generally a semimartingale) *dX*~*t*~ with a twice-differentiable function *f*. In Itō\'s lemma, the derivative of the composite function depends not only on *dX*~*t*~ and the derivative of *f* but also on the second derivative of *f*. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way. This variant of the chain rule is not an example of a functor because the two functions being composed are of different types.
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Charles Sanders Peirce
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Curl (mathematics)
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`{{Calculus |Vector}}`{=mediawiki}
In vector calculus, the **curl**, also known as **rotor**, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field.
A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes\' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.
The notation `{{math|curl '''F'''}}`{=mediawiki} is more common in North America. In the rest of the world, particularly in 20th century scientific literature, the alternative notation `{{math|rot '''F'''}}`{=mediawiki} is traditionally used, which comes from the \"rate of rotation\" that it represents. To avoid confusion, modern authors tend to use the cross product notation with the del (nabla) operator, as in `{{nowrap|<math>\nabla \times \mathbf{F}</math>,}}`{=mediawiki} which also reveals the relation between curl (rotor), divergence, and gradient operators.
Unlike the gradient and divergence, curl as formulated in vector calculus does not generalize simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This deficiency is a direct consequence of the limitations of vector calculus; on the other hand, when expressed as an antisymmetric tensor field via the wedge operator of geometric calculus, the curl generalizes to all dimensions. The circumstance is similar to that attending the 3-dimensional cross product, and indeed the connection is reflected in the notation $\nabla \times$ for the curl.
The name \"curl\" was first suggested by James Clerk Maxwell in 1871 but the concept was apparently first used in the construction of an optical field theory by James MacCullagh in 1839.
## Definition
}}
and the fingers curl along the orientation of `{{math|''C''}}`{=mediawiki} \| align = \| direction = \| alt1 = \| header = Right-hand rule }}
The curl of a vector field `{{math|'''F'''}}`{=mediawiki}, denoted by `{{math|curl '''F'''}}`{=mediawiki}, or $\nabla \times \mathbf{F}$, or `{{math|rot '''F'''}}`{=mediawiki}, is an operator that maps `{{math|[[Smooth function|''C<sup>k</sup>'']]}}`{=mediawiki} functions in `{{math|'''R'''<sup>3</sup>}}`{=mediawiki} to `{{math|''C''<sup>''k''−1</sup>}}`{=mediawiki} functions in `{{math|'''R'''<sup>3</sup>}}`{=mediawiki}, and in particular, it maps continuously differentiable functions `{{math|'''R'''<sup>3</sup> → '''R'''<sup>3</sup>}}`{=mediawiki} to continuous functions `{{math|'''R'''<sup>3</sup> → '''R'''<sup>3</sup>}}`{=mediawiki}. It can be defined in several ways, to be mentioned below:
One way to define the curl of a vector field at a point is implicitly through its components along various axes passing through the point: if $\mathbf{\hat{u}}$ is any unit vector, the component of the curl of `{{math|'''F'''}}`{=mediawiki} along the direction $\mathbf{\hat{u}}$ may be defined to be the limiting value of a closed line integral in a plane perpendicular to $\mathbf{\hat{u}}$ divided by the area enclosed, as the path of integration is contracted indefinitely around the point.
More specifically, the curl is defined at a point `{{math|''p''}}`{=mediawiki} as $(\nabla \times \mathbf{F})(p)\cdot \mathbf{\hat{u}} \ \overset{\underset{\mathrm{def}}{}}{{}={}} \lim_{A \to 0}\frac{1}{|A|}\oint_{C(p)} \mathbf{F} \cdot \mathrm{d}\mathbf{r}$ where the line integral is calculated along the boundary `{{math|''C''}}`{=mediawiki} of the area `{{math|''A''}}`{=mediawiki} containing point p, `{{math|{{abs|''A''}}}}`{=mediawiki} being the magnitude of the area. This equation defines the component of the curl of `{{math|'''F'''}}`{=mediawiki} along the direction $\mathbf{\hat{u}}$. The infinitesimal surfaces bounded by `{{math|''C''}}`{=mediawiki} have $\mathbf{\hat{u}}$ as their normal. `{{math|''C''}}`{=mediawiki} is oriented via the right-hand rule.
The above formula means that the component of the curl of a vector field along a certain axis is the *infinitesimal area density* of the circulation of the field in a plane perpendicular to that axis. This formula does not *a priori* define a legitimate vector field, for the individual circulation densities with respect to various axes *a priori* need not relate to each other in the same way as the components of a vector do; that they *do* indeed relate to each other in this precise manner must be proven separately.
To this definition fits naturally the Kelvin--Stokes theorem, as a global formula corresponding to the definition. It equates the surface integral of the curl of a vector field to the above line integral taken around the boundary of the surface.
Another way one can define the curl vector of a function `{{math|'''F'''}}`{=mediawiki} at a point is explicitly as the limiting value of a vector-valued surface integral around a shell enclosing `{{math|''p''}}`{=mediawiki} divided by the volume enclosed, as the shell is contracted indefinitely around `{{math|''p''}}`{=mediawiki}.
More specifically, the curl may be defined by the vector formula $(\nabla \times \mathbf{F})(p) \overset{\underset{\mathrm{def}}{}}{{}={}} \lim_{V \to 0}\frac{1}{|V|}\oint_S \mathbf{\hat{n}} \times \mathbf{F} \ \mathrm{d}S$ where the surface integral is calculated along the boundary `{{math|''S''}}`{=mediawiki} of the volume `{{math|''V''}}`{=mediawiki}, `{{math|{{abs|''V''}}}}`{=mediawiki} being the magnitude of the volume, and $\mathbf{\hat{n}}$ pointing outward from the surface `{{math|''S''}}`{=mediawiki} perpendicularly at every point in `{{math|''S''}}`{=mediawiki}.
In this formula, the cross product in the integrand measures the tangential component of `{{math|'''F'''}}`{=mediawiki} at each point on the surface `{{math|''S''}}`{=mediawiki}, and points along the surface at right angles to the *tangential projection* of `{{math|'''F'''}}`{=mediawiki}. Integrating this cross product over the whole surface results in a vector whose magnitude measures the overall circulation of `{{math|'''F'''}}`{=mediawiki} around `{{math|''S''}}`{=mediawiki}, and whose direction is at right angles to this circulation. The above formula says that the *curl* of a vector field at a point is the *infinitesimal volume density* of this \"circulation vector\" around the point.
To this definition fits naturally another global formula (similar to the Kelvin-Stokes theorem) which equates the volume integral of the curl of a vector field to the above surface integral taken over the boundary of the volume.
Whereas the above two definitions of the curl are coordinate free, there is another \"easy to memorize\" definition of the curl in curvilinear orthogonal coordinates, e.g. in Cartesian coordinates, spherical, cylindrical, or even elliptical or parabolic coordinates: $\begin{align}
& (\operatorname{curl}\mathbf F)_1=\frac{1}{h_2h_3}\left (\frac{\partial (h_3F_3)}{\partial u_2}-\frac{\partial (h_2F_2)}{\partial u_3}\right ), \\[5pt]
& (\operatorname{curl}\mathbf F)_2=\frac{1}{h_3h_1}\left (\frac{\partial (h_1F_1)}{\partial u_3}-\frac{\partial (h_3F_3)}{\partial u_1}\right ), \\[5pt]
& (\operatorname{curl}\mathbf F)_3=\frac{1}{h_1h_2}\left (\frac{\partial (h_2F_2)}{\partial u_1}-\frac{\partial (h_1F_1)}{\partial u_2}\right ).
\end{align}$
The equation for each component `{{math|(curl '''F''')<sub>''k''</sub>}}`{=mediawiki} can be obtained by exchanging each occurrence of a subscript 1, 2, 3 in cyclic permutation: 1 → 2, 2 → 3, and 3 → 1 (where the subscripts represent the relevant indices).
If `{{math|(''x''<sub>1</sub>, ''x''<sub>2</sub>, ''x''<sub>3</sub>)}}`{=mediawiki} are the Cartesian coordinates and `{{math|(''u''<sub>1</sub>, ''u''<sub>2</sub>, ''u''<sub>3</sub>)}}`{=mediawiki} are the orthogonal coordinates, then $h_i = \sqrt{\left (\frac{\partial x_1}{\partial u_i} \right )^2 + \left (\frac{\partial x_2}{\partial u_i} \right )^2 + \left (\frac{\partial x_3}{\partial u_i} \right )^2}$ is the length of the coordinate vector corresponding to `{{math|''u<sub>i</sub>''}}`{=mediawiki}. The remaining two components of curl result from cyclic permutation of indices: 3,1,2 → 1,2,3 → 2,3,1.
## Usage
In practice, the two coordinate-free definitions described above are rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived.
The notation $\nabla\times\mathbf{F}$ has its origins in the similarities to the 3-dimensional cross product, and it is useful as a mnemonic in Cartesian coordinates if $\nabla$ is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra.
Expanded in 3-dimensional Cartesian coordinates (see *Del in cylindrical and spherical coordinates* for spherical and cylindrical coordinate representations), $\nabla\times\mathbf{F}$ is, for $\mathbf{F}$ composed of $[F_x,F_y,F_z]$ (where the subscripts indicate the components of the vector, not partial derivatives): $\nabla \times \mathbf{F} =
\begin{vmatrix} \boldsymbol{\hat\imath} & \boldsymbol{\hat\jmath} & \boldsymbol{\hat k} \\[5mu]
{\dfrac{\partial}{\partial x}} & {\dfrac{\partial}{\partial y}} & {\dfrac{\partial}{\partial z}} \\[5mu]
F_x & F_y & F_z \end{vmatrix}$ where `{{math|'''i'''}}`{=mediawiki}, `{{math|'''j'''}}`{=mediawiki}, and `{{math|'''k'''}}`{=mediawiki} are the unit vectors for the `{{math|''x''}}`{=mediawiki}-, `{{math|''y''}}`{=mediawiki}-, and `{{math|''z''}}`{=mediawiki}-axes, respectively. This expands as follows: $\nabla \times \mathbf{F} =
\left(\frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z}\right) \boldsymbol{\hat\imath} +
\left(\frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \boldsymbol{\hat\jmath} +
\left(\frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \boldsymbol{\hat k}$
Although expressed in terms of coordinates, the result is invariant under proper rotations of the coordinate axes but the result inverts under reflection.
In a general coordinate system, the curl is given by $(\nabla \times \mathbf{F} )^k = \frac{1}{\sqrt{g}} \varepsilon^{k\ell m} \nabla_\ell F_m$ where `{{mvar|ε}}`{=mediawiki} denotes the Levi-Civita tensor, `{{math|∇}}`{=mediawiki} the covariant derivative, $g$ is the determinant of the metric tensor and the Einstein summation convention implies that repeated indices are summed over. Due to the symmetry of the Christoffel symbols participating in the covariant derivative, this expression reduces to the partial derivative: $(\nabla \times \mathbf{F} ) = \frac{1}{\sqrt{g}} \mathbf{R}_k\varepsilon^{k\ell m} \partial_\ell F_m$ where `{{math|'''R'''<sub>''k''</sub>}}`{=mediawiki} are the local basis vectors. Equivalently, using the exterior derivative, the curl can be expressed as: $\nabla \times \mathbf{F} = \left( \star \big( {\mathrm d} \mathbf{F}^\flat \big) \right)^\sharp$
Here `{{music|flat}}`{=mediawiki} and `{{music|sharp}}`{=mediawiki} are the musical isomorphisms, and `{{math|<small>★</small>}}`{=mediawiki} is the Hodge star operator. This formula shows how to calculate the curl of `{{math|'''F'''}}`{=mediawiki} in any coordinate system, and how to extend the curl to any oriented three-dimensional Riemannian manifold. Since this depends on a choice of orientation, curl is a chiral operation. In other words, if the orientation is reversed, then the direction of the curl is also reversed.
## Examples
### Example 1 {#example_1}
Suppose the vector field describes the velocity field of a fluid flow (such as a large tank of liquid or gas) and a small ball is located within the fluid or gas (the center of the ball being fixed at a certain point). If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis (oriented according to the right hand rule) points in the direction of the curl of the field at the center of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point. The curl of the vector field at any point is given by the rotation of an infinitesimal area in the *xy*-plane (for *z*-axis component of the curl), *zx*-plane (for *y*-axis component of the curl) and *yz*-plane (for *x*-axis component of the curl vector). This can be seen in the examples below.
### Example 2 {#example_2}
The vector field $\mathbf{F}(x,y,z)=y\boldsymbol{\hat{\imath}}-x\boldsymbol{\hat{\jmath}}$ can be decomposed as $F_x =y, F_y = -x, F_z =0.$
Upon visual inspection, the field can be described as \"rotating\". If the vectors of the field were to represent a linear force acting on objects present at that point, and an object were to be placed inside the field, the object would start to rotate clockwise around itself. This is true regardless of where the object is placed.
Calculating the curl: $\nabla \times \mathbf{F} =0\boldsymbol{\hat{\imath}}+0\boldsymbol{\hat{\jmath}}+ \left({\frac{\partial}{\partial x}}(-x) -{\frac{\partial}{\partial y}} y\right)\boldsymbol{\hat{k}}=-2\boldsymbol{\hat{k}}$
The resulting vector field describing the curl would at all points be pointing in the negative `{{Math|''z''}}`{=mediawiki} direction. The results of this equation align with what could have been predicted using the right-hand rule using a right-handed coordinate system. Being a uniform vector field, the object described before would have the same rotational intensity regardless of where it was placed.
### Example 3 {#example_3}
For the vector field $\mathbf{F}(x,y,z) = -x^2\boldsymbol{\hat{\jmath}}$
the curl is not as obvious from the graph. However, taking the object in the previous example, and placing it anywhere on the line `{{math|1=''x'' = 3}}`{=mediawiki}, the force exerted on the right side would be slightly greater than the force exerted on the left, causing it to rotate clockwise. Using the right-hand rule, it can be predicted that the resulting curl would be straight in the negative `{{math|''z''}}`{=mediawiki} direction. Inversely, if placed on `{{math|1=''x'' = −3}}`{=mediawiki}, the object would rotate counterclockwise and the right-hand rule would result in a positive `{{math|''z''}}`{=mediawiki} direction.
Calculating the curl: ${\nabla} \times \mathbf{F} = 0 \boldsymbol{\hat{\imath}} + 0\boldsymbol{\hat{\jmath}} + {\frac{\partial}{\partial x}}\left(-x^2\right) \boldsymbol{\hat{k}} = -2x\boldsymbol{\hat{k}}.$
The curl points in the negative `{{math|''z''}}`{=mediawiki} direction when `{{math|''x''}}`{=mediawiki} is positive and vice versa. In this field, the intensity of rotation would be greater as the object moves away from the plane `{{math|1=''x'' = 0}}`{=mediawiki}.
### Further examples {#further_examples}
- In a vector field describing the linear velocities of each part of a rotating disk in uniform circular motion, the curl has the same value at all points, and this value turns out to be exactly two times the vectorial angular velocity of the disk (oriented as usual by the right-hand rule). More generally, for any flowing mass, the linear velocity vector field at each point of the mass flow has a curl (the vorticity of the flow at that point) equal to exactly two times the *local* vectorial angular velocity of the mass about the point.
- For any solid object subject to an external physical force (such as gravity or the electromagnetic force), one may consider the vector field representing the infinitesimal force-per-unit-volume contributions acting at each of the points of the object. This force field may create a net *torque* on the object about its center of mass, and this torque turns out to be directly proportional and vectorially parallel to the (vector-valued) integral of the *curl* of the force field over the whole volume.
- Of the four Maxwell\'s equations, two---Faraday\'s law and Ampère\'s law---can be compactly expressed using curl. Faraday\'s law states that the curl of an electric field is equal to the opposite of the time rate of change of the magnetic field, while Ampère\'s law relates the curl of the magnetic field to the current and the time rate of change of the electric field.
## Identities
In general curvilinear coordinates (not only in Cartesian coordinates), the curl of a cross product of vector fields `{{math|'''v'''}}`{=mediawiki} and `{{math|'''F'''}}`{=mediawiki} can be shown to be $\nabla \times \left( \mathbf{v \times F} \right) = \Big( \left( \mathbf{ \nabla \cdot F } \right) + \mathbf{F \cdot \nabla} \Big) \mathbf{v}- \Big( \left( \mathbf{ \nabla \cdot v } \right) + \mathbf{v \cdot \nabla} \Big) \mathbf{F} \ .$
Interchanging the vector field `{{math|'''v'''}}`{=mediawiki} and `{{math|∇}}`{=mediawiki} operator, we arrive at the cross product of a vector field with curl of a vector field: $\mathbf{v \ \times } \left( \mathbf{ \nabla \times F} \right) =\nabla_\mathbf{F} \left( \mathbf{v \cdot F } \right) - \left( \mathbf{v \cdot \nabla } \right) \mathbf{F} \ ,$ where `{{math|∇<sub>'''F'''</sub>}}`{=mediawiki} is the Feynman subscript notation, which considers only the variation due to the vector field `{{math|'''F'''}}`{=mediawiki} (i.e., in this case, `{{math|'''v'''}}`{=mediawiki} is treated as being constant in space).
Another example is the curl of a curl of a vector field. It can be shown that in general coordinates $\nabla \times \left( \mathbf{\nabla \times F} \right) = \mathbf{\nabla}(\mathbf{\nabla \cdot F}) - \nabla^2 \mathbf{F} \ ,$ and this identity defines the vector Laplacian of `{{math|'''F'''}}`{=mediawiki}, symbolized as `{{math|∇<sup>2</sup>'''F'''}}`{=mediawiki}.
The curl of the gradient of *any* scalar field `{{mvar|φ}}`{=mediawiki} is always the zero vector field $\nabla \times ( \nabla \varphi ) = \boldsymbol{0}$ which follows from the antisymmetry in the definition of the curl, and the symmetry of second derivatives.
The divergence of the curl of any vector field is equal to zero: $\nabla\cdot(\nabla\times\mathbf{F}) = 0.$
If `{{mvar|φ}}`{=mediawiki} is a scalar valued function and `{{math|'''F'''}}`{=mediawiki} is a vector field, then $\nabla \times ( \varphi \mathbf{F}) = \nabla \varphi \times \mathbf{F} + \varphi \nabla \times \mathbf{F}$
## Generalizations
The vector calculus operations of grad, curl, and div are most easily generalized in the context of differential forms, which involves a number of steps. In short, they correspond to the derivatives of 0-forms, 1-forms, and 2-forms, respectively. The geometric interpretation of curl as rotation corresponds to identifying bivectors (2-vectors) in 3 dimensions with the special orthogonal Lie algebra $\mathfrak{so}(3)$ of infinitesimal rotations (in coordinates, skew-symmetric 3 × 3 matrices), while representing rotations by vectors corresponds to identifying 1-vectors (equivalently, 2-vectors) and `{{nowrap|<math>\mathfrak{so}(3)</math>,}}`{=mediawiki} these all being 3-dimensional spaces.
### Differential forms {#differential_forms}
In 3 dimensions, a differential 0-form is a real-valued function $f(x,y,z)$; a differential 1-form is the following expression, where the coefficients are functions: $a_1\,dx + a_2\,dy + a_3\,dz;$ a differential 2-form is the formal sum, again with function coefficients: $a_{12}\,dx\wedge dy + a_{13}\,dx\wedge dz + a_{23}\,dy\wedge dz;$ and a differential 3-form is defined by a single term with one function as coefficient: $a_{123}\,dx\wedge dy\wedge dz.$ (Here the `{{mvar|a}}`{=mediawiki}-coefficients are real functions of three variables; the wedge products, e.g. $\text{d}x\wedge\text{d}y$, can be interpreted as oriented plane segments, $\text{d}x\wedge\text{d}y=-\text{d}y\wedge\text{d}x$, etc.)
The exterior derivative of a `{{math|''k''}}`{=mediawiki}-form in `{{math|1='''R'''<sup>3</sup>}}`{=mediawiki} is defined as the `{{math|(''k'' + 1)}}`{=mediawiki}-form from above---and in `{{math|'''R'''<sup>''n''</sup>}}`{=mediawiki} if, e.g., $\omega^{(k)}=\sum_{1\leq i_1<i_2<\cdots<i_k\leq n} a_{i_1,\ldots,i_k} \,dx_{i_1}\wedge \cdots\wedge dx_{i_k},$ then the exterior derivative `{{math|''d''}}`{=mediawiki} leads to $d\omega^{(k)}=\sum_{\scriptstyle{j=1} \atop \scriptstyle{i_1<\cdots<i_k}}^n\frac{\partial a_{i_1,\ldots,i_k}}{\partial x_j}\,dx_j \wedge dx_{i_1}\wedge \cdots \wedge dx_{i_k}.$
The exterior derivative of a 1-form is therefore a 2-form, and that of a 2-form is a 3-form. On the other hand, because of the interchangeability of mixed derivatives, $\frac{\partial^2}{\partial x_i\,\partial x_j} = \frac{\partial^2}{\partial x_j\,\partial x_i} ,$ and antisymmetry, $d x_i \wedge d x_j = -d x_j \wedge d x_i$
the twofold application of the exterior derivative yields $0$ (the zero $k+2$-form).
Thus, denoting the space of `{{math|''k''}}`{=mediawiki}-forms by $\Omega^k(\mathbb{R}^3)$ and the exterior derivative by `{{math|''d''}}`{=mediawiki} one gets a sequence: $0 \, \overset{d}{\longrightarrow} \;
\Omega^0\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \;
\Omega^1\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \;
\Omega^2\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \;
\Omega^3\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \, 0.$
Here $\Omega^k(\mathbb{R}^n)$ is the space of sections of the exterior algebra $\Lambda^k(\mathbb{R}^n)$ vector bundle over **R**^*n*^, whose dimension is the binomial coefficient $\binom{n}{k}$; note that $\Omega^k(\mathbb{R}^3)=0$ for $k>3$ or $k<0$. Writing only dimensions, one obtains a row of Pascal\'s triangle:
$0\rightarrow 1\rightarrow 3\rightarrow 3\rightarrow 1\rightarrow 0;$
the 1-dimensional fibers correspond to scalar fields, and the 3-dimensional fibers to vector fields, as described below. Modulo suitable identifications, the three nontrivial occurrences of the exterior derivative correspond to grad, curl, and div.
Differential forms and the differential can be defined on any Euclidean space, or indeed any manifold, without any notion of a Riemannian metric. On a Riemannian manifold, or more generally pseudo-Riemannian manifold, `{{math|''k''}}`{=mediawiki}-forms can be identified with `{{math|''k''}}`{=mediawiki}-vector fields (`{{math|''k''}}`{=mediawiki}-forms are `{{math|''k''}}`{=mediawiki}-covector fields, and a pseudo-Riemannian metric gives an isomorphism between vectors and covectors), and on an *oriented* vector space with a nondegenerate form (an isomorphism between vectors and covectors), there is an isomorphism between `{{math|''k''}}`{=mediawiki}-vectors and `{{math|(''n'' − ''k'')}}`{=mediawiki}-vectors; in particular on (the tangent space of) an oriented pseudo-Riemannian manifold. Thus on an oriented pseudo-Riemannian manifold, one can interchange `{{math|''k''}}`{=mediawiki}-forms, `{{math|''k''}}`{=mediawiki}-vector fields, `{{math|(''n'' − ''k'')}}`{=mediawiki}-forms, and `{{math|(''n'' − ''k'')}}`{=mediawiki}-vector fields; this is known as Hodge duality. Concretely, on `{{math|'''R'''<sup>3</sup>}}`{=mediawiki} this is given by:
- 1-forms and 1-vector fields: the 1-form `{{math|''a<sub>x</sub> dx'' + ''a<sub>y</sub> dy'' + ''a<sub>z</sub> dz''}}`{=mediawiki} corresponds to the vector field `{{math|(''a<sub>x</sub>'', ''a<sub>y</sub>'', ''a<sub>z</sub>'')}}`{=mediawiki}.
- 1-forms and 2-forms: one replaces `{{math|''dx''}}`{=mediawiki} by the dual quantity `{{math|''dy'' ∧ ''dz''}}`{=mediawiki} (i.e., omit `{{math|''dx''}}`{=mediawiki}), and likewise, taking care of orientation: `{{math|''dy''}}`{=mediawiki} corresponds to `{{math|1=''dz'' ∧ ''dx'' = −''dx'' ∧ ''dz''}}`{=mediawiki}, and `{{math|''dz''}}`{=mediawiki} corresponds to `{{math|''dx'' ∧ ''dy''}}`{=mediawiki}. Thus the form `{{math|''a<sub>x</sub> dx'' + ''a<sub>y</sub> dy'' + ''a<sub>z</sub> dz''}}`{=mediawiki} corresponds to the \"dual form\" `{{math|''a<sub>z</sub> dx'' ∧ ''dy'' + ''a<sub>y</sub> dz'' ∧ ''dx'' + ''a<sub>x</sub> dy'' ∧ ''dz''}}`{=mediawiki}.
Thus, identifying 0-forms and 3-forms with scalar fields, and 1-forms and 2-forms with vector fields:
- grad takes a scalar field (0-form) to a vector field (1-form);
- curl takes a vector field (1-form) to a pseudovector field (2-form);
- div takes a pseudovector field (2-form) to a pseudoscalar field (3-form)
On the other hand, the fact that `{{math|1=''d''{{isup|2}} = 0}}`{=mediawiki} corresponds to the identities $\nabla\times(\nabla f) = \mathbf 0$ for any scalar field `{{mvar|f}}`{=mediawiki}, and $\nabla \cdot (\nabla \times\mathbf v)=0$ for any vector field `{{math|'''v'''}}`{=mediawiki}.
Grad and div generalize to all oriented pseudo-Riemannian manifolds, with the same geometric interpretation, because the spaces of 0-forms and `{{math|''n''}}`{=mediawiki}-forms at each point are always 1-dimensional and can be identified with scalar fields, while the spaces of 1-forms and `{{math|(''n'' − 1)}}`{=mediawiki}-forms are always fiberwise `{{math|''n''}}`{=mediawiki}-dimensional and can be identified with vector fields.
Curl does not generalize in this way to 4 or more dimensions (or down to 2 or fewer dimensions); in 4 dimensions the dimensions are `{{block indent |text = 0 → 1 → 4 → 6 → 4 → 1 → 0;}}`{=mediawiki} so the curl of a 1-vector field (fiberwise 4-dimensional) is a *2-vector field*, which at each point belongs to 6-dimensional vector space, and so one has $\omega^{(2)}=\sum_{i<k=1,2,3,4}a_{i,k}\,dx_i\wedge dx_k,$ which yields a sum of six independent terms, and cannot be identified with a 1-vector field. Nor can one meaningfully go from a 1-vector field to a 2-vector field to a 3-vector field (4 → 6 → 4), as taking the differential twice yields zero (`{{math|1=''d''{{isup|2}} = 0}}`{=mediawiki}). Thus there is no curl function from vector fields to vector fields in other dimensions arising in this way.
However, one can define a curl of a vector field as a *2-vector field* in general, as described below.
### Curl geometrically {#curl_geometrically}
2-vectors correspond to the exterior power `{{math|Λ<sup>2</sup>''V''}}`{=mediawiki}; in the presence of an inner product, in coordinates these are the skew-symmetric matrices, which are geometrically considered as the special orthogonal Lie algebra `{{math|<math>\mathfrak{so}</math>(''V'')}}`{=mediawiki} of infinitesimal rotations. This has `{{math|1=<big><big>(</big></big>{{su|p=''n''|b=2}}<big><big>)</big></big> = {{sfrac|1|2}}''n''(''n'' − 1)}}`{=mediawiki} dimensions, and allows one to interpret the differential of a 1-vector field as its infinitesimal rotations. Only in 3 dimensions (or trivially in 0 dimensions) we have `{{math|1=''n'' = {{sfrac|1|2}}''n''(''n'' − 1)}}`{=mediawiki}, which is the most elegant and common case. In 2 dimensions the curl of a vector field is not a vector field but a function, as 2-dimensional rotations are given by an angle (a scalar -- an orientation is required to choose whether one counts clockwise or counterclockwise rotations as positive); this is not the div, but is rather perpendicular to it. In 3 dimensions the curl of a vector field is a vector field as is familiar (in 1 and 0 dimensions the curl of a vector field is 0, because there are no non-trivial 2-vectors), while in 4 dimensions the curl of a vector field is, geometrically, at each point an element of the 6-dimensional Lie algebra `{{nowrap|<math>\mathfrak{so}(4)</math>.}}`{=mediawiki}
The curl of a 3-dimensional vector field which only depends on 2 coordinates (say `{{math|''x''}}`{=mediawiki} and `{{math|''y''}}`{=mediawiki}) is simply a vertical vector field (in the `{{math|''z''}}`{=mediawiki} direction) whose magnitude is the curl of the 2-dimensional vector field, as in the examples on this page.
Considering curl as a 2-vector field (an antisymmetric 2-tensor) has been used to generalize vector calculus and associated physics to higher dimensions.
## Inverse
In the case where the divergence of a vector field `{{math|'''V'''}}`{=mediawiki} is zero, a vector field `{{math|'''W'''}}`{=mediawiki} exists such that `{{math|1='''V''' = curl('''W''')}}`{=mediawiki}. This is why the magnetic field, characterized by zero divergence, can be expressed as the curl of a magnetic vector potential.
If `{{math|'''W'''}}`{=mediawiki} is a vector field with `{{math|1=curl('''W''') = '''V'''}}`{=mediawiki}, then adding any gradient vector field `{{math|grad(''f'')}}`{=mediawiki} to `{{math|'''W'''}}`{=mediawiki} will result in another vector field `{{math|'''W''' + grad(''f'')}}`{=mediawiki} such that `{{math|1=curl('''W''' + grad(''f'')) = '''V'''}}`{=mediawiki} as well. This can be summarized by saying that the inverse curl of a three-dimensional vector field can be obtained up to an unknown irrotational field with the Biot--Savart law.
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Christoph Ludwig Agricola
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**Christoph Ludwig Agricola** (5 November 1665 -- 8 August 1724) was a German landscape painter and etcher. He was born and died in Regensburg (Ratisbon).
## Life and career {#life_and_career}
Christoph Ludwig Agricola was born on 5 November 1665 in Regensburg in Germany. He trained, as many painters of the period did, by studying nature.
He spent a great part of his life in travel visiting England, the Netherlands and France, and residing for a considerable period in Naples, where he may have been influenced by Nicolas Poussin. He also stayed in Venice for several years around 1712, where he painted many works for Zaccaria Sagredo.
He died in Regensburg in 1724.
## Work
Although he primarily worked in gouache and oils, documentary sources show that he also produced a small number of etchings. He was a good draughtsman, used warm lighting and exhibited a warm, masterly brushstroke.
His numerous landscapes, chiefly cabinet pictures, are remarkable for their fidelity to nature, and especially for their skilful representation of varied phases of climate, especially nocturnal scenes and weather phenomena like thunderstorms. In composition, his style shows the influence of Nicolas Poussin: Agricola\'s work often displays idealistic scenes like Poussin\'s work. In light and colour Agricola\'s work resembles that of Claude Lorrain. His compositions often include ruins of ancient buildings in the foreground, but his favourite foreground figures were men dressed in Oriental attire. He also produced a series of etchings of birds.
His pictures can be found in Dresden, Braunschweig, Vienna, Florence, Naples and many other locations in Germany and Italy.
## Legacy
He probably tutored the artist Johann Theile and had a strong influence on him. Art historians have also noted that the work of the landscape painter Christian Johann Bendeler (1699--1728) was influenced by Agricola.
## Gallery
<File:Christoph> Ludwig Agricola (zugeschr.) - Eine Flusslandschaft mit Anglern.jpg\|*River landscape* <File:Christoph> Ludwig Agricola - Großer Hänfling und Schopfmeise.jpg\|*Greater Redpole and crested titmous; Bluethroat* <File:Christoph> Ludwig Agricola (Umkreis) - Räuber schießen auf Reisende.jpg\|*Bandits Shooting at Travellers* <File:Christoph> Ludwig Agricola - Trappe un Elster in exotischer Landschaft.jpg\|*A bustard and a magpie in an exotic landscape* <File:Christoph> Ludwig Agricola - Ein Vogel auf einem Ast.jpg\|*A bird seated on a branch* <File:Wintergezicht> met ijsvermaak, RP-T-1898-A-3549.jpg\|*Winter face with ice entertainment* <File:Christoph> Ludwig Agricola - Singvogel auf einem Nadelbaum.jpg\|*Songbird in an Evergreen*
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Cardinal number
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In mathematics, a **cardinal number**, or **cardinal** for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the Hebrew letter $\aleph$ (aleph) marked with subscript indicating their rank among the infinite cardinals.
Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of number of elements. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for two infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set---something that cannot happen with proper subsets of finite sets.
There is a transfinite sequence of cardinal numbers:
$$0, 1, 2, 3, \ldots, n, \ldots ; \aleph_0, \aleph_1, \aleph_2, \ldots, \aleph_{\alpha}, \ldots.\$$ This sequence starts with the natural numbers including zero (finite cardinals), which are followed by the aleph numbers. The aleph numbers are indexed by ordinal numbers. If the axiom of choice is true, this transfinite sequence includes every cardinal number. If the axiom of choice is not true (see `{{slink|Axiom of choice#Independence}}`{=mediawiki}), there are infinite cardinals that are not aleph numbers.
Cardinality is studied for its own sake as part of set theory. It is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.
## History
The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874--1884. Cardinality can be used to compare an aspect of finite sets. For example, the sets {1,2,3} and {4,5,6} are not *equal*, but have the *same cardinality*, namely three. This is established by the existence of a bijection (i.e., a one-to-one correspondence) between the two sets, such as the correspondence {1→4, 2→5, 3→6}.
Cantor applied his concept of bijection to infinite sets (for example the set of natural numbers **N** = {0, 1, 2, 3, \...}). Thus, he called all sets having a bijection with **N** *denumerable (countably infinite) sets*, which all share the same cardinal number. This cardinal number is called $\aleph_0$, aleph-null. He called the cardinal numbers of infinite sets transfinite cardinal numbers.
Cantor proved that any unbounded subset of **N** has the same cardinality as **N**, even though this might appear to run contrary to intuition. He also proved that the set of all ordered pairs of natural numbers is denumerable; this implies that the set of all rational numbers is also denumerable, since every rational can be represented by a pair of integers. He later proved that the set of all real algebraic numbers is also denumerable. Each real algebraic number *z* may be encoded as a finite sequence of integers, which are the coefficients in the polynomial equation of which it is a solution, i.e. the ordered n-tuple (*a*~0~, *a*~1~, \..., *a~n~*), *a~i~* ∈ **Z** together with a pair of rationals (*b*~0~, *b*~1~) such that *z* is the unique root of the polynomial with coefficients (*a*~0~, *a*~1~, \..., *a~n~*) that lies in the interval (*b*~0~, *b*~1~).
In his 1874 paper \"On a Property of the Collection of All Real Algebraic Numbers\", Cantor proved that there exist higher-order cardinal numbers, by showing that the set of real numbers has cardinality greater than that of **N**. His proof used an argument with nested intervals, but in an 1891 paper, he proved the same result using his ingenious and much simpler diagonal argument. The new cardinal number of the set of real numbers is called the cardinality of the continuum and Cantor used the symbol $\mathfrak{c}$ for it.
Cantor also developed a large portion of the general theory of cardinal numbers; he proved that there is a smallest transfinite cardinal number ($\aleph_0$, aleph-null), and that for every cardinal number there is a next-larger cardinal
$$(\aleph_1, \aleph_2, \aleph_3, \ldots).$$
His continuum hypothesis is the proposition that the cardinality $\mathfrak{c}$ of the set of real numbers is the same as $\aleph_1$. This hypothesis is independent of the standard axioms of mathematical set theory, that is, it can neither be proved nor disproved from them. This was shown in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940.
## Motivation
In informal use, a cardinal number is what is normally referred to as a *counting number*, provided that 0 is included: 0, 1, 2, \.... They may be identified with the natural numbers beginning with 0. The counting numbers are exactly what can be defined formally as the finite cardinal numbers. Infinite cardinals only occur in higher-level mathematics and logic.
More formally, a non-zero number can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence. For finite sets and sequences it is easy to see that these two notions coincide, since for every number describing a position in a sequence we can construct a set that has exactly the right size. For example, 3 describes the position of \'c\' in the sequence \<\'a\',\'b\',\'c\',\'d\',\...\>, and we can construct the set {a,b,c}, which has 3 elements.
However, when dealing with infinite sets, it is essential to distinguish between the two, since the two notions are in fact different for infinite sets. Considering the position aspect leads to ordinal numbers, while the size aspect is generalized by the cardinal numbers described here.
The intuition behind the formal definition of cardinal is the construction of a notion of the relative size or \"bigness\" of a set, without reference to the kind of members which it has. For finite sets this is easy; one simply counts the number of elements a set has. In order to compare the sizes of larger sets, it is necessary to appeal to more refined notions.
A set *Y* is at least as big as a set *X* if there is an injective mapping from the elements of *X* to the elements of *Y*. An injective mapping identifies each element of the set *X* with a unique element of the set *Y*. This is most easily understood by an example; suppose we have the sets *X* = {1,2,3} and *Y* = {a,b,c,d}, then using this notion of size, we would observe that there is a mapping:
: 1 → a
: 2 → b
: 3 → c
which is injective, and hence conclude that *Y* has cardinality greater than or equal to *X*. The element d has no element mapping to it, but this is permitted as we only require an injective mapping, and not necessarily a bijective mapping. The advantage of this notion is that it can be extended to infinite sets.
We can then extend this to an equality-style relation. Two sets *X* and *Y* are said to have the same *cardinality* if there exists a bijection between *X* and *Y*. By the Schroeder--Bernstein theorem, this is equivalent to there being *both* an injective mapping from *X* to *Y*, *and* an injective mapping from *Y* to *X*. We then write \|*X*\| = \|*Y*\|. The cardinal number of *X* itself is often defined as the least ordinal *a* with \|*a*\| = \|*X*\|. This is called the von Neumann cardinal assignment; for this definition to make sense, it must be proved that every set has the same cardinality as *some* ordinal; this statement is the well-ordering principle. It is however possible to discuss the relative cardinality of sets without explicitly assigning names to objects.
The classic example used is that of the infinite hotel paradox, also called Hilbert\'s paradox of the Grand Hotel. Supposing there is an innkeeper at a hotel with an infinite number of rooms. The hotel is full, and then a new guest arrives. It is possible to fit the extra guest in by asking the guest who was in room 1 to move to room 2, the guest in room 2 to move to room 3, and so on, leaving room 1 vacant. We can explicitly write a segment of this mapping:
: 1 → 2
: 2 → 3
: 3 → 4
: \...
: *n* → *n* + 1
: \...
With this assignment, we can see that the set {1,2,3,\...} has the same cardinality as the set {2,3,4,\...}, since a bijection between the first and the second has been shown. This motivates the definition of an infinite set being any set that has a proper subset of the same cardinality (i.e., a Dedekind-infinite set); in this case {2,3,4,\...} is a proper subset of {1,2,3,\...}.
When considering these large objects, one might also want to see if the notion of counting order coincides with that of cardinal defined above for these infinite sets. It happens that it does not; by considering the above example we can see that if some object \"one greater than infinity\" exists, then it must have the same cardinality as the infinite set we started out with. It is possible to use a different formal notion for number, called ordinals, based on the ideas of counting and considering each number in turn, and we discover that the notions of cardinality and ordinality are divergent once we move out of the finite numbers.
It can be proved that the cardinality of the real numbers is greater than that of the natural numbers just described. This can be visualized using Cantor\'s diagonal argument; classic questions of cardinality (for instance the continuum hypothesis) are concerned with discovering whether there is some cardinal between some pair of other infinite cardinals. In more recent times, mathematicians have been describing the properties of larger and larger cardinals.
Since cardinality is such a common concept in mathematics, a variety of names are in use. Sameness of cardinality is sometimes referred to as *equipotence*, *equipollence*, or *equinumerosity*. It is thus said that two sets with the same cardinality are, respectively, *equipotent*, *equipollent*, or *equinumerous*.
## Formal definition {#formal_definition}
Formally, assuming the axiom of choice, the cardinality of a set *X* is the least ordinal number α such that there is a bijection between *X* and α. This definition is known as the von Neumann cardinal assignment. If the axiom of choice is not assumed, then a different approach is needed. The oldest definition of the cardinality of a set *X* (implicit in Cantor and explicit in Frege and *Principia Mathematica*) is as the class \[*X*\] of all sets that are equinumerous with *X*. This does not work in ZFC or other related systems of axiomatic set theory because if *X* is non-empty, this collection is too large to be a set. In fact, for *X* ≠ ∅ there is an injection from the universe into \[*X*\] by mapping a set *m* to {*m*} × *X*, and so by the axiom of limitation of size, \[*X*\] is a proper class. The definition does work however in type theory and in New Foundations and related systems. However, if we restrict from this class to those equinumerous with *X* that have the least rank, then it will work (this is a trick due to Dana Scott: it works because the collection of objects with any given rank is a set).
Von Neumann cardinal assignment implies that the cardinal number of a finite set is the common ordinal number of all possible well-orderings of that set, and cardinal and ordinal arithmetic (addition, multiplication, power, proper subtraction) then give the same answers for finite numbers. However, they differ for infinite numbers. For example, $2^\omega=\omega<\omega^2$ in ordinal arithmetic while $2^{\aleph_0}>\aleph_0=\aleph_0^2$ in cardinal arithmetic, although the von Neumann assignment puts $\aleph_0=\omega$. On the other hand, Scott\'s trick implies that the cardinal number 0 is $\{\emptyset\}$, which is also the ordinal number 1, and this may be confusing. A possible compromise (to take advantage of the alignment in finite arithmetic while avoiding reliance on the axiom of choice and confusion in infinite arithmetic) is to apply von Neumann assignment to the cardinal numbers of finite sets (those which can be well ordered and are not equipotent to proper subsets) and to use Scott\'s trick for the cardinal numbers of other sets.
Formally, the order among cardinal numbers is defined as follows: \|*X*\| ≤ \|*Y*\| means that there exists an injective function from *X* to *Y*. The Cantor--Bernstein--Schroeder theorem states that if \|*X*\| ≤ \|*Y*\| and \|*Y*\| ≤ \|*X*\| then \|*X*\| = \|*Y*\|. The axiom of choice is equivalent to the statement that given two sets *X* and *Y*, either \|*X*\| ≤ \|*Y*\| or \|*Y*\| ≤ \|*X*\|.
A set *X* is Dedekind-infinite if there exists a proper subset *Y* of *X* with \|*X*\| = \|*Y*\|, and Dedekind-finite if such a subset does not exist. The finite cardinals are just the natural numbers, in the sense that a set *X* is finite if and only if \|*X*\| = \|*n*\| = *n* for some natural number *n*. Any other set is infinite.
Assuming the axiom of choice, it can be proved that the Dedekind notions correspond to the standard ones. It can also be proved that the cardinal $\aleph_0$ (aleph null or aleph-0, where aleph is the first letter in the Hebrew alphabet, represented $\aleph$) of the set of natural numbers is the smallest infinite cardinal (i.e., any infinite set has a subset of cardinality $\aleph_0$). The next larger cardinal is denoted by $\aleph_1$, and so on. For every ordinal α, there is a cardinal number $\aleph_{\alpha},$ and this list exhausts all infinite cardinal numbers.
## Cardinal arithmetic {#cardinal_arithmetic}
We can define arithmetic operations on cardinal numbers that generalize the ordinary operations for natural numbers. It can be shown that for finite cardinals, these operations coincide with the usual operations for natural numbers. Furthermore, these operations share many properties with ordinary arithmetic.
### Successor cardinal {#successor_cardinal}
If the axiom of choice holds, then every cardinal κ has a successor, denoted κ^+^, where κ^+^ \> κ and there are no cardinals between κ and its successor. (Without the axiom of choice, using Hartogs\' theorem, it can be shown that for any cardinal number κ, there is a minimal cardinal κ^+^ such that $\kappa^+\nleq\kappa.$) For finite cardinals, the successor is simply κ + 1. For infinite cardinals, the successor cardinal differs from the successor ordinal.
### Cardinal addition {#cardinal_addition}
If *X* and *Y* are disjoint, addition is given by the union of *X* and *Y*. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the same cardinality (e.g., replace *X* by *X*×{0} and *Y* by *Y*×{1}).
$$|X| + |Y| = | X \cup Y|.$$
Zero is an additive identity *κ* + 0 = 0 + *κ* = *κ*.
Addition is associative (*κ* + *μ*) + *ν* = *κ* + (*μ* + *ν*).
Addition is commutative *κ* + *μ* = *μ* + *κ*.
Addition is non-decreasing in both arguments:
$$(\kappa \le \mu) \rightarrow ((\kappa + \nu \le \mu + \nu) \mbox{ and } (\nu + \kappa \le \nu + \mu)).$$
Assuming the axiom of choice, addition of infinite cardinal numbers is easy. If either *κ* or *μ* is infinite, then
$$\kappa + \mu = \max\{\kappa, \mu\}\,.$$
#### Subtraction
Assuming the axiom of choice and, given an infinite cardinal *σ* and a cardinal *μ*, there exists a cardinal *κ* such that *μ* + *κ* = *σ* if and only if *μ* ≤ *σ*. It will be unique (and equal to *σ*) if and only if *μ* \< *σ*.
### Cardinal multiplication {#cardinal_multiplication}
The product of cardinals comes from the Cartesian product.
$$|X|\cdot|Y| = |X \times Y|$$
Zero is a multiplicative absorbing element: *κ*·0 = 0·*κ* = 0.
There are no nontrivial zero divisors: *κ*·*μ* = 0 → (*κ* = 0 or *μ* = 0).
One is a multiplicative identity: *κ*·1 = 1·*κ* = *κ*.
Multiplication is associative: (*κ*·*μ*)·*ν* = *κ*·(*μ*·*ν*).
Multiplication is commutative: *κ*·*μ* = *μ*·*κ*.
Multiplication is non-decreasing in both arguments: *κ* ≤ *μ* → (*κ*·*ν* ≤ *μ*·*ν* and *ν*·*κ* ≤ *ν*·*μ*).
Multiplication distributes over addition: *κ*·(*μ* + *ν*) = *κ*·*μ* + *κ*·*ν* and (*μ* + *ν*)·*κ* = *μ*·*κ* + *ν*·*κ*.
Assuming the axiom of choice, multiplication of infinite cardinal numbers is also easy. If either *κ* or *μ* is infinite and both are non-zero, then
$$\kappa\cdot\mu = \max\{\kappa, \mu\}.$$ Thus the product of two infinite cardinal numbers is equal to their sum.
#### Division
Assuming the axiom of choice and given an infinite cardinal *π* and a non-zero cardinal *μ*, there exists a cardinal *κ* such that *μ* · *κ* = *π* if and only if *μ* ≤ *π*. It will be unique (and equal to *π*) if and only if *μ* \< *π*.
### Cardinal exponentiation {#cardinal_exponentiation}
Exponentiation is given by
$$|X|^{|Y|} = \left|X^Y\right|,$$ where *X^Y^* is the set of all functions from *Y* to *X*. It is easy to check that the right-hand side depends only on ${|X|}$ and ${|Y|}$.
: κ^0^ = 1 (in particular 0^0^ = 1), see empty function.
: If *μ* ≥ 1, then 0^*μ*^ = 0.
: 1^*μ*^ = 1.
: *κ*^1^ = *κ*.
: *κ*^*μ*\ +\ *ν*^ = *κ*^*μ*^·*κ*^*ν*^.
: κ^*μ*\ ·\ *ν*^ = (*κ*^*μ*^)^*ν*^.
: (*κ*·*μ*)^*ν*^ = *κ*^*ν*^·*μ*^*ν*^.
Exponentiation is non-decreasing in both arguments:
: (1 ≤ *ν* and *κ* ≤ *μ*) → (*ν*^*κ*^ ≤ *ν*^*μ*^) and
: (*κ* ≤ *μ*) → (*κ*^*ν*^ ≤ *μ*^*ν*^).
2^\|*X*\|^ is the cardinality of the power set of the set *X* and Cantor\'s diagonal argument shows that 2^\|*X*\|^ \> \|*X*\| for any set *X*. This proves that no largest cardinal exists (because for any cardinal *κ*, we can always find a larger cardinal 2^*κ*^). In fact, the class of cardinals is a proper class. (This proof fails in some set theories, notably New Foundations.)
All the remaining propositions in this section assume the axiom of choice:
: If *κ* and *μ* are both finite and greater than 1, and *ν* is infinite, then *κ*^*ν*^ = *μ*^*ν*^.
: If *κ* is infinite and *μ* is finite and non-zero, then *κ*^*μ*^ = *κ*.
If 2 ≤ *κ* and 1 ≤ *μ* and at least one of them is infinite, then:
: Max (*κ*, 2^*μ*^) ≤ *κ*^*μ*^ ≤ Max (2^*κ*^, 2^*μ*^).
Using König\'s theorem, one can prove *κ* \< *κ*^cf(*κ*)^ and *κ* \< cf(2^*κ*^) for any infinite cardinal *κ*, where cf(*κ*) is the cofinality of *κ*.
#### Roots
Assuming the axiom of choice and, given an infinite cardinal *κ* and a finite cardinal *μ* greater than 0, the cardinal *ν* satisfying $\nu^\mu = \kappa$ will be $\kappa$.
#### Logarithms
Assuming the axiom of choice and, given an infinite cardinal *κ* and a finite cardinal *μ* greater than 1, there may or may not be a cardinal *λ* satisfying $\mu^\lambda = \kappa$. However, if such a cardinal exists, it is infinite and less than *κ*, and any finite cardinality *ν* greater than 1 will also satisfy $\nu^\lambda = \kappa$.
The logarithm of an infinite cardinal number *κ* is defined as the least cardinal number *μ* such that *κ* ≤ 2^*μ*^. Logarithms of infinite cardinals are useful in some fields of mathematics, for example in the study of cardinal invariants of topological spaces, though they lack some of the properties that logarithms of positive real numbers possess.
## The continuum hypothesis {#the_continuum_hypothesis}
The continuum hypothesis (CH) states that there are no cardinals strictly between $\aleph_0$ and $2^{\aleph_0}.$ The latter cardinal number is also often denoted by $\mathfrak{c}$; it is the cardinality of the continuum (the set of real numbers). In this case $2^{\aleph_0} = \aleph_1.$
Similarly, the generalized continuum hypothesis (GCH) states that for every infinite cardinal $\kappa$, there are no cardinals strictly between $\kappa$ and $2^\kappa$. Both the continuum hypothesis and the generalized continuum hypothesis have been proved to be independent of the usual axioms of set theory, the Zermelo--Fraenkel axioms together with the axiom of choice (ZFC).
Indeed, Easton\'s theorem shows that, for regular cardinals $\kappa$, the only restrictions ZFC places on the cardinality of $2^\kappa$ are that $\kappa < \operatorname{cf}(2^\kappa)$, and that the exponential function is non-decreasing.
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Cecil B. DeMille
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**Cecil Blount DeMille** (`{{IPAc-en|'|s|ɛ|s|əl|_|d|ə|ˈ|m|ɪ|l}}`{=mediawiki}; August 12, 1881`{{spnd}}`{=mediawiki}January 21, 1959) was an American filmmaker and actor. Between 1914 and 1958, he made 70 features, both silent and sound films. He is acknowledged as a founding father of American cinema and the most commercially successful producer-director in film history, with many films dominating the box office three or four at a time. His films were distinguished by their epic scale and by his cinematic showmanship. His silent films included social dramas, comedies, Westerns, farces, morality plays, and historical pageants. He was an active Freemason and member of Prince of Orange Lodge #16 in New York City.
DeMille was born in Ashfield, Massachusetts, where his parents were vacationing for the summer. He grew up in New York City. He began his career as a stage actor in 1900. He later began to write and direct stage plays, a few with his older brother William de Mille, and some with Jesse L. Lasky, who was then a vaudeville producer.
DeMille\'s first film, *The Squaw Man* (1914), was the first full-length feature film shot in Hollywood. Its interracial love story was commercially successful, and the film marked Hollywood as the new home of the U.S. film industry. It had previously been based in New York and New Jersey. Based on continued film successes, DeMille founded Famous Players Lasky which was later reverse merged into Paramount Pictures with Lasky and Adolph Zukor. His first biblical epic, *The Ten Commandments* (1923), was both a critical and commercial success; it held the Paramount revenue record for 25 years.
DeMille directed *The King of Kings* (1927), a biography of Jesus, which gained approval for its sensitivity and reached more than 800 million viewers. *The Sign of the Cross* (1932) is said to be the first sound film to integrate all aspects of cinematic technique. *Cleopatra* (1934) was his first film to be nominated for the Academy Award for Best Picture.
After more than 30 years in film production, DeMille reached a pinnacle in his career with *Samson and Delilah* (1949), a biblical epic that became the highest-grossing film of 1950. Along with biblical and historical narratives, he also directed films oriented toward \"neo-naturalism\", which tried to portray the laws of man fighting the forces of nature.
DeMille received his first nomination for the Academy Award for Best Director for his circus drama *The Greatest Show on Earth* (1952), which won both the Academy Award for Best Picture and the Golden Globe Award for Best Motion Picture -- Drama. His last and best-known film, *The Ten Commandments* (1956), also a Best Picture Academy Award nominee, and it is the eighth-highest-grossing film of all time, adjusted for inflation.
In addition to his Best Picture Awards, DeMille received an Academy Honorary Award for his film contributions, the Palme d\'Or (posthumously) for *Union Pacific* (1939), a DGA Award for Lifetime Achievement, and the Irving G. Thalberg Memorial Award. He was the first recipient of the Golden Globe Cecil B. DeMille Award, which was named in his honor. DeMille\'s reputation had a renaissance in the 2010s, and his work has influenced numerous other films and directors.
## Biography
### 1881--1899: early years {#early_years}
Cecil Blount DeMille was of paternal Dutch ancestry. His surname was spelled de Mil`{{refn|group=note|There are several variants of DeMille's surname. His family's [[Dutch people|Dutch]] surname, originally spelled '' de Mil''.}}`{=mediawiki} before his grandfather William added an \"le\" for \"visual symmetry\".
As an adult, Cecil De Mille adopted the spelling *DeMille* because he believed it would look better on a marquee, but continued to use *de Mille* in private life. The family name *de Mille* was used by his children Cecilia, John, Richard, and Katherine. Cecil\'s brother, William, and his daughters, Margaret and Agnes, as well as DeMille\'s granddaughter, Cecilia de Mille Presley, also used the *de Mille* spelling.
DeMille was born on August 12, 1881, in a boarding house on Main Street in Ashfield, Massachusetts, where his parents had been vacationing for the summer. On September 1, 1881, the family returned with the newborn DeMille to their flat in New York. DeMille was named after his grandmothers Cecelia Wolff and Margarete Blount. He was the second of three children of Henry Churchill de Mille (September 4, 1853 -- February 10, 1893) and his wife, Matilda Beatrice deMille (née Samuel; January 30, 1853 -- October 8, 1923), known as Beatrice. His older brother, William C. deMille, was born on July 25, 1878.
Henry de Mille, whose ancestors were of English and Dutch-Belgian descent, was a North Carolina-born dramatist, actor, and lay reader in the Episcopal Church. In New York, Henry also taught English at Columbia College (now Columbia University). He worked as a playwright, administrator, and faculty member during the early years of the American Academy of Dramatic Arts, established in New York City in 1884. Henry de Mille frequently collaborated with David Belasco in playwriting; their best-known collaborations included \"The Wife\", \"Lord Chumley\", \"The Charity Ball\", and \"Men and Women\".
Cecil B. DeMille\'s mother, Beatrice, a literary agent and scriptwriter, was the daughter of German Jews. She had emigrated from England with her parents in 1871 when she was 18; the newly arrived family settled in Brooklyn, New York, where they maintained a middle-class, English-speaking household.
DeMille\'s parents met as members of a music and literary society in New York. Henry was a tall, red-headed student. Beatrice was intelligent, educated, forthright, and strong-willed. They married on July 1, 1876, despite Beatrice\'s parents\' objections because of the young couple\'s differing religions; Beatrice converted to Episcopalianism.
DeMille was a brave and confident child. He gained his love of theater while watching his father and Belasco rehearse their plays. A lasting memory for DeMille was a lunch with his father and actor Edwin Booth. As a child, DeMille created an alter ego, Champion Driver, a Robin Hood-like character, evidence of his creativity and imagination.
His father and his family had lived in Washington, North Carolina, until Henry built a three-story Victorian-style house for his family in Pompton Lakes, New Jersey ; they named this estate \"Pamlico\". John Philip Sousa was a friend of the family, and DeMille recalled throwing mud balls in the air so neighbor Annie Oakley could practice her shooting. DeMille\'s sister, Agnes, was born on April 23, 1891; his mother nearly did not survive the birth. Agnes died on February 11, 1894, from spinal meningitis.`{{refn|group=note|DeMille's niece and William deMille's daughter [[Agnes de Mille]] was a famed dancer-choreographer.<ref>{{cite magazine |last= Acocella |first=Joan |title=Agnes DeMille's Artistic Justice |url=https://www.newyorker.com/books/page-turner/agnes-de-milles-artistic-justice |access-date=May 23, 2019 |magazine=The New Yorker |date=November 5, 2015}}</ref>}}`{=mediawiki}
DeMille\'s parents operated a private school in Pompton Lakes and attended Christ Episcopal Church. DeMille recalled that this church was the place where he visualized the story of his 1923 version of *The Ten Commandments*.
On January 8, 1893, at age 40, Henry de Mille died suddenly from typhoid fever, leaving Beatrice with three children. To provide for her family, she opened the Henry C. de Mille School for Girls in her home in February 1893. The aim of the school was to teach young women to properly understand and fulfill the women\'s duty to themselves, their home, and their country. Beatrice had \"enthusiastically supported\" Henry\'s theatrical aspirations. She later became the second female play broker on Broadway. On Henry\'s deathbed, he told his wife that he did not want his sons to become playwrights. DeMille\'s mother sent him to Pennsylvania Military College (now Widener University) in Chester, Pennsylvania, at age 15. He fled the school to join the Spanish--American War, but failed to meet the age requirement. At the military college, even though his grades were average, he reportedly excelled in personal conduct.
DeMille attended the American Academy of Dramatic Arts (tuition-free due to his father\'s service to the academy). He graduated in 1900, and for graduation, his performance was the play *The Arcady Trail*. In the audience was Charles Frohman, who cast DeMille in his play *Hearts are Trumps*, DeMille\'s Broadway debut.
### 1900--1912: theater
#### Charles Frohman, Constance Adams, and David Belasco {#charles_frohman_constance_adams_and_david_belasco}
Cecil B. DeMille began his career as an actor on stage in 1900 in the theatrical company of Charles Frohman. He debuted on February 21, 1900, in the play *Hearts Are Trumps* at New York\'s Garden Theater. In 1901, DeMille starred in productions of *A Repentance*, *To Have and to Hold*, and *Are You a Mason?* At age 21, he married Constance Adams on August 16, 1902, at Adams\'s father\'s home in East Orange, New Jersey. The wedding party was small. Beatrice DeMille\'s family did not attend. Simon Louvish suggests that this was to conceal DeMille\'s partial Jewish heritage. Adams was 29 years old at the time of the marriage. They had met in a theater in Washington D.C. while they were both acting in *Hearts Are Trumps*.
They were sexually incompatible; according to DeMille, Adams was too \"pure\" to \"feel such violent and evil passions\" as he. DeMille had more violent sexual preferences and fetishes than his wife. Adams allowed DeMille to have several long-term mistresses during their marriage as an outlet while maintaining an appearance of a faithful marriage. One of DeMille\'s affairs was with his screenwriter Jeanie MacPherson. Despite his reputation for extramarital affairs, DeMille did not like to have affairs with his stars, as he believed it would cause him to lose control as a director. He once said he maintained his self-control when Gloria Swanson sat on his lap, and refused to touch her.
In 1902, he played a small part in *Hamlet*. Publicists wrote that he became an actor in order to learn how to direct and produce, but DeMille admitted that he became an actor in order to pay the bills. From 1904 to 1905, he attempted to make a living as a stock theater actor with his wife, Constance. DeMille made a 1905 reprise in *Hamlet* as Osric. In the summer of 1905, DeMille joined the stock cast at the Elitch Theatre in Denver, Colorado. He appeared in 11 of the 15 plays presented that season, all in minor roles. Maude Fealy was the featured actress in several productions that summer and developed a lasting friendship with DeMille. (He later cast her in *The Ten Commandments*.)
His brother, William, was establishing himself as a playwright and sometimes invited DeMille to collaborate. DeMille and William collaborated on *The Genius*, *The Royal Mounted*, and *After Five*. None of these was very successful. William de Mille was most successful when he worked alone.
DeMille and his brother at times worked with the legendary impresario David Belasco, who had been a friend and collaborator of their father. DeMille later adapted Belasco\'s *The Girl of the Golden West*, *Rose of the Rancho*, and *The Warrens of Virginia* into films. He was credited with the conception of Belasco\'s *The Return of Peter Grimm*. *The Return of Peter Grimm* sparked controversy, because Belasco had taken DeMille\'s unnamed screenplay, changed the characters, and named it *The Return of Peter Grimm*, producing and presenting it as his own work. DeMille was credited in small print as \"based on an idea by Cecil DeMille\". The play was successful, and DeMille was distraught that his childhood idol had plagiarized his work.
#### Losing interest in theater {#losing_interest_in_theater}
DeMille performed on stage with actors he later directed in films: Charlotte Walker, Mary Pickford, and Pedro de Cordoba. He also produced and directed plays. His 1905 performance in *The Prince Chap* as the Earl of Huntington was well received by audiences.
DeMille wrote a few of his own plays in between stage performances, but his playwriting was less successful. His first play was *The Pretender-A Play in a Prologue and 4 Acts* set in 17th-century Russia. Another unperformed play he wrote was *Son of the Winds*, a mythological Native American story. Life was difficult for DeMille and his wife as traveling actors, but travel allowed him to experience parts of the United States he had not yet seen. DeMille sometimes worked with the director E. H. Sothern, who influenced DeMille\'s later perfectionism. In 1907, due to a scandal with one of Beatrice\'s students, Evelyn Nesbit, the Henry de Mille School lost students. The school closed, and Beatrice filed for bankruptcy. DeMille wrote another play originally called *Sergeant Devil May Care* and renamed *The Royal Mounted*. He also toured with the Standard Opera Company, but there are few records of his singing ability.
On November 5, 1908, Constance and DeMille had a daughter, Cecilia, their only biological child. In the 1910s, DeMille began directing and producing other writers\' plays.
DeMille was poor and struggled to find work. Consequently, his mother hired him for her agency, The DeMille Play Company, and taught him how to be an agent and a playwright. He became the agency\'s manager and later a junior partner with his mother. In 1911, DeMille became acquainted with vaudeville producer Jesse Lasky when Lasky was searching for a writer for his new musical. He initially sought out William deMille. William had been a successful playwright, but DeMille was suffering from the failure of his plays *The Royal Mounted* and *The Genius*.
Beatrice introduced Lasky to Cecil DeMille instead. The collaboration of DeMille and Lasky produced a successful musical, *California*, which opened in New York in January 1912. Another DeMille-Lasky production that opened in January 1912 was *The Antique Girl*. In the spring of 1913, DeMille found success producing *Reckless Age* by Lee Wilson, a play about a high-society girl wrongly accused of manslaughter, starring Frederick Burton and Sydney Shields. But changes in the theater rendered DeMille\'s melodramas obsolete before they were produced, and true theatrical success eluded him. He produced many flops. Having become uninterested in working in theater, DeMille became ignited by passion for film when he watched the 1912 French film *Les Amours de la reine Élisabeth*.
### 1913--1914: entering films {#entering_films}
Desiring a change of scene, DeMille, Lasky, Sam Goldfish (later Samuel Goldwyn), and a group of East Coast businessmen created the Jesse L. Lasky Feature Play Company in 1913, of which DeMille became director-general. Lasky and DeMille were said to have sketched out the organization of the company on the back of a restaurant menu. As director-general, DeMille\'s job was to make the films. In addition to directing, he was the supervisor and consultant for the first year of films the company made. Sometimes, he directed scenes for other directors at the company in order to release films on time. Moreover, he co-authored other Lasky Company scripts and created screen adaptations that others directed.
The Lasky Play Company tried to recruit William de Mille, but he rejected the offer because he did not believe there was any promise in a film career. When William found out that DeMille had begun working in the motion picture industry, he wrote his brother a letter, saying that he was disappointed that Cecil was willing \"to throw away \[his\] future\" when he was \"born and raised in the finest traditions of the theater\".
The Lasky Company wanted to attract high-class audiences to their films, so it began producing films from literary works. The company bought the rights to Edwin Milton Royle\'s play *The Squaw Man* and cast Dustin Farnum in the lead role. It offered Farnum a choice between a quarter stock in the company or \$250 in weekly salary. Farnum chose the salary. Already \$15,000 in debt to Royle for the screenplay of *The Squaw Man*, Lasky\'s relatives bought the \$5,000 stock to save the Lasky Company from bankruptcy. With no knowledge of filmmaking, DeMille was introduced to observe the process at film studios. He was eventually introduced to Oscar Apfel, a stage director who had been a director with the Edison Company.
On December 12, 1913, DeMille, his cast, and crew boarded a Southern Pacific train bound for Flagstaff via New Orleans. His tentative plan was to shoot a film in Arizona, but he felt that Arizona lacked the Western look they were searching for. They also learned that other filmmakers were successfully shooting in Los Angeles, even in winter. He continued to Los Angeles. Once there, he chose not to shoot in Edendale, where many studios were, but in Hollywood. DeMille rented a barn to function as their film studio. Filming began on December 29, 1913, and lasted three weeks. Apfel filmed most of *The Squaw Man* due to DeMille\'s inexperience, but DeMille learned quickly and was particularly adept at impromptu screenwriting as necessary. He made his first film run 60 minutes, as long as a short play. *The Squaw Man* (1914), co-directed by Apfel, was a sensation, and it established the Lasky Company. It was the first feature-length film made in Hollywood. There were problems with the perforation of the film stock, and it was discovered the DeMille had brought a cheap British film perforator that had punched in 65 holes per foot instead of the industry standard of 64. Lasky and DeMille convinced film pioneer Siegmund Lubin of the Lubin Manufacturing Company to have his experienced technicians reperforate the film.
This was the first American feature film, according to its release date. D. W. Griffith\'s *Judith of Bethulia* was filmed earlier than *The Squaw Man*, but released later. This as the only film in which DeMille shared director\'s credit with Apfel.
*The Squaw Man* was a success, which led to the eventual founding of Paramount Pictures and Hollywood becoming the \"film capital of the world\". The film grossed more than ten times its budget after its New York premiere in February 1914. DeMille\'s next project was to aid Apfel in directing *Brewster\'s Millions*, which was wildly successful. In December 1914, Constance Adams brought home John DeMille, a 15-month-old boy, whom the couple legally adopted three years later. Biographer Scott Eyman suggested that she may have decided to adopt after recently having had a miscarriage.
### 1915--1928: silent era {#silent_era}
#### Westerns, Paradise, and World War I {#westerns_paradise_and_world_war_i}
Cecil B. DeMille\'s second film, credited exclusively to him, was *The Virginian*. It is the earliest of DeMille\'s films available in a quality, color-tinted video format, but that version is actually a 1918 rerelease. The Lasky Company\'s first few years were spent making films nonstop. DeMille directed 20 films by 1915. The most successful films during this period were *Brewster\'s Millions* (co-directed by DeMille), *Rose of the Rancho*, and *The Ghost Breaker*. DeMille adapted Belasco\'s dramatic lighting techniques to film technology, mimicking moonlight with U.S. cinema\'s first attempts at \"motivated lighting\" in *The Warrens of Virginia*. This was the first of a few film collaborations with his brother William. They struggled to adapt the play from the stage to the set. After the film was shown, viewers complained that the shadows and lighting prevented the audience from seeing the actors\' full faces and said they would pay only half price. Sam Goldwyn suggested that if they called it \"Rembrandt\" lighting, the audience would pay double the price. Additionally, because of DeMille\'s cordiality after the *Peter Grimm* incident, DeMille was able to rekindle his partnership with Belasco. He adapted several of Belasco\'s screenplays into film.
DeMille\'s most successful film was *The Cheat*; his direction in the film was acclaimed. In 1916, exhausted from three years of nonstop filmmaking, DeMille purchased land in the Angeles National Forest for a ranch that would become his getaway. He called this place \"Paradise\", declaring it a wildlife sanctuary; no shooting of animals besides snakes was allowed. His wife did not like Paradise, so DeMille often brought his mistresses there with him, including actress Julia Faye. In 1921, DeMille purchased a yacht he called *The Seaward*.
While filming *The Captive* in 1915, an extra, Charles Chandler, died on set when another extra failed to heed DeMille\'s orders to unload all guns for rehearsal. DeMille instructed the guilty man to leave town and never revealed his name. Lasky and DeMille maintained Chandler\'s widow on the payroll and, according to leading actor House Peters Sr., DeMille refused to stop production for Chandler\'s funeral. Peters said that he encouraged the cast to attend the funeral with him anyway since DeMille would not be able to shoot the film without him. On July 19, 1916, the Jesse Lasky Feature Play Company merged with Adolph Zukor\'s Famous Players Film Company, becoming Famous Players--Lasky. Zukor became president, Lasky vice president, DeMille director-general, and Goldwyn chairman of the board. Famous Players--Lasky later fired Goldwyn for frequent clashes with Lasky, DeMille, and Zukor. While on a European vacation in 1921, DeMille contracted rheumatic fever in Paris. He was confined to bed and unable to eat. His poor physical condition upon his return home affected the production of his 1922 film *Manslaughter*. According to Richard Birchard, DeMille\'s weakened state during production may have led to the film being received as uncharacteristically substandard.
During World War I, the Famous Players--Lasky organized a military company underneath the National Guard, the Home Guard, made up of film studio employees, with DeMille as captain. Eventually, the Guard was enlarged to a battalion and recruited soldiers from other film studios. They took time off weekly to practice military drills. Additionally, during the war, DeMille volunteered for the Justice Department\'s Intelligence Office, investigating friends, neighbors, and others he came in contact with in connection with the Famous Players--Lasky. He also volunteered for the Intelligence Office during World War II. DeMille considered enlisting in World War I, but stayed in the U.S. and made films. He did take a few months to set up a movie theater for the French front. Famous Players--Lasky donated the films. DeMille and Adams adopted Katherine Lester in 1920, whom Adams had found in the orphanage she directed.`{{Refn|group=note|Katherine's father had been killed in [[World War I]] and her mother had died of [[tuberculosis]].<ref>{{harvnb|Louvish|2007|p=185}}; {{harvnb|Eyman|2010|p=162}}</ref> To DeMille's dismay, Katherine became an actress; however, she ultimately gained his approval. In 1936 she married actor Anthony Quinn.<ref>{{cite news |last=Bergan |first=Ronald |title=Anthony Quinn: Colourful Hollywood star who built a career playing ethnic heroes and villains |url=https://www.theguardian.com/news/2001/jun/05/guardianobituaries.filmnews |work=The Guardian |date=June 5, 2001 |access-date=May 24, 2019}}</ref>}}`{=mediawiki} In 1922, the couple adopted Richard deMille.
#### Scandalous dramas, Biblical epics, and departure from Paramount {#scandalous_dramas_biblical_epics_and_departure_from_paramount}
Film started becoming more sophisticated and the Lasky company\'s subsequent films were criticized for primitive and unrealistic set design. Consequently, Beatrice deMille introduced the Famous Players--Lasky to Wilfred Buckland, whom DeMille knew from his time at the American Academy of Dramatic Arts, and he became DeMille\'s art director. William deMille reluctantly became a story editor. William later converted from theater to Hollywood and spent the rest of his career as a film director. DeMille frequently remade his own films. In 1917, he remade *The Squaw Man* (1918), only four years after the original. Despite its quick turnaround, the film was fairly successful. DeMille\'s second remake at MGM in 1931 was a failure.
After five years and 30 hit films, DeMille became the American film industry\'s most successful director. In the silent era, he was renowned for *Male and Female* (1919), *Manslaughter* (1922), *The Volga Boatman* (1926), and *The Godless Girl* (1928). His trademark scenes included bathtubs, lion attacks, and Roman orgies. Many of his films featured scenes in two-color Technicolor. In 1923, DeMille released the modern melodrama *The Ten Commandments*, a significant change from his previous irreligious films. The film was produced on a budget of \$600,000, Paramount\'s most expensive production. This concerned Paramount executives, but the film was the studio\'s highest-grossing film. It held the Paramount record for 25 years until DeMille broke the record again.
In the early 1920s, scandal surrounded Paramount; religious groups and the media opposed portrayals of immorality in films. A censorship board called the Hays Code was established. DeMille\'s film *The Affairs of Anatol* came under fire. Furthermore, DeMille argued with Zukor over his extravagant and over-budget production costs. Consequently, DeMille left Paramount in 1924 despite having helped establish it. He joined the Producers Distributing Corporation. His first film in the new production company, DeMille Pictures Corporation, was *The Road to Yesterday* in 1925. He directed and produced four films on his own, working with Producers Distributing Corporation because he found front office supervision too restricting. Aside from *The King of Kings,* none of DeMille\'s films away from Paramount were successful. *The King of Kings* established DeMille as \"master of the grandiose and of biblical sagas\". Considered at the time the most successful Christian film of the silent era, DeMille calculated that it had been viewed over 800 million times around the world. After the release of DeMille\'s *The Godless Girl*, silent films in America became obsolete, and DeMille was forced to shoot a shoddy final reel with the new sound production technique. Although this final reel looked so different from the first 11 reels that it appeared to be from another movie, according to Simon Louvish, the film is one of DeMille\'s strangest and most \"DeMillean\" film.
The immense popularity of DeMille\'s silent films enabled him to branch out into other areas. The Roaring Twenties were the boom years and DeMille took full advantage, opening the Mercury Aviation Company, one of America\'s first commercial airlines. He was also a real estate speculator, an underwriter of political campaigns, vice president of Bank of America, and vice president of the Commercial National Trust and Savings Bank in Los Angeles, where he approved loans for other filmmakers. In 1916, DeMille purchased a mansion in Hollywood. Charlie Chaplin lived next door for a time, and after he moved, DeMille purchased the other house and combined the estates.
### 1929--1956: sound era {#sound_era}
#### MGM and return to Paramount {#mgm_and_return_to_paramount}
When \"talking pictures\" were invented in 1928, DeMille made a successful transition, offering his own innovations to the painful process; he devised a microphone boom and a soundproof camera blimp. He also popularized the camera crane. His first three sound films, *Dynamite*, *Madame Satan*, and his 1931 remake of *The Squaw Man*, were produced at Metro-Goldwyn-Mayer. These films were critically and financially unsuccessful. He had completely adapted to the production of sound film despite the film\'s poor dialogue. After his contract ended at MGM, he left, but no production studios would hire him. He attempted to create a guild of a half a dozen directors with the same creative desires called the Director\'s Guild, but the idea failed due to lack of funding and commitment. Moreover, the Internal Revenue Service audited DeMille due to issues with his production company. This was, according to DeMille, the lowest point of his career. He traveled abroad to find employment until he was offered a deal at Paramount.
In 1932, DeMille returned to Paramount at Lasky\'s request, bringing with him his own production unit. His first film back at Paramount, *The Sign of the Cross*, was also his first success since leaving Paramount besides *The King of Kings*. Zukor approved DeMille\'s return on the condition that DeMille not exceed his production budget of \$650,000 for *The Sign of the Cross*. Produced in eight weeks without exceeding budget, the film was financially successful. *The Sign of the Cross* was the first film to integrate all cinematic techniques. The film was considered a \"masterpiece\" and surpassed the quality of other sound films of the time. DeMille followed this epic with two dramas released in 1933 and 1934, *This Day and Age* and *Four Frightened People*. These were box-office disappointments, though *Four Frightened People* received good reviews. DeMille stuck to large-budget spectaculars for the rest of his career.
#### Politics and *Lux Radio Theatre* {#politics_and_lux_radio_theatre}
DeMille was outspoken about his Episcopalian integrity, but his private life included mistresses and adultery. He was a conservative Republican activist, becoming more conservative as he aged. He was known as anti-union and worked to prevent the unionization of film production studios. But according to DeMille himself, he was not anti-union and belonged to a few unions. He said he was rather against union leaders such as Walter Reuther and Harry Bridges, whom he compared to dictators. He supported Herbert Hoover and in 1928 made his largest campaign donation to Hoover. But DeMille also liked Franklin D. Roosevelt, finding him charismatic, tenacious, and intelligent, and agreeing with Roosevelt\'s abhorrence of Prohibition. DeMille lent Roosevelt a car for his 1932 United States presidential election campaign and voted for him. He never again voted for a Democratic candidate in a presidential election.
From June 1, 1936, until January 22, 1945, DeMille hosted and directed *Lux Radio Theatre*, a weekly digest of current feature films. Broadcast on the Columbia Broadcasting System (CBS) from 1935 to 1954, *Lux Radio* was one of the most popular weekly shows in radio history. While DeMille was host, the show had 40 million weekly listeners and DeMille had an annual salary of \$100,000. From 1936 to 1945, he produced, hosted, and directed every show, with the occasional exception of a guest director. He resigned from *Lux Radio* because he refused to pay a dollar to the American Federation of Radio Artists (AFRA), on the principle that no organization had the right to \"levy a compulsory assessment upon any member\".
DeMille sued the union for reinstatement but lost. He appealed to the California Supreme Court and lost again. When the AFRA expanded to television, DeMille was banned from television appearances. Consequently, he formed the DeMille Foundation for Political Freedom to campaign for the right to work. He gave speeches across the nation for the next few years. DeMille\'s primary criticism was of closed shops, but later included criticism of communism and unions in general. The U.S. Supreme Court declined to review his case, but DeMille lobbied for the Taft--Hartley Act, which passed. It prohibited denying anyone the right to work if they refuse to pay a political assessment. But the law did not apply retroactively, so DeMille\'s television and radio appearance ban lasted the rest of his life, though he was permitted to appear on radio or television to publicize a movie. William Keighley replaced him. DeMille never worked in radio again.
#### Adventure films and dramatic spectacles {#adventure_films_and_dramatic_spectacles}
In 1939, DeMille\'s *Union Pacific* was successful through DeMille\'s collaboration with the Union Pacific Railroad. The Union Pacific gave DeMille access to historical data, early period trains, and expert crews, adding to the film\'s authenticity. During pre-production, DeMille was dealing with his first serious health issue. In March 1938, he underwent a major emergency prostatectomy. He had a post-surgery infection from which he nearly did not recover, citing streptomycin as his saving grace. The surgery caused him to suffer from sexual dysfunction for the rest of his life, according to some family members. After his surgery and the success of *Union Pacific*, DeMille first used three-strip Technicolor in 1940, in *North West Mounted Police*. DeMille wanted to film in Canada, but due to budget constraints, the film was instead shot in Oregon and Hollywood. Critics were impressed with the visuals but found the scripts dull, calling it DeMille\'s \"poorest Western\". Despite the criticism, it was Paramount\'s highest-grossing film of the year. Audiences liked its highly saturated color, so DeMille made no further black-and-white features. DeMille was anti-communist and abandoned a project in 1940 to film Ernest Hemingway\'s *For Whom the Bell Tolls* due to its communist themes, even though he had already paid \$100,000 for the rights to the novel. He was so eager to produce the film that he hadn\'t yet read it. He claimed he abandoned the project in order to complete a different project, but it was actually to preserve his reputation and avoid appearing reactionary. While concurrently filmmaking, he served during World War II at age 60 as his neighborhood air-raid warden.
In 1942, DeMille worked with Jeanie MacPherson and William deMille to produce a film, *Queen of Queens*, that was intended to be about Mary, mother of Jesus. After reading the screenplay, Daniel A. Lord warned DeMille that Catholics would find the film too irreverent while non-Catholics would consider it Catholic propaganda. Consequently, the film was never made. MacPherson worked as a scriptwriter on many of DeMille\'s films. In 1938, DeMille supervised the film compilation *Land of Liberty* as the American film industry\'s contribution to the 1939 New York World\'s Fair. He used clips from his own films in it. *Land of Liberty* was not high-grossing, but it was well-received, and DeMille was asked to shorten its running time to allow for more showings per day. MGM distributed the film in 1941 and donated profits to World War II relief charities. In 1942, DeMille released Paramount\'s most successful film, *Reap the Wild Wind*. It had a large budget and many special effects, including an electronically operated giant squid. After working on it, DeMille was the master of ceremonies at a rally organized by David O. Selznick in the Los Angeles Coliseum in support of the Dewey--Bricker presidential ticket as well as Governor Earl Warren of California.`{{refn|group=note| The gathering drew 93,000, with short speeches by [[Hedda Hopper]] and [[Walt Disney]]. Among those in attendance were [[Ann Sothern]], [[Ginger Rogers]], [[Randolph Scott]], [[Adolphe Menjou]], [[Gary Cooper]], and [[Walter Pidgeon]]. Though the rally drew a good response, most Hollywood celebrities who took a public position sided with the [[Franklin Roosevelt|Roosevelt]]-[[Harry Truman|Truman]] ticket.<ref name="David M. Jordan 2011 pp. 231-232">David M. Jordan, ''FDR, Dewey, and the Election of 1944'' (Bloomington and Indianapolis: Indiana University Press, 2011), pp. 231–232.</ref>}}`{=mediawiki} DeMille\'s 1947 film *Unconquered* had the longest running time (146 minutes), longest filming schedule (102 days), and largest budget (\$5 million). Its sets and effects were so realistic that 30 extras needed to be hospitalized due to a scene with fireballs and flaming arrows. It was commercially very successful.
DeMille\'s next film, *Samson and Delilah* (1949), was Paramount\'s highest-grossing film up to that time. A Biblical epic with sex, it was a characteristically DeMille film. 1952\'s *The Greatest Show on Earth* became Paramount\'s highest-grossing film to that point and won the Academy Award for Best Picture and the Academy Award for Best Story. It began production in 1949. Ringling Brothers-Barnum and Bailey were paid \$250,000 for use of the title and facilities. DeMille toured with the circus while helping write the script. Noisy and bright, the film was not well-liked by critics but was an audience favorite. In 1953, DeMille signed a contract with Prentice Hall to publish an autobiography. He reminisced into a voice recorder, the recording was transcribed, and the information was organized by topic. Art Arthur also interviewed people for the autobiography. DeMille did not like the biography\'s first draft, saying he thought the person portrayed in it was an egotistical \"SOB\". In the early 1950s, Allen Dulles and Frank Wisner recruited DeMille to serve on the board of the anti-communist National Committee for a Free Europe, the public face of the organization that oversaw Radio Free Europe. In 1954, Secretary of the Air Force Harold E. Talbott asked DeMille for help designing the cadet uniforms at the newly established United States Air Force Academy. DeMille\'s designs, most notably that of the cadet parade uniform, were praised by Air Force and Academy leadership, adopted, and still worn.
#### Final works and unrealized projects {#final_works_and_unrealized_projects}
In 1952, DeMille sought approval for a lavish remake of his 1923 silent film *The Ten Commandments*. He went before the Paramount board of directors, which was mostly Jewish-American. The board rejected his proposal, even though his last two films, *Samson and Delilah* and *The Greatest Show on Earth*, had been record-breaking hits. Adolph Zukor convinced the board to change its mind on the grounds of morality. DeMille did not have an exact budget proposal for the project, and it promised to be the most costly in U.S. film history. Still, the board unanimously approved it. *The Ten Commandments*, released in 1956, was DeMille\'s final film. It was the longest (3 hours, 39 minutes) and most expensive (\$13 million) film in Paramount history. Production began in October 1954. The Exodus scene was filmed on-site in Egypt with four Technicolor-VistaVision cameras filming 12,000 people. Filming continued in 1955 in Paris and Hollywood on 30 different sound stages. They even expanded to RKO sound studios for filming. Post-production lasted a year, and the film premiered in Salt Lake City. Nominated for an Academy Award for Best Picture, it grossed over \$80 million, which surpassed the gross of *The Greatest Show on Earth* and every other film in history except *Gone with the Wind*. DeMille offered ten percent of his profit to the crew, a unique practice at the time.
On November 7, 1954, while in Egypt filming the Exodus sequence for *The Ten Commandments*, DeMille (who was 73) climbed a 107 ft ladder to the top of the set and had a serious heart attack. Despite the urging of his associate producer, DeMille wanted to return to the set right away. He developed a plan with his doctor to allow him to continue directing while reducing his physical stress. DeMille completed the film, but his health was diminished by several more heart attacks. His daughter Cecilia took over as director as DeMille sat behind the camera with Loyal Griggs as the cinematographer. This film was his last.
Due to his frequent heart attacks, DeMille asked his son-in-law, actor Anthony Quinn, to direct a remake of his 1938 film *The Buccaneer*. DeMille served as executive producer, overseeing producer Henry Wilcoxon. Despite a cast led by Charlton Heston and Yul Brynner, the 1958 film *The Buccaneer* was a disappointment. DeMille attended its Santa Barbara premiere in December 1958. He was unable to attend its Los Angeles premiere. In the months before his death, DeMille was researching a film biography of Robert Baden-Powell, the founder of the Scout Movement. DeMille asked David Niven to star in the film, but it was never made. DeMille also was planning a film about the space race and a biblical epic based on the Book of Revelation. His autobiography was mostly complete when he died, and was published in November 1959.
#### Death
DeMille suffered a series of heart attacks from June 1958 to January 1959, and died on January 21, 1959, following an attack. His funeral was held on January 23 at St. Stephen\'s Episcopal Church. He was entombed at the Hollywood Memorial Cemetery (now known as Hollywood Forever). After his death, news outlets such as *The New York Times*, the *Los Angeles Times*, and *The Guardian* called DeMille a \"pioneer of movies\", \"the greatest creator and showman of our industry\", and \"the founder of Hollywood\". DeMille left his multi-million dollar estate in Los Feliz, Los Angeles, in Laughlin Park to his daughter Cecilia because his wife had dementia and was unable to care for an estate. She died a year later. His personal will drew a line between Cecilia and his three adopted children, with Cecilia receiving a majority of DeMille\'s inheritance and estate. The other three children were surprised by this, as DeMille had not treated them differently in life. Cecilia lived in the house until her death in 1984. The house was auctioned by his granddaughter Cecilia DeMille Presley, who also lived there in the late 1980s.`{{refn|group=note|The estate cycled through several different homeowners for the next 30 years until it was bought by American actress [[Angelina Jolie]] in 2017 for nearly $25 million.<ref name="jolie">{{cite news |last=David |first=Mark |title=Angelina Jolie Buys Cecil B. DeMille's Estate at Record-Shattering Price |url=https://variety.com/2017/dirt/real-estalker/angelina-jolie-cecil-b-demille-estate-laughlin-park-1202451889/ |access-date=June 26, 2019 |work=Variety |date=June 2, 2017}}</ref>}}`{=mediawiki}
## Filmmaking
### Influences
DeMille believed his first influences to be his parents, Henry and Beatrice DeMille. His playwright father introduced him to the theater at a young age. Henry was heavily influenced by the work of Charles Kingsley, whose ideas trickled down to DeMille. DeMille noted that his mother had a \"high sense of the dramatic\" and was determined to continue the artistic legacy of her husband after he died. Beatrice became a play broker and author\'s agent, influencing DeMille\'s early life and career. DeMille\'s father worked with David Belasco who was a theatrical producer, impresario, and playwright. Belasco was known for adding realistic elements in his plays such as real flowers, food, and aromas that could transport his audiences into the scenes. While working in theatre, DeMille used real fruit trees in his play *California*, as influenced by Belasco. Similar to Belasco, DeMille\'s theatre revolved around entertainment rather than artistry. Generally, Belasco\'s influence of DeMille\'s career can be seen in DeMille\'s showmanship and narration. E. H. Sothern\'s early influence on DeMille\'s work can be seen in DeMille\'s perfectionism. DeMille recalled that one of the most influential plays he saw was *Hamlet*, directed by Sothern.
### Method
DeMille\'s filmmaking process always began with extensive research. Next, he would work with writers to develop the story that he was envisioning. Then, he would help writers construct a script. Finally, he would leave the script with artists and allow them to create artistic depictions and renderings of each scene. Plot and dialogue were not a strong point of DeMille\'s films. Consequently, he focused his efforts on his films\' visuals. He worked with visual technicians, editors, art directors, costume designers, cinematographers, and set carpenters in order to perfect the visual aspects of his films. With his editor, Anne Bauchens, DeMille used editing techniques to allow the visual images to bring the plot to climax rather than dialogue. DeMille had large and frequent office conferences to discuss and examine all aspects of the working film including story-boards, props, and special effects.
DeMille rarely gave direction to actors; he preferred to \"office-direct\", where he would work with actors in his office, going over characters and reading through scripts. Any problems on the set were often fixed by writers in the office rather than on the set. DeMille did not believe a large movie set was the place to discuss minor character or line issues. DeMille was particularly adept at directing and managing large crowds in his films. Martin Scorsese recalled that DeMille had the skill to maintain control of not only the lead actors in a frame but the many extras in the frame as well. DeMille was adept at directing \"thousands of extras\", and many of his pictures include spectacular set pieces: the toppling of the pagan temple in *Samson and Delilah*; train wrecks in *The Road to Yesterday*, *Union Pacific* and *The Greatest Show on Earth*; the destruction of an airship in *Madam Satan*; and the parting of the Red Sea in both versions of *The Ten Commandments*. In his early films, DeMille experimented with photographic light and shade, which created dramatic shadows instead of glare. His specific use of lighting, influenced by his mentor David Belasco, was for the purpose of creating \"striking images\" and heightening \"dramatic situations\". DeMille was unique in using this technique. In addition to his use of volatile and abrupt film editing, his lighting and composition were innovative for the time period as filmmakers were primarily concerned with a clear, realistic image. Another important aspect of DeMille\'s editing technique was to put the film away for a week or two after an initial edit in order to re-edit the picture with a fresh mind. This allowed for the rapid production of his films in the early years of the Lasky Company. The cuts were sometimes rough, but the movies were always interesting.
DeMille often edited in a manner that favored psychological space rather than physical space through his cuts. In this way, the characters\' thoughts and desires are the visual focus rather than the circumstances regarding the physical scene. As DeMille\'s career progressed, he increasingly relied on artist Dan Sayre Groesbeck\'s concept, costume, and storyboard art. Groesbeck\'s art was circulated on set to give actors and crew members a better understanding of DeMille\'s vision. His art was even shown at Paramount meetings when pitching new films. DeMille adored the art of Groesbeck, even hanging it above his fireplace, but film staff found it difficult to convert his art into three-dimensional sets. As DeMille continued to rely on Groesbeck, the nervous energy of his early films transformed into more steady compositions of his later films. While visually appealing, this made the films appear more old-fashioned.
Composer Elmer Bernstein described DeMille as \"sparing no effort\" when filmmaking. Bernstein recalled that DeMille would scream, yell, or flatter---whatever it took to achieve the perfection he required in his films. DeMille was painstakingly attentive to details on set and was as critical of himself as he was of his crew. Costume designer Dorothy Jeakins, who worked with DeMille on *The Ten Commandments* (1956), said that he was skilled in humiliating people. Jeakins admitted that she received quality training from him, but that it was necessary to become a perfectionist on a DeMille set to avoid being fired. DeMille had an authoritarian persona on set; he required absolute attention from the cast and crew. He had a band of assistants who catered to his needs. He would speak to the entire set, sometimes enormous with countless numbers of crew members and extras, via a microphone to maintain control of the set. He was disliked by many inside and outside of the film industry for his cold and controlling reputation.
DeMille was known for autocratic behavior on the set, singling out and berating extras who were not paying attention. Many of these displays were thought to be staged, however, as an exercise in discipline. He despised actors who were unwilling to take physical risks, especially when he had first demonstrated that the required stunt would not harm them. This occurred with Victor Mature in *Samson and Delilah*. Mature refused to wrestle Jackie the Lion, even though DeMille had just tussled with the lion, proving that he was tame. DeMille told the actor that he was \"one hundred percent yellow\". Paulette Goddard\'s refusal to risk personal injury in a scene involving fire in *Unconquered* cost her DeMille\'s favor and a role in *The Greatest Show on Earth*. DeMille did receive help in his films, notably from Alvin Wyckoff, who shot forty-three of DeMille\'s films; brother William deMille who would occasionally serve as his screenwriter; and Jeanie Macpherson, who served as DeMille\'s exclusive screenwriter for fifteen years; and Eddie Salven, DeMille\'s favorite assistant director.
DeMille made stars of unknown actors: Gloria Swanson, Bebe Daniels, Rod La Rocque, William Boyd, Claudette Colbert, and Charlton Heston. He also cast established stars such as Gary Cooper, Robert Preston, Paulette Goddard and Fredric March in multiple pictures. DeMille cast some of his performers repeatedly, including Henry Wilcoxon, Julia Faye, Joseph Schildkraut, Ian Keith, Charles Bickford, Theodore Roberts, Akim Tamiroff, and William Boyd. DeMille was credited by actor Edward G. Robinson with saving his career following his eclipse in the Hollywood blacklist.
### Style and themes {#style_and_themes}
Cecil B. DeMille\'s film production career evolved from critically significant silent films to financially significant sound films. He began his career with reserved yet brilliant melodramas; from there, his style developed into marital comedies with outrageously melodramatic plots. In order to attract a high-class audience, DeMille based many of his early films on stage melodramas, novels, and short stories. He began the production of epics earlier in his career until they began to solidify his career in the 1920s. By 1930, DeMille had perfected his film style of mass-interest spectacle films with Western, Roman, or Biblical themes. DeMille was often criticized for making his spectacles too colorful and for being too occupied with entertaining the audience rather than accessing the artistic and auteur possibilities that film could provide. However, others interpreted DeMille\'s work as visually impressive, thrilling, and nostalgic. Along the same lines, critics of DeMille often qualify him by his later spectacles and fail to consider several decades of ingenuity and energy that defined him during his generation. Throughout his career, he did not alter his films to better adhere to contemporary or popular styles. Actor Charlton Heston admitted DeMille was, \"terribly unfashionable\" and Sidney Lumet called DeMille, \"the cheap version of D. W. Griffith\", adding that DeMille, \"\[didn\'t have\]\...an original thought in his head\", though Heston added that DeMille was much more than that. According to Scott Eyman, DeMille\'s films were at the same time masculine and feminine due to his thematic adventurousness and his eye for the extravagant. DeMille\'s distinctive style can be seen through camera and lighting effects as early as *The Squaw Man* with the use of daydream images; moonlight and sunset on a mountain; and side-lighting through a tent flap. In the early age of cinema, DeMille differentiated the Lasky Company from other production companies due to the use of dramatic, low-key lighting they called \"Lasky lighting\" and marketed as \"Rembrandt lighting\" to appeal to the public. DeMille achieved international recognition for his unique use of lighting and color tint in his film *The Cheat*. DeMille\'s 1956 version of *The Ten Commandments*, according to director Martin Scorsese, is renowned for its level of production and the care and detail that went into creating the film. He stated that *The Ten Commandments* was the final culmination of DeMille\'s style.
DeMille was interested in art and his favorite artist was Gustave Doré; DeMille based some of his most well-known scenes on the work of Doré. DeMille was the first director to connect art to filmmaking; he created the title of \"art director\" on the film set. DeMille was also known for his use of special effects without the use of digital technology. Notably, DeMille had cinematographer John P. Fulton create the parting of the Red Sea scene in his 1956 film *The Ten Commandments*, which was one of the most expensive special effects in film history, and has been called by Steven Spielberg \"the greatest special effect in film history\". The actual parting of the sea was created by releasing 360,000 gallons of water into a huge water tank split by a U-shaped trough, overlaying it with a film of a giant waterfall that was built on the Paramount backlot, and playing the clip backward.
Aside from his Biblical and historical epics, which are concerned with how man relates to God, some of DeMille\'s films contained themes of \"neo-naturalism\", which portray the conflict between the laws of man and the laws of nature. Although he is known for his later \"spectacular\" films, his early films are held in high regard by critics and film historians. DeMille discovered the possibilities of the \"bathroom\" or \"boudoir\" in the film without being \"vulgar\" or \"cheap\". DeMille\'s films *Male and Female*, *Why Change Your Wife?*, and *The Affairs of Anatol* can be retrospectively described as high camp and are categorized as \"early DeMille films\" due to their particular style of production and costume and set design. However, his earlier films *The Captive*, *Kindling*, *Carmen*, and *The Whispering Chorus* are more serious films. It is difficult to typify DeMille\'s films into one specific genre. His first three films were Westerns, and he filmed many Westerns throughout his career. However, throughout his career, he filmed comedies, periodic and contemporary romances, dramas, fantasies, propaganda, Biblical spectacles, musical comedies, suspense, and war films. At least one DeMille film can represent each film genre. DeMille produced the majority of his films before the 1930s, and by the time sound films were invented, film critics saw DeMille as antiquated, with his best filmmaking years behind him.
DeMille\'s films contained many similar themes throughout his career. However, the films of his silent era were often thematically different from the films of his sound era. His silent-era films often included the \"battle of the sexes\" theme due to the era of women\'s suffrage and the enlarging role of women in society. Moreover, before his religious-themed films, many of his silent era films revolved around \"husband-and-wife-divorce-and-remarry satires\", considerably more adult-themed. According to Simon Louvish, these films reflected DeMille\'s inner thoughts and opinions about marriage and human sexuality. Religion was a theme that DeMille returned to throughout his career. Of his seventy films, five revolved around stories of the Bible and the New Testament; however many others, while not direct retellings of Biblical stories, had themes of faith and religious fanaticism in films such as *The Crusades* and *The Road to Yesterday*. Western and frontier American were also themes that DeMille returned to throughout his career. His first several films were Westerns, and he produced a chain of westerns during the sound era. Instead of portraying the danger and anarchy of the West, he portrayed the opportunity and redemption found in Western America. Another common theme in DeMille\'s films is the reversal of fortune and the portrayal of the rich and the poor, including the war of the classes and man versus society conflicts such as in *The Golden Chance* and *The Cheat*. In relation to his own interests and sexual preferences, sadomasochism was a minor theme present in some of his films. Another minor characteristic of DeMille\'s films include train crashes, which can be found in several of his films.
## Legacy
Known as the father of the Hollywood motion picture industry, Cecil B. DeMille made 70 films including several box-office hits. DeMille is one of the more commercially successful film directors in history, with his films before the release of *The Ten Commandments* estimated to have grossed \$650 million worldwide. Adjusted for inflation, DeMille\'s remake of *The Ten Commandments* is the eighth highest-grossing film in the world.
According to Sam Goldwyn, critics did not like DeMille\'s films, but the audiences did, and \"they have the final word\". Similarly, scholar David Blanke, argued that DeMille had lost the respect of his colleagues and film critics by his late film career. However, his final films maintained that DeMille was still respected by his audiences. Five of DeMille\'s films were the highest-grossing films at the year of their release, with only Spielberg topping him with six of his films as the highest-grossing films of the year. DeMille\'s highest-grossing films include: *The Sign of the Cross* (1932), *Unconquered* (1947), *Samson and Delilah* (1949), *The Greatest Show on Earth* (1952), and *The Ten Commandments* (1956). Director Ridley Scott has been called \"the Cecil B. DeMille of the digital era\" due to his classical and medieval epics.
Despite his box-office success, awards, and artistic achievements, DeMille has been dismissed and ignored by critics both during his life and posthumously. He was consistently criticized for producing shallow films without talent or artistic care. Compared to other directors, few film scholars have taken the time to academically analyze his films and style. During the French New Wave, critics began to categorize certain filmmakers as auteurs such as Howard Hawks, John Ford, and Raoul Walsh. DeMille was omitted from the list, thought to be too unsophisticated and antiquated to be considered an auteur. However, Simon Louvish wrote \"he was the complete master and auteur of his films\", and Anton Kozlovic called him the \"unsung American auteur\". Andrew Sarris, a leading proponent of the auteur theory, ranked DeMille highly as an auteur in the \"Far Side of Paradise\", just below the \"Pantheon\". Sarris added that despite the influence of the styles of contemporary directors throughout his career, DeMille\'s style remained unchanged. Robert Birchard wrote that one could argue the auteurship of DeMille on the basis that DeMille\'s thematic and visual style remained consistent throughout his career. However, Birchard acknowledged that Sarris\'s point was more likely that DeMille\'s style was behind the development of film as an art form. Meanwhile, Sumiko Higashi sees DeMille as \"not only a figure who was shaped and influenced by the forces of his era but as a filmmaker who left his own signature on the culture industry.\" The critic Camille Paglia has called *The Ten Commandments* one of the ten greatest films of all time.
DeMille was one of the first directors to become a celebrity in his own right. He cultivated the image of the omnipotent director, complete with megaphone, riding crop, and jodhpurs. He was known for his unique working wardrobe, which included riding boots, riding pants, and soft, open necked shirts. Joseph Henabery recalled that DeMille looked like \"a king on a throne surrounded by his court\" while directing films on a camera platform.
DeMille was liked by some of his fellow directors and disliked by others, though his actual films were usually dismissed by his peers as a vapid spectacle. Director John Huston intensely disliked both DeMille and his films. \"He was a thoroughly bad director\", Huston said. \"A dreadful showoff. Terrible. To diseased proportions.\" Said fellow director William Wellman: \"Directorially, I think his pictures were the most horrible things I\'ve ever seen in my life. But he put on pictures that made a fortune. In that respect, he was better than any of us.\" Producer David O. Selznick wrote: \"There has appeared only one Cecil B. DeMille. He is one of the most extraordinarily able showmen of modern times. However much I may dislike some of his pictures, it would be very silly of me, as a producer of commercial motion pictures, to demean for an instant his unparalleled skill as a maker of mass entertainment.\" Salvador Dalí wrote that DeMille, Walt Disney, and the Marx Brothers were \"the three great American Surrealists\". DeMille appeared as himself in numerous films, including the MGM comedy *Free and Easy*. He often appeared in his coming-attraction trailers and narrated many of his later films, even stepping on screen to introduce *The Ten Commandments*. DeMille was immortalized in Billy Wilder\'s *Sunset Boulevard* when Gloria Swanson spoke the line: \"All right, Mr. DeMille. I\'m ready for my close-up.\" DeMille plays himself in the film. DeMille\'s reputation had a renaissance in the 2010s.
As a filmmaker, DeMille was the aesthetic inspiration of many directors and films due to his early influence during the crucial development of the film industry. DeMille\'s early silent comedies influenced the comedies of Ernst Lubitsch and Charlie Chaplin\'s *A Woman of Paris*. Additionally, DeMille\'s epics such as *The Crusades* influenced Sergei Eisenstein\'s *Alexander Nevsky*. Moreover, DeMille\'s epics inspired directors such as Howard Hawks, Nicholas Ray, Joseph L. Mankiewicz, and George Stevens to try producing epics. Cecil B. DeMille has influenced the work of several well-known directors. Alfred Hitchcock cited DeMille\'s 1921 film *Forbidden Fruit* as an influence of his work and one of his top ten favorite films. DeMille has influenced the careers of many modern directors. Martin Scorsese cited *Unconquered*, *Samson and Delilah*, and *The Greatest Show on Earth* as DeMille films that have imparted lasting memories on him. Scorsese said he had viewed *The Ten Commandments* forty or fifty times. Famed director Steven Spielberg stated that DeMille\'s *The Greatest Show on Earth* was one of the films that influenced him to become a filmmaker. Furthermore, DeMille influenced about half of Spielberg\'s films, including *War of the Worlds*.`{{refn|group=note|DeMille had considered making the film himself. He bought the rights to the novel in 1925 but abandoned the project in pre-production.<ref>{{cite book |last=Flynn |first=John L. |title=War of the Worlds: From Wells to Spielberg |url=https://books.google.com/books?id=T0aCSs1-23sC&q=cecil+b+demille+%22war+of+the+worlds%22&pg=PA56 |publisher=Galactic Books |location=Owings Mills, MD |date=2005 |page=56 |isbn=0976940000 |access-date=July 1, 2019}}</ref>}}`{=mediawiki} *The Ten Commandments* inspired DreamWorks Animation\'s later film about Moses, *The Prince of Egypt*. As one of the establishing members of Paramount Pictures and co-founder of Hollywood, DeMille had a role in the development of the film industry. Consequently, the name \"DeMille\" has become synonymous with filmmaking.
Publicly Episcopalian, DeMille drew on his Christian and Jewish ancestors to convey a message of tolerance. DeMille received more than a dozen awards from Christian and Jewish religious and cultural groups, including B\'nai B\'rith. However, not everyone received DeMille\'s religious films favorably. DeMille was accused of antisemitism after the release of *The King of Kings*, and director John Ford despised DeMille for what he saw as \"hollow\" biblical epics meant to promote DeMille\'s reputation during the politically turbulent 1950s. In response to the claims, DeMille donated some of the profits from *The King of Kings* to charity. In the 2012 *Sight & Sound* poll, both DeMille\'s *Samson and Delilah* and 1923 version of *The Ten Commandments* received votes, but did not make the top 100 films. Although many of DeMille\'s films are available on DVD and Blu-ray release, only 20 of his silent films are commercially available on DVD.`{{refn|group=note|In the 1950s, Paramount sold its entire pre-1948 film library, including those of DeMille, to [[EMKA]]. Consequently, most of DeMille's pre-1948 films no longer belong to Paramount.<ref>{{cite journal |last=White |first=Timothy R. |title=Life After Divorce: The Corporate Strategy of Paramount Pictures Corporation in the 1950s |journal=Film History |date=1988 |volume=2 |issue=2 |page=114 |jstor=3815029}}</ref>}}`{=mediawiki}
### Commemoration and tributes {#commemoration_and_tributes}
The original Lasky-DeMille Barn in which *The Squaw Man* was filmed was converted into a museum named the \"Hollywood Heritage Museum\". It opened on December 13, 1985, and features some of DeMille\'s personal artifacts. The Lasky-DeMille Barn was dedicated as a California historical landmark in a ceremony on December 27, 1956; DeMille was the keynote speaker. It was listed on the National Register of Historic Places in 2014. The Dunes Center in Guadalupe, California, contains an exhibition of artifacts uncovered in the desert near Guadalupe from DeMille\'s set of his 1923 version of *The Ten Commandments*, known as the \"Lost City of Cecil B. DeMille\".`{{refn|group=note|The set was discovered by Peter Brosnan after hearing a rumor in 1982 that DeMille had ordered the enormous set to be buried after filming rather than taken away. A documentary titled ''The Lost City of Cecil B. DeMille'' follows the story of Brosnan's 30-year journey to find and uncover the set.<ref>{{cite news |last=Linden |first=Sheri |title="The Lost City of Cecil B. DeMille": Film Review |url=https://www.hollywoodreporter.com/review/lost-city-cecil-b-demille-1011412 |work=The Hollywood Reporter |date=June 13, 2017 |access-date=July 10, 2019}}</ref>}}`{=mediawiki} Donated by the Cecil B. DeMille Foundation in 2004, the moving image collection of Cecil B. DeMille is held at the Academy Film Archive and includes home movies, outtakes, and never-before-seen test footage.
In summer 2019, The Friends of the Pompton Lakes Library hosted a Cecil B DeMille film festival to celebrate DeMille\'s achievements and connection to Pompton Lakes. They screened four of his films at Christ Church, where DeMille and his family attended church when they lived there. Two schools have been named after him: Cecil B. DeMille Middle School, in Long Beach, California, which was closed and demolished in 2010 to make way for a new high school; and Cecil B. DeMille Elementary School in Midway City, California. The former film building at Chapman University in Orange, California, is named in honor of DeMille. During the Apollo 11 mission, Buzz Aldrin referred to himself in one instance as \"Cecil B. DeAldrin\", as a humorous nod to DeMille. The title of the 2000 John Waters film *Cecil B. Demented* alludes to DeMille.
DeMille\'s legacy is maintained by his granddaughter Cecilia DeMille Presley who serves as the president of the Cecil B. DeMille Foundation, which strives to support higher education, child welfare, and film in Southern California. In 1963, the Cecil B. DeMille Foundation donated the \"Paradise\" ranch to the Hathaway Foundation, which cares for emotionally disturbed and abused children. A large collection of DeMille\'s materials including scripts, storyboards, and films resides at Brigham Young University in L. Tom Perry Special Collections.
## Awards and recognition {#awards_and_recognition}
Cecil B. DeMille received many awards and honors, especially later in his career.
In August 1941, DeMille was honored with a block in the forecourt of Grauman\'s Chinese Theatre.
The American Academy of Dramatic Arts honored DeMille with an Alumni Achievement Award in 1958.
In 1957, DeMille gave the commencement address for the graduation ceremony of Brigham Young University, wherein he received an honorary Doctorate of Letter degree. Additionally, in 1958, he received an honorary Doctorate of Law degree from Temple University.
From the film industry, DeMille received the Irving G. Thalberg Memorial Award at the Academy Awards in 1953, and a Lifetime Achievement Award from the Directors Guild of America Award the same year. In the same ceremony, DeMille received a nomination from Directors Guild of America Award for Outstanding Directorial Achievement in Motion Pictures for *The Greatest Show on Earth*. In 1952, DeMille was awarded the first Cecil B. DeMille Award at the Golden Globes. An annual award, the Golden Globe\'s Cecil B. DeMille Award recognizes lifetime achievement in the film industry.`{{refn|group=note|Later recipients of the award include [[Kirk Douglas]], [[Robert Redford]], [[Lauren Bacall]].<ref>{{cite web |title=Academy Alum Cecil B. DeMille, The Founding Father of Hollywood Filmmaking |url=https://www.aada.edu/article/academy-alum-cecil-b-demille-the-founding-father-of-hollywood-filmmaking |website=The American Academy of Dramatic Arts |publisher=American Academy of Dramatic Arts |access-date=May 29, 2019}}</ref> [[Jeff Bridges]] was the 2019 Cecil B. DeMille Award winner.<ref>{{cite news |title=Jeff Bridges to Receive Cecil B. DeMille Award at 2019 Golden Globes |url=https://variety.com/2018/film/news/jeff-bridges-cecil-b-demille-award-golden-globes-2019-1203090682/ |access-date=May 29, 2019 |work=Variety |publisher=Variety Media |date=December 17, 2018}}</ref>}}`{=mediawiki} For his contribution to the motion picture and radio industry, DeMille has two stars on the Hollywood Walk of Fame. The first, for radio contributions, is located at 6240 Hollywood Blvd. The second star is located at 1725 Vine Street.
DeMille received two Academy Awards: an Honorary Award for \"37 years of brilliant showmanship\" in 1950 and a Best Picture award in 1953 for *The Greatest Show on Earth*. DeMille received a Golden Globe Award for Best Director and was additionally nominated for the Best Director category at the 1953 Academy Awards for the same film. He was further nominated in the Best Picture category for *The Ten Commandments* at the 1957 Academy Awards. DeMille\'s *Union Pacific* received a Palme d\'Or in retrospect at the 2002 Cannes Film Festival.
Two of DeMille\'s films have been selected for preservation in the National Film Registry by the United States Library of Congress: *The Cheat* (1915) and *The Ten Commandments* (1956).
## Filmography
DeMille made 70 features, 52 of which are silent. The first 24 of his silents were produced during the first three years of his career (1913--1916). Eight of his films were \"epics\" with five classified as \"Biblical\". Six of DeMille\'s films --- *The Arab*, *The Wild Goose Chase*, *The Dream Girl*, *The Devil-Stone*, *We Can\'t Have Everything*, and *The Squaw Man* (1918) --- were destroyed by nitrate decomposition, and are considered lost. *The Ten Commandments* is broadcast every Saturday at Passover in the United States on the ABC Television Network.
### Directed features {#directed_features}
Filmography obtained from *Fifty Hollywood Directors*.
**Silent films** **Sound films** `{{div col|colwidth=22em|content=
* ''[[Dynamite (1929 film)|Dynamite]]'' (1929)
* ''[[Madam Satan]]'' (1930)
* ''[[The Squaw Man (1931 film)|The Squaw Man]]'' (1931)
* ''[[The Sign of the Cross (1932 film)|The Sign of the Cross]]'' (1932)
* ''[[This Day and Age (film)|This Day and Age]]'' (1933)
* ''[[Four Frightened People]]'' (1934)
* ''[[Cleopatra (1934 film)|Cleopatra]]'' (1934)
* ''[[The Crusades (1935 film)|The Crusades]]'' (1935)
* ''[[The Plainsman]]'' (1936)
* ''[[The Buccaneer (1938 film)|The Buccaneer]]'' (1938)
* ''[[Union Pacific (film)|Union Pacific]]'' (1939)
* ''[[North West Mounted Police (film)|North West Mounted Police]]'' (1940)
* ''[[Reap the Wild Wind]]'' (1942)
* ''[[The Story of Dr. Wassell]]'' (1944)
* ''[[Unconquered (1947 film)|Unconquered]]'' (1947)
* ''[[Samson and Delilah (1949 film)|Samson and Delilah]]'' (1949)
* ''[[The Greatest Show on Earth (film)|The Greatest Show on Earth]]'' (1952)
* ''[[The Ten Commandments (1956 film)|The Ten Commandments]]'' (1956)
}}`{=mediawiki}
### Directing or producing credit {#directing_or_producing_credit}
These are films which DeMille produced or assisted in directing, credited or uncredited.
- *Brewster\'s Millions* (1914, lost)
- *The Master Mind* (1914)
- *The Only Son* (1914, lost)
- *The Man on the Box* (1914)
- *The Ghost Breaker* (1914, lost)
- *After Five* (1915)
- *Nan of Music Mountain* (1917)
- *Chicago* (1927, Producer, uncredited)
- *When Worlds Collide* (1951, executive producer)
- *The War of the Worlds* (1953, executive producer)
- *The Buccaneer* (1958, producer)
### Acting and cameos {#acting_and_cameos}
DeMille frequently made cameos as himself in other Paramount films. Additionally, he often starred in prologues and special trailers that he created for his films, having an opportunity to personally address the audience.
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Chinese Islamic cuisine
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**Chinese Islamic cuisine** consists of variations of regionally popular foods that are typical of Han Chinese cuisine, in particular to make them halal. Dishes borrow ingredients from Middle Eastern, Turkic, Iranian and South Asian cuisines, notably mutton and spices. Much like other northern Chinese cuisines, Chinese Islamic cuisine uses wheat noodles as the staple, rather than rice. Chinese Islamic dishes include clear-broth beef noodle soup and *chuanr*.
The Hui (ethnic Chinese Muslims), Bonan, Dongxiang, Salar and Uyghurs of China, as well as the Dungans of Central Asia and the Panthays of Burma, collectively contribute to Chinese Islamic cuisine.
## History
Due to the large Muslim population in Western China, many Chinese restaurants cater to or are run by Muslims. Northern Chinese Islamic cuisine originated in China proper. It is heavily influenced by Beijing cuisine, with nearly all cooking methods identical and differs only in material due to religious restrictions. As a result, northern Islamic cuisine is often included in home Beijing cuisine though seldom in east coast restaurants.
During the Yuan dynasty, halal and kosher methods of slaughtering animals and preparing food was banned and forbidden by the Mongol emperors, starting with Genghis Khan who banned Muslims and Jews from slaughtering their animals their own way and made them follow the Mongol method.
> Among all the \[subject\] alien peoples only the Hui-hui say \"we do not eat Mongol food.\" \[Cinggis Qa\'an replied:\] \"By the aid of heaven we have pacified you; you are our slaves. Yet you do not eat our food or drink. How can this be right?\" He thereupon made them eat. \"If you slaughter sheep, you will be considered guilty of a crime.\" He issued a regulation to that effect \... \[In 1279/1280 under Qubilai\] all the Muslims say: "if someone else slaughters \[the animal\] we do not eat.\" Because the poor people are upset by this, from now on, Musuluman \[Muslim\] Huihui and Zhuhu \[Jewish\] Huihui, no matter who kills \[the animal\] will eat \[it\] and must cease slaughtering sheep themselves, and cease the rite of circumcision.
Traditionally, there is a distinction between Northern and Southern Chinese Islamic cuisine despite both using lamb and mutton. Northern Chinese Islamic cuisine relies heavily on beef, but rarely ducks, geese, shrimp or seafood, while southern Islamic cuisine is the reverse. The reason for this difference is due to availability of the ingredients. Oxen have been long used for farming and Chinese governments have frequently strictly prohibited the slaughter of oxen for food. However, due to the geographic proximity of the northern part of China to minority-dominated regions that were not subjected to such restrictions, beef could be easily purchased and transported to Northern China. At the same time, ducks, geese and shrimp are rare in comparison to Southern China due to the arid climate of Northern China.
A Chinese Islamic restaurant (`{{zh|t=淸眞菜館|p=qīngzhēn càiguǎn}}`{=mediawiki}) can be similar to a Mandarin restaurant with the exception that there is no pork on the menu and the dishes are primarily noodle/soup based.
In most major eastern cities in China, there are very limited Islamic/Halal restaurants, which are typically run by migrants from Western China (e.g., Uyghurs). They primarily offer inexpensive noodle soups only. These restaurants are typically decorated with Islamic motifs such as Islamic writing.
Another difference is that lamb and mutton dishes are more commonly available than in other Chinese restaurants, due to the greater prevalence of these meats in the cuisine of Western Chinese regions. (Refer to image 1.)
Other Muslim ethnic minorities like the Bonan, Dongxiang, Salar and Tibetan Muslims have their own cuisines as well. Dongxiang people operate their own restaurants serving their cuisine.
Many cafeterias (canteens) at Chinese universities have separate sections or dining areas for Muslim students (Hui or Western Chinese minorities), typically labeled \"qingzhen\". Student ID cards sometimes indicate whether a student is Muslim and will allow access to these dining areas or will allow access on special occasions such as the Eid feast following Ramadan.
Several Hui restaurants serving Chinese Islamic cuisine exist in Los Angeles. San Francisco, despite its huge number of Chinese restaurants, appears to have only one whose cuisine would qualify as halal.
Many Chinese Hui Muslims who moved from Yunnan to Burma (Myanmar) are known as Panthays operate restaurants and stalls serving Chinese Islamic cuisine such as noodles. Chinese Hui Muslims from Yunnan who moved to Thailand are known as Chin Haw and they also own restaurants and stalls serving Chinese Islamic food.
In Central Asia, Dungan people, descendants of Hui, operate restaurants serving Chinese Islamic cuisine, which is respectively referred to as *Dungan cuisine* there. They cater to Chinese businessmen. Chopsticks are used by Dungans. The cuisine of the Dungan resembles northwestern Chinese cuisine.
Most Chinese regard Hui halal food as cleaner than food made by non-Muslims so their restaurants are popular in China. Hui who migrated to Northeast China (Manchuria) after the Chuang Guandong opened many new inns and restaurants to cater to travelers, which were regarded as clean.
The Hui who migrated to Taiwan operate Qingzhen restaurants and stalls serving Chinese Islamic cuisine in Taipei and other big cities.
The Thai Department of Export Promotion claims that \"China\'s halal food producers are small-scale entrepreneurs whose products have little value added and lack branding and technology to push their goods to international standards\" to encourage Thai private sector halal producers to market their products in China.
A 1903-started franchise serving Muslim food is Dong Lai Shun in Hankou.
400 meters have to be kept as a distance from each restaurant serving beef noodles to another of its type if they belong to Hui Muslims, since Hui have a pact between each other in Ningxia, Gansu and Shaanxi.
Halal restaurants are checked up upon by clerics from mosques.
Halal food manufacture has been sanctioned by the government of the Ningxia Autonomous Region.
## Famous dishes {#famous_dishes}
### Lamian
**Lamian** (`{{zh|s=拉面|t=拉麪|p=lāmiàn}}`{=mediawiki}, Dungan: Ламян) is a Chinese dish of hand-made noodles, usually served in a beef or mutton-flavored soup (湯麪, даңмян, tāngmiàn), but sometimes stir-fried (炒麪, Чаомян, chǎomiàn) and served with a tomato-based sauce. Literally, 拉, ла (lā) means to pull or stretch, while 麪, мян (miàn) means noodle. The hand-making process involves taking a lump of dough and repeatedly stretching it to produce a single very long noodle. There exists a local variant in Lanzhou, the Lanzhou beef noodles, also known as Lanzhou lamian.
Words that begin with L are not native to Turkic --- läghmän is a loanword as stated by Uyghur linguist Abdlikim: It is of Chinese derivation and not originally Uyghur.
### Beef noodle soup {#beef_noodle_soup}
**Beef noodle soup** is a noodle soup dish composed of stewed beef, beef broth, vegetables and wheat noodles. It exists in various forms throughout East and Southeast Asia. It was created by the Hui people during the Qing dynasty of China.
In the west, this food may be served in a small portion as a soup. In China, a large bowl of it is often taken as a whole meal with or without any side dish.
### Chuanr
**Chuanr** (Chinese: 串儿, Dungan: Чўанр, Pinyin: chuànr (shortened from \"chuan er\"), \"*kebab*\"), originating in the Xinjiang (新疆) province of China and in recent years has been disseminated throughout the rest of that country, most notably in Beijing. It is a product of the Chinese Islamic cuisine of the Uyghur (维吾尔) people and other Chinese Muslims. Yang rou chuan or lamb kebabs, is particularly popular.
### Suan cai {#suan_cai}
**Suan cai** is a traditional fermented vegetable dish, similar to Korean kimchi and German sauerkraut, used in a variety of ways. It consists of pickled Chinese cabbage. Suan cai is a unique form of pao cai due to the material used and the method of production. Although *suan cai* is not exclusive to Chinese Islamic cuisine, it is used in Chinese Islamic cuisine to top off noodle soups, especially beef noodle soup.
### Nang
*Nang* (Chinese: 馕, Dungan: Нәң) is a type of round unleavened bread, topped with sesame. It is similar to South and Central Asia naan.
## Image gallery {#image_gallery}
<File:Beef> noodle.JPG\|Beef noodle served <File:Peking> Duck.jpg\|Peking duck served at a halal restaurant in Beijing <File:5658-Linxia-City-niang-pi.jpg>\|*Niang pi* (酿皮, Няң пы), a popular vegetarian noodle cold dish in Linxia
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Teochew cuisine
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**Teochew cuisine**, also known as **Chiuchow cuisine**, **Chaozhou cuisine** or **Teo-swa cuisine**, originated from the Chaoshan region in the eastern part of China\'s Guangdong Province, which includes the cities of Chaozhou, Shantou and Jieyang. Teochew cuisine bears more similarities to that of Fujian cuisine, particularly Southern Min cuisine, due to the similarity of Teochew\'s and Fujian\'s culture, language, and their geographic proximity to each other. However, Teochew cuisine is also influenced by Cantonese cuisine in its style and technique.
## Background
Teochew cuisine is well known for its seafood and vegetarian dishes. Its use of flavouring is much less heavy-handed than most other Chinese cuisines and depends much on the freshness and quality of the ingredients for taste and flavour. As a delicate cuisine, oil is not often used in large quantities and there is a relatively heavy emphasis on poaching, steaming and braising, as well as the common Chinese method of stir-frying. Teochew cuisine is also known for serving congee (`{{zh|c=糜|p=mí|labels=no}}`{=mediawiki}; or *mue*), in addition to steamed rice or noodles with meals. The Teochew **mue** is rather different from the Cantonese counterpart, being very watery with the rice sitting loosely at the bottom of the bowl, while the Cantonese dish is more a thin gruel.
Authentic Teochew restaurants serve very strong oolong tea called Tieguanyin in very tiny cups before and after the meal. Presented as *gongfu* tea, the tea has a thickly bittersweet taste, colloquially known as *gam gam* (`{{zh|c=甘甘|p=gān gān|labels=no}}`{=mediawiki}).
A condiment that is popular in Fujian and Taiwanese cuisine and commonly associated with cuisine of certain Teochew groups is shacha sauce (`{{zh|s=沙茶酱|t=沙茶醬|p=shāchá jiàng|labels=no}}`{=mediawiki}). It is made from soybean oil, garlic, shallots, chilies, brill fish and dried shrimp. The paste has a savoury and slightly spicy taste. As an ingredient, it has multiple uses: as a base for soups, as a rub for barbecued meats, as a seasoning for stir-fried dishes, or as a component for dipping sauces.
In addition to soy sauce (widely used in all Chinese cuisines), Teochew people also use fish sauce in their cooking.
Teochew chefs often use a special stock called siang teng (`{{zh|s=上汤|t=上湯|p=shàngtāng|labels=no}}`{=mediawiki}), literally translates from the Teochew dialect as \"superior broth\". This stock remains on the stove and is continuously replenished. Portrayed in popular media, some Hong Kong chefs allegedly use the same superior broth that is preserved for decades. This stock can as well be seen on Chaozhou TV\'s cooking programmes.
There is a notable feast in Teochew cuisine called **jiat dot** (`{{zh|c=食桌|p=shízhuō|l=food table|labels=no}}`{=mediawiki}). A myriad of dishes are often served, which include shark fin soup, bird\'s nest soup, lobster, steamed fish, roasted suckling pig and braised goose.
Teochew chefs take pride in their skills of vegetable carving, and carved vegetables are used as garnishes on cold dishes and on the banquet table.
Teochew cuisine is also known for a late night meal known as *meh siao* (`{{zh|c=夜宵|p=yèxiāo|labels=no}}`{=mediawiki}) or *daa laang* (`{{zh|c=打冷|p=dǎléng|labels=no}}`{=mediawiki}) among the Cantonese. Teochew people enjoy eating out close to midnight in restaurants or at roadside food stalls. Some dai pai dong-like eateries stay open till dawn.
Unlike the typical menu selections of many other Chinese cuisines, Teochew restaurant menus often have a dessert section.
Many people of Teochew origin, also known as Teochiu or Teochew people, have settled in Hong Kong and places in Southeast Asia like Malaysia, Singapore, Cambodia and Thailand. Influences they bring can be noted in Singaporean cuisine and that of other settlements. A large number of Teochew people have also settled in Taiwan, evident in Taiwanese cuisine. Other notable Teochew diaspora communities are in Vietnam, Cambodia and France. A popular noodle soup in both Vietnam and Cambodia, known as hu tieu, originated from the Teochew . There is also a large diaspora of Teochew people (most were from Southeast Asia) in the United States - particularly in California. There is a Teochew Chinese Association in Paris called L\'Amicale des Teochews en France.
## Notable dishes {#notable_dishes}
English Traditional Chinese Simplified Chinese Pinyin Peng\'im Description
------------------------------------------------- --------------------- -------------------- ----------------- ----------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Bak chor mee / *bhah4 co3 mi7* Boiled noodles, dried and mixed with variety sauce such as soy sauce, chilli sauce and lard topped with vegetables, sliced onion, minced pork, mushrooms and fish balls or fishcakes.
Bak kut teh / *nêg8 gug4 dê5* A hearty soup that, at its simplest, consists of meaty pork ribs in a complex broth of herbs and spices (including star anise, cinnamon, cloves, danggui, fennel seeds and garlic), boiled together with pork bones for hours. Dark and light soy sauce may also be added to the soup during the cooking stages. Some Teochew families like to add extra Chinese herbs such as yuzhu (rhizome of Solomon\'s seal) and juzhi (buckthorn fruit) for a sweeter, slightly stronger flavoured soup. The dish is usually eaten with rice or noodles (sometimes as a noodle soup), and often served with fried dough fritters. Garnish includes chopped coriander or green onions and a sprinkling of fried shallots. A variation of bak kut `{{not a typo|teh}}`{=mediawiki} uses chicken instead of pork, which then becomes chik kut teh. Bak kut `{{not a typo|teh}}`{=mediawiki} is particularly popular in Southeast Asian countries such as Singapore and Malaysia.
Braised varieties Teochew cuisine is noted for its variety of braised dishes, which includes geese, duck, pork, bean curd and offal.
Chai tau kueh A savoury fried cake, made of white radish and rice flour. It is commonly stir-fried with soy sauce, eggs, garlic, spring onion and occasionally dried shrimp.
Chwee kueh Cup-shaped steamed rice cakes topped with chopped preserved/salted radish.
Crystal balls A steamed dessert with a variety of fillings such as yellow milk (`{{zh|s=奶黄|t=奶黃|p=nǎihuáng|labels=no}}`{=mediawiki}; *ni ng*, ni7 ng5), yam paste (`{{zh|c=芋泥|p=yùní|labels=no}}`{=mediawiki}; *or ni*, ou7 ni5) or bean paste made from mung beans or azuki beans (red beans). They are similar to mochi.
Deep-Fried tofu A simple deep fried tofu dish, and was later adopted by Guangzhou\'s residents. First, deep-fry slices of fresh firm tofu until they are golden, and then serve with salted water dip (ingredients are boiling water, salt, and chopped Chinese chives). In modern times, some Teochew people now use the air fryer to prepare them for convenience and reduction of the amount of fat and calories in the food.
Fish balls / fishcakes / fish dumplings (*her ee*) / *he7 guê2* (*her kueh*) / *he7 gieu2* (*her kiaw*) This fish paste made into balls, cakes and dumplings can be cooked in many ways but are often served in Teochew-style noodle and soups.
Fish ball noodle soup (*her ee mee*) Any of several kinds of egg and rice noodles may be served either in a light fish-flavoured broth or dry, along with fishballs, fishcakes, beansprouts and lettuce.
Flavored-potted goose A well-known braised goose dish, often accompanised by tofu.
Fried beef balls (*za ghu bak ee*) A simple deep-fired beef ball dish serves with dipping sauce such as shacha sauce or salted water dip (ingredients are boiling water, salt, and chopped Chinese chives). In modern times, some Teochew people now use the air fryer to prepare them for convenience and reduction of the amount of fat and calories in the food.
Fun guo A type of steamed dumplings. This is usually filled with dried radish, garlic chives, ground pork, dried shrimp, shiitake mushrooms and peanuts. The dumpling wrapper is made from a mixture of flour or plant starches mixed together with water. In Cantonese, these are called *chiu chow fun guo* (`{{zh|c=潮州粉果|p=Cháozhōu fěnguǒ|labels=no}}`{=mediawiki}), in which the Chinese character *粿* is replaced by *果*.
Head of mustard greens with mushrooms A dish of *Brassica juncea* (Chinese mustard) and shiitake (Chinese black mushrooms) in a soup. Originally a vegetarian soup, it often added with diced pork belly and other ingredients.
Kway chap (*kueh chap*) A dish of flat, broad rice sheets in a soup made from dark soy sauce served with pig offal, braised duck meat, various kinds of bean curd, preserved salted vegetables and braised hard-boiled eggs.
Marinating pork head / Braised pig head Clean and braise pork head in soy sauce and rock sugar. Cilantro, garlic, ginger, chilies, star anise and other spices may also added.
Mee pok (*mee pok*) A popular noodle dish served with minced pork, braised mushrooms, fishballs, dumplings, sauce and other garnish.
Oolong tea (*Ou-leeng `{{not a typo|teh}}`{=mediawiki}*) Tieguanyin is one of the most popular Teochew teas. However, the Teochew people prefer their own brand of Oolong tea, which is the *hong wang dan cong teh* (`{{zh|s=凤凰单丛茶|t=鳳凰單丛茶|p=fènghuáng dāncóng chá|labels=no}}`{=mediawiki}).
Oyster omelette (*or lua*) A dish of omelette cooked with fresh raw oysters, tapioca starch and eggs. Teochew-style oyster omelette is usually deep fried and very crisp. Dip condiments are fish sauce and pepper or chili sauce.
Pan-fried marinated fish A pan-fried dish of marinated fish, typically using Larimichthys crocea as the main ingredient but can use other alternatives such as a white croaker, Japanese sea bass or other types of bass, or tilefish.
Patriotic soup (Protect the Country Dish) Developed during the Mongol conquest of the Song dynasty and named by Song\'s last emperor Zhao Bing. A simple soup boiled with stir-fried leaf vegetable (commonly sweet potato leaves since the Ming dynasty but also can use amaranth, spinach, Ipomoea aquatica or other leafy greens as alternatives) and edible mushrooms (preferably straw mushrooms) and broth (vegetable, chicken, or beef).
Pig\'s organ soup (Pork offal soup) (*ter zap terng*)
Popiah (薄饼) (*po piah*) A fresh (non-fried) spring roll usually eaten during the Qingming Festival. The skin is a soft, thin paper-like crepe made from wheat flour. The filling is mainly finely grated and steamed or stir-fried turnip, yam bean (jicama), which has been cooked with a combination of other ingredients such as bean sprouts, French beans, and lettuce leaves, depending on the individual vendor, along with grated carrots, slices of Chinese sausage, thinly sliced fried tofu, chopped peanuts or peanut powder, fried shallots and shredded omelette. Other common variations of popiah include pork (lightly seasoned and stir-fried), shrimp or crab meat. It is eaten in accompaniment with a sweet sauce (often a bean sauce, a blended soy sauce or hoisin sauce or a shrimp paste sauce).
Pork jelly (*ter ka dang*) Braised pig\'s leg made into jelly form, sliced and served cold.
Prawns sautéed with olive vegetables A dish of deep-fried prawns
Raw Pickled Seafood There are various kinds of Chaoshan fresh seafoods pickles, such as raw pickled crab, raw pickled blood clams, raw pickled shrimp, raw pickled prawns, raw pickled mantis shrimp. Seafoods are steeped in a pickling bath made of vinegar, salt, soy sauce, wine, cilantro, garlic, ginger, chilies and other spices.
Red peach cake (*ang tao kueh*, *ung toh kway*) Pink hue rice flour skin wrapped with flavorful glutinous rice. Pressed on a nicely designed peach shaped wooden mould, and then steam the dumpling to perfection. You can eat it freshly steamed, or pan-fried.
Salted vegetable duck soup (*kiam cai ak terng*) A soup boiled with duck, preserved salted vegetable, tomatoes and preserved sour plum.
Scalding (hot water dipping) blood clams Wash the blood clams and then soak them in cold salted water to let them release sands inside their body. Boil a pot of water, add some coriander, carefully pour the blood clams into the boiling water, dip them in hot water for 10 seconds and they are ready to eat.
Sichuan pepper chicken A traditionally deep-fried chicken dish, usually accompanied with leafy green from *Lysimachia clethroides*, known as pearl vegetable (*珍珠菜*). However, *Lysimachia clethroides*\'s leaves are unavailable to use in culinary outside of China, but basil, spinach, or other leafy green vegetables can be substitutes to them in preparation of the dish.
Sliced Cuttlefish on Ice with Wasabi Sauce Clean the cuttlefish, remove the skin, internal organs and head and boil it in 80^o^C salty water for 10 minutes. Soak it in ice water for 5 minutes after cook. Pat dry with kitchen towel and slice it. Place the slices on top of a dish with a thick layer of ice. When eating, pick up the cuttlefish slices with chopsticks and dip them in mustard and soy sauce.
Spring rolls with prawn or minced meat fillings (heh gerng) / *siê1 geng2*, *sio1 geng2* (sio gerng) / *ngou6 hiang1* (ngo hiang) Mixed pork and prawn paste (sometimes fish), seasoned with five-spice powder, wrapped and rolled in a bean curd skin and deep-fried or pan-fried. It is sometimes referred to as Teochew-style spring roll in restaurant menus.
Steamed chives dumplings They are sometimes sautéed to give them a crispy texture.
Steamed goose
Taro paste (orh ni / orh nee) A traditional Teochew dessert made primarily from taro. The taro is steamed and then mashed into a thick paste, which forms the base of the dessert. Pumpkin is also added for sweetness and to create a smoother consistency. Lard or fried onion oil is then added for fragrance. The dessert is traditionally sweetened with water chestnut syrup, and served with ginkgo nuts. Modern versions of the dessert include the addition of coconut cream and sweet corn. The dessert is commonly served at traditional Teochew wedding banquet dinners as the last course, marking the end of the banquet.
Teochew chicken *Cháozhōu jī* *dio7/diê7 ziu1 goi1* (Teochew koi) A dish of sliced chicken
Teochew cold crab (Teochew ngang hoi) The whole crab is first steamed then served chilled. The species of crab most commonly used is *Charybdis cruciata*.
Teochew cold fish (Teochew he bung) Steam fish with ginger slices, let it cool down to room temperature, then remove the ginger slices and keep it in refrigerator for at least 2 hours.
Teochew hot pot / Teochew steamboat (Teochew zuang lou) A dish where fresh, thinly sliced ingredients are placed into a simmering flavourful broth to cook and then dipped into various mixed sauces, usually with Shacha and soy sauce as its main components. Ingredients often include leafy vegetables, yam, tofu, pomfret and other seafood, beef balls, fish balls, pork balls, mushrooms and Chinese noodles, among others. Teochew hot pot, like other Chinese hot pots, is served in a large communal metal pot at the center of the dining table.
Teochew Oyster Congee Teochew congee with oysters and minced pork
Teochew rice noodle soup (Teochew kuay teow) A quintessential Teochew-style noodle soup that is also particularly popular in Vietnam and Cambodia (known respectively as *hủ tiếu /hủ tíu * and គុយទាវ *kuyteav*), through the influx of Teochew immigrants. It is a dish of yellow egg noodles and thin rice noodles served in a delicate, fragrant soup with meatballs, other various meats, seafood (such as shrimp), fried fishcake slices, quail eggs, blanched Chinese cabbage and sometimes offal. The soup base is typically made of pork or chicken bones and dried squid. Just before serving, the noodle soup is garnished with fried minced garlic, fried shallots, thinly sliced scallions and fresh cilantro (coriander) sprigs. For those who enjoy their noodle soup with added depth, the solid ingredients may be dipped into Shacha sauce or Teochew chilli oil.
Teochew-style congee (Teochew mue) A rice soup that has a more watery texture as compared to the Cantonese congee. It is commonly served with various salty accompaniments such as salted vegetables (*kiam chai*), preserved radish (*chai por*), black Chinese olives (*烏橄欖*), olive grits (*橄欖糝*), boiled salted duck eggs, fried salted fish and fried peanuts.
Teochew-style steamed pomfret (Teochew chue chioh her) Silvery pomfret steamed with preserved salted vegetables, lard and sour plums.
Yusheng (her sae) A raw fish salad (similar to ceviche or sashimi) whose typical ingredients include fresh salmon, white radish, carrot, red pepper (capsicum), ginger, kaffir lime leaves, Chinese parsley, chopped peanuts, toasted sesame seeds, Chinese shrimp crackers or fried dried shrimp, and five-spice powder, with the dressing primarily made from plum sauce. It is customarily served as an appetiser to bring good luck for the new year and is usually eaten on the seventh day of the Lunar New Year.
## Gallery
<File:HK> Wan Chai 春園街 Spring Garden Lane night Chiu Chow food shop window.jpg\|\"Flavor potted\" goose (*滷水鵝*) <File:Teochew> Sweet Yam Paste - After Stirring.jpg\|Taro paste (*芋泥*) <File:Shui> jing bao zz.JPG\|Crystal balls (*水晶包*) <File:Teochew> pomfret.jpg\|Steamed fish (*炊魚*) <File:Oyster> omelette.jpg\|Oyster omelette (*蚝烙*) <File:Khanom> kuichai.jpg\|Fried chive dumplings (*韭菜粿*) <File:Song> dynasty\'s \'patriotic soup\' (prepared in Clovis California) 宋朝的"護國菜"（在加利福尼亞克洛維斯市製備）。.jpg\|Patriotic Soup (Protect the Country Dish (*護國菜*)) <File:Fried> Tofu (炸豆腐).jpg\|A dish of fried tofu (*炸豆腐*) with dipping sauce. <File:Teochew> rice noodle soup (潮州粿條).jpg\|Teochew rice noodle soup (*潮州粿條*). <File:Sautéed> Prawns with Olive Vegetables (欖菜焗蝦).jpg\|Sautéed prawns with olive vegetables (*欖菜焗蝦*) . <File:Teochew> Hotpot (prepared in Clovis California) 潮州火鍋（在加利福尼亞克洛維斯市製備）.jpg\|Teochew hotpot (*潮州火鍋*) <File:Sichuan> pepper chicken - air-fried version (川椒雞 - 氣炸版).jpg\|Sichuan pepper chicken (*川椒雞*) <File:Mixed> Bak Kut Teh - Teochew Bak Kut Teh (4590434658).jpg\|Bak Kut Teh (肉骨茶)
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Co-NP
|
In computational complexity theory, **co-NP** is a complexity class. A decision problem X is a member of co-NP if and only if its complement `{{overline|X}}`{=mediawiki} is in the complexity class NP. The class can be defined as follows: a decision problem is in co-NP if and only if for every *no*-instance we have a polynomial-length \"certificate\" and there is a polynomial-time algorithm that can be used to verify any purported certificate.
That is, **co-NP** is the set of decision problems where there exists a polynomial `{{tmath|p(n)}}`{=mediawiki} and a polynomial-time bounded Turing machine *M* such that for every instance *x*, *x* is a *no*-instance if and only if: for some possible certificate *c* of length bounded by `{{tmath|p(n)}}`{=mediawiki}, the Turing machine *M* accepts the pair `{{math|(''x'', ''c'')}}`{=mediawiki}.
## Complementary problems {#complementary_problems}
While an NP problem asks whether a given instance is a *yes*-instance, its *complement* asks whether an instance is a *no*-instance, which means the complement is in co-NP. Any *yes*-instance for the original NP problem becomes a *no*-instance for its complement, and vice versa.
### Unsatisfiability
An example of an NP-complete problem is the Boolean satisfiability problem: given a Boolean formula, is it *satisfiable* (is there a possible input for which the formula outputs true)? The complementary problem asks: \"given a Boolean formula, is it *unsatisfiable* (do all possible inputs to the formula output false)?\". Since this is the *complement* of the satisfiability problem, a certificate for a *no*-instance is the same as for a *yes*-instance from the original NP problem: a set of Boolean variable assignments which make the formula true. On the other hand, a certificate of a *yes*-instance for the complementary problem (whatever form it might take) would be equally as complex as for the *no*-instance of the original NP satisfiability problem.
## co-NP-completeness {#co_np_completeness}
A problem *L* is co-NP-complete if and only if *L* is in co-NP and for any problem in co-NP, there exists a polynomial-time reduction from that problem to *L*.
### Tautology reduction {#tautology_reduction}
Determining if a formula in propositional logic is a tautology is co-NP-complete: that is, if the formula evaluates to true under every possible assignment to its variables.
## Relationship to other classes {#relationship_to_other_classes}
P, the class of polynomial time solvable problems, is a subset of both NP and co-NP. P is thought to be a strict subset in both cases. Because P is closed under complementation, and NP and co-NP are complementary, it cannot be strict in one case and not strict in the other: if P equals NP, it must also equal co-NP, and vice versa.
NP and co-NP are also thought to be unequal, and their equality would imply the collapse of the polynomial hierarchy PH to NP. If they are unequal, then no NP-complete problem can be in co-NP and no co-NP-complete problem can be in NP. This can be shown as follows. Suppose for the sake of contradiction there exists an NP-complete problem `{{mathcal|X}}`{=mediawiki} that is in co-NP. Since all problems in NP can be reduced to `{{mathcal|X}}`{=mediawiki}, it follows that for every problem in NP, we can construct a non-deterministic Turing machine that decides its complement in polynomial time; i.e., `{{tmath|\textsf{NP} \subseteq \textsf{co-NP} }}`{=mediawiki}. From this, it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co-NP; i.e., `{{tmath|\textsf{co-NP} \subseteq \textsf{NP} }}`{=mediawiki}. Thus `{{tmath|1=\textsf{co-NP} = \textsf{NP} }}`{=mediawiki}. The proof that no co-NP-complete problem can be in NP if `{{tmath|\textsf{NP} \neq \textsf{co-NP} }}`{=mediawiki} is symmetrical.
co-NP is a subset of PH, which itself is a subset of PSPACE.
### Integer factorization {#integer_factorization}
An example of a problem that is known to belong to both NP and co-NP (but not known to be in P) is Integer factorization: given positive integers *m* and *n*, determine if *m* has a factor less than *n* and greater than one. Membership in NP is clear; if *m* does have such a factor, then the factor itself is a certificate. Membership in co-NP is also straightforward: one can just list the prime factors of *m*, all greater or equal to *n*, which the verifier can confirm to be valid by multiplication and the AKS primality test. It is presently not known whether there is a polynomial-time algorithm for factorization, equivalently that integer factorization is in P, and hence this example is interesting as one of the most natural problems known to be in NP and co-NP but not known to be in P.
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6,193 |
Constantin von Tischendorf
|
*Pandoc failed*: ```
Error at (line 262, column 1):
unexpected end of input
expecting white space
```
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6,199 |
Convention on Fishing and Conservation of the Living Resources of the High Seas
|
The **Convention on Fishing and Conservation of Living Resources of the High Seas** is an agreement that was designed to solve through international cooperation the problems involved in the conservation of living resources of the high seas, considering that because of the development of modern technology some of these resources are in danger of being overexploited. The convention opened for signature on 29 April 1958 and entered into force on 20 March 1966.
## Participation
*Parties* -- (39): Australia, Belgium, Bosnia and Herzegovina, Burkina Faso, Cambodia, Colombia, Republic of the Congo, Denmark, Dominican Republic, Fiji, Finland, France, Haiti, Jamaica, Kenya, Lesotho, Madagascar, Malawi, Malaysia, Mauritius, Mexico, Montenegro, Netherlands, Nigeria, Portugal, Senegal, Serbia, Sierra Leone, Solomon Islands, South Africa, Spain, Switzerland, Thailand, Tonga, Trinidad and Tobago, Uganda, United Kingdom, United States, Venezuela.
*Countries that have signed, but not yet ratified* -- (21): Afghanistan, Argentina, Bolivia, Canada, Costa Rica, Cuba, Ghana, Iceland, Indonesia, Iran, Ireland, Israel, Lebanon, Liberia, Nepal, New Zealand, Pakistan, Panama, Sri Lanka, Tunisia, Uruguay.
| 2025-06-20T00:00:00 |
6,200 |
Convention on Long-Range Transboundary Air Pollution
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`{{Pollution sidebar}}`{=mediawiki}
The **Convention on Long-Range Transboundary Air Pollution**, often abbreviated as **Air Convention** or **CLRTAP**, is intended to protect the human environment against air pollution and to gradually reduce and prevent air pollution, including long-range transboundary air pollution. It is implemented by the European Monitoring and Evaluation Programme (EMEP), directed by the United Nations Economic Commission for Europe (UNECE).
The convention opened for signature on `{{Format date|1979|Nov|13}}`{=mediawiki}, and entered into force on `{{Format date|1983|3|16}}`{=mediawiki}.
## Secretariat
The Convention, which now has 51 Parties, identifies the Executive Secretary of the United Nations Economic Commission for Europe (UNECE) as its secretariat. The current parties to the Convention are shown on the map.
The Convention is implemented by the European Monitoring and Evaluation Programme (EMEP) (short for *Co-operative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe*). Results of the EMEP programme are published on the EMEP website, [www.emep.int](http://www.emep.int/).
## Procedure
The aim of the Convention is that Parties shall endeavour to limit and, as far as possible, gradually reduce and prevent air pollution including long-range transboundary air pollution. Parties develop policies and strategies to combat the discharge of air pollutants through exchanges of information, consultation, research and monitoring.
The Parties meet annually at sessions of the Executive Body to review ongoing work and plan future activities including a workplan for the coming year. The three main subsidiary bodies -- the Working Group on Effects, the Steering Body to EMEP and the Working Group on Strategies and Review -- as well as the Convention\'s Implementation Committee, report to the Executive Body each year.
Currently, the Convention\'s priority activities include review and possible revision of its most recent protocols, implementation of the Convention and its protocols across the entire UNECE region (with special focus on Eastern Europe, the Caucasus and Central Asia and South-East Europe) and sharing its knowledge and information with other regions of the world.
## Protocols
Since 1979 the Convention on Long-range Transboundary Air Pollution has addressed some of the major environmental problems of the UNECE region through scientific collaboration and policy negotiation. The Convention has been extended by eight protocols that identify specific measures to be taken by Parties to cut their emissions of air pollutants:
- Protocol on Long-Term Financing of the Cooperative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe (EMEP) (1984)
- 1985 Helsinki Protocol on the Reduction of Sulphur Emissions
- Nitrogen Oxide Protocol (1988)
- Volatile Organic Compounds Protocol (1991)
- 1994 Oslo Protocol on Further Reduction of Sulphur Emissions
- Protocol on Heavy Metals (1998)
- Aarhus Protocol on Persistent Organic Pollutants (1998)
- 1999 Gothenburg Protocol to Abate Acidification, Eutrophication and Ground-level Ozone (1999)
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6,203 |
Environmental Modification Convention
|
The **Environmental Modification Convention** (**ENMOD**), formally the **Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques**, is an international treaty prohibiting the military or other hostile use of environmental modification techniques having widespread, long-lasting or severe effects. It opened for signature on 18 May 1977 in Geneva and entered into force on 5 October 1978.
The Convention bans weather warfare, which is the use of weather modification techniques for the purposes of inducing damage or destruction. The Convention on Biological Diversity of 2010 would also ban some forms of weather modification or geoengineering.
Many states do not regard this as a complete ban on the use of herbicides in warfare, such as Agent Orange, but it does require case-by-case consideration.
## Parties
The convention was signed by 48 states; 16 of the signatories have not ratified. As of 2022 the convention has 78 state parties.
## History
The problem of artificial modification of the environment for military or other hostile purposes was brought to the international agenda in the early 1970s. Following the US decision of July 1972 to renounce the use of climate modification techniques for hostile purposes, the 1973 resolution by the US Senate calling for an international agreement \"prohibiting the use of any environmental or geophysical modification activity as a weapon of war\", and an in-depth review by the Department of Defense of the military aspects of weather and other environmental modification techniques, US decided to seek agreement with the Soviet Union to explore the possibilities of an international agreement.
In July 1974, US and USSR agreed to hold bilateral discussions on measures to overcome the danger of the use of environmental modification techniques for military purposes and three subsequent rounds of discussions in 1974 and 1975. In August 1975, US and USSR tabled identical draft texts of a convention at the Conference of the Committee on Disarmament (CCD), Conference on Disarmament, where intensive negotiations resulted in a modified text and understandings regarding four articles of this Convention in 1976.
The convention was approved by Resolution 31/72 of the General Assembly of the United Nations on 10 December 1976, by 96 to 8 votes with 30 abstentions.
## Environmental Modification Technique {#environmental_modification_technique}
Environmental Modification Technique includes any technique for changing -- through the deliberate manipulation of natural processes -- the dynamics, composition or structure of the earth, including its biota, lithosphere, hydrosphere and atmosphere, or of outer space.
## Structure of ENMOD {#structure_of_enmod}
The Convention contains ten articles and one Annex on the Consultative Committee of Experts. Integral part of the convention are also the Understandings relating to articles I, II, III and VIII. These Understandings are not incorporated into the convention but are part of the negotiating record and were included in the report transmitted by the Conference of the Committee on Disarmament to the United Nations General Assembly in September 1976 Report of the Conference of the Committee on Disarmament, Volume I, General Assembly Official records: Thirty-first session, Supplement No. 27 (A/31/27), New York, United Nations, 1976, pp. 91--92.
## Anthropogenic climate change {#anthropogenic_climate_change}
ENMOD treaty members are responsible for 83% of carbon dioxide emissions since the treaty entered into force in 1978. The ENMOD treaty could potentially be used by ENMOD member states seeking climate-change loss and damage compensation from other ENMOD member states at the International Court of Justice. With the knowledge that carbon dioxide emissions can enhance extreme weather events, the continued unmitigated greenhouse gas emissions from some ENMOD member states could be viewed as 'reckless' in the context of deliberately declining emissions from other ENMOD member states. It is unclear whether the International Court of Justice will consider the ENMOD treaty when it issues a legal opinion on international climate change obligations requested by the United Nations General Assembly on 29 March 2023.
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Charles Ancillon
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**Charles Ancillon** (28 July 1659`{{snd}}`{=mediawiki}5 July 1715) was a French jurist and diplomat.
## Life
Ancillon was born in Metz into a distinguished family of Huguenots. His father, David Ancillon (1617--1692), was obliged to leave France on the revocation of the Edict of Nantes, and became pastor of the French Protestant community in Berlin.
Ancillon studied law at Marburg, Geneva and Paris, where he was called to the bar. At the request of the Huguenots at Metz, he pleaded its cause at the court of King Louis XIV, urging that it should be excepted in the revocation of the Edict of Nantes, but his efforts were unsuccessful, and he joined his father in Berlin. He was at once appointed by Elector Frederick III \"*juge et directeur de colonie de Berlin*.\" He also became the first headmaster of Französisches Gymnasium Berlin. Before this, he had published several works on the revocation of the Edict of Nantes and its consequences, but his literary capacity was mediocre, his style stiff and cold, and it was his personal character rather than his reputation as a writer that earned him the confidence of the elector.
In 1687 Ancillon was appointed head of the so-called *Academie des nobles,* the principal educational establishment of the state; later on, as councillor of embassy, he took part in the negotiations which led to the assumption of the title of \"King in Prussia\" by the elector. In 1699 he succeeded Samuel Pufendorf as historiographer to the elector, and the same year replaced his uncle Joseph Ancillon as judge of all the French refugees in the Margraviate of Brandenburg.
Ancillon is mainly remembered for what he did for education in Brandenburg-Prussia, and the share he took, in co-operation with Gottfried Leibniz, in founding the Academy of Berlin. Of his fairly numerous works the most valued is the \"*Histoire de l\'etablissement des Francais refugies dans les etats de Brandebourg*\" published in Berlin in 1690.
## Family
- Friedrich Ancillon, his grandson, a Prussian historian and statesman
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Context-sensitive grammar
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A **context-sensitive grammar** (**CSG**) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSGs are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.
A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equivalent), but it does make a difference in terms of what grammars are structurally considered context-sensitive; the latter issue was analyzed by Chomsky in 1963.
Chomsky introduced context-sensitive grammars as a way to describe the syntax of natural language where it is often the case that a word may or may not be appropriate in a certain place depending on the context. Walter Savitch has criticized the terminology \"context-sensitive\" as misleading and proposed \"non-erasing\" as better explaining the distinction between a CSG and an unrestricted grammar.
Although it is well known that certain features of languages (e.g. cross-serial dependency) are not context-free, it is an open question how much of CSGs\' expressive power is needed to capture the context sensitivity found in natural languages. Subsequent research in this area has focused on the more computationally tractable mildly context-sensitive languages. The syntaxes of some visual programming languages can be described by context-sensitive graph grammars.
## Formal definition {#formal_definition}
### Formal grammar {#formal_grammar}
Let us notate a formal grammar as $G = (N, \Sigma, P, S)$, with $N$ a set of nonterminal symbols, $\Sigma$ a set of terminal symbols, $P$ a set of production rules, and $S \in N$ the start symbol.
A string $u \in (N \cup \Sigma)^*$ *directly yields*, or *directly derives to*, a string $v \in (N \cup \Sigma)^*$, denoted as $u \Rightarrow v$, if *v* can be obtained from *u* by an application of some production rule in *P*, that is, if $u = \gamma L \delta$ and $v = \gamma R \delta$, where $(L \to R) \in P$ is a production rule, and $\gamma, \delta \in (N \cup \Sigma)^*$ is the unaffected left and right part of the string, respectively. More generally, *u* is said to *yield*, or *derive to*, *v*, denoted as $u \Rightarrow^* v$, if *v* can be obtained from *u* by repeated application of production rules, that is, if $u = u_0 \Rightarrow ... \Rightarrow u_n = v$ for some *n* ≥ 0 and some strings $u_1, ..., u_{n-1} \in (N \cup \Sigma)^*$. In other words, the relation $\Rightarrow^*$ is the reflexive transitive closure of the relation $\Rightarrow$.
The **language** of the grammar *G* is the set of all terminal-symbol strings derivable from its start symbol, formally: $L(G) = \{ w \in \Sigma^* \mid S \Rightarrow^* w \}$. Derivations that do not end in a string composed of terminal symbols only are possible, but do not contribute to *L*(*G*).
### Context-sensitive grammar {#context_sensitive_grammar}
A formal grammar is **context-sensitive** if each rule in *P* is either of the form $S \to \varepsilon$ where $\varepsilon$ is the empty string, or of the form
: α*A*β → αγβ
with *A* ∈ *N*, $\alpha, \beta\in (N \cup \Sigma \setminus\{S\})^*$, and $\gamma\in (N \cup \Sigma \setminus\{S\})^+$.
The name *context-sensitive* is explained by the α and β that form the context of *A* and determine whether *A* can be replaced with γ or not. By contrast, in a context-free grammar, no context is present: the left hand side of every production rule is just a nonterminal.
The string γ is not allowed to be empty. Without this restriction, the resulting grammars become equal in power to unrestricted grammars.
### (Weakly) equivalent definitions {#weakly_equivalent_definitions}
A noncontracting grammar is a grammar in which for any production rule, of the form *u* → *v*, the length of *u* is less than or equal to the length of *v*.
Every context-sensitive grammar is noncontracting, while every noncontracting grammar can be converted into an equivalent context-sensitive grammar; the two classes are weakly equivalent.
Some authors use the term *context-sensitive grammar* to refer to noncontracting grammars in general.
The **left-context**- and **right-context**-sensitive grammars are defined by restricting the rules to just the form α*A* → αγ and to just *A*β → γβ, respectively. The languages generated by these grammars are also the full class of context-sensitive languages. The equivalence was established by Penttonen normal form.
## Examples
### *a^n^b^n^c^n^*
The following context-sensitive grammar, with start symbol *S*, generates the canonical non-context-free language { *a^n^b^n^c^n^* \| *n* ≥ 1 } :
----------- ----- --------- ------- ----- ----- -----
1\. *S* → *a* *B* *C*
2\. *S* → *a* *S* *B*
3\. *C* *B* → *C* *Z*
4\. *C* *Z* → *W* *Z*
5\. *W* *Z* → *W* *C*
6\. *W* *C* → *B* *C*
7\. *a* *B* → *a* *b*
8\. *b* *B* → *b* *b*
9\. *b* *C* → *b* *c*
10\. *c* *C* → *c* *c*
----------- ----- --------- ------- ----- ----- -----
Rules 1 and 2 allow for blowing-up *S* to *a*^*n*^*BC*(*BC*)^*n*−1^; rules 3 to 6 allow for successively exchanging each *CB* to *BC* (four rules are needed for that since a rule *CB* → *BC* wouldn\'t fit into the scheme α*A*β → αγβ); rules 7--10 allow replacing a non-terminal *B* or *C* with its corresponding terminal *b* or *c*, respectively, provided it is in the right place. A generation chain for *`{{not a typo|aaabbbccc}}`{=mediawiki}* is:
: *S*
: →~2~ `{{not a typo|'''aSBC'''}}`{=mediawiki}
: →~2~ `{{not a typo|''a'''aSBC'''BC''}}`{=mediawiki}
: →~1~ `{{not a typo|''aa'''aBC'''BCBC''}}`{=mediawiki}
: →~3~ `{{not a typo|''aaaB'''CZ'''CBC''}}`{=mediawiki}
: →~4~ `{{not a typo|''aaaB'''WZ'''CBC''}}`{=mediawiki}
: →~5~ `{{not a typo|''aaaB'''WC'''CBC''}}`{=mediawiki}
: →~6~ `{{not a typo|''aaaB'''BC'''CBC''}}`{=mediawiki}
: →~3~ `{{not a typo|''aaaBBC'''CZ'''C''}}`{=mediawiki}
: →~4~ `{{not a typo|''aaaBBC'''WZ'''C''}}`{=mediawiki}
: →~5~ `{{not a typo|''aaaBBC'''WC'''C''}}`{=mediawiki}
: →~6~ `{{not a typo|''aaaBBC'''BC'''C''}}`{=mediawiki}
: →~3~ `{{not a typo|''aaaBB'''CZ'''CC''}}`{=mediawiki}
: →~4~ `{{not a typo|''aaaBB'''WZ'''CC''}}`{=mediawiki}
: →~5~ `{{not a typo|''aaaBB'''WC'''CC''}}`{=mediawiki}
: →~6~ `{{not a typo|''aaaBB'''BC'''CC''}}`{=mediawiki}
: →~7~ `{{not a typo|''aa'''ab'''BBCCC''}}`{=mediawiki}
: →~8~ `{{not a typo|''aaa'''bb'''BCCC''}}`{=mediawiki}
: →~8~ `{{not a typo|''aaab'''bb'''CCC''}}`{=mediawiki}
: →~9~ `{{not a typo|''aaabb'''bc'''CC''}}`{=mediawiki}
: →~10~ `{{not a typo|''aaabbb'''cc'''C''}}`{=mediawiki}
: →~10~ `{{not a typo|''aaabbbc'''cc'''''}}`{=mediawiki}
:
### *a^n^b^n^c^n^d^n^*, etc. {#anbncndn_etc.}
More complicated grammars can be used to parse { *a^n^b^n^c^n^d^n^* \| *n* ≥ 1 }, and other languages with even more letters. Here we show a simpler approach using non-contracting grammars: Start with a kernel of regular productions generating the sentential forms $(ABCD)^{n}abcd$ and then include the non contracting productions $p_{Da} : Da\rightarrow aD$, $p_{Db} : Db\rightarrow bD$, $p_{Dc} : Dc\rightarrow cD$, $p_{Dd} : Dd\rightarrow dd$, $p_{Ca} : Ca\rightarrow aC$, $p_{Cb} : Cb\rightarrow bC$, $p_{Cc} : Cc\rightarrow cc$, $p_{Ba} : Ba\rightarrow aB$, $p_{Bb} : Bb\rightarrow bb$, $p_{Aa} : Aa\rightarrow aa$.
### *a^m^b^n^c^m^d^n^*
A non contracting grammar (for which there is an equivalent CSG) for the language $L_{Cross} = \{ a^mb^nc^{m}d^{n} \mid m \ge 1, n \ge 1 \}$ is defined by
$$p_0 : S \rightarrow RT$$,
$$p_1 : R\rightarrow aRC | aC$$,
$$p_3 : T\rightarrow BTd | Bd$$,
$$p_5 : CB\rightarrow BC$$,
$$p_6 : aB\rightarrow ab$$,
$$p_7 : bB\rightarrow bb$$,
$$p_8 : Cd\rightarrow cd$$, and
$$p_9 : Cc\rightarrow cc$$.
With these definitions, a derivation for $a^3b^2c^3d^2$ is: $S
\Rightarrow_{p_0} RT
\Rightarrow_{p^{2}_{1}p_{2}} a^3C^3T
\Rightarrow_{p_{3}p_{4} } a^3C^3B^2d^2
\Rightarrow_{p^{6}_{5} } a^3B^2C^3d^2
\Rightarrow_{p_{6}p_{7} } a^3b^2C^3d^2
\Rightarrow_{p_{8}p^{2}_{9}} a^3b^2c^3d^2$.
### *a*^2^*i*^^
A noncontracting grammar for the language { *a*^2^*i*^^ \| *i* ≥ 1 } is constructed in Example 9.5 (p. 224) of (Hopcroft, Ullman, 1979):
1. $S\rightarrow [ACaB]$
2. \\begin{cases}
\\ \[Ca\]a\\rightarrow aa\[Ca\] \\\\ \\ \[Ca\]\[aB\]\\rightarrow aa\[CaB\] \\\\ \\ \[ACa\]a\\rightarrow \[Aa\]a\[Ca\] \\\\ \\ \[ACa\]\[aB\]\\rightarrow \[Aa\]a\[CaB\] \\\\ \\ \[ACaB\]\\rightarrow \[Aa\]\[aCB\] \\\\ \\ \[CaB\]\\rightarrow a\[aCB\] \\end{cases}
1. $[aCB]\rightarrow [aDB]$
2. $[aCB]\rightarrow [aE]$
3. \\begin{cases}
\\ a\[Da\]\\rightarrow \[Da\]a \\\\ \\ \[aDB\]\\rightarrow \[DaB\] \\\\ \\ \[Aa\]\[Da\]\\rightarrow \[ADa\]a \\\\ \\ a\[DaB\]\\rightarrow \[Da\]\[aB\] \\\\ \\ \[Aa\]\[DaB\]\\rightarrow \[ADa\]\[aB\] \\end{cases}
1. $[ADa]\rightarrow [ACa]$
2. \\begin{cases}
\\ a\[Ea\]\\rightarrow \[Ea\]a \\\\ \\ \[aE\]\\rightarrow \[Ea\] \\\\ \\ \[Aa\]\[Ea\]\\rightarrow \[AEa\]a \\end{cases}
1. $[AEa]\rightarrow a$
## Kuroda normal form {#kuroda_normal_form}
Every context-sensitive grammar which does not generate the empty string can be transformed into a weakly equivalent one in Kuroda normal form. \"Weakly equivalent\" here means that the two grammars generate the same language. The normal form will not in general be context-sensitive, but will be a noncontracting grammar.
The Kuroda normal form is an actual normal form for non-contracting grammars.
## Properties and uses {#properties_and_uses}
### Equivalence to linear bounded automaton {#equivalence_to_linear_bounded_automaton}
A formal language can be described by a context-sensitive grammar if and only if it is accepted by some linear bounded automaton (LBA). In some textbooks this result is attributed solely to Landweber and Kuroda. Others call it the Myhill--Landweber--Kuroda theorem. (Myhill introduced the concept of deterministic LBA in 1960. Peter S. Landweber published in 1963 that the language accepted by a deterministic LBA is context sensitive. Kuroda introduced the notion of non-deterministic LBA and the equivalence between LBA and CSGs in 1964.)
it is still an open question whether every context-sensitive language can be accepted by a *deterministic* LBA.
### Closure properties {#closure_properties}
Context-sensitive languages are closed under complement. This 1988 result is known as the Immerman--Szelepcsényi theorem. Moreover, they are closed under union, intersection, concatenation, substitution, inverse homomorphism, and Kleene plus.
Every recursively enumerable language *L* can be written as *h*(*L*) for some context-sensitive language *L* and some string homomorphism *h*.
### Computational problems {#computational_problems}
The decision problem that asks whether a certain string *s* belongs to the language of a given context-sensitive grammar *G*, is PSPACE-complete. Moreover, there are context-sensitive grammars whose languages are PSPACE-complete. In other words, there is a context-sensitive grammar *G* such that deciding whether a certain string *s* belongs to the language of *G* is PSPACE-complete (so *G* is fixed and only *s* is part of the input of the problem).
The emptiness problem for context-sensitive grammars (given a context-sensitive grammar *G*, is *L*(*G*)=∅ ?) is undecidable.
### As model of natural languages {#as_model_of_natural_languages}
Savitch has proven the following theoretical result, on which he bases his criticism of CSGs as basis for natural language: for any recursively enumerable set *R*, there exists a context-sensitive language/grammar *G* which can be used as a sort of proxy to test membership in *R* in the following way: given a string *s*, *s* is in *R* if and only if there exists a positive integer *n* for which *sc^n^* is in G, where *c* is an arbitrary symbol not part of *R*.
It has been shown that nearly all natural languages may in general be characterized by context-sensitive grammars, but the whole class of CSGs seems to be much bigger than natural languages. Worse yet, since the aforementioned decision problem for CSGs is PSPACE-complete, that makes them totally unworkable for practical use, as a polynomial-time algorithm for a PSPACE-complete problem would imply P=NP.
It was proven that some natural languages are not context-free, based on identifying so-called cross-serial dependencies and unbounded scrambling phenomena. However this does not necessarily imply that the class of CSGs is necessary to capture \"context sensitivity\" in the colloquial sense of these terms in natural languages. For example, linear context-free rewriting systems (LCFRSs) are strictly weaker than CSGs but can account for the phenomenon of cross-serial dependencies; one can write a LCFRS grammar for {*a^n^b^n^c^n^d^n^* \| *n* ≥ 1} for example.
Ongoing research on computational linguistics has focused on formulating other classes of languages that are \"mildly context-sensitive\" whose decision problems are feasible, such as tree-adjoining grammars, combinatory categorial grammars, coupled context-free languages, and linear context-free rewriting systems. The languages generated by these formalisms properly lie between the context-free and context-sensitive languages.
More recently, the class PTIME has been identified with range concatenation grammars, which are now considered to be the most expressive of the mild-context sensitive language classes.
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Connected space
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In topology and related branches of mathematics, a **connected space** is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that distinguish topological spaces.
A subset of a topological space $X$ is a `{{visible anchor|connected set}}`{=mediawiki} if it is a connected space when viewed as a subspace of $X$.
Some related but stronger conditions are path connected, simply connected, and $n$-connected. Another related notion is locally connected, which neither implies nor follows from connectedness.
## Formal definition {#formal_definition}
A topological space $X$ is said to be `{{visible anchor|disconnected}}`{=mediawiki} if it is the union of two disjoint non-empty open sets. Otherwise, $X$ is said to be connected. A subset of a topological space is said to be connected if it is connected under its subspace topology. Some authors exclude the empty set (with its unique topology) as a connected space, but this article does not follow that practice.
For a topological space $X$ the following conditions are equivalent:
1. $X$ is connected, that is, it cannot be divided into two disjoint non-empty open sets.
2. The only subsets of $X$ which are both open and closed (clopen sets) are $X$ and the empty set.
3. The only subsets of $X$ with empty boundary are $X$ and the empty set.
4. $X$ cannot be written as the union of two non-empty separated sets (sets for which each is disjoint from the other\'s closure).
5. All continuous functions from $X$ to $\{ 0, 1 \}$ are constant, where $\{ 0, 1 \}$ is the two-point space endowed with the discrete topology.
Historically this modern formulation of the notion of connectedness (in terms of no partition of $X$ into two separated sets) first appeared (independently) with N.J. Lennes, Frigyes Riesz, and Felix Hausdorff at the beginning of the 20th century. See `{{harv|Wilder|1978}}`{=mediawiki} for details.
### Connected components {#connected_components}
Given some point $x$ in a topological space $X,$ the union of any collection of connected subsets such that each contains $x$ will once again be a connected subset. The connected component of a point $x$ in $X$ is the union of all connected subsets of $X$ that contain $x;$ it is the unique largest (with respect to $\subseteq$) connected subset of $X$ that contains $x.$ The maximal connected subsets (ordered by inclusion $\subseteq$) of a non-empty topological space are called the connected components of the space. The components of any topological space $X$ form a partition of $X$: they are disjoint, non-empty and their union is the whole space. Every component is a closed subset of the original space. It follows that, in the case where their number is finite, each component is also an open subset. However, if their number is infinite, this might not be the case; for instance, the connected components of the set of the rational numbers are the one-point sets (singletons), which are not open. Proof: Any two distinct rational numbers $q_1<q_2$ are in different components. Take an irrational number $q_1 < r < q_2,$ and then set $A = \{q \in \Q : q < r\}$ and $B = \{q \in \Q : q > r\}.$ Then $(A,B)$ is a separation of $\Q,$ and $q_1 \in A, q_2 \in B$. Thus each component is a one-point set.
Let $\Gamma_x$ be the connected component of $x$ in a topological space $X,$ and $\Gamma_x'$ be the intersection of all clopen sets containing $x$ (called quasi-component of $x$). Then $\Gamma_x \subset \Gamma'_x$ where the equality holds if $X$ is compact Hausdorff or locally connected.
### Disconnected spaces {#disconnected_spaces}
A space in which all components are one-point sets is called `{{visible anchor|totally disconnected}}`{=mediawiki}. Related to this property, a space $X$ is called `{{visible anchor|totally separated}}`{=mediawiki} if, for any two distinct elements $x$ and $y$ of $X$, there exist disjoint open sets $U$ containing $x$ and $V$ containing $y$ such that $X$ is the union of $U$ and $V$. Clearly, any totally separated space is totally disconnected, but the converse does not hold. For example, take two copies of the rational numbers $\Q$, and identify them at every point except zero. The resulting space, with the quotient topology, is totally disconnected. However, by considering the two copies of zero, one sees that the space is not totally separated. In fact, it is not even Hausdorff, and the condition of being totally separated is strictly stronger than the condition of being Hausdorff.
## Examples
- The closed interval $[0, 2)$ in the standard subspace topology is connected; although it can, for example, be written as the union of $[0, 1)$ and $[1, 2),$ the second set is not open in the chosen topology of $[0, 2).$
- The union of $[0, 1)$ and $(1, 2]$ is disconnected; both of these intervals are open in the standard topological space $[0, 1) \cup (1, 2].$
- $(0, 1) \cup \{ 3 \}$ is disconnected.
- A convex subset of $\R^n$ is connected; it is actually simply connected.
- A Euclidean plane excluding the origin, $(0, 0),$ is connected, but is not simply connected. The three-dimensional Euclidean space without the origin is connected, and even simply connected. In contrast, the one-dimensional Euclidean space without the origin is not connected.
- A Euclidean plane with a straight line removed is not connected since it consists of two half-planes.
- $\R$, the space of real numbers with the usual topology, is connected.
- The Sorgenfrey line is disconnected.
- If even a single point is removed from $\mathbb{R}$, the remainder is disconnected. However, if even a countable infinity of points are removed from $\R^n$, where $n \geq 2,$ the remainder is connected. If $n\geq 3$, then $\R^n$ remains simply connected after removal of countably many points.
- Any topological vector space, e.g. any Hilbert space or Banach space, over a connected field (such as $\R$ or $\Complex$), is simply connected.
- Every discrete topological space with at least two elements is disconnected, in fact such a space is totally disconnected. The simplest example is the discrete two-point space.
- On the other hand, a finite set might be connected. For example, the spectrum of a discrete valuation ring consists of two points and is connected. It is an example of a Sierpiński space.
- The Cantor set is totally disconnected; since the set contains uncountably many points, it has uncountably many components.
- If a space $X$ is homotopy equivalent to a connected space, then $X$ is itself connected.
- The topologist\'s sine curve is an example of a set that is connected but is neither path connected nor locally connected.
- The general linear group $\operatorname{GL}(n, \R)$ (that is, the group of $n$-by-$n$ real, invertible matrices) consists of two connected components: the one with matrices of positive determinant and the other of negative determinant. In particular, it is not connected. In contrast, $\operatorname{GL}(n, \Complex)$ is connected. More generally, the set of invertible bounded operators on a complex Hilbert space is connected.
- The spectra of commutative local ring and integral domains are connected. More generally, the following are equivalent
1. The spectrum of a commutative ring $R$ is connected
2. Every finitely generated projective module over $R$ has constant rank.
3. $R$ has no idempotent $\ne 0, 1$ (i.e., $R$ is not a product of two rings in a nontrivial way).
An example of a space that is not connected is a plane with an infinite line deleted from it. Other examples of disconnected spaces (that is, spaces which are not connected) include the plane with an annulus removed, as well as the union of two disjoint closed disks, where all examples of this paragraph bear the subspace topology induced by two-dimensional Euclidean space.
## Path connectedness {#path_connectedness}
A `{{visible anchor|path-connected space}}`{=mediawiki} is a stronger notion of connectedness, requiring the structure of a path. A path from a point $x$ to a point $y$ in a topological space $X$ is a continuous function $f$ from the unit interval $[0,1]$ to $X$ with $f(0)=x$ and $f(1)=y$. A `{{visible anchor|path-component}}`{=mediawiki} of $X$ is an equivalence class of $X$ under the equivalence relation which makes $x$ equivalent to $y$ if and only if there is a path from $x$ to $y$. The space $X$ is said to be path-connected (or pathwise connected or $\mathbf{0}$-connected) if there is exactly one path-component. For non-empty spaces, this is equivalent to the statement that there is a path joining any two points in $X$. Again, many authors exclude the empty space.
Every path-connected space is connected. The converse is not always true: examples of connected spaces that are not path-connected include the extended long line $L^*$ and the topologist\'s sine curve.
Subsets of the real line $\R$ are connected if and only if they are path-connected; these subsets are the intervals and rays of $\R$. Also, open subsets of $\R^n$ or $\C^n$ are connected if and only if they are path-connected. Additionally, connectedness and path-connectedness are the same for finite topological spaces.
## Arc connectedness {#arc_connectedness}
A space $X$ is said to be arc-connected or arcwise connected if any two topologically distinguishable points can be joined by an arc, which is an embedding $f : [0, 1] \to X$. An arc-component of $X$ is a maximal arc-connected subset of $X$; or equivalently an equivalence class of the equivalence relation of whether two points can be joined by an arc or by a path whose points are topologically indistinguishable.
Every Hausdorff space that is path-connected is also arc-connected; more generally this is true for a $\Delta$-Hausdorff space, which is a space where each image of a path is closed. An example of a space which is path-connected but not arc-connected is given by the line with two origins; its two copies of $0$ can be connected by a path but not by an arc.
Intuition for path-connected spaces does not readily transfer to arc-connected spaces. Let $X$ be the line with two origins. The following are facts whose analogues hold for path-connected spaces, but do not hold for arc-connected spaces:
- Continuous image of arc-connected space may not be arc-connected: for example, a quotient map from an arc-connected space to its quotient with countably many (at least 2) topologically distinguishable points cannot be arc-connected due to too small cardinality.
- Arc-components may not be disjoint. For example, $X$ has two overlapping arc-components.
- Arc-connected product space may not be a product of arc-connected spaces. For example, $X \times \mathbb{R}$ is arc-connected, but $X$ is not.
- Arc-components of a product space may not be products of arc-components of the marginal spaces. For example, $X \times \mathbb{R}$ has a single arc-component, but $X$ has two arc-components.
- If arc-connected subsets have a non-empty intersection, then their union may not be arc-connected. For example, the arc-components of $X$ intersect, but their union is not arc-connected.
## Local connectedness {#local_connectedness}
A topological space is said to be locally connected at a point $x$ if every neighbourhood of $x$ contains a connected open neighbourhood. It is locally connected if it has a base of connected sets. It can be shown that a space $X$ is locally connected if and only if every component of every open set of $X$ is open.
Similarly, a topological space is said to be `{{visible anchor|locally path-connected}}`{=mediawiki} if it has a base of path-connected sets. An open subset of a locally path-connected space is connected if and only if it is path-connected. This generalizes the earlier statement about $\R^n$ and $\C^n$, each of which is locally path-connected. More generally, any topological manifold is locally path-connected. Locally connected does not imply connected, nor does locally path-connected imply path connected. A simple example of a locally connected (and locally path-connected) space that is not connected (or path-connected) is the union of two separated intervals in $\R$, such as $(0,1) \cup (2,3)$.
A classic example of a connected space that is not locally connected is the so-called topologist\'s sine curve, defined as $T = \{(0,0)\} \cup \left\{ \left(x, \sin\left(\tfrac{1}{x}\right)\right) : x \in (0, 1] \right\}$, with the Euclidean topology induced by inclusion in $\R^2$.
## Set operations {#set_operations}
The intersection of connected sets is not necessarily connected.
The union of connected sets is not necessarily connected, as can be seen by considering $X=(0,1) \cup (1,2)$.
Each ellipse is a connected set, but the union is not connected, since it can be partitioned into two disjoint open sets $U$ and $V$.
This means that, if the union $X$ is disconnected, then the collection $\{X_i\}$ can be partitioned into two sub-collections, such that the unions of the sub-collections are disjoint and open in $X$ (see picture). This implies that in several cases, a union of connected sets `{{em|is}}`{=mediawiki} necessarily connected. In particular:
1. If the common intersection of all sets is not empty ($\bigcap X_i \neq \emptyset$), then obviously they cannot be partitioned to collections with disjoint unions. Hence the union of connected sets with non-empty intersection is connected.
2. If the intersection of each pair of sets is not empty ($\forall i,j: X_i \cap X_j \neq \emptyset$) then again they cannot be partitioned to collections with disjoint unions, so their union must be connected.
3. If the sets can be ordered as a \"linked chain\", i.e. indexed by integer indices and $\forall i: X_i \cap X_{i+1} \neq \emptyset$, then again their union must be connected.
4. If the sets are pairwise-disjoint and the quotient space $X / \{X_i\}$ is connected, then `{{mvar|X}}`{=mediawiki} must be connected. Otherwise, if $U \cup V$ is a separation of `{{mvar|X}}`{=mediawiki} then $q(U) \cup q(V)$ is a separation of the quotient space (since $q(U), q(V)$ are disjoint and open in the quotient space).
The set difference of connected sets is not necessarily connected. However, if $X \supseteq Y$ and their difference $X \setminus Y$ is disconnected (and thus can be written as a union of two open sets $X_1$ and $X_2$), then the union of $Y$ with each such component is connected (i.e. $Y \cup X_{i}$ is connected for all $i$).
## Theorems
- **Main theorem of connectedness** : Let $X$ and $Y$ be topological spaces and let $f:X\rightarrow Y$ be a continuous function. If $X$ is (path-)connected then the image $f(X)$ is (path-)connected. This result can be considered a generalization of the intermediate value theorem.
- Every path-connected space is connected.
- In a locally path-connected space, every open connected set is path-connected.
- Every locally path-connected space is locally connected.
- A locally path-connected space is path-connected if and only if it is connected.
- The closure of a connected subset is connected. Furthermore, any subset between a connected subset and its closure is connected.
- The connected components are always closed (but in general not open)
- The connected components of a locally connected space are also open.
- The connected components of a space are disjoint unions of the path-connected components (which in general are neither open nor closed).
- Every quotient of a connected (resp. locally connected, path-connected, locally path-connected) space is connected (resp. locally connected, path-connected, locally path-connected).
- Every product of a family of connected (resp. path-connected) spaces is connected (resp. path-connected).
- Every open subset of a locally connected (resp. locally path-connected) space is locally connected (resp. locally path-connected).
- Every manifold is locally path-connected.
- Arc-wise connected space is path connected, but path-wise connected space may not be arc-wise connected
- Continuous image of arc-wise connected set is arc-wise connected.
## Graphs
Graphs have path connected subsets, namely those subsets for which every pair of points has a path of edges joining them. However, it is not always possible to find a topology on the set of points which induces the same connected sets. The 5-cycle graph (and any $n$-cycle with $n>3$ odd) is one such example.
As a consequence, a notion of connectedness can be formulated independently of the topology on a space. To wit, there is a category of connective spaces consisting of sets with collections of connected subsets satisfying connectivity axioms; their morphisms are those functions which map connected sets to connected sets `{{harv|Muscat|Buhagiar|2006}}`{=mediawiki}. Topological spaces and graphs are special cases of connective spaces; indeed, the finite connective spaces are precisely the finite graphs.
However, every graph can be canonically made into a topological space, by treating vertices as points and edges as copies of the unit interval (see topological graph theory#Graphs as topological spaces). Then one can show that the graph is connected (in the graph theoretical sense) if and only if it is connected as a topological space.
## Stronger forms of connectedness {#stronger_forms_of_connectedness}
There are stronger forms of connectedness for topological spaces, for instance:
- If there exist no two disjoint non-empty open sets in a topological space $X$, $X$ must be connected, and thus hyperconnected spaces are also connected.
- Since a simply connected space is, by definition, also required to be path connected, any simply connected space is also connected. If the \"path connectedness\" requirement is dropped from the definition of simple connectivity, a simply connected space does not need to be connected.
- Yet stronger versions of connectivity include the notion of a contractible space. Every contractible space is path connected and thus also connected.
In general, any path connected space must be connected but there exist connected spaces that are not path connected. The deleted comb space furnishes such an example, as does the above-mentioned topologist\'s sine curve.
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Contraction mapping
|
In mathematics, a **contraction mapping**, or **contraction** or **contractor**, on a metric space (*M*, *d*) is a function *f* from *M* to itself, with the property that there is some real number $0 \leq k < 1$ such that for all *x* and *y* in *M*,
$$d(f(x),f(y)) \leq k\,d(x,y).$$ The smallest such value of *k* is called the **Lipschitz constant** of *f*. Contractive maps are sometimes called **Lipschitzian maps**. If the above condition is instead satisfied for *k* ≤ 1, then the mapping is said to be a non-expansive map.
More generally, the idea of a contractive mapping can be defined for maps between metric spaces. Thus, if (*M*, *d*) and (*N*, *d*\') are two metric spaces, then $f:M \rightarrow N$ is a contractive mapping if there is a constant $0 \leq k < 1$ such that
$$d'(f(x),f(y)) \leq k\,d(x,y)$$ for all *x* and *y* in *M*.
Every contraction mapping is Lipschitz continuous and hence uniformly continuous (for a Lipschitz continuous function, the constant *k* is no longer necessarily less than 1).
A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any *x* in *M* the iterated function sequence *x*, *f* (*x*), *f* (*f* (*x*)), *f* (*f* (*f* (*x*))), \... converges to the fixed point. This concept is very useful for iterated function systems where contraction mappings are often used. Banach\'s fixed-point theorem is also applied in proving the existence of solutions of ordinary differential equations, and is used in one proof of the inverse function theorem.
Contraction mappings play an important role in dynamic programming problems.
## Firmly non-expansive mapping {#firmly_non_expansive_mapping}
A non-expansive mapping with $k=1$ can be generalized to a **firmly non-expansive mapping** in a Hilbert space $\mathcal{H}$ if the following holds for all *x* and *y* in $\mathcal{H}$:
$$\|f(x)-f(y) \|^2 \leq \, \langle x-y, f(x) - f(y) \rangle.$$ where
$$d(x,y) = \|x-y\|$$.
This is a special case of $\alpha$ averaged nonexpansive operators with $\alpha = 1/2$. A firmly non-expansive mapping is always non-expansive, via the Cauchy--Schwarz inequality.
The class of firmly non-expansive maps is closed under convex combinations, but not compositions. This class includes proximal mappings of proper, convex, lower-semicontinuous functions, hence it also includes orthogonal projections onto non-empty closed convex sets. The class of firmly nonexpansive operators is equal to the set of resolvents of maximally monotone operators. Surprisingly, while iterating non-expansive maps has no guarantee to find a fixed point (e.g. multiplication by -1), firm non-expansiveness is sufficient to guarantee global convergence to a fixed point, provided a fixed point exists. More precisely, if $\operatorname{Fix}f := \{x \in \mathcal{H} \ | \ f(x) = x\} \neq \varnothing$, then for any initial point $x_0 \in \mathcal{H}$, iterating
$(\forall n \in \mathbb{N})\quad x_{n+1} = f(x_n)$
yields convergence to a fixed point $x_n \to z \in \operatorname{Fix} f$. This convergence might be weak in an infinite-dimensional setting.
## Subcontraction map {#subcontraction_map}
A **subcontraction map** or **subcontractor** is a map *f* on a metric space (*M*, *d*) such that
$$d(f(x), f(y)) \leq d(x,y);$$
$$d(f(f(x)),f(x)) < d(f(x),x) \quad \text{unless} \quad x = f(x).$$
If the image of a subcontractor *f* is compact, then *f* has a fixed point.
## Locally convex spaces {#locally_convex_spaces}
In a locally convex space (*E*, *P*) with topology given by a set *P* of seminorms, one can define for any *p* ∈ *P* a *p*-contraction as a map *f* such that there is some *k*~*p*~ \< 1 such that `{{nowrap|''p''(''f''(''x'') − ''f''(''y''))}}`{=mediawiki} ≤ `{{nowrap|''k<sub>p</sub> p''(''x'' − ''y'')}}`{=mediawiki}. If *f* is a *p*-contraction for all *p* ∈ *P* and (*E*, *P*) is sequentially complete, then *f* has a fixed point, given as limit of any sequence *x*~*n*+1~ = *f*(*x*~*n*~), and if (*E*, *P*) is Hausdorff, then the fixed point is unique.
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Condensation polymer
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In polymer chemistry, **condensation polymers** are any kind of polymers whose process of polymerization involves a condensation reaction (i.e. a small molecule, such as water or methanol, is produced as a byproduct). Natural proteins as well as some common plastics such as nylon and PETE are formed in this way. Condensation polymers are formed by polycondensation, when the polymer is formed by condensation reactions between species of all degrees of polymerization, or by condensative chain polymerization, when the polymer is formed by sequential addition of monomers to an active site in a chain reaction. The main alternative forms of polymerization are chain polymerization and polyaddition, both of which give addition polymers.
Condensation polymerization is a form of step-growth polymerization. Linear polymers are produced from bifunctional monomers, i.e. compounds with two reactive end-groups. Common condensation polymers include polyesters, polyamides such as nylon, polyacetals, and proteins.
## Polyamides
One important class of condensation polymers are polyamides. They arise from the reaction of carboxylic acid and an amine. Examples include nylons and proteins. When prepared from amino-carboxylic acids, e.g. amino acids, the stoichiometry of the polymerization includes co-formation of water:
: n H~2~N-X-CO~2~H → \[HN-X-C(O)\]~n~ + (n-1) H~2~O
When prepared from diamines and dicarboxylic acids, e.g. the production of nylon 66, the polymerization produces two molecules of water per repeat unit:
: n H~2~N-X-NH~2~ + n HO~2~C-Y-CO~2~H → \[HN-X-NHC(O)-Y-C(O)\]~n~ + (2n-1) H~2~O
:
## Polyesters
Another important class of condensation polymers are polyesters. They arise from the reaction of a carboxylic acid and an alcohol. An example is polyethyleneterephthalate, the common plastic PET (recycling #1 in the USA):
: n HO-X-OH + n HO~2~C-Y-CO~2~H → \[O-X-O~2~C-Y-C(O)\]~n~ + (2n-1) H~2~O
## Safety and environmental considerations {#safety_and_environmental_considerations}
Condensation polymers tend to be more biodegradable than addition polymers. The peptide or ester bonds between monomers can be hydrolysed, especially in the presence of catalysts or bacterial enzymes.
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Timeline of computing
|
**Timeline of computing** presents events in the history of computing organized by year and grouped into six topic areas: predictions and concepts, first use and inventions, hardware systems and processors, operating systems, programming languages, and new application areas.
**Detailed computing timelines**: before 1950, 1950--1979, 1980--1989, 1990--1999, 2000--2009, 2010--2019, 2020--present
\_\_TOC\_\_
## Graphical timeline {#graphical_timeline}
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List of cartoonists
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This is a **list of cartoonists**, visual artists who specialize in drawing cartoons. This list includes only notable cartoonists and is not meant to be exhaustive. Note that the word \'cartoon\' only took on its modern sense after its use in Punch magazine in the 1840s - artists working earlier than that are more correctly termed \'caricaturists\',
## Notable cartoonists {#notable_cartoonists}
- Scott Adams, *Dilbert*
- Charles Addams (1938--1988), macabre cartoons featured in *The New Yorker* and elsewhere
- Attila Adorjany
- Sarah Andersen, known for *Sarah\'s Scribbles*
- Barry Appleby
- Dan Piraro
- Sergio Aragonés, known for his contributions to *Mad*
- Graciela Aranis (1908--1996), Chilean painter, cartoonist
- Peter Arno (1904--1968), cartoons featured in *The New Yorker* and elsewhere
- Arotxa (Rodolfo Arotxarena)
- Jim Bamber, cartoonist of *Autosport*, magazine specialising in motor sports
- Edgar Henry Banger
- Carl Barks, inventor of *Duckburg* and many of its characters like *Scrooge McDuck* and *Gladstone Gander*; Fantagraphics Books called him \"the Hans Christian Andersen of comic books.\"
- Sumanta Baruah
- Aminollah Rezaei
- Niko Barun
- Nancy Beiman, \"FurBabies\"
- Darrin Bell, *Candorville* and *Rudy Park*
- Steve Bell, *The Guardian* (UK)
- Stephen Bentley, \"Herb and Jamaal\"
- Jim Benton, known for his cartoons on reddit, GoComics, and Instagram as well as *It\'s Happy Bunny*,*Dear Dumb Diary*,*Franny K Stein*,*Catwad*,*Batman Squad*,*Attack of the Stuff*
- Oscar Berger, *Aesop\'s Foibles (1947)*; active 1920s--1960s
- Mark Beyer, *Amy and Jordan*, *Agony*
- Brumsic Brandon Jr., \"Luther\"; with his daughter Barbara Brandon-Croft, first family of cartoonists (father/daughter) to each be nationally syndicated in the U.S. mainstream press
- Barbara Brandon-Croft, \"Where I\'m Coming From\"; first Black woman cartoonist to be nationally syndicated in the U.S. mainstream press
- Berkeley Breathed, *Bloom County* and *Outland*
- Frédéric-Antonin Breysse
- Ed Brubaker
- Henry Bunbury 18th Century British caricaturist
- Tom Bunk, cartoonist for *Mad*
- Stanley Burnside, *Sideburns*
- Mark Burrier
- John Byrne
- Al Capp, *Li\'l Abner*
- Tom Cheney, staff cartoonist for *The New Yorker*
- Edgar Church
- Chester Commodore, political cartoonist
- George Cruikshank 19th Century British caricaturist
- Isaac Cruikshank 18th Century British caricaturist
- Isaac Robert Cruikshank 19th Century British caricaturist
- Robert Crumb, *Mr. Natural*, *Fritz the Cat*, *Keep on Truckin\'*
- Natalie d\'Arbeloff
- Jack Davis
- Jim Davis, *Garfield*
- Abner Dean
- Arifur Rahman
- Narayan Debnath, Indian cartoonist known for *Handa Bhonda*, *Bantul the Great*, and *Nonte Phonte*
- Richard Decker, *The New Yorker*
- Walt Disney, *Mickey Mouse*, *Donald Duck*
- Ralph Waddell Douglass
- Stan Drake
- George du Maurier, also the author of Trilby
- Robert W. Edgren, American political cartoonist known for his \"Sketches from Death\" from the Spanish--American War
- Will Eisner, *The Spirit*
- Otto Eppers
- Charles Evenden
- Lyonel Feininger, rare fine artist who did strips, *The Kin-der-Kids* and *Wee Willie Winkie\'s World*
- Rod Filbrandt
- David Fletcher
- Ellen Forney
- André François
- André Franquin, *Spirou et Fantasio*, *Gaston Lagaffe*, *Marsupilami*
- Yuliy Abramovich Ganf, Soviet Russian
- Eddie Germano
- Denis Gifford, strips in *Whizzer and Chips*, *Knockout*, *Marvelman*
- Carl Giles
- James Gillray, 18th century British, called \"the father of the political cartoon\".
- John Glashan, *Genius*
- Rube Goldberg, cartoons of complex and convoluted machines doing very simple tasks.
- Larry Gonick, *The Cartoon History of the Universe series, Kokopelli & Company*
- Cleven \"Goodie\" Goudeau, known for his pioneering Afrocentric images on greeting cards
- Jimmy Gownley, *Amelia Rules! series, Simon & Schuster*
- Bud Grace, \"Ernie/Piranha Club\"
- Mel Graff, "The Adventures of Patsy", "Secret Agent X-9"
- Matt Groening, *Life in Hell*, *The Simpsons*, *Futurama*
- Sam Gross, for his *The New Yorker* work, plus many other magazines
- Shekhar Gurera, well known for his quirky cartoons about India\'s political and social trends
- William Haefeli
- Martin Handford, *Where\'s Wally?*
- Steven Harris
- Butch Hartman, *The Fairly OddParents*, *T.U.F.F. Puppy*, *Danny Phantom*, *Bunsen Is a Beast*
- Andrew Kennaway Henderson
- Henfil, Brazilian cartoonist
- Hergé, *The Adventures of Tintin*
- George Herriman, *Krazy Kat*
- Herblock American cartoonist
- Watson Heston
- Stephen Hillenburg (1961--2018), *SpongeBob SquarePants*
- Bill Hinds, \"Tank McNamara\"
- Dick Hodgins, Jr.
- William Hogarth, English pictorial satirist and editorial cartoonist; credited with pioneering western sequential art; work ranged from realistic portraiture to comic strip
- Bill Holbrook, *On the Fastrack*, *Safe Havens*, and *Kevin and Kell*
- Nicole Hollander, *Sylvia*
- John Holmstrom
- Geoff \"Jeff\" Hook, Australian
- George William Houghton, British golf cartoonist
- Jim Hummel
- Edgar Pierre Jacobs, *Blake and Mortimer*
- Al Jaffee, *Mad*
- Kirk Jarvinen
- S. Jithesh, World\'s Fastest Performing Cartoonist
- Herbert Johnson
- Mike Judge, *Beavis and Butt-head*, *King of the Hill*, *The Goode Family*
- Arja Kajermo
- Avi Katz
- Bil Keane, \"Family Circus\"
- Jeff Keane. \"Family Circus\"
- Walt Kelly, *Pogo*
- Rik Kemp
- Molly Kiely
- Wyncie King
- Jeff Kinney, *Diary of a Wimpy Kid*
- Rick Kirkman, \"Baby Blues\"
- Heinrich Kley
- B. Kliban
- John Kricfalusi, *The Ren & Stimpy Show*
- Abril Lamarque
- Gary Larson, *The Far Side*
- Rick Law, *Beyond the Veil*
- R K Laxman, cartoonist for *The Times of India*, India
- Mell Lazarus. \"Momma, Miss Peach\"
- John Leech, 19th-century *Punch* cartoonist
- Jonathan Lemon, *Alley Oop*
- Michael Leunig, Australian
- Arnold Levin
- David Liljemark
- Neil Lonsdale (1907--1989), New Zealand editorial cartoonist
- David Low, New Zealand political cartoonist and caricaturist
- Jay Lynch
- Trey Parker and Matt Stone, *South Park*
- Seth MacFarlane, *Family Guy*, *American Dad!*, *The Cleveland Show*
- Manjul, *India Today*, *The Economic Times* and *Daily News and Analysis*
- Bob Mankoff, *The New Yorker*
- Jack Markow
- Don Martin, \"Mad\"
- Enrico Mazzanti
- Scott McCloud, *Zot!*, *Understanding Comics*
- Aaron McGruder, *The Boondocks*
- Ronald Michaud
- Yevgeniy Migunov
- Mario Miranda, *The Economic Times*, India
- Shigeru Mizuki, *Ge Ge Ge no Kitaro*, master of horror of Japanese manga
- Guillermo Mordillo
- Arthur Moreland
- Lorin Morgan-Richards
- Morris, *Lucky Luke*
- Joe Murray, *Rocko\'s Modern Life* and *Camp Lazlo!*
- Rachel Nabors
- Ogden Nash
- Nigar Nazar, first female cartoonist of the Muslim world, creator of cartoon character \"Gogi\"
- Roy Nelson
- Richard Newton, 18th century British caricaturist
- Mana Neyestani, Iranian cartoonist
- Ajit Ninan, *India Today* and *The Times of India*
- Floyd Norman
- Murray Olderman, sports columnist, author of 14 books, National Cartoonist Society Sports Cartoon Award for 1974 and 1978
- Jack Edward Oliver
- Jackie Ormes, \"Torchy Brown in \'Dixie to Harlem\", \"Candy\", \"Patty-Jo \'n\' Ginger\", \"Torchy in \'Hearbeats\'\"; first Black woman cartoonist to be published nationally in the U.S. (not via syndication)
- Bruce Ozella
- Paul Palnik, American Jewish cartoonist
- Gary Panter
- Virgil Franklin Partch, known as \"VIP;\" leading American gag cartoonist from the 1940s to the 1980s
- Alan Stuart Paterson, New Zealand cartoonist
- Andrea Pazienza
- René Pellos, French cartoonist
- Bob Penuelas, *Wilbur Kookmeyer*
- Camillus Perera
- Bruce Petty
- Peyo, *The Smurfs*, *Steven Strong*, *Johan and Peewit*
- S. D. Phadnis, Indian cartoonist
- Ziraldo Alves Pinto, Brazilian cartoonist
- Hugo Pratt, *Corto Maltese*
- Ken Pyne
- Quino (Joaquín Salvador Lavado), Argentine cartoonist and social satirist, known for *Mafalda*
- Jacki Randall
- Roy Raymonde, 20th Century English cartoonist whose work appeared principally in Punch (magazine) and Playboy
- Bob Rich, American award-winning cartoonist
- Danny Antonucci, Canadian animator famous for the animated show *Ed, Edd n Eddy*
- Pat Ventura, cartoonist who created shorts for *Nickelodeon* and *Cartoon Network*
- Maxwell Atoms, the creator of *The Grim Adventures of Billy & Mandy*
- W. Heath Robinson, British satirist known for drawings of convoluted machines, similar to Rube Goldberg
- Christine Roche
- Artie Romero
- Ed \"Big Daddy\" Roth
- Thomas Rowlandson 18th Century British caricaturist
- Martin Rowson British political cartoonist
- Øystein Runde
- Malik Sajad Indian cartoonist, author of graphic novel *Munnu - A Boy from Kashmir*\'
- Armando Salas
- Gerald Scarfe ( political)
- Jerry Scott, \"Baby Blues, Zits\"
- Ronald Searle, St Trinians, Molesworth, *The Rake\'s Progress*, editorial work
- Elzie Crisler Segar, *Popeye*
- Sempé
- Claude Serre
- James Affleck Shepherd
- Lee Sheppard
- Gilbert Shelton
- Mahmoud Shokraye
- Shel Silverstein
- Posy Simmonds, *The Silent Three of St Botolph\'s*, *Gemma Bovery*
- Siné
- Vishavjit Singh
- Jeff Smith, *Bone*, *RASL*, *Shazam!: The Monster Society of Evil*, *Little Mouse Gets Ready*
- Mauricio de Sousa, *Monica\'s Gang*, *Chuck Billy \'n\' Folks*, *The Cavern Clan*
- Art Spiegelman, author of *Maus*; co-editor of *RAW* magazine
- Dan Spiegle
- George Sprod, *Punch* and other publications
- Ralph Steadman, editorial cartoonist and book illustrator
- Ralph Stein
- Saul Steinberg
- Jay Stephens
- Matt Stone, with Trey Parker, co-creator of *South Park*
- Jakob Martin Strid
- Ed Subitzky, known for his *National Lampoon* work, also *The New York Times*
- Joost Swarte, Dutch comic artist known for his ligne claire or clear line style of drawing
- Betty Swords
- Les Tanner, political cartoonist
- Howard Tayler, pioneered web-cartooning as a profession
- Raina Telgemeier
- Osamu Tezuka, *Astro Boy*, *Phoenix*; known as the \"God\" of Japanese manga who defined modern Japanese cartooning
- Bal Thackeray, formed a political party in India
- Lefred Thouron
- Morrie Turner, credited with the first multicultural syndicated cartoon strip
- Albert Uderzo, *Asterix*
- Jim Unger, Canadian cartoonist: *Herman*
- Willy Vandersteen, *Spike and Suzy*, *De Rode Ridder*
- Joan Vizcarra
- Vicco von Bülow, *Loriot*
- Keith Waite, New Zealand-born English editorial cartoonist
- Mort Walker, *Beetle Bailey*, *Hi and Lois*
- Arthur Watts
- Ben Wicks, Canadian cartoonist and illustrator: *The Outsider*, *Wicks*
- S. Clay Wilson, *Zap Comix*, *Underground Comix*
- Shannon Wright
- Rhie Won-bok
- Bianca Xunise, \"Six Chix\"; first nonbinary cartoonist to be nationally syndicated in the U.S. mainstream press
- Art Young
- José Zabala-Santos
- Zapiro
## Cartoonists of comic strips {#cartoonists_of_comic_strips}
- Scott Adams, *Dilbert*
- Alex Akerbladh
- Bill Amend, *FoxTrot*
- George Baker, *Sad Sack*
- Tom Batiuk, *Funky Winkerbean*
- Murray Ball, *Footrot Flats*
- Darrin Bell, *Candorville*, *Rudy Park*
- Stephen Bentley, \"Herb and Jamaal\"
- Jerry Bittle
- Boulet, pseudonym of French cartoonist Gilles Roussel
- Brumsic Brandon Jr., \"Luther\"
- Barbara Brandon-Croft, \"Where I\'m Coming From\"
- Berkeley Breathed, *Bloom County* (1980s American social-political), *Outland*, *Opus*
- Dave Breger, *Mister Breger*
- Dik Browne, *Hi and Lois*, *Hägar the Horrible*
- Ernie Bushmiller, *Nancy*
- Milton Caniff, *Terry and the Pirates*, *Steve Canyon*
- Al Capp, *Li\'l Abner*
- Ad Carter, *Just Kids*
- Jok Church, *You Can With Beakman and Jax*
- Francis Cleetus, *It\'s Geek 2 Me*
- Mitch Clem, *Nothing Nice to Say*, *San Antonio Rock City*
- Darby Conley, *Get Fuzzy*
- Joan Cornellà
- Dave Coverly, *Speed Bump*
- Max Crivello
- Alex Raymond, *Flash Gordon*, *Jungle Jim*, *Rip Kirby*
- Stan Cross, *The Potts*
- Stacy Curtis, *Cul de Sac*
- Lyman Dally, *Max Rep*
- Harry Grant Dart
- Lou Darvas
- Jim Davis, *Gnorm Gnat*, *Garfield*, *U.S. Acres*, a *Mr. Potato Head* comic strip
- Reginald Ben Davis
- Derf Backderf (John Backderf)
- Brad Diller
- J. C. Duffy, *The Fusco Brothers*
- Edwina Dumm
- Frank Dunne
- Benita Epstein, *Six Chix*
- Larry Feign, *The World of Lily Wong*
- Norm Feuti, *Retail*
- George Fett, *Sniffy and Norbert*
- Charles Fincher, creator of *Thadeus & Weez* and *The Daily Scribble*
- Bud Fisher, *Mutt and Jeff*
- Ham Fisher, *Joe Palooka*
- Evelyn Flinders, *The Silent Three*
- Harold Rudolf Foster, *Prince Valiant* and *Tarzan*
- J.D. Frazer, *User Friendly*
- David Füleki, *78 Tage auf der Straße des Hasses*
- Paul Gilligan, *Pooch Cafe*
- Erich von Götha de la Rosière
- Chester Gould, *Dick Tracy*
- Bud Grace, \"Ernie/Piranha Club\", \"Babs and Aldo\"
- Mel Graff, "The Adventures of Patsy", "Secret Agent X-9"
- Bill Griffith, *Zippy the Pinhead*
- Milt Gross
- Cathy Guisewite, *Cathy*
- Nicholas Gurewitch, *Perry Bible Fellowship*
- Alex Hallatt
- Johnny Hart, *B.C.*, *The Wizard of Id*
- Bill Hinds, *Tank McNamara*, *Cleats*, *Buzz Beamer*
- Bill Holman, *Smokey Stover*
- Daniel Hulet
- Billy Ireland
- Tatsuya Ishida, *Sinfest*
- Tove and Lars Jansson, *The Moomins*
- Ferd Johnson, *Moon Mullins*
- Kerry G. Johnson, *Harambee Hills*, caricaturist and children\'s book illustrator
- Russell Johnson, *Mister Oswald*
- Lynn Johnston, *For Better or For Worse*
- Eric Jolliffe, *Andy*
- Bil Keane, *Family Circus*
- Jeff Keane, *Family Circus*
- Walt Kelly, *Pogo*
- James Kemsley, *Ginger Meggs*
- Hank Ketcham, *Dennis the Menace*
- Kazu Kibuishi, *Copper*
- Frank King, *Gasoline Alley*
- Rick Kirkman, \"Baby Blues\"
- Keith Knight, *The K Kronicles*
- Charles Kuhn, *Grandma*
- Fred Lasswell, *Barney Google*
- Mell Lazarus, \"Momma, Miss Peach\"
- Virginio Livraghi
- Les Lumsdon, \"Basil\", \"Nipper\", \"Caspar\"
- Edgar Martin
- Clifford McBride, *Napoleon*
- Winsor McCay, *Little Nemo*
- Patrick McDonnell, *Mutts*
- Brian McFadden, *Big Fat Whale*
- Aaron McGruder, creator of the controversial strip *The Boondocks*
- George McManus, *Bringing Up Father*
- Caesar Meadows
- Dale Messick, *Brenda Starr*
- Tim Molloy
- Bill Murray, *Sonny Boy*
- Fred Negro, *Pub Strip*
- Chris Onstad, *Achewood*
- Jackie Ormes, \"Torchy Brown in \'Dixie to Harlem\'\", \"Torchy in \'Heartbeats\'\"
- Phil Ortiz
- Frode Øverli, *Pondus*
- Nina Paley, *Nina\'s Adventures*, *Fluff*, *The Hots*
- Brant Parker, *The Wizard of Id*
- Stephan Pastis, *Pearls Before Swine*
- Charles Peattie and Russell Taylor, *Alex*
- Mike Peters, *Mother Goose & Grimm*
- Keats Petree
- Stan Pitt, *Larry Flynn, Detective*
- Vic Pratt
- Dariush Ramezani
- John Rivas, *Bonzzo*
- Valentina Romeo, *Jonathan Steele*, *Dylan Dog*, *Morgan Lost*, *Nathan Never*
- Leigh Rubin, *Rubes*
- Warren Sattler, *Grubby*, *Billy the Kid* and *Yang*, as well as contributing artist for *Barnaby* daily, *The Jackson Twins*, *Bringing Up Father* and *Hi and Lois*
- Charles M. Schulz, *Peanuts*, *Young Pillars*
- Jerry Scott, \"Baby Blues, Zits, Nancy\"
- Caroll Spinney, *Harvey*
- Lee W. Stanley, *The Old Home Town*
- Cliff Sterrett, *Polly and Her Pals*
- Kris Straub, *Starslip Crisis*, *Checkerboard Nightmare*
- Henry Matthew Talintyre
- Harold Tamblyn-Watts
- Russell Taylor and Charles Peattie, *Alex*
- Richard Thompson, *Cul de Sac*
- Jim Toomey, *Sherman\'s Lagoon*
- Harry J. Tuthill, *The Bungle Family*
- Gustave Verbeek, *The Upside Downs*, *The Terrors of the Tiny Tads*
- Mort Walker, *Beetle Bailey*, *Hi and Lois*
- Bill Watterson, *Calvin and Hobbes*
- Bob Weber, *Moose & Molly*
- Monty Wedd, *Ned Kelly*
- Alex Williams, *Queen\'s Counsel*
- Tom Wilson, *Ziggy*
## Cartoonists of single-panel cartoons {#cartoonists_of_single_panel_cartoons}
- Charles Addams
- Gene Ahern
- Glen Baxter
- Belsky
- Jim Benton
- Rupert Besley
- Charles Boyce, *Compu-Toon*
- Barry Bradfield
- Sheree Bradford-Lea
- Bo Brown
- Ivan Brunetti
- John Callahan
- Irwin Caplan
- Patrick Chappatte (Chappatte)
- Roz Chast
- Chumy Chúmez
- Mariza Dias Costa
- Wilbur Dawbarn
- Chon Day
- Donelan
- Denise Dorrance
- Nick Downes
- Mort Drucker
- Vladimir Flórez
- Stanley Arthur Franklin
- Carl Giles (Giles), *Daily Express*
- Ted Goff
- Bud Grace
- Sam Gross
- Dick Guindon
- William Haefeli
- Jessica Hagy
- Baron Halpenny
- Sidney Harris
- William Haselden
- Bill Hoest
- Judy Horacek
- Stan Hunt
- Hank Ketcham
- Ted Key
- John F. Knott, creator of Old Man Texas, Dallas Morning News, 1905-1957
- Clyde Lamb
- Gary Larson
- Mel Lazarus
- Robert Leighton
- George Lichty
- Mike Lynch
- Lorin Morgan-Richards
- Fred Neher
- John Norment
- Don Orehek
- Jackie Ormes, \"Candy\", \"Patty-Jo \'n\' Ginger\"
- W. B. Park
- Virgil Partch
- Dave Pascal
- Mad Peck
- Matt Percival
- Martin Perscheid
- Josefina Tanganelli Plana
- Gardner Rea
- John Reiner
- Dan Reynolds
- Mischa Richter
- Victoria Roberts
- Burr Shafer
- Vahan Shirvanian
- Chris Slane
- Grant Snider
- Dan Steffan
- James Thurber
- Jerry Van Amerongen
- H. T. Webster
- Gluyas Williams
- J. R. Williams, *Out Our Way*
- Gahan Wilson
- George Wolfe
- Kevin Woodcock
- Bianca Xunise
- Bill Yates
- ZAK, pseudonym of Belgian cartoonist Jacques Moeraert
- Zero
## Cartoonists of comic books {#cartoonists_of_comic_books}
- Carlo Ambrosini
- Jack Herbert
- Sergio Aragonés, *Mad*; creator of *Groo the Wanderer*
- Daniel A. Baker
- Ken Battefield
- Jim Benton, *Catwad*,*Batman Squad*,*Attack of the Stuff*
- Bill Benulis, *War is Hell*
- Steve Bialik
- François Bourgeon, *Le Cycle de Cyann*
- Anna Brandoli
- Reg Bunn
- Ben Caldwell, creator of the Dare Detectives
- Aldo Capitanio
- Onofrio Catacchio
- Domitille Collardey
- Carlo Cossio, *Dick Fulmine*
- Jason Craig
- Hugleikur Dagsson
- Dame Darcy, creator of *Meat Cake*
- Patryck de Froidmont
- Gianni De Luca, *Commissario Spada*
- Dan DeCarlo, *Archie*, *Josie and the Pussycats*, *Sabrina, the Teenage Witch*
- Kim Deitch creator of *Waldo the Cat* and comic novels
- Vince Deporter, DC Comics; Nickelodeon, Spirou (Belgium)
- Julie Doucet, creator of *Dirty Plotte*, *My New York Diary*
- Will Elder, *Mad*, *Little Annie Fanny* in *Playboy*
- Steve Fiorilla, mini-comics
- Andy Fish
- Brad W. Foster, creator of *Mechthings* mini-comics, *The Mechthings*, *Adventures of Olivia* mini-comics
- Chandra Free
- Vernon Grant, creator of *The Love Rangers*
- Dick Hafer
- Marc Hansen, creator of Ralph Snart
- Los Bros Hernandez, creators of *Love and Rockets*
- Don Hillsman II
- Yvonne Hutton
- Al Jaffee, *Mad*, *Snappy Answers to Stupid Questions*
- Robyn E. Kenealy
- Helena Klakocar
- Andrea Kruis
- Harvey Kurtzman, founding editor of *Mad*
- Antonio Lara de Gavilán
- Selena Lin
- Craig McKay
- Mark Marderosian
- David Messer, adaptations of *Macbeth* and the *Tempest*
- Erika Moen
- Colonel Moutarde
- Art Nugent
- Gaman Palem
- Fung Chin Pang
- Power Paola
- Eduardo Vañó Pastor
- Craig Phillips
- Darren Sanchez
- Seth, creator of *Palookaville*
- Ravi Shankar
- Pran Kumar Sharma, *Chacha Chaudhary*
- Jeff Smith, *Bone Book*
- Cal Sobrepeña
- Fermín Solís
- Hans Steinbach
- Kazimir Strzepek
- Ramon Torrents
- Przemysław Truściński
- Jhonen Vasquez, *Johnny the Homicidal Maniac*, *Squee!*, *I Feel Sick*, *Everything Can be Beaten*, *Fillerbunny*, *Bad Art Collection*, *Happy Noodle Boy*
- Wally Wood, *Mad*
- Chao Yat
- Carlos Zéfiro
- Laura Zuccheri, *Ken Parker*, *Julia-le avventure di una criminologa*
### Cartoonists of action/superhero comic books {#cartoonists_of_actionsuperhero_comic_books}
- Kyle Baker, creator of *Why I Hate Saturn*
- Barry Bradfield, *Batman: The Animated Homepage*
- Jack Cole, creator of Plastic Man, later set the style for cartoons in *Playboy*
- Alan Davis, creator of ClanDestine
- Steve Ditko, creator of many Marvel Comics, including Spider-Man and Doctor Strange, with editor Stan Lee
- Will Eisner, creator of *The Spirit*, teacher, publisher, one of the first to popularize the term *graphic novel*, in his book *A Contract with God*
- Bob Kane, creator of The Batman with writer Bill Finger
- Jack Kirby, creator of Captain America with his partner Joe Simon, and many other comics
- Erik Larsen, creator of *Savage Dragon*
- Rob Liefeld, creator of *Deadpool* and *Youngblood*
- Jim McDermott
- Todd McFarlane, creator of *Spawn*
- Shawn McManus
- Mike Mignola, creator of *Hellboy*
- Frank Miller, creator of *Sin City*
- James O\'Barr, creator of *The Crow*
- Paul Palnik, creator of *The God of Cartoons*
- Whilce Portacio
- Humberto Ramos
- Roberto Raviola, creator of *La Compagnia della Forca*
- Shelby Robertson
- Alberto Saichann
- Tim Sale
- Horacio Sandoval
- Marc Silvestri, creator of *Cyberforce* and *The Darkness*
- Dave Sim, creator of Cerebus
- Jeff Smith, creator of *Bone*
- Ed Tourriol
- Alain Voss
| 2025-06-20T00:00:00 |
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Chemical reaction
|
A **chemical reaction** is a process that leads to the chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
The substance (or substances) initially involved in a chemical reaction are called reactants or reagents. Chemical reactions are usually characterized by a chemical change, and they yield one or more products, which usually have properties different from the reactants. Reactions often consist of a sequence of individual sub-steps, the so-called elementary reactions, and the information on the precise course of action is part of the reaction mechanism. Chemical reactions are described with chemical equations, which symbolically present the starting materials, end products, and sometimes intermediate products and reaction conditions.
Chemical reactions happen at a characteristic reaction rate at a given temperature and chemical concentration. Some reactions produce heat and are called exothermic reactions, while others may require heat to enable the reaction to occur, which are called endothermic reactions. Typically, reaction rates increase with increasing temperature because there is more thermal energy available to reach the activation energy necessary for breaking bonds between atoms.
A reaction may be classified as redox in which oxidation and reduction occur or non-redox in which there is no oxidation and reduction occurring. Most simple redox reactions may be classified as a combination, decomposition, or single displacement reaction.
Different chemical reactions are used during chemical synthesis in order to obtain the desired product. In biochemistry, a consecutive series of chemical reactions (where the product of one reaction is the reactant of the next reaction) form metabolic pathways. These reactions are often catalyzed by protein enzymes. Enzymes increase the rates of biochemical reactions, so that metabolic syntheses and decompositions impossible under ordinary conditions can occur at the temperature and concentrations present within a cell.
The general concept of a chemical reaction has been extended to reactions between entities smaller than atoms, including nuclear reactions, radioactive decays and reactions between elementary particles, as described by quantum field theory.
## History
Chemical reactions such as combustion in fire, fermentation and the reduction of ores to metals were known since antiquity. Initial theories of transformation of materials were developed by Greek philosophers, such as the Four-Element Theory of Empedocles stating that any substance is composed of the four basic elements -- fire, water, air and earth. In the Middle Ages, chemical transformations were studied by alchemists. They attempted, in particular, to convert lead into gold, for which purpose they used reactions of lead and lead-copper alloys with sulfur.
The artificial production of chemical substances already was a central goal for medieval alchemists. Examples include the synthesis of ammonium chloride from organic substances as described in the works (c. 850--950) attributed to Jābir ibn Ḥayyān, or the production of mineral acids such as sulfuric and nitric acids by later alchemists, starting from c. 1300. The production of mineral acids involved the heating of sulfate and nitrate minerals such as copper sulfate, alum and saltpeter. In the 17th century, Johann Rudolph Glauber produced hydrochloric acid and sodium sulfate by reacting sulfuric acid and sodium chloride. With the development of the lead chamber process in 1746 and the Leblanc process, allowing large-scale production of sulfuric acid and sodium carbonate, respectively, chemical reactions became implemented into the industry. Further optimization of sulfuric acid technology resulted in the contact process in the 1880s, and the Haber process was developed in 1909--1910 for ammonia synthesis.
From the 16th century, researchers including Jan Baptist van Helmont, Robert Boyle, and Isaac Newton tried to establish theories of experimentally observed chemical transformations. The phlogiston theory was proposed in 1667 by Johann Joachim Becher. It postulated the existence of a fire-like element called \"phlogiston\", which was contained within combustible bodies and released during combustion. This proved to be false in 1785 by Antoine Lavoisier who found the correct explanation of the combustion as a reaction with oxygen from the air.
Joseph Louis Gay-Lussac recognized in 1808 that gases always react in a certain relationship with each other. Based on this idea and the atomic theory of John Dalton, Joseph Proust had developed the law of definite proportions, which later resulted in the concepts of stoichiometry and chemical equations.
Regarding the organic chemistry, it was long believed that compounds obtained from living organisms were too complex to be obtained synthetically. According to the concept of vitalism, organic matter was endowed with a \"vital force\" and distinguished from inorganic materials. This separation was ended however by the synthesis of urea from inorganic precursors by Friedrich Wöhler in 1828. Other chemists who brought major contributions to organic chemistry include Alexander William Williamson with his synthesis of ethers and Christopher Kelk Ingold, who, among many discoveries, established the mechanisms of substitution reactions.
## Characteristics
The general characteristics of chemical reactions are:
- Evolution of a gas
- Formation of a precipitate
- Change in temperature
- Change in state
## Equations
Chemical equations are used to graphically illustrate chemical reactions. They consist of chemical or structural formulas of the reactants on the left and those of the products on the right. They are separated by an arrow (→) which indicates the direction and type of the reaction; the arrow is read as the word \"yields\". The tip of the arrow points in the direction in which the reaction proceeds. A double arrow (`{{eqm}}`{=mediawiki}) pointing in opposite directions is used for equilibrium reactions. Equations should be balanced according to the stoichiometry, the number of atoms of each species should be the same on both sides of the equation. This is achieved by scaling the number of involved molecules (A, B, C and D in a schematic example below) by the appropriate integers *a, b, c* and *d*.
:
More elaborate reactions are represented by reaction schemes, which in addition to starting materials and products show important intermediates or transition states. Also, some relatively minor additions to the reaction can be indicated above the reaction arrow; examples of such additions are water, heat, illumination, a catalyst, etc. Similarly, some minor products can be placed below the arrow, often with a minus sign. Retrosynthetic analysis can be applied to design a complex synthesis reaction. Here the analysis starts from the products, for example by splitting selected chemical bonds, to arrive at plausible initial reagents. A special arrow (⇒) is used in retro reactions.
## Elementary reactions {#elementary_reactions}
The elementary reaction is the smallest division into which a chemical reaction can be decomposed, it has no intermediate products. Most experimentally observed reactions are built up from many elementary reactions that occur in parallel or sequentially. The actual sequence of the individual elementary reactions is known as reaction mechanism. An elementary reaction involves a few molecules, usually one or two, because of the low probability for several molecules to meet at a certain time.
The most important elementary reactions are unimolecular and bimolecular reactions. Only one molecule is involved in a unimolecular reaction; it is transformed by isomerization or a dissociation into one or more other molecules. Such reactions require the addition of energy in the form of heat or light. A typical example of a unimolecular reaction is the cis--trans isomerization, in which the cis-form of a compound converts to the trans-form or vice versa.
In a typical dissociation reaction, a bond in a molecule splits (**ruptures**) resulting in two molecular fragments. The splitting can be homolytic or heterolytic. In the first case, the bond is divided so that each product retains an electron and becomes a neutral radical. In the second case, both electrons of the chemical bond remain with one of the products, resulting in charged ions. Dissociation plays an important role in triggering chain reactions, such as hydrogen--oxygen or polymerization reactions.
: AB -\> A + B
: Dissociation of a molecule AB into fragments A and B
For bimolecular reactions, two molecules collide and react with each other. Their merger is called chemical synthesis or an addition reaction.
: A + B -\> AB
Another possibility is that only a portion of one molecule is transferred to the other molecule. This type of reaction occurs, for example, in redox and acid-base reactions. In redox reactions, the transferred particle is an electron, whereas in acid-base reactions it is a proton. This type of reaction is also called metathesis.
: HA + B -\> A + HB
for example
: NaCl + AgNO3 -\> NaNO3 + AgCl(v)
## Chemical equilibrium {#chemical_equilibrium}
Most chemical reactions are reversible; that is, they can and do run in both directions. The forward and reverse reactions are competing with each other and differ in reaction rates. These rates depend on the concentration and therefore change with the time of the reaction: the reverse rate gradually increases and becomes equal to the rate of the forward reaction, establishing the so-called chemical equilibrium. The time to reach equilibrium depends on parameters such as temperature, pressure, and the materials involved, and is determined by the minimum free energy. In equilibrium, the Gibbs free energy of reaction must be zero. The pressure dependence can be explained with the Le Chatelier\'s principle. For example, an increase in pressure due to decreasing volume causes the reaction to shift to the side with fewer moles of gas.
The reaction yield stabilizes at equilibrium but can be increased by removing the product from the reaction mixture or changed by increasing the temperature or pressure. A change in the concentrations of the reactants does not affect the equilibrium constant but does affect the equilibrium position.
## Thermodynamics
Chemical reactions are determined by the laws of thermodynamics. Reactions can proceed by themselves if they are exergonic, that is if they release free energy. The associated free energy change of the reaction is composed of the changes of two different thermodynamic quantities, enthalpy and entropy:
:; $\Delta G = \Delta H - T \cdot \Delta S$.
:
: `{{mvar|G}}`{=mediawiki}: free energy, `{{mvar|H}}`{=mediawiki}: enthalpy, `{{mvar|T}}`{=mediawiki}: temperature, `{{mvar|S}}`{=mediawiki}: entropy, `{{math|Δ}}`{=mediawiki}: difference (change between original and product)
Reactions can be exothermic, where Δ*H* is negative and energy is released. Typical examples of exothermic reactions are combustion, precipitation and crystallization, in which ordered solids are formed from disordered gaseous or liquid phases. In contrast, in endothermic reactions, heat is consumed from the environment. This can occur by increasing the entropy of the system, often through the formation of gaseous or dissolved reaction products, which have higher entropy. Since the entropy term in the free-energy change increases with temperature, many endothermic reactions preferably take place at high temperatures. On the contrary, many exothermic reactions such as crystallization occur preferably at lower temperatures. A change in temperature can sometimes reverse the sign of the enthalpy of a reaction, as for the carbon monoxide reduction of molybdenum dioxide:
: 2CO(g) + MoO2(s) -\> 2CO2(g) + Mo(s); $\Delta H^o = +21.86 \ \text{kJ at 298 K}$
This reaction to form carbon dioxide and molybdenum is endothermic at low temperatures, becoming less so with increasing temperature. Δ*H*° is zero at `{{val|1855|ul=K}}`{=mediawiki}, and the reaction becomes exothermic above that temperature.
Changes in temperature can also reverse the direction tendency of a reaction. For example, the water gas shift reaction
: CO(g) + H2O({v}) \<=\> CO2(g) + H2(g)
is favored by low temperatures, but its reverse is favored by high temperatures. The shift in reaction direction tendency occurs at `{{val|1100|u=K}}`{=mediawiki}.
Reactions can also be characterized by their internal energy change, which takes into account changes in the entropy, volume and chemical potentials. The latter depends, among other things, on the activities of the involved substances.
:; ${d}U = T\cdot {d}S - p\cdot {d}V + \mu\cdot {d}n$
:
: `{{mvar|U}}`{=mediawiki}: internal energy, `{{mvar|S}}`{=mediawiki}: entropy, `{{mvar|p}}`{=mediawiki}: pressure, `{{mvar|μ}}`{=mediawiki}: chemical potential, `{{mvar|n}}`{=mediawiki}: number of molecules, `{{mvar|d}}`{=mediawiki}: small change sign
## Kinetics
The speed at which reactions take place is studied by reaction kinetics. The rate depends on various parameters, such as:
- Reactant concentrations, which usually make the reaction happen at a faster rate if raised through increased collisions per unit of time. Some reactions, however, have rates that are *independent* of reactant concentrations, due to a limited number of catalytic sites. These are called zero order reactions.
- Surface area available for contact between the reactants, in particular solid ones in heterogeneous systems. Larger surface areas lead to higher reaction rates.
- Pressure -- increasing the pressure decreases the volume between molecules and therefore increases the frequency of collisions between the molecules.
- Activation energy, which is defined as the amount of energy required to make the reaction start and carry on spontaneously. Higher activation energy implies that the reactants need more energy to start than a reaction with lower activation energy.
- Temperature, which hastens reactions if raised, since higher temperature increases the energy of the molecules, creating more collisions per unit of time,
- The presence or absence of a catalyst. Catalysts are substances that make weak bonds with reactants or intermediates and change the pathway (mechanism) of a reaction which in turn increases the speed of a reaction by lowering the activation energy needed for the reaction to take place. A catalyst is not destroyed or changed during a reaction, so it can be used again.
- For some reactions, the presence of electromagnetic radiation, most notably ultraviolet light, is needed to promote the breaking of bonds to start the reaction. This is particularly true for reactions involving radicals.
Several theories allow calculating the reaction rates at the molecular level. This field is referred to as reaction dynamics. The rate *v* of a first-order reaction, which could be the disintegration of a substance A, is given by:
: $v= -\frac {d[\ce{A}]}{dt}= k \cdot [\ce{A}].$
Its integration yields:
: $\ce{[A]}(t) = \ce{[A]}_{0} \cdot e^{-k\cdot t}.$
Here *k* is the first-order rate constant, having dimension 1/time, \[A\](*t*) is the concentration at a time *t* and \[A\]~0~ is the initial concentration. The rate of a first-order reaction depends only on the concentration and the properties of the involved substance, and the reaction itself can be described with a characteristic half-life. More than one time constant is needed when describing reactions of higher order. The temperature dependence of the rate constant usually follows the Arrhenius equation:
$$k = k_0 e^{{-E_a}/{k_{B}T}}$$
where *E*~a~ is the activation energy and *k*~B~ is the Boltzmann constant. One of the simplest models of reaction rate is the collision theory. More realistic models are tailored to a specific problem and include the transition state theory, the calculation of the potential energy surface, the Marcus theory and the Rice--Ramsperger--Kassel--Marcus (RRKM) theory.
## Reaction types {#reaction_types}
### Four basic types {#four_basic_types}
#### Synthesis
In a synthesis reaction, two or more simple substances combine to form a more complex substance. These reactions are in the general form: A + B-\>AB
Two or more reactants yielding one product is another way to identify a synthesis reaction. One example of a synthesis reaction is the combination of iron and sulfur to form iron(II) sulfide: 8Fe + S8-\>8FeS
Another example is simple hydrogen gas combined with simple oxygen gas to produce a more complex substance, such as water.
#### Decomposition
A decomposition reaction is when a more complex substance breaks down into its more simple parts. It is thus the opposite of a synthesis reaction and can be written as AB-\>A + B
One example of a decomposition reaction is the electrolysis of water to make oxygen and hydrogen gas: 2H2O-\>2H2 + O2
#### Single displacement {#single_displacement}
In a single displacement reaction, a single uncombined element replaces another in a compound; in other words, one element trades places with another element in a compound. These reactions come in the general form of: A + BC-\>AC + B
One example of a single displacement reaction is when magnesium replaces hydrogen in water to make solid magnesium hydroxide and hydrogen gas: Mg + 2H2O-\>Mg(OH)2 (v) + H2 (\^)
#### Double displacement {#double_displacement}
In a double displacement reaction, the anions and cations of two compounds switch places and form two entirely different compounds. These reactions are in the general form: AB + CD-\>AD + CB
For example, when barium chloride (BaCl~2~) and magnesium sulfate (MgSO~4~) react, the SO~4~^2−^ anion switches places with the 2Cl^−^ anion, giving the compounds BaSO~4~ and MgCl~2~.
Another example of a double displacement reaction is the reaction of lead(II) nitrate with potassium iodide to form lead(II) iodide and potassium nitrate: Pb(NO3)2 + 2KI-\>PbI2(v) + 2KNO3
### Forward and backward reactions {#forward_and_backward_reactions}
According to Le Chatelier\'s Principle, reactions may proceed in the forward or reverse direction until they end or reach equilibrium.
#### Forward reactions {#forward_reactions}
Reactions that proceed in the forward direction (from left to right) to approach equilibrium are often called spontaneous reactions, that is, $\Delta G$ is negative, which means that if they occur at constant temperature and pressure, they decrease the Gibbs free energy of the reaction. They require less energy to proceed in the forward direction. Reactions are usually written as forward reactions in the direction in which they are spontaneous. Examples:
- Reaction of hydrogen and oxygen to form water.
: \+ `{{chem|O|2}}`{=mediawiki} `{{eqm}}`{=mediawiki} `{{chem|2H|2|O}}`{=mediawiki}
- Dissociation of acetic acid in water into acetate ions and hydronium ions.
: \+ `{{chem|H|2|O}}`{=mediawiki} `{{eqm}}`{=mediawiki} `{{chem|CH|3|COO|-}}`{=mediawiki} + `{{chem|H|3|O|+}}`{=mediawiki}
#### Backward reactions {#backward_reactions}
Reactions that proceed in the backward direction to approach equilibrium are often called non-spontaneous reactions, that is, $\Delta G$ is positive, which means that if they occur at constant temperature and pressure, they increase the Gibbs free energy of the reaction. They require input of energy to proceed in the forward direction. Examples include:
- Charging a normal DC battery (consisting of electrolytic cells) from an external electrical power source
- Photosynthesis driven by absorption of electromagnetic radiation usually in the form of sunlight
: \+ `{{underset| water |H<sub>2</sub>O}}`{=mediawiki} + `{{underset|light energy|photons}}`{=mediawiki} → `{{underset|carbohydrate|[CH<sub>2</sub>O]}}`{=mediawiki} + `{{underset| oxygen |O<sub>2</sub>}}`{=mediawiki}
### Combustion
In a combustion reaction, an element or compound reacts with an oxidant, usually oxygen, often producing energy in the form of heat or light. Combustion reactions frequently involve a hydrocarbon. For instance, the combustion of 1 mole (114 g) of octane in oxygen C8H18(l) + 25/2 O2(g)-\>8CO2 + 9H2O(l)
releases 5500 kJ. A combustion reaction can also result from carbon, magnesium or sulfur reacting with oxygen. 2Mg(s) + O2-\>2MgO(s) S(s) + O2(g)-\>SO2(g)
### Oxidation and reduction {#oxidation_and_reduction}
Redox reactions can be understood in terms of the transfer of electrons from one involved species (reducing agent) to another (oxidizing agent). In this process, the former species is *oxidized* and the latter is *reduced*. Though sufficient for many purposes, these descriptions are not precisely correct. Oxidation is better defined as an increase in oxidation state of atoms and reduction as a decrease in oxidation state. In practice, the transfer of electrons will always change the oxidation state, but there are many reactions that are classed as \"redox\" even though no electron transfer occurs (such as those involving covalent bonds).
In the following redox reaction, hazardous sodium metal reacts with toxic chlorine gas to form the ionic compound sodium chloride, or common table salt: 2Na(s) + Cl2(g)-\>2NaCl(s)
In the reaction, sodium metal goes from an oxidation state of 0 (a pure element) to +1: in other words, the sodium lost one electron and is said to have been oxidized. On the other hand, the chlorine gas goes from an oxidation of 0 (also a pure element) to −1: the chlorine gains one electron and is said to have been reduced. Because the chlorine is the one reduced, it is considered the electron acceptor, or in other words, induces oxidation in the sodium -- thus the chlorine gas is considered the oxidizing agent. Conversely, the sodium is oxidized or is the electron donor, and thus induces a reduction in the other species and is considered the *reducing agent*.
Which of the involved reactants would be a reducing or oxidizing agent can be predicted from the electronegativity of their elements. Elements with low electronegativities, such as most metals, easily donate electrons and oxidize -- they are reducing agents. On the contrary, many oxides or ions with high oxidation numbers of their non-oxygen atoms, such as `{{chem|link=hydrogen peroxide|H|2|O|2}}`{=mediawiki}, `{{chem|link=permanganate|MnO|4|-}}`{=mediawiki}, `{{chem|link=chromium trioxide|CrO|3}}`{=mediawiki}, `{{chem|link=dichromate|Cr|2|O|7|2-}}`{=mediawiki}, or `{{chem|link=Osmium(VIII) oxide|OsO|4}}`{=mediawiki}, can gain one or two extra electrons and are strong oxidizing agents.
For some main-group elements the number of electrons donated or accepted in a redox reaction can be predicted from the electron configuration of the reactant element. Elements try to reach the low-energy noble gas configuration, and therefore alkali metals and halogens will donate and accept one electron, respectively. Noble gases themselves are chemically inactive.
The overall redox reaction can be balanced by combining the oxidation and reduction half-reactions multiplied by coefficients such that the number of electrons lost in the oxidation equals the number of electrons gained in the reduction.
An important class of redox reactions are the electrolytic electrochemical reactions, where electrons from the power supply at the negative electrode are used as the reducing agent and electron withdrawal at the positive electrode as the oxidizing agent. These reactions are particularly important for the production of chemical elements, such as chlorine or aluminium. The reverse process, in which electrons are released in redox reactions and chemical energy is converted to electrical energy, is possible and used in batteries.
### Complexation
In complexation reactions, several ligands react with a metal atom to form a coordination complex. This is achieved by providing lone pairs of the ligand into empty orbitals of the metal atom and forming dipolar bonds. The ligands are Lewis bases, they can be both ions and neutral molecules, such as carbon monoxide, ammonia or water. The number of ligands that react with a central metal atom can be found using the 18-electron rule, saying that the valence shells of a transition metal will collectively accommodate 18 electrons, whereas the symmetry of the resulting complex can be predicted with the crystal field theory and ligand field theory. Complexation reactions also include ligand exchange, in which one or more ligands are replaced by another, and redox processes which change the oxidation state of the central metal atom.
### Acid--base reactions {#acidbase_reactions}
In the Brønsted--Lowry acid--base theory, an acid--base reaction involves a transfer of protons (H^+^) from one species (the acid) to another (the base). When a proton is removed from an acid, the resulting species is termed that acid\'s conjugate base. When the proton is accepted by a base, the resulting species is termed that base\'s conjugate acid. In other words, acids act as proton donors and bases act as proton acceptors according to the following equation: \\underset{acid}{HA} + \\underset{base}{B} \<=\> \\underset{conjugated\\ base}{A\^-} + \\underset{conjugated\\ acid}{HB+}
The reverse reaction is possible, and thus the acid/base and conjugated base/acid are always in equilibrium. The equilibrium is determined by the acid and base dissociation constants (*K*~a~ and *K*~b~) of the involved substances. A special case of the acid-base reaction is the neutralization where an acid and a base, taken at the exact same amounts, form a neutral salt.
Acid-base reactions can have different definitions depending on the acid-base concept employed. Some of the most common are:
- Arrhenius definition: Acids dissociate in water releasing H~3~O^+^ ions; bases dissociate in water releasing OH^−^ ions.
- Brønsted--Lowry definition: Acids are proton (H^+^) donors, bases are proton acceptors; this includes the Arrhenius definition.
- Lewis definition: Acids are electron-pair acceptors, and bases are electron-pair donors; this includes the Brønsted-Lowry definition.
### Precipitation
Precipitation is the formation of a solid in a solution or inside another solid during a chemical reaction. It usually takes place when the concentration of dissolved ions exceeds the solubility limit and forms an insoluble salt. This process can be assisted by adding a precipitating agent or by the removal of the solvent. Rapid precipitation results in an amorphous or microcrystalline residue and a slow process can yield single crystals. The latter can also be obtained by recrystallization from microcrystalline salts.
### Solid-state reactions {#solid_state_reactions}
Reactions can take place between two solids. However, because of the relatively small diffusion rates in solids, the corresponding chemical reactions are very slow in comparison to liquid and gas phase reactions. They are accelerated by increasing the reaction temperature and finely dividing the reactant to increase the contacting surface area.
### Reactions at the solid/gas interface {#reactions_at_the_solidgas_interface}
The reaction can take place at the solid\|gas interface, surfaces at very low pressure such as ultra-high vacuum. Via scanning tunneling microscopy, it is possible to observe reactions at the solid\|gas interface in real space, if the time scale of the reaction is in the correct range. Reactions at the solid\|gas interface are in some cases related to catalysis.
### Photochemical reactions {#photochemical_reactions}
In photochemical reactions, atoms and molecules absorb energy (photons) of the illumination light and convert it into an excited state. They can then release this energy by breaking chemical bonds, thereby producing radicals. Photochemical reactions include hydrogen--oxygen reactions, radical polymerization, chain reactions and rearrangement reactions.
Many important processes involve photochemistry. The premier example is photosynthesis, in which most plants use solar energy to convert carbon dioxide and water into glucose, disposing of oxygen as a side-product. Humans rely on photochemistry for the formation of vitamin D, and vision is initiated by a photochemical reaction of rhodopsin. In fireflies, an enzyme in the abdomen catalyzes a reaction that results in bioluminescence. Many significant photochemical reactions, such as ozone formation, occur in the Earth atmosphere and constitute atmospheric chemistry.
## Catalysis
In catalysis, the reaction does not proceed directly, but through a reaction with a third substance known as catalyst. Although the catalyst takes part in the reaction, forming weak bonds with reactants or intermediates, it is returned to its original state by the end of the reaction and so is not consumed. However, it can be inhibited, deactivated or destroyed by secondary processes. Catalysts can be used in a different phase (heterogeneous) or in the same phase (homogeneous) as the reactants. In heterogeneous catalysis, typical secondary processes include coking where the catalyst becomes covered by polymeric side products. Additionally, heterogeneous catalysts can dissolve into the solution in a solid-liquid system or evaporate in a solid--gas system. Catalysts can only speed up the reaction -- chemicals that slow down the reaction are called inhibitors. Substances that increase the activity of catalysts are called promoters, and substances that deactivate catalysts are called catalytic poisons. With a catalyst, a reaction that is kinetically inhibited by high activation energy can take place in the circumvention of this activation energy.
Heterogeneous catalysts are usually solids, powdered in order to maximize their surface area. Of particular importance in heterogeneous catalysis are the platinum group metals and other transition metals, which are used in hydrogenations, catalytic reforming and in the synthesis of commodity chemicals such as nitric acid and ammonia. Acids are an example of a homogeneous catalyst, they increase the nucleophilicity of carbonyls, allowing a reaction that would not otherwise proceed with electrophiles. The advantage of homogeneous catalysts is the ease of mixing them with the reactants, but they may also be difficult to separate from the products. Therefore, heterogeneous catalysts are preferred in many industrial processes.
## Reactions in organic chemistry {#reactions_in_organic_chemistry}
In organic chemistry, in addition to oxidation, reduction or acid-base reactions, a number of other reactions can take place which involves covalent bonds between carbon atoms or carbon and heteroatoms (such as oxygen, nitrogen, halogens, etc.). Many specific reactions in organic chemistry are name reactions designated after their discoverers.
One of the most industrially important reactions is the cracking of heavy hydrocarbons at oil refineries to create smaller, simpler molecules. This process is used to manufacture gasoline. Specific types of organic reactions may be grouped by their reaction mechanisms (particularly substitution, addition and elimination) or by the types of products they produce (for example, methylation, polymerisation and halogenation).
### Substitution
In a substitution reaction, a functional group in a particular chemical compound is replaced by another group. These reactions can be distinguished by the type of substituting species into a nucleophilic, electrophilic or radical substitution. `{{multiple image | direction = vertical | image1 = SN1 reaction mechanism.png|width1 = 300|image2 = SN2 reaction mechanism.png|width2 = 300| caption1 = S<sub>N</sub>1 mechanism| caption2 = S<sub>N</sub>2 mechanism}}`{=mediawiki}
In the first type, a nucleophile, an atom or molecule with an excess of electrons and thus a negative charge or partial charge, replaces another atom or part of the \"substrate\" molecule. The electron pair from the nucleophile attacks the substrate forming a new bond, while the leaving group departs with an electron pair. The nucleophile may be electrically neutral or negatively charged, whereas the substrate is typically neutral or positively charged. Examples of nucleophiles are hydroxide ion, alkoxides, amines and halides. This type of reaction is found mainly in aliphatic hydrocarbons, and rarely in aromatic hydrocarbon. The latter have high electron density and enter nucleophilic aromatic substitution only with very strong electron withdrawing groups. Nucleophilic substitution can take place by two different mechanisms, S~N~1 and S~N~2. In their names, S stands for substitution, N for nucleophilic, and the number represents the kinetic order of the reaction, unimolecular or bimolecular. `{{multiple image | direction = vertical
| align = right
| width = 120
| image1= Walden-inversion-3D-balls.png
|caption1=The three steps of an [[SN2 reaction|S<sub>N</sub>2 reaction]]. The nucleophile is green and the leaving group is red
|image2=SN2-Walden-before-and-after-horizontal-3D-balls.png
|caption2=S<sub>N</sub>2 reaction causes stereo inversion (Walden inversion)
}}`{=mediawiki}
The S~N~1 reaction proceeds in two steps. First, the leaving group is eliminated creating a carbocation. This is followed by a rapid reaction with the nucleophile.
In the S~N~2 mechanisms, the nucleophile forms a transition state with the attacked molecule, and only then the leaving group is cleaved. These two mechanisms differ in the stereochemistry of the products. S~N~1 leads to the non-stereospecific addition and does not result in a chiral center, but rather in a set of geometric isomers (*cis/trans*). In contrast, a reversal (Walden inversion) of the previously existing stereochemistry is observed in the S~N~2 mechanism.
Electrophilic substitution is the counterpart of the nucleophilic substitution in that the attacking atom or molecule, an electrophile, has low electron density and thus a positive charge. Typical electrophiles are the carbon atom of carbonyl groups, carbocations or sulfur or nitronium cations. This reaction takes place almost exclusively in aromatic hydrocarbons, where it is called electrophilic aromatic substitution. The electrophile attack results in the so-called σ-complex, a transition state in which the aromatic system is abolished. Then, the leaving group, usually a proton, is split off and the aromaticity is restored. An alternative to aromatic substitution is electrophilic aliphatic substitution. It is similar to the nucleophilic aliphatic substitution and also has two major types, S~E~1 and S~E~2.
In the third type of substitution reaction, radical substitution, the attacking particle is a radical. This process usually takes the form of a chain reaction, for example in the reaction of alkanes with halogens. In the first step, light or heat disintegrates the halogen-containing molecules producing radicals. Then the reaction proceeds as an avalanche until two radicals meet and recombine.
:;X. + R-H -\> X-H + R.
:;R. + X2 -\> R-X + X.
:
: Reactions during the chain reaction of radical substitution
### Addition and elimination {#addition_and_elimination}
The addition and its counterpart, the elimination, are reactions that change the number of substituents on the carbon atom, and form or cleave multiple bonds. Double and triple bonds can be produced by eliminating a suitable leaving group. Similar to the nucleophilic substitution, there are several possible reaction mechanisms that are named after the respective reaction order. In the E1 mechanism, the leaving group is ejected first, forming a carbocation. The next step, the formation of the double bond, takes place with the elimination of a proton (deprotonation). The leaving order is reversed in the E1cb mechanism, that is the proton is split off first. This mechanism requires the participation of a base. Because of the similar conditions, both reactions in the E1 or E1cb elimination always compete with the S~N~1 substitution.
The E2 mechanism also requires a base, but there the attack of the base and the elimination of the leaving group proceed simultaneously and produce no ionic intermediate. In contrast to the E1 eliminations, different stereochemical configurations are possible for the reaction product in the E2 mechanism, because the attack of the base preferentially occurs in the anti-position with respect to the leaving group. Because of the similar conditions and reagents, the E2 elimination is always in competition with the S~N~2-substitution.
The counterpart of elimination is an addition where double or triple bonds are converted into single bonds. Similar to substitution reactions, there are several types of additions distinguished by the type of the attacking particle. For example, in the electrophilic addition of hydrogen bromide, an electrophile (proton) attacks the double bond forming a carbocation, which then reacts with the nucleophile (bromine). The carbocation can be formed on either side of the double bond depending on the groups attached to its ends, and the preferred configuration can be predicted with the Markovnikov\'s rule. This rule states that \"In the heterolytic addition of a polar molecule to an alkene or alkyne, the more electronegative (nucleophilic) atom (or part) of the polar molecule becomes attached to the carbon atom bearing the smaller number of hydrogen atoms.\"
If the addition of a functional group takes place at the less substituted carbon atom of the double bond, then the electrophilic substitution with acids is not possible. In this case, one has to use the hydroboration--oxidation reaction, wherein the first step, the boron atom acts as electrophile and adds to the less substituted carbon atom. In the second step, the nucleophilic hydroperoxide or halogen anion attacks the boron atom.
While the addition to the electron-rich alkenes and alkynes is mainly electrophilic, the nucleophilic addition plays an important role in the carbon-heteroatom multiple bonds, and especially its most important representative, the carbonyl group. This process is often associated with elimination so that after the reaction the carbonyl group is present again. It is, therefore, called an addition-elimination reaction and may occur in carboxylic acid derivatives such as chlorides, esters or anhydrides. This reaction is often catalyzed by acids or bases, where the acids increase the electrophilicity of the carbonyl group by binding to the oxygen atom, whereas the bases enhance the nucleophilicity of the attacking nucleophile.
Nucleophilic addition of a carbanion or another nucleophile to the double bond of an alpha, beta-unsaturated carbonyl compound can proceed via the Michael reaction, which belongs to the larger class of conjugate additions. This is one of the most useful methods for the mild formation of C--C bonds.
Some additions which can not be executed with nucleophiles and electrophiles can be succeeded with free radicals. As with the free-radical substitution, the radical addition proceeds as a chain reaction, and such reactions are the basis of the free-radical polymerization.
### Other organic reaction mechanisms {#other_organic_reaction_mechanisms}
`{{multiple image | direction = vertical
| align = right
| width = 220
| image1= Diels Alder Mechanismus.svg
|caption1=Mechanism of a Diels-Alder reaction
| image2= Diels Alder Orbitale.svg
|caption2=Orbital overlap in a Diels-Alder reaction}}`{=mediawiki}
In a rearrangement reaction, the carbon skeleton of a molecule is rearranged to give a structural isomer of the original molecule. These include hydride shift reactions such as the Wagner-Meerwein rearrangement, where a hydrogen, alkyl or aryl group migrates from one carbon to a neighboring carbon. Most rearrangements are associated with the breaking and formation of new carbon-carbon bonds. Other examples are sigmatropic reaction such as the Cope rearrangement.
Cyclic rearrangements include cycloadditions and, more generally, pericyclic reactions, wherein two or more double bond-containing molecules form a cyclic molecule. An important example of cycloaddition reaction is the Diels--Alder reaction (the so-called \[4+2\] cycloaddition) between a conjugated diene and a substituted alkene to form a substituted cyclohexene system.
Whether a certain cycloaddition would proceed depends on the electronic orbitals of the participating species, as only orbitals with the same sign of wave function will overlap and interact constructively to form new bonds. Cycloaddition is usually assisted by light or heat. These perturbations result in a different arrangement of electrons in the excited state of the involved molecules and therefore in different effects. For example, the \[4+2\] Diels-Alder reactions can be assisted by heat whereas the \[2+2\] cycloaddition is selectively induced by light. Because of the orbital character, the potential for developing stereoisomeric products upon cycloaddition is limited, as described by the Woodward--Hoffmann rules.
## Biochemical reactions {#biochemical_reactions}
Biochemical reactions are mainly controlled by complex proteins called enzymes, which are usually specialized to catalyze only a single, specific reaction. The reaction takes place in the active site, a small part of the enzyme which is usually found in a cleft or pocket lined by amino acid residues, and the rest of the enzyme is used mainly for stabilization. The catalytic action of enzymes relies on several mechanisms including the molecular shape (\"induced fit\"), bond strain, proximity and orientation of molecules relative to the enzyme, proton donation or withdrawal (acid/base catalysis), electrostatic interactions and many others.
The biochemical reactions that occur in living organisms are collectively known as metabolism. Among the most important of its mechanisms is the anabolism, in which different DNA and enzyme-controlled processes result in the production of large molecules such as proteins and carbohydrates from smaller units. Bioenergetics studies the sources of energy for such reactions. Important energy sources are glucose and oxygen, which can be produced by plants via photosynthesis or assimilated from food and air, respectively. All organisms use this energy to produce adenosine triphosphate (ATP), which can then be used to energize other reactions. Decomposition of organic material by fungi, bacteria and other micro-organisms is also within the scope of biochemistry.
## Applications
Chemical reactions are central to chemical engineering, where they are used for the synthesis of new compounds from natural raw materials such as petroleum, mineral ores, and oxygen in air. It is essential to make the reaction as efficient as possible, maximizing the yield and minimizing the number of reagents, energy inputs and waste. Catalysts are especially helpful for reducing the energy required for the reaction and increasing its reaction rate.
Some specific reactions have their niche applications. For example, the thermite reaction is used to generate light and heat in pyrotechnics and welding. Although it is less controllable than the more conventional oxy-fuel welding, arc welding and flash welding, it requires much less equipment and is still used to mend rails, especially in remote areas.
## Monitoring
Mechanisms of monitoring chemical reactions depend strongly on the reaction rate. Relatively slow processes can be analyzed in situ for the concentrations and identities of the individual ingredients. Important tools of real-time analysis are the measurement of pH and analysis of optical absorption (color) and emission spectra. A less accessible but rather efficient method is the introduction of a radioactive isotope into the reaction and monitoring how it changes over time and where it moves to; this method is often used to analyze the redistribution of substances in the human body. Faster reactions are usually studied with ultrafast laser spectroscopy where utilization of femtosecond lasers allows short-lived transition states to be monitored at a time scaled down to a few femtoseconds.
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Casiquiare canal
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The **Casiquiare river** or **canal** (`{{IPA|es|kasiˈkjaɾe}}`{=mediawiki}) is a natural distributary of the upper Orinoco flowing southward into the Rio Negro, in Venezuela, South America. As such, it forms a unique natural canal between the Orinoco and Amazon river systems. It is the world\'s largest river of the kind that links two major river systems, a so-called bifurcation. The area forms a water divide, more dramatically at regional flood stage.
## Etymology
The name *Casiquiare*, first used in that form by Manuel Román, likely derives from the Ye\'kuana language name of the river, *Kashishiwadi*.
## Discovery
The first European to describe it was Spanish Jesuit missionary and explorer Cristóbal Diatristán de Acuña in 1639.
In 1744 a Jesuit priest named Manuel Román, while ascending the Orinoco River in the region of La Esmeralda, met some Portuguese slave-traders from the settlements on the Rio Negro. The Portuguese insisted they were not in Spanish territory but on a tributary of the Amazon; they invited Román back with them to prove their claim. He accompanied them on their return, by way of the Casiquiare canal, and afterwards retraced his route to the Orinoco. Along the way, he made first contact with the Ye\'kuana people, whom he enlisted to help in his journey. Charles Marie de La Condamine, seven months later, was able to give to the *Académie française* an account of Father Román\'s voyage, and thus confirm the existence of this waterway, first reported by Father Acuña in 1639.
Little credence was given to Román\'s statement until it was verified, in 1756, by the Spanish Boundary-line Commission of José Yturriaga and Solano. In 1800 German scientist Alexander von Humboldt and French botanist Aimé Bonpland explored the river. `{{citation needed span|During a 1924–25 expedition, [[Alexander H. Rice Jr.]] of [[Harvard University]] traveled up the Orinoco, traversed the Casiquiare canal, and descended the Rio Negro to the Amazon at Manaus. It was the first expedition to use aerial photography and [[shortwave radio]] for mapping of the region.|reason=Rice's WP article indicates he explored the Casiquiare Canal in 1919, and the use of aerial photography and shortwave radio was on a later expedition elsewhere.|date=November 2024}}`{=mediawiki} In 1968 the Casiquiare was navigated by an SRN6 hovercraft during a The Geographical Journal expedition.
## Geography
The origin of the Casiquiare, at the River Orinoco, is 9 mi below the mission of La Esmeralda at 3 8 18.5 N 65 52 42.5 W region:VE-X_type:landmark display=inline, and about 123 m above sea level. Its mouth at the Rio Negro, an affluent of the Amazon River, is near the town of San Carlos and is 91 m above sea level.
The general course is south-west, and its length, including windings, is about 200 mi. Its width, at its bifurcation with the Orinoco, is approximately 300 ft, with a current towards the Rio Negro of 0.75 mph. However, as it gains in volume from the very numerous tributary streams, large and small, that it receives en route, its velocity increases, and in the wet season reaches 5 mph, even 8 mph in certain stretches. It broadens considerably as it approaches its mouth, where it is about 1750 ft wide. The volume of water the Casiquiare captures from the Orinoco is small in comparison to what it accumulates in its course. Nevertheless, the geological processes are ongoing, and evidence points to a slow and gradual increase in the size of Casiquiare. It is likely that stream capture is in progress, i.e. what currently is the uppermost Orinoco basin, including Cunucunuma River, eventually will be entirely diverted by the Casiquiare into the Amazon basin.
In flood time, it is said to have a second connection with the Rio Negro by a branch, which it throws off to the westward, called the Itinivini, which leaves it at a point about 50 mi above its mouth. In the dry season, it has shallows, and is obstructed by sandbanks, a few rapids and granite rocks. Its shores are densely wooded, and the soil more fertile than that along the Rio Negro. The general slope of the plains through which the canal runs is south-west, but those of the Rio Negro slope south-east.
The Casiquiare is not a sluggish canal on a flat tableland, but a great, rapid river which, if its upper waters had not found contact with the Orinoco, perhaps by cutting back, would belong entirely to the Negro branch of the Amazon.
To the west of the Casiquiare, there is a much shorter and easier portage between the Orinoco and Amazon basins, called the isthmus of Pimichin, which is reached by ascending the Temi branch of the Atabapo River, an affluent of the Orinoco. Although the Temi is somewhat obstructed, it is believed that it could easily be made navigable for small craft. The isthmus is 10 mi across, with undulating ground, nowhere over 50 ft high, with swamps and marshes. In the early 20th century, it was much used for the transit of large canoes, which were hauled across it from the Temi River and reached the Rio Negro by a little stream called the Pimichin.
## Hydrographic divide {#hydrographic_divide}
The Casiquiare canal -- Orinoco River hydrographic divide is a representation of the hydrographic water divide that delineates the separation between the Orinoco Basin and the Amazon Basin. (The Orinoco Basin flows west--north--northeast into the Caribbean; the Amazon Basin flows east into the western Atlantic in the extreme northeast of Brazil.)
Essentially the river divide is a west-flowing, upriver section of Venezuela\'s Orinoco River with an outflow to the south into the Amazon Basin. This named outflow is the Casiquiare canal, which, as it heads downstream (southerly), picks up speed and also accumulates water volume.
The greatest manifestation of the divide is during floods. During flood stage, the Casiquiare\'s main outflow point into the Rio Negro is supplemented by an overflow that is a second, and more minor, entry river bifurcation into the Rio Negro and upstream from its major, common low-water entry confluence with the Rio Negro. At flood, the river becomes an area flow source, far more than a narrow confined river.
The Casiquiare canal connects the upper Orinoco, 9 mi below the mission of Esmeraldas, with the Rio Negro affluent of the Amazon River near the town of San Carlos.
The simplest description (besides the entire area-floodplain) of the water divide is a \"south-bank Orinoco River strip\" at the exit point of the Orinoco, also the origin of the Casiquiare canal. However, during the Orinoco\'s flood stage, that single, simply defined \"origin of the canal\" is turned into a region, and an entire strip along the southern bank of the Orinoco River.
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Cuboctahedron
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A **cuboctahedron** is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e., an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron.
## Construction
The cuboctahedron can be constructed in many ways:
- Its construction can be started by attaching two regular triangular cupolas base-to-base. This is similar to one of the Johnson solids, triangular orthobicupola. The difference is that the triangular orthobicupola is constructed with one of the cupolas twisted so that similar polygonal faces are adjacent, whereas the cuboctahedron is not. As a result, the cuboctahedron may also called the *triangular gyrobicupola*.
- Its construction can be started from a cube or a regular octahedron, marking the midpoints of their edges, and cutting off all the vertices at those points. This process is known as rectification, making the cuboctahedron being named the *rectified cube* and *rectified octahedron*.
- An alternative construction is by cutting off all vertices (truncation) of a regular tetrahedron and beveling the edges. This process is termed cantellation, lending the cuboctahedron an alternate name of *cantellated tetrahedron*.
From all of these constructions, the cuboctahedron has 14 faces: 8 equilateral triangles and 6 squares. It also has 24 edges and 12 vertices.
The Cartesian coordinates for the vertices of a cuboctahedron with edge length $\sqrt{2}$ centered at the origin are: $(\pm 1, \pm 1, 0), \qquad (\pm 1, 0, \pm 1), \qquad (0, \pm 1, \pm 1).$
## Properties
### Measurement and other metric properties {#measurement_and_other_metric_properties}
The surface area of a cuboctahedron $A$ can be determined by summing all the area of its polygonal faces. The volume of a cuboctahedron $V$ can be determined by slicing it off into two regular triangular cupolas, summing up their volume. Given that the edge length $a$, its surface area and volume are: $\begin{align}
A &= \left(6+2\sqrt{3}\right)a^2 &&\approx 9.464a^2 \\
V &= \frac{5 \sqrt{2}}{3} a^3 &&\approx 2.357a^3.
\end{align}$
The dihedral angle of a cuboctahedron can be calculated with the angle of triangular cupolas. The dihedral angle of a triangular cupola between square-to-triangle is approximately 125°, that between square-to-hexagon is 54.7°, and that between triangle-to-hexagon is 70.5°. Therefore, the dihedral angle of a cuboctahedron between square-to-triangle, on the edge where the base of two triangular cupolas are attached is 54.7° + 70.5° approximately 125°. Therefore, the dihedral angle of a cuboctahedron between square-to-triangle is approximately 125°.
Buckminster Fuller found that the cuboctahedron is the only polyhedron in which the distance between its center to the vertex is the same as the length of its edges. In other words, it has the same length vectors in three-dimensional space, known as *vector equilibrium*. The rigid struts and the flexible vertices of a cuboctahedron may also be transformed progressively into a regular icosahedron, regular octahedron, regular tetrahedron. Fuller named this the *jitterbug transformation*.
A cuboctahedron has the Rupert property, meaning there is a polyhedron of the same or larger size that can pass through its hole.
### Symmetry and classification {#symmetry_and_classification}
The cuboctahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. The cuboctahedron has two symmetries, resulting from the constructions as has mentioned above: the same symmetry as the regular octahedron or cube, the octahedral symmetry $\mathrm{O}_\mathrm{h}$, and the same symmetry as the regular tetrahedron, tetrahedral symmetry $\mathrm{T}_\mathrm{d}$. The polygonal faces that meet for every vertex are two equilateral triangles and two squares, and the vertex figure of a cuboctahedron is 3.4.3.4. The dual of a cuboctahedron is rhombic dodecahedron.
### Radial equilateral symmetry {#radial_equilateral_symmetry}
In a cuboctahedron, the long radius (center to vertex) is the same as the edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Its center is like the apical vertex of a canonical pyramid: one edge length away from *all* the other vertices. (In the case of the cuboctahedron, the center is in fact the apex of 6 square and 8 triangular pyramids). This radial equilateral symmetry is a property of only a few uniform polytopes, including the two-dimensional hexagon, the three-dimensional cuboctahedron, and the four-dimensional 24-cell and 8-cell (tesseract). *Radially equilateral* polytopes are those that can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge. Therefore, all the interior elements which meet at the center of these polytopes have equilateral triangle inward faces, as in the dissection of the cuboctahedron into 6 square pyramids and 8 tetrahedra.
Each of these radially equilateral polytopes also occurs as cells of a characteristic space-filling tessellation: the tiling of regular hexagons, the rectified cubic honeycomb (of alternating cuboctahedra and octahedra), the 24-cell honeycomb and the tesseractic honeycomb, respectively. Each tessellation has a dual tessellation; the cell centers in a tessellation are cell vertices in its dual tessellation. The densest known regular sphere-packing in two, three and four dimensions uses the cell centers of one of these tessellations as sphere centers.
Because it is radially equilateral, the cuboctahedron\'s center is one edge length distant from the 12 vertices.
## Configuration matrix {#configuration_matrix}
The cuboctahedron can be represented as a configuration matrix with elements grouped by symmetry transitivity classes. A configuration matrix is a matrix in which the rows and columns correspond to the elements of a polyhedron as in the vertices, edges, and faces. The diagonal of a matrix denotes the number of each element that appears in a polyhedron, whereas the non-diagonal of a matrix denotes the number of the column\'s elements that occur in or at the row\'s element.
The cuboctahedron has 1 transitivity class of 12 vertices, 1 class of 24 edges, and 2 classes of faces: 8 triangular and 6 square; each element in a matrix\'s diagonal. The 24 edges can be seen in 4 central hexagons.
With octahedral symmetry (orbifold 432), the squares have the 4-fold symmetry, triangles the 3-fold symmetry, and vertices the 2-fold symmetry. With tetrahedral symmetry (orbifold 332) the 24 vertices split into 2 edge classes, and the 8 triangles split into 2 face classes. The square symmetry is reduced to 2-fold.
+---------------------------+----------------------------------------------+
| Octahedral symmetry (432) | |
+===========================+==============================================+
| | -------------- ------ ------ ------ ------ |
| | \(432\) v~1~ e~1~ f~1~ f~2~ |
| | v~1\ (Z~2~)~ 12 \|4 \|2 \|2 |
| | e~1~ \|2 24 \|1 \|1 |
| | f~1\ (Z~3~)~ \|3 \|3 8 \* |
| | f~2\ (Z~4~)~ \|4 \|4 \* 6 |
| | -------------- ------ ------ ------ ------ |
| | |
| | : Configuration |
+---------------------------+----------------------------------------------+
## Graph
The skeleton of a cuboctahedron may be represented as the graph, one of the Archimedean graph. It has 12 vertices and 24 edges. It is quartic graph, which is four vertices connecting each vertex.
The graph of a cuboctahedron may be constructed as the line graph of the cubical graph, making it becomes the locally linear graph.
The 24 edges can be partitioned into 2 sets isomorphic to tetrahedral symmetry. The edges can also be partitioned into 4 hexagonal cycles, representing centrosymmetry, with only opposite vertices and edges in the same transitivity class.
+------------------------------+------------------------+----------------------+
| Octahedral (48 automorphism) | | Tetrahedral (24 aut) |
+==============================+========================+======================+
| | ------ ------ ------ | |
| | \\ v~1~ e~1~ | |
| | v~1~ 12 \|4 | |
| | e~1~ \|2 24 | |
| | ------ ------ ------ | |
| | | |
| | : Configuration | |
+------------------------------+------------------------+----------------------+
## Related polyhedra and honeycomb {#related_polyhedra_and_honeycomb}
The cuboctahedron shares its skeleton with the two nonconvex uniform polyhedra, the cubohemioctahedron and octahemioctahedron. These polyhedrons are constructed from the skeleton of a cuboctahedron in which the four hexagonal planes bisect its diagonal, intersecting its interior. Adding six squares or eight equilateral triangles results in the cubohemicotahedron or octahemioctahedron, respectively.
The cuboctahedron 2-covers the tetrahemihexahedron, which accordingly has the same abstract vertex figure (two triangles and two squares: $3 \cdot 4 \cdot 3 \cdot 4$) and half the vertices, edges, and faces. (The actual vertex figure of the tetrahemihexahedron is $3 \cdot 4 \cdot \frac{3}{2} \cdot 4$, with the $\frac{a}{2}$ factor due to the cross.)
The cuboctahedron can be dissected into 6 square pyramids and 8 tetrahedra meeting at a central point. This dissection is expressed in the tetrahedral-octahedral honeycomb where pairs of square pyramids are combined into octahedra.
## Appearance
The cuboctahedron was probably known to Plato: Heron\'s *Definitiones* quotes Archimedes as saying that Plato knew of a solid made of 8 triangles and 6 squares.
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Christian Goldbach
|
**Christian Goldbach** (`{{IPAc-en|ˈ|ɡ|oʊ|l|d|b|ɑː|k}}`{=mediawiki} `{{respell|GOHLD|bahk}}`{=mediawiki}, `{{IPA|de|ˈkʁɪsti̯a(ː)n ˈɡɔltbax|lang}}`{=mediawiki}; 18 March 1690 -- 20 November 1764) was a Prussian mathematician connected with some important research mainly in number theory; he also studied law and took an interest in and a role in the Russian court. After traveling around Europe in his early life, he landed in Russia in 1725 as a professor at the newly founded Saint Petersburg Academy of Sciences. Goldbach jointly led the academy in 1737. However, he relinquished duties in the academy in 1742 and worked in the Russian Ministry of Foreign Affairs until his death in 1764. He is remembered today for Goldbach\'s conjecture and the Goldbach--Euler Theorem. He had a close friendship with famous mathematician Leonhard Euler, serving as inspiration for Euler\'s mathematical pursuits.
## Biography
### Early life {#early_life}
Born in the Duchy of Prussia\'s capital Königsberg, part of Brandenburg-Prussia, Goldbach was the son of a pastor. He studied at the Royal Albertus University. After finishing his studies he went on long educational trips from 1710 to 1724 through Europe, visiting other German states, England, the Netherlands, Italy, and France, meeting with many famous mathematicians, such as Gottfried Leibniz, Leonhard Euler, and Nicholas I Bernoulli. These acquaintances started Goldbach\'s interest in mathematics. He briefly attended Oxford University in 1713 and, while he was there, Goldbach studied mathematics with John Wallis and Isaac Newton. Also, Goldbach\'s travels fostered his interest in philology, archaeology, metaphysics, ballistics, and medicine. Between 1717 and 1724, Goldbach published his first few papers which, while minor, credited his mathematical ability. Back in Königsberg, he became acquainted with Georg Bernhard Bilfinger and Jakob Hermann.
### Saint Petersburg Academy of Sciences {#saint_petersburg_academy_of_sciences}
Goldbach followed Bilfinger and Hermann to the newly opened St. Petersburg Academy of Sciences in 1725. Christian Wolff had invited and had written recommendations for all the Germans who traveled to Saint Petersburg for the academy except Goldbach. Goldbach wrote to the president-designate of the academy, petitioning for a position in the academy, using his past publications and knowledge in medicine and law as qualifications. Goldbach was then hired to a five-year contract as a professor of mathematics and historian of the academy. As historian of the academy, he recorded each academy meeting from the opening of the school in 1725 until January 1728. Goldbach worked with famous mathematicians like Leonhard Euler, Daniel Bernoulli, Johann Bernoulli, and Jean le Rond d\'Alembert. Goldbach also played a part in Euler\'s decision to academically pursue mathematics instead of medicine, cementing mathematics as the premier research field of the academy in the 1730s.
### Russian government work {#russian_government_work}
In 1728, when Peter II became Tsar of Russia, Goldbach became Peter II and Anna\'s, Peter II\'s cousin, tutor. Peter II moved the Russian court from St. Petersburg to Moscow in 1729, so Goldbach followed him to Moscow. Goldbach started a correspondence with Euler in 1729, in which some of Goldbach\'s most important mathematics contributions can be found. Upon Peter II\'s death in 1730, Goldbach stopped teaching but continued to assist Empress Anna. In 1732, Goldbach returned to the St. Petersburg Academy of Sciences and stayed in the Russian government when Anna moved the court back to St. Petersburg. Upon return to the academy, Goldbach was named corresponding secretary. With Goldbach\'s return, his friend Euler continued his teaching and research at the academy as well. Then, in 1737, Goldbach and J.D. Schumacher took over the administration of the academy. Also, Goldbach took on duty in Russian court under Empress Anna. He managed to retain his influence in court after the death of Anna and the rule of Empress Elizabeth. In 1742 he entered the Russian Ministry of Foreign Affairs, stepping away from the academy once more. Goldbach was gifted land and increased salary for his good work and rise in the Russian government. In 1760, Goldbach created new guidelines for the education of the royal children which would remain in place for 100 years. He died on 20 November 1764, aged 74, in Moscow.
Christian Goldbach was multilingual -- he wrote a diary in German and Latin, his letters were written in German, Latin, French, and Italian and for official documents he used Russian, German and Latin.
## Contributions
Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach\'s conjecture. He also studied and proved some theorems on perfect powers, such as the Goldbach--Euler theorem, and made several notable contributions to analysis. He also proved a result concerning Fermat numbers that is called Goldbach\'s theorem.
### Impact on Euler {#impact_on_euler}
It is Goldbach and Euler\'s correspondence that contains some of Goldbach\'s most important contributions to mathematics, specifically number theory. Goldbach and Euler\'s friendship survived Goldbach\'s move to Moscow in 1728 and communication ensued. Their correspondence spanned 196 letters over 35 years written in Latin, German, and French. These letters spanned a wide range of topics, including various mathematics topics. Goldbach was the leading influence on Euler\'s interest and work in number theory. Most of the letters discuss Euler\'s research in number theory as well as differential calculus. Until the late 1750s, Euler\'s correspondence on his number theory research was almost exclusively with Goldbach. Goldbach\'s earlier mathematical work and ideas in letters to Euler directly influenced some of Euler\'s work. In 1729, Euler solved two problems pertaining to sequences which had stumped Goldbach. Ensuingly, Euler outlined the solutions to Goldbach. Also, in 1729 Goldbach closely approximated the Basel problem, which prompted Euler\'s interest and concurring breakthrough solution. Goldbach, through his letters, kept Euler focused on number theory in the 1730s by discussing Fermat\'s conjecture with Euler. Euler subsequently offered a proof to the conjecture, crediting Goldbach with introducing him to the subfield. Euler proceeded to write 560 writings, published posthumously in four volumes of Opera omnia, with Goldbach\'s influence guiding some of the writings. Goldbach\'s famous conjecture and his writings with Euler prove him to be one of a handful of mathematicians who understood complex number theory in light of Fermat\'s revolutionary ideas on the topic.
## Works
- \(1729\) *De transformatione serierum*
- \(1732\) *De terminis generalibus serierum*
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Convex set
|
In geometry, a set of points is **convex** if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex.
The boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a given subset `{{mvar|A}}`{=mediawiki} of Euclidean space is called the convex hull of `{{mvar|A}}`{=mediawiki}. It is the smallest convex set containing `{{mvar|A}}`{=mediawiki}.
A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets. The branch of mathematics devoted to the study of properties of convex sets and convex functions is called convex analysis.
Spaces in which convex sets are defined include the Euclidean spaces, the affine spaces over the real numbers, and certain non-Euclidean geometries.
## Definitions
Let `{{mvar|S}}`{=mediawiki} be a vector space or an affine space over the real numbers, or, more generally, over some ordered field (this includes Euclidean spaces, which are affine spaces). A subset `{{mvar|C}}`{=mediawiki} of `{{mvar|S}}`{=mediawiki} is **convex** if, for all `{{mvar|x}}`{=mediawiki} and `{{mvar|y}}`{=mediawiki} in `{{mvar|C}}`{=mediawiki}, the line segment connecting `{{mvar|x}}`{=mediawiki} and `{{mvar|y}}`{=mediawiki} is included in `{{mvar|C}}`{=mediawiki}.
This means that the affine combination `{{math|(1 − ''t'')''x'' + ''ty''}}`{=mediawiki} belongs to `{{mvar|C}}`{=mediawiki} for all `{{mvar|x,y}}`{=mediawiki} in `{{mvar|C}}`{=mediawiki} and `{{mvar|t}}`{=mediawiki} in the interval `{{math|[0, 1]}}`{=mediawiki}. This implies that convexity is invariant under affine transformations. Further, it implies that a convex set in a real or complex topological vector space is path-connected (and therefore also connected).
A set `{{mvar|C}}`{=mediawiki} is **`{{visible anchor|strictly convex}}`{=mediawiki}** if every point on the line segment connecting `{{mvar|x}}`{=mediawiki} and `{{mvar|y}}`{=mediawiki} other than the endpoints is inside the topological interior of `{{mvar|C}}`{=mediawiki}. A closed convex subset is strictly convex if and only if every one of its boundary points is an extreme point.
A set `{{mvar|C}}`{=mediawiki} is **absolutely convex** if it is convex and balanced.
### Examples
The convex subsets of `{{math|'''R'''}}`{=mediawiki} (the set of real numbers) are the intervals and the points of `{{math|'''R'''}}`{=mediawiki}. Some examples of convex subsets of the Euclidean plane are solid regular polygons, solid triangles, and intersections of solid triangles. Some examples of convex subsets of a Euclidean 3-dimensional space are the Archimedean solids and the Platonic solids. The Kepler-Poinsot polyhedra are examples of non-convex sets.
### Non-convex set {#non_convex_set}
A set that is not convex is called a *non-convex set*. A polygon that is not a convex polygon is sometimes called a concave polygon, and some sources more generally use the term *concave set* to mean a non-convex set, but most authorities prohibit this usage.
The complement of a convex set, such as the epigraph of a concave function, is sometimes called a *reverse convex set*, especially in the context of mathematical optimization.
## Properties
Given `{{mvar|r}}`{=mediawiki} points `{{math|''u''<sub>1</sub>, ..., ''u<sub>r</sub>''}}`{=mediawiki} in a convex set `{{mvar|S}}`{=mediawiki}, and `{{mvar|r}}`{=mediawiki} nonnegative numbers `{{math|''λ''<sub>1</sub>, ..., ''λ<sub>r</sub>''}}`{=mediawiki} such that `{{math|''λ''<sub>1</sub> + ... + ''λ<sub>r</sub>'' {{=}}`{=mediawiki} 1}}, the affine combination $\sum_{k=1}^r\lambda_k u_k$ belongs to `{{mvar|S}}`{=mediawiki}. As the definition of a convex set is the case `{{math|1=''r'' = 2}}`{=mediawiki}, this property characterizes convex sets.
Such an affine combination is called a convex combination of `{{math|''u''<sub>1</sub>, ..., ''u<sub>r</sub>''}}`{=mediawiki}. The **convex hull** of a subset `{{mvar|S}}`{=mediawiki} of a real vector space is defined as the intersection of all convex sets that contain `{{mvar|S}}`{=mediawiki}. More concretely, the convex hull is the set of all convex combinations of points in `{{mvar|S}}`{=mediawiki}. In particular, this is a convex set.
A *(bounded) convex polytope* is the convex hull of a finite subset of some Euclidean space `{{math|'''R'''<sup>''n''</sup>}}`{=mediawiki}.
### Intersections and unions {#intersections_and_unions}
The collection of convex subsets of a vector space, an affine space, or a Euclidean space has the following properties:
1. The empty set and the whole space are convex.
2. The intersection of any collection of convex sets is convex.
3. The *union* of a collection of convex sets is convex if those sets form a chain (a totally ordered set) under inclusion. For this property, the restriction to chains is important, as the union of two convex sets need not be convex.
### Closed convex sets {#closed_convex_sets}
Closed convex sets are convex sets that contain all their limit points. They can be characterised as the intersections of *closed half-spaces* (sets of points in space that lie on and to one side of a hyperplane).
From what has just been said, it is clear that such intersections are convex, and they will also be closed sets. To prove the converse, i.e., every closed convex set may be represented as such intersection, one needs the supporting hyperplane theorem in the form that for a given closed convex set `{{mvar|C}}`{=mediawiki} and point `{{mvar|P}}`{=mediawiki} outside it, there is a closed half-space `{{mvar|H}}`{=mediawiki} that contains `{{mvar|C}}`{=mediawiki} and not `{{mvar|P}}`{=mediawiki}. The supporting hyperplane theorem is a special case of the Hahn--Banach theorem of functional analysis.
### Face of a convex set {#face_of_a_convex_set}
A **face** of a convex set $C$ is a convex subset $F$ of $C$ such that whenever a point $p$ in $F$ lies strictly between two points $x$ and $y$ in $C$, both $x$ and $y$ must be in $F$. Equivalently, for any $x,y\in C$ and any real number $0<t<1$ such that $(1-t)x+ty$ is in $F$, $x$ and $y$ must be in $F$. According to this definition, $C$ itself and the empty set are faces of $C$; these are sometimes called the *trivial faces* of $C$. An **extreme point** of $C$ is a point that is a face of $C$.
Let $C$ be a convex set in $\R^n$ that is compact (or equivalently, closed and bounded). Then $C$ is the convex hull of its extreme points. More generally, each compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points (the Krein--Milman theorem).
For example:
- A triangle in the plane (including the region inside) is a compact convex set. Its nontrivial faces are the three vertices and the three edges. (So the only extreme points are the three vertices.)
- The only nontrivial faces of the closed unit disk $\{ (x,y) \in \R^2: x^2+y^2 \leq 1 \}$ are its extreme points, namely the points on the unit circle $S^1 = \{ (x,y) \in \R^2: x^2+y^2=1 \}$.
### Convex sets and rectangles {#convex_sets_and_rectangles}
Let `{{mvar|C}}`{=mediawiki} be a convex body in the plane (a convex set whose interior is non-empty). We can inscribe a rectangle *r* in `{{mvar|C}}`{=mediawiki} such that a homothetic copy *R* of *r* is circumscribed about `{{mvar|C}}`{=mediawiki}. The positive homothety ratio is at most 2 and: $\tfrac{1}{2} \cdot\operatorname{Area}(R) \leq \operatorname{Area}(C) \leq 2\cdot \operatorname{Area}(r)$\
### Blaschke-Santaló diagrams {#blaschke_santaló_diagrams}
The set $\mathcal{K}^2$ of all planar convex bodies can be parameterized in terms of the convex body diameter *D*, its inradius *r* (the biggest circle contained in the convex body) and its circumradius *R* (the smallest circle containing the convex body). In fact, this set can be described by the set of inequalities given by $2r \le D \le 2R$ $R \le \frac{\sqrt{3}}{3} D$ $r + R \le D$ $D^2 \sqrt{4R^2-D^2} \le 2R (2R + \sqrt{4R^2 -D^2})$ and can be visualized as the image of the function *g* that maps a convex body to the `{{math|'''R'''<sup>2</sup>}}`{=mediawiki} point given by (*r*/*R*, *D*/2*R*). The image of this function is known a (*r*, *D*, *R*) Blachke-Santaló diagram. Alternatively, the set $\mathcal{K}^2$ can also be parametrized by its width (the smallest distance between any two different parallel support hyperplanes), perimeter and area.
### Other properties {#other_properties}
Let *X* be a topological vector space and $C \subseteq X$ be convex.
- $\operatorname{Cl} C$ and $\operatorname{Int} C$ are both convex (i.e. the closure and interior of convex sets are convex).
- If $a \in \operatorname{Int} C$ and $b \in \operatorname{Cl} C$ then $[a, b[ \, \subseteq \operatorname{Int} C$ (where $[a, b[ \, := \left\{ (1 - r) a + r b : 0 \leq r < 1 \right\}$).
- If $\operatorname{Int} C \neq \emptyset$ then:
- $\operatorname{cl} \left( \operatorname{Int} C \right) = \operatorname{Cl} C$, and
- $\operatorname{Int} C = \operatorname{Int} \left( \operatorname{Cl} C \right) = C^i$, where $C^{i}$ is the algebraic interior of *C*.
## Convex hulls and Minkowski sums {#convex_hulls_and_minkowski_sums}
### Convex hulls {#convex_hulls}
Every subset `{{mvar|A}}`{=mediawiki} of the vector space is contained within a smallest convex set (called the *convex hull* of `{{mvar|A}}`{=mediawiki}), namely the intersection of all convex sets containing `{{mvar|A}}`{=mediawiki}. The convex-hull operator Conv() has the characteristic properties of a closure operator:
- *extensive*: `{{math|''S'' ⊆ Conv(''S'')}}`{=mediawiki},
- *non-decreasing*: `{{math|''S'' ⊆ ''T''}}`{=mediawiki} implies that `{{math|Conv(''S'') ⊆ Conv(''T'')}}`{=mediawiki}, and
- *idempotent*: `{{math|Conv(Conv(''S'')) {{=}}`{=mediawiki} Conv(*S*)}}.
The convex-hull operation is needed for the set of convex sets to form a lattice, in which the \"*join*\" operation is the convex hull of the union of two convex sets $\operatorname{Conv}(S)\vee\operatorname{Conv}(T) = \operatorname{Conv}(S\cup T) = \operatorname{Conv}\bigl(\operatorname{Conv}(S)\cup\operatorname{Conv}(T)\bigr).$ The intersection of any collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice.
### Minkowski addition {#minkowski_addition}
In a real vector-space, the *Minkowski sum* of two (non-empty) sets, `{{math|''S''<sub>1</sub>}}`{=mediawiki} and `{{math|''S''<sub>2</sub>}}`{=mediawiki}, is defined to be the set `{{math|''S''<sub>1</sub> + ''S''<sub>2</sub>}}`{=mediawiki} formed by the addition of vectors element-wise from the summand-sets $S_1+S_2=\{x_1+x_2: x_1\in S_1, x_2\in S_2\}.$ More generally, the *Minkowski sum* of a finite family of (non-empty) sets `{{math|''S<sub>n</sub>''}}`{=mediawiki} is the set formed by element-wise addition of vectors $\sum_n S_n = \left \{ \sum_n x_n : x_n \in S_n \right \}.$
For Minkowski addition, the *zero set* `{{math|{0} }}`{=mediawiki} containing only the zero vector `{{math|0}}`{=mediawiki} has special importance: For every non-empty subset S of a vector space $S+\{0\}=S;$ in algebraic terminology, `{{math|{0} }}`{=mediawiki} is the identity element of Minkowski addition (on the collection of non-empty sets).
### Convex hulls of Minkowski sums {#convex_hulls_of_minkowski_sums}
Minkowski addition behaves well with respect to the operation of taking convex hulls, as shown by the following proposition:
Let `{{math|''S''<sub>1</sub>, ''S''<sub>2</sub>}}`{=mediawiki} be subsets of a real vector-space, the convex hull of their Minkowski sum is the Minkowski sum of their convex hulls $\operatorname{Conv}(S_1+S_2)=\operatorname{Conv}(S_1)+\operatorname{Conv}(S_2).$
This result holds more generally for each finite collection of non-empty sets: $\text{Conv}\left ( \sum_n S_n \right ) = \sum_n \text{Conv} \left (S_n \right).$
In mathematical terminology, the operations of Minkowski summation and of forming convex hulls are commuting operations.
### Minkowski sums of convex sets {#minkowski_sums_of_convex_sets}
The Minkowski sum of two compact convex sets is compact. The sum of a compact convex set and a closed convex set is closed.
The following famous theorem, proved by Dieudonné in 1966, gives a sufficient condition for the difference of two closed convex subsets to be closed. It uses the concept of a **recession cone** of a non-empty convex subset *S*, defined as: $\operatorname{rec} S = \left\{ x \in X \, : \, x + S \subseteq S \right\},$ where this set is a convex cone containing $0 \in X$ and satisfying $S + \operatorname{rec} S = S$. Note that if *S* is closed and convex then $\operatorname{rec} S$ is closed and for all $s_0 \in S$, $\operatorname{rec} S = \bigcap_{t > 0} t (S - s_0).$
**Theorem** (Dieudonné). Let *A* and *B* be non-empty, closed, and convex subsets of a locally convex topological vector space such that $\operatorname{rec} A \cap \operatorname{rec} B$ is a linear subspace. If *A* or *B* is locally compact then *A* − *B* is closed.
## Generalizations and extensions for convexity {#generalizations_and_extensions_for_convexity}
The notion of convexity in the Euclidean space may be generalized by modifying the definition in some or other aspects. The common name \"generalized convexity\" is used, because the resulting objects retain certain properties of convex sets.
### Star-convex (star-shaped) sets {#star_convex_star_shaped_sets}
Let `{{mvar|C}}`{=mediawiki} be a set in a real or complex vector space. `{{mvar|C}}`{=mediawiki} is **star convex (star-shaped)** if there exists an `{{math|''x''<sub>0</sub>}}`{=mediawiki} in `{{mvar|C}}`{=mediawiki} such that the line segment from `{{math|''x''<sub>0</sub>}}`{=mediawiki} to any point `{{mvar|y}}`{=mediawiki} in `{{mvar|C}}`{=mediawiki} is contained in `{{mvar|C}}`{=mediawiki}. Hence a non-empty convex set is always star-convex but a star-convex set is not always convex.
### Orthogonal convexity {#orthogonal_convexity}
An example of generalized convexity is **orthogonal convexity**.
A set `{{mvar|S}}`{=mediawiki} in the Euclidean space is called **orthogonally convex** or **ortho-convex**, if any segment parallel to any of the coordinate axes connecting two points of `{{mvar|S}}`{=mediawiki} lies totally within `{{mvar|S}}`{=mediawiki}. It is easy to prove that an intersection of any collection of orthoconvex sets is orthoconvex. Some other properties of convex sets are valid as well.
### Non-Euclidean geometry {#non_euclidean_geometry}
The definition of a convex set and a convex hull extends naturally to geometries which are not Euclidean by defining a geodesically convex set to be one that contains the geodesics joining any two points in the set.
### Order topology {#order_topology}
Convexity can be extended for a totally ordered set `{{mvar|X}}`{=mediawiki} endowed with the order topology.
Let `{{math|''Y'' ⊆ ''X''}}`{=mediawiki}. The subspace `{{mvar|Y}}`{=mediawiki} is a convex set if for each pair of points `{{math|''a'', ''b''}}`{=mediawiki} in `{{mvar|Y}}`{=mediawiki} such that `{{math|''a'' ≤ ''b''}}`{=mediawiki}, the interval `{{math|[''a'', ''b''] {{=}}`{=mediawiki} {*x* ∈ *X* {{!}} *a* ≤ *x* ≤ *b*} }} is contained in `{{mvar|Y}}`{=mediawiki}. That is, `{{mvar|Y}}`{=mediawiki} is convex if and only if for all `{{math|''a'', ''b''}}`{=mediawiki} in `{{mvar|Y}}`{=mediawiki}, `{{math|''a'' ≤ ''b''}}`{=mediawiki} implies `{{math|[''a'', ''b''] ⊆ ''Y''}}`{=mediawiki}.
A convex set is `{{em|not}}`{=mediawiki} connected in general: a counter-example is given by the subspace {1,2,3} in `{{math|'''Z'''}}`{=mediawiki}, which is both convex and not connected.
### Convexity spaces {#convexity_spaces}
The notion of convexity may be generalised to other objects, if certain properties of convexity are selected as axioms.
Given a set `{{mvar|X}}`{=mediawiki}, a **convexity** over `{{mvar|X}}`{=mediawiki} is a collection `{{math|''𝒞''}}`{=mediawiki} of subsets of `{{mvar|X}}`{=mediawiki} satisfying the following axioms:
1. The empty set and `{{mvar|X}}`{=mediawiki} are in `{{math|''𝒞''}}`{=mediawiki}.
2. The intersection of any collection from `{{math|''𝒞''}}`{=mediawiki} is in `{{math|''𝒞''}}`{=mediawiki}.
3. The union of a chain (with respect to the inclusion relation) of elements of `{{math|''𝒞''}}`{=mediawiki} is in `{{math|''𝒞''}}`{=mediawiki}.
The elements of `{{math|''𝒞''}}`{=mediawiki} are called convex sets and the pair `{{math|(''X'', ''𝒞'')}}`{=mediawiki} is called a **convexity space**. For the ordinary convexity, the first two axioms hold, and the third one is trivial.
For an alternative definition of abstract convexity, more suited to discrete geometry, see the *convex geometries* associated with antimatroids.
### Convex spaces {#convex_spaces}
Convexity can be generalised as an abstract algebraic structure: a space is convex if it is possible to take convex combinations of points.
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6,298 |
Cupola
|
}} thumb\|upright=1.6\|Cupolas on the towers of Montefiascone Cathedral, Italy
In architecture, a **cupola** (`{{IPAc-en|ˈ|k|(|j|)|uː|p|ə|l|ə}}`{=mediawiki}) is a relatively small, usually dome-like structure on top of a building often crowning a larger roof or dome. Cupolas often serve as a roof lantern to admit light and air or as a lookout.
The word derives, via Italian, from lower Latin *cupula* (classical Latin *cupella*), `{{etymology|grc|''{{wikt-lang|grc|κύπελλον}}'' ({{grc-transl|κύπελλον}})|small cup}}`{=mediawiki} (Latin *cupa*), indicating a vault resembling an upside-down cup.
The cylindrical drum underneath a larger cupola is called a tholobate.
## Background
The cupola evolved during the Renaissance from the older oculus. Being weatherproof, the cupola was better suited to the wetter climates of northern Europe. The chhatri, seen in Indian architecture, fits the definition of a cupola when it is used atop a larger structure.
Cupolas often serve as a belfry, belvedere, or roof lantern above a main roof. In other cases they may crown a spire, tower, or turret. Barns often have cupolas for ventilation.
Cupolas can also appear as small buildings in their own right.
The square, dome-like segment of a North American railroad train caboose that contains the second-level or \"angel\" seats is also called a cupola.
<File:White> marble cupolas cap minarets at the Tomb of Jahangir.jpg\|White marble cupolas cap minarets at the Tomb of Jahangir in Lahore, Pakistan <File:Santa> Maria del Fiore, Duomo.JPG\|The dome of Florence Cathedral with a roof lanternat the top <File:Cupola> ceiling Synagogue Gyor Hungary.jpg\|Interior of cupola ceiling in the old Synagogue of Győr, Hungary. <File:Great> Mosque Minaret - Kairouan, Tunisia.jpg\|Ribbed cupola crowns the minaret of the Mosque of Uqba, in Kairouan, Tunisia. <File:Cupola> - Armenian Orthodox church in Lvov.jpg\|Inside of Armenian Orthodox church cupola in Lviv, Ukraine. <File:ISS> STS130 Cupola view of Algeria coast.jpg\|View from the interior of the Cupola module on the International Space Station. <File:Brivio.church.cupola.jpg>\|Trompe-l\'œil painting of a cupola in a church in Northern Italy (Brivio)
## On armoured vehicles {#on_armoured_vehicles}
The term cupola can also refer to the protrusions atop an armoured fighting vehicle due to their distinctive dome-like appearance. They allow crew or personnel to observe, offering very good all round vision, or even field weaponry, without being exposed to incoming fire. Later designs, however, became progressively flatter and less prominent as technology evolved to allow designers to reduce the profile of their vehicles.
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Chupacabra
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The **chupacabra** or ***chupacabras*** (`{{IPA|es|tʃupaˈkaβɾas}}`{=mediawiki}, literally \'goat-sucker\', from *chupa*, \'sucks\', and *cabras*, \'goats\') is a legendary creature, or cryptid, in the folklore of parts of the Americas. The name comes from the animal\'s purported vampirism `{{Ndash}}`{=mediawiki} the chupacabra is said to attack and drink the blood of livestock, including goats.
Physical descriptions of the creature vary. In Puerto Rico and in Hispanic America it is generally described as a heavy creature, reptilian and alien-like, roughly the size of a small bear, and with a row of spines reaching from the neck to the base of the tail, while in the Southwestern United States it is depicted as more dog-like.
Initial sightings and accompanying descriptions first occurred in Puerto Rico in 1995. The creature has since been reported as far north as Maine, as far south as Chile, and even outside the Americas in countries like Russia and the Philippines. All of the reports are anecdotal and have been disregarded as uncorroborated or lacking evidence. Sightings in northern Mexico and the Southern United States have been verified as canids afflicted by mange.
## Name
can be literally translated as \'goat-sucker\', from *chupar* (\'to suck\') and *cabras* (\'goats\'). It is known as both *chupacabras* and *chupacabra* throughout the Americas, with the former being the original name, and the latter a regularization. The name is attributed to Puerto Rican comedian Silverio Pérez, who coined the label in 1995 while commenting on the attacks as a San Juan radio deejay.
## History
In 1975, a series of livestock killings in the small town of Moca, Puerto Rico were attributed to *el vampiro de Moca* (\'the vampire of Moca\'). Initially, it was suspected that the killings were committed by a Satanic cult; later more killings were reported around the island, and many farms reported loss of animal life. Each of the animals was reported to have had its body bled dry through a series of small circular incisions.
The first reported attack eventually attributed to the actual chupacabras occurred in March 1995. Eight sheep were discovered dead in Puerto Rico, each with three puncture wounds in the chest area and reportedly completely drained of blood. A few months later, in August, an eyewitness named Madelyne Tolentino reported seeing the creature in the Puerto Rican town of Canóvanas, where as many as 150 farm animals and pets were reportedly killed.
Puerto Rican comedian and entrepreneur Silverio Pérez is credited with coining the term *chupacabras* soon after the first incidents were reported in the press. Shortly after the first reported incidents in Puerto Rico, other animal deaths were reported in other countries, such as Argentina, Bolivia, Brazil, Chile, Colombia, Dominican Republic, El Salvador, Honduras, Mexico, Nicaragua, Panama, Peru, and the United States.
In 2019 a video recorded by *Mundo Ovni* showed the results of a supposed attack on chickens in the Seburuquillo sector of Lares, Puerto Rico.
## Reputed origin {#reputed_origin}
A five-year investigation by Benjamin Radford, documented in his 2011 book *Tracking the Chupacabra*, concluded that the description given by the original eyewitness in Puerto Rico, Madelyne Tolentino, was based on the creature Sil in the 1995 science-fiction horror film *Species*. The alien creature Sil is nearly identical to Tolentino\'s chupacabra eyewitness account and she had seen the movie before her report: \"It was a creature that looked like the chupacabra, with spines on its back and all\... The resemblance to the chupacabra was really impressive\", Tolentino reported. Radford revealed that Tolentino \"believed that the creatures and events she saw in *Species* were happening in reality in Puerto Rico at the time\", and therefore concludes that \"the most important chupacabra description cannot be trusted\". This, Radford believes, seriously undermines the credibility of the chupacabra as a real animal.
The reports of blood-sucking by the chupacabra were never confirmed by a necropsy, the only way to conclude that the animal was drained of blood. Dr. David Morales, a Puerto Rican veterinarian with the Department of Agriculture, analyzed 300 reported victims of the chupacabra and found that they had not been bled dry.
Radford divided the chupacabra reports into two categories: the reports from Puerto Rico and Latin America, where animals were attacked and it is supposed their blood was extracted; and the reports in the United States of mammals, mostly dogs and coyotes with mange, that people call \"chupacabra\" due to their unusual appearance.
In 2010, University of Michigan biologist Barry O\'Connor concluded that all the chupacabra reports in the United States were simply coyotes infected with the parasite *Sarcoptes scabiei*, whose symptoms would explain most of the features of the chupacabra: they would be left with little fur, thickened skin, and a rank odor. O\'Connor theorized that the attacks on goats occurred \"because these animals are greatly weakened, \[so\] they\'re going to have a hard time hunting. So they may be forced into attacking livestock because it\'s easier than running down a rabbit or a deer.\" Both dogs and coyotes can kill and not consume the prey, either because they are inexperienced, or due to injury or difficulty in killing the prey. The prey can survive the attack and die afterwards from internal bleeding or circulatory shock. The presence of two holes in the neck, corresponding with the canine teeth, are to be expected since this is the only way that most land carnivores have to catch their prey. There are reports of stray Mexican hairless dogs being mistaken for chupacabras.
## Appearance
The most common description of the chupacabra is that of a reptile-like creature, said to have leathery or scaly greenish-gray skin and sharp spines or quills running down its back. It is said to be approximately 3 to high, and stands and hops in a fashion similar to that of a kangaroo. This description was the chief one given to the few Puerto Rican reports in 1995 that claimed to have sighted the creature, with similar reports in parts of Chile and Argentina following.
Another common description of the chupacabra is of a strange breed of wild dog. This form is mostly hairless and has a pronounced spinal ridge, unusually pronounced eye sockets, fangs, and claws. This description started to appear in the early 2000s from reports trailing north from the Yucatán Peninsula, northern Mexico, and then into the United States; becoming the predominant description since. Unlike conventional predators, the chupacabra is said to drain all of the animal\'s blood (and sometimes organs) usually through three holes in the shape of a downwards-pointing triangle, but sometimes through only one or two holes.
## Plausibility of existence {#plausibility_of_existence}
The chupacabra panic first started in late 1995, Puerto Rico: farmers were mass reporting the mysterious killings of various livestock. In these reports, the farmers recalled two puncture wounds on the animal carcasses. Chupacabra killings were soon associated with a seemingly untouched animal carcass other than puncture wounds which were said to be used to suck the blood out of the victim. Reports of such killings began to spread around and eventually out of the country, reaching areas such as Mexico, Brazil, Chile, and the Southern area of the United States.
Most notably, these areas experience frequent, and extreme dry seasons; in the cases of the Puerto Rican reports of 1995 and the Mexican reports of 1996, both countries were currently experiencing or dealing with the aftermath of severe droughts. Investigations carried out in both countries at this time noted a certain dramatic violence in these killings. These environmental conditions could provide a simple explanation for the livestock killings: wild predators losing their usual prey to the drought, therefore being forced to hunt the livestock of farmers for sustenance. Thus, the same theory can be applied to many of the other \'chupacabra\' attacks: that the dry weather had created a more competitive environment for native predators, leading them to prey on livestock to survive. Such an idea can also explain the increased violence in the killings; hungry and desperate predators are driven to hunt livestock to avoid starvation, causing an increase in both the number of livestock killings, and the viciousness of each one.
Evidence of such is provided in page 179 of Benjamin Radford\'s book, *Tracking the Chupacabra: The Vampire Beast in Fact, Fiction, and Folklore.* Radford\'s chart highlights ten significant reports of chupacabra attacks, seven of which had a carcass recovered and examined; these autopsies concluded the causes of death as various animal attacks, as displayed though the animal DNA found on the carcasses. Radford provides further evidence in pages 161-162 of his book, displaying animals who are proven to have fallen victim to regular coyote attacks; thus, explaining that it is not unusual for an animal carcass to be left uneaten while only displaying puncture wounds and/or minimal signs of attack.
The plausibility of the chupacabra\'s existence is also discredited by the varying descriptions of the creature. Depending on the reported sighting, the creature is described with thick skin or fur, wings or no wings, a long tail or no tail, is bat-like, dog-like, or even alien-like. Evidently, the chupacabra has a wide variety of descriptions; to the point where it is hard to believe that all the sightings are of the same creature. A very likely explanation for this phenomenon is that individuals who had heard of the newly popular chupacabra had the creature\'s name fresh in their mind before they happened to see a strange looking animal. They then resort to make sense of their encounter by labelling it as the recently \'discovered\' monster, instead of a more realistic explanation. For example, some scientists hypothesize that what many believe to be a chupacabra is a wild or domestic dog affected by mange, a disease causing a thick buildup of skin and hair loss.
## Related legends {#related_legends}
The \"Ozark Howler\", a large bear-like animal, is the subject of a similar legend.
The Peuchens of Chile also share similarities in their supposed habits, but instead of being dog-like they are described as winged snakes. This legend may have originated from the vampire bat, an animal endemic to the region.
In the Philippines the Sigbin shares many of the chupacabra\'s descriptions.
In 2018 there were reports of suspected chupacabras in Manipur, India. Many domestic animals and poultry were killed in a manner similar to other chupacabra attacks, and several people reported that they had seen creatures. Forensic experts opined that street dogs were responsible for mass killing of domestic animals and poultry after studying the remnants of a corpse.
## Media
- A chupacabra is referred to in the 2009 novel *Drive Your Plow Over the Bones of the Dead*.
- The debut album by Imani Coppola is titled *Chupacabra*.
- In *Indigenous* (2014), the chupacabra is the main antagonist.
- The myth of the chupacabra is mocked in a 2012 episode of the cartoon series *South Park*, titled \"Jewpacabra\", in which antisemitic main character Eric Cartman claims to have seen a Jewish Chupacabra that kills children on Easter.
- The chupacabra was included as one of several vinyl figurines in Cryptozoic Entertainment\'s Cryptkins blind box toy line in 2018. A redesigned series of figurines, including an updated chupacabra, was released in August 2020.
- The search for a chupacabra was featured in the 1997 *The X-Files* episode \"El Mundo Gira\".
- \"Chupacabra\" was the title of the midseason finale of season 4 of the supernatural drama television series *Grimm*, in December 2014.
- *Teen Titans Academy*, a DC Comics book, has a bat-like metahuman called Chupacabra, whose alter ego is Diego Pérez, named in honour of George Pérez (the artist that initially illustrated the Teen Titans).
- A 1999 episode of *Futurama* features a monster called \"El Chupanibre\".
- In the *Jackie Chan Adventures* episode \"The Curse of El Chupacabra\", Jackie Chan\'s friend El Toro gets scratched and infected by a Chupacabra, causing him to transform into another Chupacabra every night, much like a werewolf.
- In season 3 of *Workaholics* called \"To Kill a Chupacabraj\", Blake finds what he believes to be the deceased corpse of the Rancho Chupacabra in the pool, though it turns out to be the neighbor\'s dog.
- In the Netflix original series *The Imperfects*, the character of Juan Ruiz transforms into a chupacabra whenever anyone he cares about is in danger.
- The 2016 film *La leyenda del Chupacabras* features the titular Chupacabra initially as an antagonist before revealing the creature is merely trying to rescue its family.
- The Brazilian Chupa-Cu legend created in 2017 takes its cues from the chupacabra.
- A \"Chupakabura\" plays the role of a tourism mascot for the fictional town of Manoyama in P.A. Works\' 2017 anime *Sakura Quest*. The spelling and pronunciation relates to a retired mascot called \"Kabura Kid\", whose name was a pun alluding to the Japanese word for turnips.
- The 2023 film *Chupa* is about a chupacabra that is saved from scientists who want to capture it to prove it is real and exploit it for medicine.
- The 2010-2011 *Super Sentai* series *Tensou Sentai Goseiger*\'s main antagonist Brajira of the Messiah assumes the guise Buredoran of the Chupacabra when working with the Yuumajuu, the villain faction of the second arc that is based on cryptids.
- The Ukrainian news program TSN used to broadcast fake news about the Chupacabra when no interesting news were there to broadcast.
- In a short titled \"Mission: Chupacabras\" from *Helluva Boss*, a Mexican goat-farmer mistakes Blitzo for a chupacabra and tries to sell him.
- *Chupacabra vs. The Alamo*, a 2013 made-for-TV movie.
- *Guns of El Chupacabra*, a 1997 martial arts based monster film.
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Fire (classical element)
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**Fire** is one of the four classical elements along with earth, water and air in ancient Greek philosophy and science. Fire is considered to be both hot and dry and, according to Plato, is associated with the tetrahedron.
## Greek and Roman tradition {#greek_and_roman_tradition}
Fire is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with the qualities of energy, assertiveness, and passion. In one Greek myth, Prometheus stole *fire* from the gods to protect the otherwise helpless humans, but was punished for this charity.
Fire was one of many *archai* proposed by the pre-Socratics, most of whom sought to reduce the cosmos, or its creation, to a single substance. Heraclitus `{{nowrap|(c. 535 BCE –}}`{=mediawiki} `{{nowrap|c. 475 BCE)}}`{=mediawiki} considered *fire* to be the most fundamental of all elements. He believed fire gave rise to the other three elements: \"All things are an interchange for fire, and fire for all things, just like goods for gold and gold for goods.\" He had a reputation for obscure philosophical principles and for speaking in riddles. He described how fire gave rise to the other elements as the: \"upward-downward path\", (*ὁδὸς ἄνω κάτω*), a \"hidden harmony\" or series of transformations he called the \"turnings of fire\", (*πυρὸς τροπαὶ*), first into *sea*, and half that *sea* into *earth*, and half that *earth* into rarefied *air*. This is a concept that anticipates both the four classical elements of Empedocles and Aristotle\'s transmutation of the four elements into one another.
> This world, which is the same for all, no one of gods or men has made. But it always was and will be: an ever-living fire, with measures of it kindling, and measures going out.
Heraclitus regarded the soul as being a mixture of fire and water, with fire being the more noble part and water the ignoble aspect. He believed the goal of the soul is to be rid of water and become pure fire: the dry soul is the best and it is worldly pleasures that make the soul \"moist\". He was known as the \"weeping philosopher\" and died of hydropsy, a swelling due to abnormal accumulation of fluid beneath the skin.
However, Empedocles of Akragas `{{nowrap|(c. 495 –}}`{=mediawiki} `{{nowrap|c. 435 BCE)}}`{=mediawiki}, is best known for having selected all elements as his *archai* and by the time of Plato `{{nowrap|(427–}}`{=mediawiki}`{{nowrap|347 BCE)}}`{=mediawiki}, the four Empedoclian elements were well established. In the *Timaeus*, Plato\'s major cosmological dialogue, the Platonic solid he associated with fire was the tetrahedron which is formed from four triangles and contains the least volume with the greatest surface area. This also makes fire the element with the smallest number of sides, and Plato regarded it as appropriate for the heat of fire, which he felt is sharp and stabbing, (like one of the points of a tetrahedron).
Plato\'s student Aristotle `{{nowrap|(384–}}`{=mediawiki}`{{nowrap|322 BCE)}}`{=mediawiki} did not maintain his former teacher\'s geometric view of the elements, but rather preferred a somewhat more naturalistic explanation for the elements based on their traditional qualities. Fire the hot and dry element, like the other elements, was an abstract principle and not identical with the normal solids, liquids and combustion phenomena we experience:
> What we commonly call fire. It is not really fire, for fire is an excess of heat and a sort of ebullition; but in reality, of what we call air, the part surrounding the earth is moist and warm, because it contains both vapour and a dry exhalation from the earth.
According to Aristotle, the four elements rise or fall toward their natural place in concentric layers surrounding the center of the Earth and form the terrestrial or sublunary spheres.
In ancient Greek medicine, each of the four humours became associated with an element. Yellow bile was the humor identified with fire, since both were hot and dry. Other things associated with fire and yellow bile in ancient and medieval medicine included the season of summer, since it increased the qualities of heat and aridity; the choleric temperament (of a person dominated by the yellow bile humour); the masculine; and the eastern point of the compass.
In alchemy the chemical element of sulfur was often associated with fire and its alchemical symbol and its symbol was an upward-pointing triangle. In alchemic tradition, metals are incubated by fire in the womb of the Earth and alchemists only accelerate their development.
## Indian tradition {#indian_tradition}
Agni is a Hindu and Vedic deity. The word *agni* is Sanskrit for fire (noun), cognate with Latin *ignis* (the root of English *ignite*), Russian *огонь* (fire), pronounced *agon*. Agni has three forms: fire, lightning and the sun.
Agni is one of the most important of the Vedic gods. He is the god of fire and the accepter of sacrifices. The sacrifices made to Agni go to the deities because Agni is a messenger from and to the other gods. He is ever-young, because the fire is re-lit every day, yet he is also immortal. In Indian tradition fire is also linked to Surya or the Sun and Mangala or Mars, and with the south-east direction.
Teukāya ekendriya is a name used in Jain tradition which refers to Jīvas said to be reincarnated as fire.
## Ceremonial magic {#ceremonial_magic}
Fire and the other Greek classical elements were incorporated into the Golden Dawn system. Philosophus (4=7) is the elemental grade attributed to fire; this grade is also attributed to the Qabalistic Sephirah Netzach and the planet Venus. The elemental weapon of fire is the Wand. Each of the elements has several associated spiritual beings. The archangel of fire is Michael, the angel is Aral, the ruler is Seraph, the king is Djin, and the fire elementals (following Paracelsus) are called salamanders. Fire is considered to be active; it is represented by the symbol for Leo and it is referred to the lower right point of the pentacle in the Supreme Invoking Ritual of the Pentacle. Many of these associations have since spread throughout the occult community.
## Tarot
Fire in tarot symbolizes conversion or passion. Many references to fire in tarot are related to the usage of fire in the practice of alchemy, in which the application of fire is a prime method of conversion, and everything that touches fire is changed, often beyond recognition. The symbol of fire was a cue pointing towards transformation, the chemical variant being the symbol delta, which is also the classical symbol for fire. Conversion symbolized can be good, for example, refining raw crudities to gold, as seen in The Devil. Conversion can also be bad, as in The Tower, symbolizing a downfall due to anger. Fire is associated with the suit of rods/wands, and as such, represents passion from inspiration. As an element, fire has mixed symbolism because it represents energy, which can be helpful when controlled, but volatile if left unchecked.
## Modern witchcraft {#modern_witchcraft}
Fire is one of the five elements that appear in most Wiccan traditions influenced by the Golden Dawn system of magic, and Aleister Crowley\'s mysticism, which was in turn inspired by the Golden Dawn.
## Freemasonry
In freemasonry, fire is present, for example, during the ceremony of winter solstice, a symbol also of renaissance and energy. Freemasonry takes the ancient symbolic meaning of fire and recognizes its double nature: creation, light, on the one hand, and destruction and purification, on the other.
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Air (classical element)
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**Air** or **Wind** is one of the four classical elements along with water, earth and fire in ancient Greek philosophy and in Western alchemy.
## Greek and Roman tradition {#greek_and_roman_tradition}
According to Plato, it is associated with the octahedron; air is considered to be both hot and wet. The ancient Greeks used two words for air: *aer* meant the dim lower atmosphere, and *aether* meant the bright upper atmosphere above the clouds. Plato, for instance writes that \"So it is with air: there is the brightest variety which we call *aether*, the muddiest which we call mist and darkness, and other kinds for which we have no name\....\" Among the early Greek Pre-Socratic philosophers, Anaximenes (mid-6th century BCE) named air as the *arche*. A similar belief was attributed by some ancient sources to Diogenes Apolloniates (late 5th century BCE), who also linked air with intelligence and soul (*psyche*), but other sources claim that his *arche* was a substance between air and fire. Aristophanes parodied such teachings in his play *The Clouds* by putting a prayer to air in the mouth of Socrates.
Air was one of many *archai* proposed by the Pre-socratics, most of whom tried to reduce all things to a single substance. However, Empedocles of Acragas (c. 495-c. 435 BCE) selected four *archai* for his four roots: air, fire, water, and earth. Ancient and modern opinions differ as to whether he identified air by the divine name Hera, Aidoneus or even Zeus. Empedocles' roots became the four classical elements of Greek philosophy. Plato (427--347 BCE) took over the four elements of Empedocles. In the *Timaeus*, his major cosmological dialogue, the Platonic solid associated with air is the octahedron which is formed from eight equilateral triangles. This places air between fire and water which Plato regarded as appropriate because it is intermediate in its mobility, sharpness, and ability to penetrate. He also said of air that its minuscule components are so smooth that one can barely feel them.
Plato\'s student Aristotle (384--322 BCE) developed a different explanation for the elements based on pairs of qualities. The four elements were arranged concentrically around the center of the universe to form the sublunary sphere. According to Aristotle, air is both hot and wet and occupies a place between fire and water among the elemental spheres. Aristotle definitively separated air from aether. For him, aether was an unchanging, almost divine substance that was found only in the heavens, where it formed celestial spheres.
### Humorism and temperaments {#humorism_and_temperaments}
------------- ------------ ----------- ------------- ------------- ---------------- -----------------
**Humour** **Season** **Ages** **Element** **Organ** **Qualities** **Temperament**
Blood spring infancy air liver moist and warm sanguine
Yellow bile summer youth fire gallbladder warm and dry choleric
Black bile autumn adulthood earth spleen dry and cold melancholic
Phlegm winter old age water brain/lungs cold and moist phlegmatic
------------- ------------ ----------- ------------- ------------- ---------------- -----------------
In ancient Greek medicine, each of the four humours became associated with an element. Blood was the humor identified with air, since both were hot and wet. Other things associated with air and blood in ancient and medieval medicine included the season of spring, since it increased the qualities of heat and moisture; the sanguine temperament (of a person dominated by the blood humour); hermaphrodite (combining the masculine quality of heat with the feminine quality of moisture); and the northern point of the compass.
### Alchemy
thumb\|upright=0.4\|Alchemical symbol for air The alchemical symbol for air is an upward-pointing triangle, bisected by a horizontal line.
## Modern reception {#modern_reception}
The Hermetic Order of the Golden Dawn, founded in 1888, incorporates air and the other Greek classical elements into its teachings. The elemental weapon of air is the dagger which must be painted yellow with magical names and sigils written upon it in violet. Each of the elements has several associated spiritual beings. The archangel of air is Raphael, the angel is Chassan, the ruler is Ariel, the king is Paralda, and the air elementals (following Paracelsus) are called sylphs. Air is considerable and it is referred to the upper left point of the pentagram in the Supreme Invoking Ritual of the Pentagram. Many of these associations have since spread throughout the occult community.
In the Golden Dawn and many other magical systems, each element is associated with one of the cardinal points and is placed under the care of guardian Watchtowers. The Watchtowers derive from the Enochian system of magic founded by Dee. In the Golden Dawn, they are represented by the Enochian elemental tablets. Air is associated with the east, which is guarded by the First Watchtower.
Air is one of the five elements that appear in most Wiccan and Pagan traditions. Wicca in particular was influenced by the Golden Dawn system of magic and Aleister Crowley\'s mysticism.
## Parallels in non-Western traditions {#parallels_in_non_western_traditions}
Air is not one of the traditional five Chinese classical elements. Nevertheless, the ancient Chinese concept of *Qi* or *chi* is believed to be close to that of air. *Qi* is believed to be part of every living thing that exists, as a kind of \"life force\" or \"spiritual energy\". It is frequently translated as \"energy flow\", or literally as \"air\" or \"breath\". (For example, *tiānqì*, literally \"sky breath\", is the Chinese word for \"weather\"). The concept of qi is often reified, however no scientific evidence supports its existence.
The element air also appears as a concept in the Buddhist philosophy which has an ancient history in China.
Some Western modern occultists equate the Chinese classical element of metal with *air*, others with wood due to the elemental association of wind and wood in the bagua.
Enlil was the god of air in ancient Sumer. Shu was the ancient Egyptian deity of air and the husband of Tefnut, goddess of moisture. He became an emblem of strength by virtue of his role in separating Nut from Geb. Shu played a primary role in the Coffin Texts, which were spells intended to help the deceased reach the realm of the afterlife safely. On the way to the sky, the spirit had to travel through the air as one spell indicates: \"I have gone up in Shu, I have climbed on the sunbeams.\"
According to Jain beliefs, the element air is inhabited by one-sensed beings or spirits called vāyukāya ekendriya, sometimes said to inhabit various kinds of winds such as whirlwinds, cyclones, monsoons, west winds and trade winds. Prior to reincarnating into another lifeform, spirits can remain as vāyukāya ekendriya from anywhere between one instant to up to three-thousand years, depending on the karma of the spirits.
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Earth (classical element)
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**Earth** is one of the classical elements, in some systems being one of the four along with air, fire, and water.
## European tradition {#european_tradition}
thumb\|left\|upright=0.7\|*Earth* (1681) by Benoît Massou, a statue of the *Grande Commande*, with allegorical attributes inspired by Cesare Ripa's *Iconologia*. Earth is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with qualities of heaviness, matter and the terrestrial world. Due to the hero cults, and chthonic underworld deities, the element of *earth* is also associated with the sensual aspects of both life and death in later occultism.
Empedocles of Acragas `{{nowrap|(c. 495 –}}`{=mediawiki} `{{nowrap|c. 435 BCE)}}`{=mediawiki} proposed four *archai* by which to understand the cosmos: *fire*,*air*, *water*, and *earth*. Plato (427--347 BCE) believed the elements were geometric forms (the platonic solids) and he assigned the cube to the element of *earth* in his dialogue *Timaeus*. Aristotle (384--322 BCE) believed *earth* was the heaviest element, and his theory of *natural place* suggested that any *earth--laden* substances, would fall quickly, straight down, towards the center of the *cosmos*.
In Classical Greek and Roman myth, various goddesses represented the Earth, seasons, crops and fertility, including Demeter and Persephone; Ceres; the Horae (goddesses of the seasons), and Proserpina; and Hades (Pluto) who ruled the souls of dead in the Underworld.
In ancient Greek medicine, each of the four humours became associated with an element. Black bile was the humor identified with earth, since both were cold and dry. Other things associated with earth and black bile in ancient and medieval medicine included the season of fall, since it increased the qualities of cold and aridity; the melancholic temperament (of a person dominated by the black bile humour); the feminine; and the southern point of the compass.
thumb\|left\|upright=0.4\|Alchemical symbol for earth
In alchemy, earth was believed to be primarily dry, and secondarily cold, (as per Aristotle). Beyond those classical attributes, the chemical substance salt, was associated with earth and its alchemical symbol was a downward-pointing triangle, bisected by a horizontal line.
## Indian tradition {#indian_tradition}
**Prithvi** (Sanskrit: *`{{IAST|pṛthvī}}`{=mediawiki}*, also *`{{IAST|pṛthivī}}`{=mediawiki}*) is the Hindu *earth* and mother goddess. According to one such tradition, she is the personification of the Earth itself; according to another, its actual mother, being *Prithvi Tattwa*, the essence of the element earth.
As *Prithvi Mata*, or \"Mother Earth\", she contrasts with *Dyaus Pita*, \"father sky\". In the Rigveda, *earth* and sky are frequently addressed as a duality, often indicated by the idea of two complementary \"half-shells.\" In addition, the element Earth is associated with Budha or Mercury who represents communication, business, mathematics and other practical matters.
Jainism mentions one-sensed beings or spirits believed to inhabit the element earth sometimes classified as pṛthvīkāya ekendriya.
## Ceremonial magic {#ceremonial_magic}
Earth and the other Greek classical elements were incorporated into the Golden Dawn system. Zelator is the elemental grade attributed to earth; this grade is also attributed to the Sephirot of Malkuth. The elemental weapon of earth is the Pentacle. Each of the elements has several associated spiritual beings. The archangel of earth is Uriel, the angel is Phorlakh, the ruler is Kerub, the king is Ghob, and the earth elementals (following Paracelsus) are called gnomes. Earth is considered to be passive; it is represented by the symbol for Taurus, and it is referred to the lower left point of the pentagram in the Supreme Invoking Ritual of the Pentagram. Many of these associations have since spread throughout the occult community.
It is sometimes represented by its Tattva or by a downward pointing triangle with a horizontal line through it.
## Modern witchcraft {#modern_witchcraft}
Earth is one of the five elements that appear in most Wiccan and Pagan traditions. Wicca in particular was influenced by the Golden Dawn system of magic, and Aleister Crowley\'s mysticism which was in turn inspired by the Golden Dawn.
## Other traditions {#other_traditions}
*Earth* is represented in the Aztec religion by a house; to the Hindus, a lotus; to the Scythians, a plough; to the Greeks, a wheel; and in Christian iconography; bulls and birds.
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Blue Jam
|
***Blue Jam*** was an ambient, surreal dark comedy and horror radio programme created and directed by Chris Morris. It was broadcast on BBC Radio 1 in the early hours of the morning, for three series from 1997 to 1999.
The programme gained cult status due to its unique mix of surreal monologue, ambient soundtrack, synthesised voices, heavily edited broadcasts and recurring sketches. It featured vocal performances of Kevin Eldon, Julia Davis, Mark Heap, David Cann and Amelia Bullmore, with Morris himself delivering disturbing monologues, one of which was revamped and made into the BAFTA-winning short film *My Wrongs #8245--8249 & 117*. Writers who contributed to the programme included Graham Linehan, Arthur Mathews, Peter Baynham, David Quantick, Jane Bussmann, Robert Katz and the cast.
The programme was adapted into the TV series *Jam*, which aired in 2000.
## Production
On his inspiration for making the show, Morris commented: \"It was so singular, and it came from a mood, quite a desolate mood. I had this misty, autumnal, boggy mood anyway, so I just went with that. But no doubt getting to the end of something like *Brass Eye*, where you\'ve been forced to be a sort of surrogate lawyer, well, that\'s the most creatively stifling thing you could possibly do.\" Morris also described the show as being \"like the nightmares you have when you fall asleep listening to the BBC World Service\" (a reference to the World Service also appears in one of the monologues read by Morris).
Morris originally requested that the show be broadcast at 3 a.m. on Radio 1 \"because at that hour, on insomniac radio, the amplitude of terrible things is enormously overblown\". As a compromise, the show was broadcast at midnight without much promotion. Morris reportedly included sketches too graphic or transgressive for radio that he knew would be cut so as to make his other material seem less transgressive in comparison. During the airing of episode 6 of series one, a re-editing of the Archbishop of Canterbury\'s speech at Princess Diana\'s funeral was deemed too offensive for broadcast, and was switched with a different episode as it aired.
## Format and style {#format_and_style}
Each episode opened (and closed) with a short spoken monologue (delivered by Morris) describing, in surreal, broken language, various bizarre feelings and situations (for example: \"when you sick so sad you cry, and in crying cry a whole leopard from your eye\"), set to ambient music interspersed with short clips of other songs and sounds. The introduction would always end with \"welcome in Blue Jam\", inviting the listener, who is presumably experiencing such feelings, to get lost in the program. (This format was replicated in the television adaptation *Jam*, often reusing opening monologues from series 3 of the radio series.) The sketches within dealt with heavy and taboo topics, such as murder, suicide, missing or dead children, and rape.
### Common recurring sketches {#common_recurring_sketches}
- **Doctor** (played by David Cann): \"The Doctor\" is a seemingly \"normal\" physician working in a standard British medical practice. However, he has a habit of treating his patients in bizarre and often disturbing ways, such as prescribing heroin for a sore jaw, kissing patients on various body parts to make swellings go away, making a man with a headache jump up and down to make his penis swing (while mirroring the patient\'s bewildered jumping himself) and making a patient leave and go into the next room so he can examine him over the telephone. His name is revealed to be **Michael Perlin** in several sketches.
- **The Monologue Man** (played by Chris Morris): Short stories, often up to 10 minutes in length, written from the perspective of a lonely and socially inept man. Each story usually involves the protagonist\'s acquaintance Suzy in some capacity.
- **Michael Alexander St. John**: A parody of hyperbolic and pun-laden radio presenting, St. John presents items such as the top 10 singles charts and the weekend\'s gigs in an incongruous upper class English accent
- **Bad Sex**: Short clips of two lovers (played by Julia Davis and Kevin Eldon) making increasingly bizarre erotic requests of one another, such as to \"shit your leg off\" and \"make your spunk come out green\".
- **The Interviewer** (played by Chris Morris): conducting real interviews with celebrities such as Andrew Morton and Jerry Springer, Morris confuses and mocks his subjects with ambiguous and odd questions.
- **Mr. Ventham** (played by Mark Heap): An extremely awkward man who requires one-to-one consultations with **Mr. Reilly** (played by David Cann), who seems to be his psychologist, for the most banal of matters.
- **Unflustered Parents** (David Cann and Julia Davis): A middle class couple that seem quite ambivalent to the fact their young son has been abducted from school or that their pet lions are eating their neighbours
The sketches not listed are often in the style of a documentary; characters speak as if being interviewed about a recent event. In one sketch, a character voiced by Morris describes a man attempting to commit suicide by jumping off a second-story balcony repeatedly; in another, an angry man (Eldon) shouts about how his car, after being picked up from the garage, is only four feet long.
### Radio stings {#radio_stings}
Morris included a series of \'radio stings\', bizarre sequences of sounds and prose as a parody of modern DJs\' own soundbites and self-advertising pieces. Each one revolves around a contemporary DJ, such as Chris Moyles, Jo Whiley and Mark Goodier, typically involving each DJ dying in a graphic way or going mad in some form -- for example, Chris Moyles covering himself in jam and hanging himself from the top of a building.
## Episodes
Three series were produced, with a total of eighteen episodes. All episodes were originally broadcast weekly on BBC Radio 1. Series 1 was broadcast from 14 November to 19 December 1997; series 2 was broadcast from 27 March to 1 May 1998; and series 3 broadcast from 21 January to 25 February 1999.
- Series 1 -- (Fridays) 14 November 1997 to 19 December 1997, from 00:00 to 01:00.
- Series 2 -- (Fridays) 27 March 1998 to 1 May 1998, from 01:00 to 02:00.
- Series 3 -- (Thursdays) 21 January 1999 to 25 February 1999, from 00:00 to 01:00.
The first five episodes of series 1 of *Blue Jam* were repeated by BBC Radio 4 Extra in February and March 2014, and series 2 was rebroadcast in December.
## Music
*Blue Jam* features songs, generally of a downtempo nature, interspersed between (and sometimes during) sketches. Artists featured includes Massive Attack, Air, Morcheeba, The Chemical Brothers, Björk, Aphex Twin, Everything But the Girl and Dimitri from Paris, as well as various non-electronic artists including Sly and the Family Stone, Serge Gainsbourg, The Cardigans and Eels.
## Reception
*Blue Jam* was favourably reviewed on several occasions by *The Guardian* and also received a positive review by *The Independent*.
Digital Spy wrote in 2014: \"It\'s a heady cocktail that provokes an odd, unsettling reaction in the listener, yet *Blue Jam* is still thumpingly and frequently laugh-out-loud hilarious.\" *Hot Press* called it \"as odd as comedy gets\".
## CD release {#cd_release}
A CD of a number of *Blue Jam* sketches was released on 23 October 2000 by record label Warp. Although the CD claims to have 22 tracks, the last one, \"www.bishopslips.com\", is not a track, but rather a reference to the \"Bishopslips\" sketch, which was cut in the middle of a broadcast. Most of the sketches on the CD were remade for *Jam*.
Track listing
1. \"Blue Jam Intro\"
2. \"Doc Phone\"
3. \"Lamacq sting\"
4. \"4 ft Car\"
5. \"Suicide Journalist\"
6. \"Acupuncture\"
7. \"Bad Sex\"
8. \"Mayo Sting\"
9. \"Unflustered Parents\"
10. \"Moyles Sting\"
11. \"TV Lizards\"
12. \"Doc Cock\"
13. \"Hobbs Sting\"
14. \"Morton Interview\"
15. \"Fix It Girl\"
16. \"Porn\"
17. \"Kids Party\"
18. \"Club News\"
19. \"Whiley Sting\"
20. \"Little Girl Balls\"
21. \"Blue Jam Outro\"
22. \"www.bishopslips.com\" (not a real track)
## Related shows {#related_shows}
*Blue Jam* was later made for television and broadcast on Channel 4 as *Jam*. It used unusual editing techniques to achieve an unnerving ambience in keeping with the radio show. Many of the sketches were lifted from the radio version, even to the extent of simply setting images to the radio soundtrack. A subsequent \"re-mixed\" airing, called *Jaaaaam* was even more extreme in its use of post-production gadgetry, often heavily distorting the footage.
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Clement Martyn Doke
|
**Clement Martyn Doke** (16 May 1893 in Bristol, United Kingdom -- 24 February 1980 in East London, South Africa) was a South African linguist working mainly on African languages. Realizing that the grammatical structures of Bantu languages are quite different from those of European languages, he was one of the first African linguists of his time to abandon the Euro-centric approach to language description for a more locally grounded one. A most prolific writer, he published a string of grammars, several dictionaries, comparative work, and a history of Bantu linguistics.
## Early life and career {#early_life_and_career}
The Doke family had been engaged in missionary activity for the Baptist Church for some generations. His father, Reverend Joseph J. Doke, left England and travelled to South Africa in 1882, where he met and married Agnes Biggs. They returned to England, where Clement was born as the third of four children. The family moved to New Zealand and eventually returned to South Africa in 1903, where it later settled in Johannesburg.
At the age of 18, Clement received a bachelor\'s degree from Transvaal University College in Pretoria (now the University of Pretoria). He decided to devote his life to missionary activity. In 1913, he accompanied his father on a tour of north-western Rhodesia, to an area called Lambaland, now known as Ilamba. It is at the watershed of the Congo and Zambesi rivers. Part of the district lay in Northern Rhodesia and part of the Belgian Congo. The Cape-Cairo Railway threaded through its eastern portion; otherwise, most travel had to be on foot.
The Reverend William Arthur Phillips of the Nyasa Industrial Mission in Blantyre had established a Baptist mission there in 1905; it served an area of 25000 sqmi and 50,000 souls. The Dokes were supposed to investigate whether the mission in Lambaland could be taken over by the Baptist Union of South Africa. It was on that trip that Doke\'s father contracted enteric fever and died soon afterwards. Mahatma Gandhi attended the memorial service and addressed the congregation. Clement assumed his father\'s role.
The South African Baptists decided to take over Kafulafuta Mission, and its founder, Reverend Phillips, remained as superintendent. Clement Doke returned to Kafulafuta as missionary in 1914, followed by his sister Olive two years later.
## Study of Lamba {#study_of_lamba}
At first, Clement Doke was frustrated by his inability to communicate with the Lamba. The only written material available at the time was a translation of Jonah and a collection of 47 hymns. Soon, however, he mastered the language and published his first book, *Ifintu Fyakwe Lesa* (\"The Things of God, a Primer of Scripture Knowledge\") in 1917. He enrolled in Johannesburg as the extension of Transvaal University College for an MA degree. His thesis was published as *The Grammar of the Lamba language*. The book is couched in traditional grammatical terms, as Doke had not yet established his innovative method to analyse and describe the Bantu languages. His later *Textbook of Lamba Grammar* is far superior in that respect.
Doke was also interested in ethnology. In 1931 he compiled *The Lambas of Northern Rhodesia*, which remains one of the outstanding ethnographic descriptions of the peoples of Central Africa. For Doke, literacy was part of evangelisation since it was required so that people to appreciate the Bible\'s message, but it was only after his retirement that he completed the translation of the Bible into Lamba. It was published under the title of *Amasiwi AwaLesa* (\"The Words of God\") in 1959.
## University of the Witwatersrand {#university_of_the_witwatersrand}
In 1919, Doke married Hilda Lehmann, who accompanied him back to Lambaland. Both contracted malaria during their work, and she was forbidden to return to Lambaland. Clement Doke also realised that his field work could not continue much longer, and he left in 1921. He was recruited by the newly founded University of the Witwatersrand. So that he could secure a qualification as a lecturer, the family moved to England, where he registered at the School of Oriental and African Studies. His major languages were Lamba and Luba, but as no suitable examiner was available, he eventually had to change his language to Zulu.
Doke took up his appointment in the new Department of Bantu Studies at the University of Witwatersrand in 1923. In 1925 he received his D.Litt. for his doctoral thesis *The Phonetics of the Zulu Language* and was promoted to Senior Lecturer. In 1931 he was appointed to the Chair of Bantu Studies and thus headed the Department of Bantu Studies. The department acted as a catalyst for the admission of Africans to the university. As early as 1925 a limited number were admitted to the vacation course in African Studies. Doke supported the appointment of Benedict Wallet Vilakazi as member of the staff, as he believed a native speaker was essential for acquiring a language. That provoked a storm of criticism and controversy from the public. Both of them collaborated on the *Zulu-English Dictionary*. First published in 1948, it is still one of the best examples of lexicography for any Bantu language.
At the request of the government of Southern Rhodesia, Doke investigated the range of dialect diversity among the languages of the country and made recommendations for *Unified Shona*, which formed the basis for Standard Shona. He devised a unified orthography based on the Zezuru, Karanga and Manyika dialects. However, Doke\'s orthography was never fully accepted, and the South African government introduced an alternative, which left Shona with two competing orthographies between 1935 and 1955.
During his tenure, Doke developed and promoted a method of linguistic analysis and description of the Bantu languages that was based upon the structure of these languages. The \"Dokean model\" continues to be one of the dominant models of linguistic description in Southern and Central Africa. His classification of the Bantu languages was for many years the dominant view of the interrelations among the African languages. He was also an early describer of Khoisan and Bantu click consonants, devising phonetic symbols for a number of them.
Doke served the University of the Witwatersrand until his retirement in 1953. He was awarded the honorary degree of Doctor of Letters by Rhodes University and the honorary degree of Doctor of Laws by the University of the Witwatersrand in 1972.
The former missionary always remained devoted to the Baptist Church. He was elected President of the South African Baptist Union in 1949 and spent a year visiting churches and mission stations. He used his presidential address in condemning the recently established apartheid policy: *I solemnly warn the Government that the spirit behind their apartheid legislation, and the way in which they are introducing discriminatory measures of all types today, will bring disaster upon this fair land of ours.*
## Selected publications {#selected_publications}
- *Ifintu Fyakwe Lesa* (The Things of God, a Primer of Scripture Knowledge in Lamba), 1917.
- An outline of the phonetics of the language of the ʗhũ̬꞉ Bushman of the North-West Kalahari. *Bantu Studies*. 2: 129--166, 1925. `{{doi|10.1080/02561751.1923.9676181}}`{=mediawiki} [1](https://archive.org/details/african-studies_1923-1926_2/page/129/mode/1up)
- *The phonetics of the Zulu language*. University of the Witwatersrand Press, 1969 \[1926\]. [2](https://storage.lib.uchicago.edu/pres/2009/pres2009-0344.pdf)
- *The Lambas of Northern Rhodesia: A Study of their Customs and Beliefs*. London: George G. Harrap, 1931.
- *Report on the Unification of the Shona Dialects*. Government of Southern Rhodesia: Government Blue Book, 1931.
- *Bantu linguistic terminology*. London; New York Longmans, Green, 1935.
- *Textbook of Lamba Grammar*. Johannesburg: Witwatersrand University Press, 1938.
- *Outline grammar of Bantu*. Johannesburg: University of the Witwatersrand, 1943.
- *Zulu--English Dictionary*. Johannesburg: Witwatersrand University Press, 1948. (with Benedict Wallet Vilakazi)
- *The Southern Bantu languages*. London; New York: Oxford University Press, 1954.
- *Amasiwi AwaLesa* (The Words of God in Lamba), 1959.
- *Contributions to the history of Bantu linguistics*. Johannesburg: Witwatersrand University Press, 1961 (with D. T. Cole).
- *Trekking in South Central Africa 1913--1919*. Johannesburg: Witwatersrand University Press, 1993.
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Carl Meinhof
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**Carl Friedrich Michael Meinhof** (23 July 1857 -- 11 February 1944) was a German linguist and one of the first linguists to study African languages.
## Early years and career {#early_years_and_career}
Meinhof was born in Barzwitz near Rügenwalde in the Province of Pomerania, Kingdom of Prussia. He studied at the University of Tübingen and at the University of Greifswald. In 1905 he became professor at the School of Oriental Studies in Berlin. On 5 May 1933 he became a member of the Nazi Party.
## Works
His most notable work was developing comparative grammar studies of the Bantu languages, building on the pioneering work of Wilhelm Bleek. In his work, Meinhof looked at the common Bantu languages such as Swahili and Zulu to determine similarities and differences.
In his work, Meinhof looked at noun classes with all Bantu languages having at least 10 classes and with 22 classes of nouns existing throughout the Bantu languages, though his definition of noun class differs slightly from the accepted one, considering the plural form of a word as belonging to a different class from the singular form (thus leading, for example, to consider a language like French as having four classes instead of two). While no language has all 22 (later: 23) classes active, Venda has 20, Lozi has 18, and Ganda has 16 or 17 (depending on whether the locative class 23 *e-* is included). All Bantu languages have a noun class specifically for humans (sometimes including other animate beings).
Meinhof also examined other African languages, including groups classified at the time as Kordofanian, Bushman, Khoikhoi, and Hamitic.
Meinhof developed a comprehensive classification scheme for African languages. His classification was the standard one for many years (Greenberg 1955:3). It was replaced by those of Joseph Greenberg in 1955 and in 1963. His ideas influenced the notation of African-language phonetics as advanced in the mid-nineteenth century by the Egyptologist Karl Richard Lepsius and gave rise to what some called the \"Meinhof-Lepsius system\" of diacritical markers.
In 1902, Meinhof made recordings of East African music. These are among the first recordings made of traditional African music.
## Controversial views {#controversial_views}
In 1912, Carl Meinhof published *Die Sprachen der Hamiten* (The Languages of the Hamites). He used the term Hamitic. Meinhof\'s system of classification of the Hamitic languages was based on a belief that \"speakers of Hamitic became largely coterminous with cattle herding peoples with essentially Caucasian origins, intrinsically different from and superior to the \'Negroes of Africa\'.\" However, in the case of the so-called Nilo-Hamitic languages (a concept he introduced), it was based on the typological feature of gender and a \"fallacious theory of language mixture.\" Meinhof did this in spite of earlier work by scholars such as Lepsius and Johnston demonstrating that the languages which he would later dub \"Nilo-Hamitic\" were in fact Nilotic languages with numerous similarities in vocabulary with other Nilotic languages.
## Family
Carl Meinhof was the great-uncle (the brother of the grandfather) of Ulrike Meinhof, a well known German journalist, who later became a founding member of the Red Army Faction (RAF), a left-wing militant group operating chiefly in West Germany in the 1970s and 1980s.
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Cucurbitaceae
|
The **Cucurbitaceae** (`{{IPAc-en|k|j|uː|ˌ|k|ɜːr|b|ɪ|ˈ|t|eɪ|s|iː|ˌ|iː}}`{=mediawiki}), also called **cucurbits** or the **gourd** family, are a plant family consisting of about 965 species in 101 genera. Those of most agricultural, commercial or nutritional value to humans include:
- *Cucurbita* -- squash, pumpkin, zucchini (courgette), some gourds.
- *Lagenaria* -- calabash (bottle gourd) and other, ornamental gourds.
- *Citrullus* -- watermelon (*C. lanatus*, *C. colocynthis*), plus several other species.
- *Cucumis* -- cucumber (*C. sativus*); various melons and vines.
- *Momordica* -- bitter melon.
- *Luffa* -- commonly called \'luffa\' or 'luffa squash\'; sometimes spelled loofah. Young fruits may be cooked; when fully ripened, they become fibrous and unpalatable, thus becoming the source of the loofah scrubbing sponge.
- *Cyclanthera* -- Caigua.
- *Gerrardanthus* --- the species *G. macrorhizus* has gained some popularity as an ornamental caudiciform plant.
- *Xerosicyos* --- the silver dollar vine (*Xerosicyos danguyi*) is popular amongst horticulturists and plant collectors.
The plants in this family are grown around the tropics and in temperate areas of the world, where those with edible fruits were among the earliest cultivated plants in both the Old and New Worlds. The family Cucurbitaceae ranks among the highest of plant families for number and percentage of species used as human food. The name *Cucurbitaceae* comes to international scientific vocabulary from Neo-Latin, from *Cucurbita*, the type genus, + *-aceae*, a standardized suffix for plant family names in modern taxonomy. The genus name comes from the Classical Latin word *`{{wikt-lang|la|cucurbita}}`{=mediawiki}*, meaning \"gourd\".
## Description
Most of the plants in this family are annual vines, but some are woody lianas, thorny shrubs, or trees (*Dendrosicyos*). Many species have large, yellow or white flowers. The stems are hairy and pentangular. Tendrils are present at 90° to the leaf petioles at nodes. Leaves are exstipulate, alternate, simple palmately lobed or palmately compound. The flowers are unisexual, with male and female flowers on different plants (dioecious) or on the same plant (monoecious). The female flowers have inferior ovaries. The fruit is often a kind of modified berry called a pepo.`{{R|SCHAEFER}}`{=mediawiki}
## Fossil history {#fossil_history}
One of the oldest fossil cucurbits so far is †*Cucurbitaciphyllum lobatum* from the Paleocene epoch, found at Shirley Canal, Montana. It was described for the first time in 1924 by the paleobotanist Frank Hall Knowlton. The fossil leaf is palmate, trilobed with rounded lobal sinuses and an entire or serrate margin. It has a leaf pattern similar to the members of the genera *Kedrostis*, *Melothria* and *Zehneria*.
## Classification
### Tribal classification {#tribal_classification}
The most recent classification of Cucurbitaceae delineates 15 tribes:
- **Tribe Gomphogyneae Benth. & Hook.f.**
- *Alsomitra* (Blume) Spach (1 sp.)
- *Bayabusua* (1 sp.)
- *Gomphogyne* Griff. (2 spp.)
- *Gynostemma* Blume (10 spp.)
- *Hemsleya* Cogn. ex F.B.Forbes & Hemsl. (30 spp.)
- *Neoalsomitra* Hutch. (12 spp.)
- **Tribe Triceratieae A.Rich.**
- *Cyclantheropsis* Harms (3 spp.)
- *Fevillea* L. (8 spp.)
- *Pteropepon* (Cogn.) Cogn. (5 spp.)
- *Sicydium* Schltdl. (9 spp.)
- **Tribe Zanonieae Benth. & Hook.f.**
- *Gerrardanthus* Harvey in Hook.f. (3--5 spp.)
- *Siolmatra* Baill. (1 sp.)
- *Xerosicyos* Humbert (5 spp.)
- *Zanonia* L. (1 sp.)
- **Tribe Actinostemmateae H.Schaef. & S.S.Renner**
- *Actinostemma* Griff. (3 spp.)
- *Bolbostemma* `{{small|Franquet}}`{=mediawiki} (2 spp.)
- **Tribe Indofevilleeae H.Schaef. & S.S.Renner**
- *Indofevillea* Chatterjee (2 sp.)
- **Tribe Thladiantheae H.Schaef. & S.S.Renner**
- *Baijiania* A.M.Lu & J.Q.Li (30 spp.)
- *Sinobaijiania* `{{small|C.Jeffrey & W.J.de Wilde}}`{=mediawiki} (5 spp.)
- *Thladiantha* Bunge 1833 (5 spp.)
- **Tribe Siraitieae H. Schaef. & S.S. Renner**
- *Siraitia* Merr. (3--4 spp.)
- **Tribe Momordiceae H.Schaef. & S.S.Renner**
- *Momordica* L. (60 spp.)
- **Tribe Joliffieae Schrad.**
- *Ampelosicyos* Thouars (5 spp.)
- *Cogniauxia* Baill. (2 spp.)
- *Telfairia* Hook. (3 spp.)
- **Tribe Bryonieae Dumort.**
- *Austrobryonia* H.Schaef. (4 spp.)
- *Bryonia* L. (10 spp.)
- *Ecballium* A.Rich. (1 sp.)
- **Tribe Schizopeponeae C.Jeffrey**
- *Herpetospermum* Wall. ex Hook.f. (3 spp.)
- *Schizopepon* Maxim. (6--8 spp.)
- **Tribe Sicyoeae Schrad.**
- *Brandegea* Cogn. (1 sp.)
- *Cyclanthera* Schrad. (40 spp.)
- *Echinocystis* Torr. & A.Gray (1 sp.)
- *Echinopepon* Naudin (19 spp.)
- *Hanburia* Seem. (7 spp.)
- *Hodgsonia* Hook.f. & Thomson (2 spp.)
- *Linnaeosicyos* H.Schaef. & Kocyan (1 sp.)
- *Luffa* Mill. (5--7 spp.)
- *Marah* Kellogg (7 spp.)
- *Microsechium* `{{small|Naudin}}`{=mediawiki} (4 spp.)
- *Nothoalsomitra* Hutch. (1 sp.)
- *Parasicyos* `{{small|Dieterle}}`{=mediawiki} (2 sp.)
- *Sechiopsis* `{{small|Naudin}}`{=mediawiki} (5 spp.)
- *Sicyocaulis* `{{small|Wiggins}}`{=mediawiki} (1 sp.)
- *Sicyos* L. (64 spp., including *Frantzia* Pittier and *Sechium* P.Browne)
- *Sicyosperma* `{{small| A.Gray}}`{=mediawiki} (1 sp.)
- *Trichosanthes* L. (≤100 spp.)
- **Tribe Coniandreae Endl.**
- *Apodanthera* Arn. (16 spp.)
- *Bambekea* Cogn. (1 sp.)
- *Ceratosanthes* Adans. (4 spp.)
- *Corallocarpus* Welw. ex Benth. & Hook.f. (17 spp.)
- *Cucurbitella* Walp. (1 sp.)
- *Dendrosicyos* Balf.f. (1 sp.)
- *Doyerea* Grosourdy (1 sp.)
- *Eureiandra* Hook.f. (8 spp.)
- *Gurania* (Schltdl.) Cogn. (37 spp.)
- *Halosicyos* Mart.Crov (1 sp.)
- *Helmontia* Cogn. (2--4 spp.)
- *Ibervillea* Greene (8 spp.)
- *Kedrostis* Medik. (28 spp.)
- *Psiguria* Neck. ex Arn. (6--12 spp.)
- *Seyrigia* Keraudren (6 spp.)
- *Trochomeriopsis* Cogn. (1 sp.)
- *Wilbrandia* Silva Manso (5 spp.)
- **Tribe Benincaseae Ser.**
- *Acanthosicyos* Welw. ex Hook.f. (1 sp.)
- *Benincasa* Savi (2 spp., including *Praecitrullus* Pangalo)
- *Blastania* `{{small|Kotschy & Peyr.}}`{=mediawiki} (3 spp., including *Ctenolepis* Hook.f.)
- *Borneosicyos* (1--2 spp.)
- *Cephalopentandra* Chiov. (1 sp.)
- *Citrullus* Schrad. (4 spp.)
- *Coccinia* Wight & Arn. (30 spp.)
- *Cucumis* L. (65 spp.)
- *Dactyliandra* Hook.f. (2 spp.)
- *Diplocyclos* (Endl.) T.Post & Kuntze (4 spp.)
- *Indomelothria* (2 spp.)
- *Khmeriosicyos* (1 sp.)
- *Lagenaria* Ser. (6 spp.)
- *Lemurosicyos* Keraudren (1 sp.)
- *Melothria* L. (12 spp., including *M. scabra*)
- *Muellerargia* Cogn. (2 sp.)
- *Oreosyce* `{{small|Hook.f.}}`{=mediawiki} (1 sp.)
- *Papuasicyos* (8 spp.)
- *Peponium* Engl. (20 spp.)
- *Raphidiocystis* Hook.f. (5 spp.)
- *Ruthalicia* C.Jeffrey (2 spp.)
- *Scopellaria* W.J.de Wilde & Duyfjes (2 spp.)
- *Solena* Lour. (3 spp.)
- *Trochomeria* Hook.f. (8 spp.)
- *Zehneria* Endl. (*ca.* 60 spp.)
- **Tribe Cucurbiteae Ser.**
- *Abobra* Naudin (1 sp.)
- *Calycophysum* H.Karst. & Triana (5 spp.)
- *Cayaponia* Silva Manso (74 spp.)
- *Cionosicys* Griseb. (4--5 spp.)
- *Cucurbita* L. (15 spp.)
- *Penelopeia* Urb. (2 spp.)
- *Peponopsis* Naudin (1 sp.)
- *Polyclathra* Bertol. (6 spp.)
- *Schizocarpum* Schrad. (11 spp.)
- *Selysia* Cogn. (4 spp.)
- *Sicana* Naudin (4 spp.)
- *Tecunumania* Standl. & Steyerm. (1 sp.)
### Systematics
Modern molecular phylogenetics suggest the following relationships:
Detailed Cladogram showing Cucurbitaceae phylogeny
-----------------------------------------------------------------
{{Clade\|style=line-height:90%;font-size:90%; \<!\--\|2={{clade
## Pests and diseases {#pests_and_diseases}
Sweet potato whitefly is the vector of a number of cucurbit viruses that cause yellowing symptoms throughout the southern United States.
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Chorded keyboard
|
A **keyset** or **chorded keyboard** (also called a chorded keyset, *chord keyboard* or *chording keyboard*) is a computer input device that allows the user to enter characters or commands formed by pressing several keys together, like playing a \"chord\" on a piano. The large number of combinations available from a small number of keys allows text or commands to be entered with one hand, leaving the other hand free. A secondary advantage is that it can be built into a device (such as a pocket-sized computer or a bicycle handlebar) that is too small to contain a normal-sized keyboard.
A chorded keyboard minus the board, typically designed to be used while held in the hand, is called a keyer. Douglas Engelbart introduced the chorded keyset as a computer interface in 1968 at what is often called \"The Mother of All Demos\".
## Principles of operation {#principles_of_operation}
Each key is mapped to a number and then can be mapped to a corresponding letter or command. By pressing two or more keys together the user can generate many combinations. In Engelbart\'s original mapping, he used five keys: 1, 2, 4, 8, 16. The keys were mapped as follows: a = 1, b = 2, c = 3, d = 4, and so on. If the user pressed keys 1 and 2 simultaneously, and then released the keys, 1 and 2 would be added to 3, and since C is the 3rd letter of the alphabet, and the letter \"c\" appeared. Unlike pressing a chord on a piano, the chord is recognized only after all the keys or mouse buttons are released. Since Engelbart introduced the keyset, several different designs have been developed based on similar concepts.
As a crude example, each finger might control one key which corresponds to one bit in a byte, so that using seven keys and seven fingers, one could enter any character in the ASCII set---if the user could remember the binary codes. Due to the small number of keys required, chording is easily adapted from a desktop to mobile environment.
Practical devices generally use simpler chords for common characters (*e.g.,* Baudot), or may have ways to make it easier to remember the chords (*e.g.,* Microwriter), but the same principles apply. These portable devices first became popular with the wearable computer movement in the 1980s.
Thad Starner from Georgia Institute of Technology and others published numerous studies showing that two-handed chorded text entry was faster and yielded fewer errors than on a QWERTY keyboard. Currently stenotype machines hold the record for fastest word entry. Many stenotype users can reach 300 words per minute. However, stenographers typically train for three years before reaching professional levels of speed and accuracy.
## History
The earliest known chord keyboard was part of the \"five-needle\" telegraph operator station, designed by Wheatstone and Cooke in 1836, in which any two of the five needles could point left or right to indicate letters on a grid. It was designed to be used by untrained operators (who would determine which keys to press by looking at the grid), and was not used where trained telegraph operators were available. The first widespread use of a chord keyboard was in the stenotype machine used by court reporters, which was invented in 1868 and is still in use. The output of the stenotype was originally a phonetic code that had to be transcribed later (usually by the same operator who produced the original output), rather than arbitrary text---automatic conversion software is now commonplace.
In 1874, the five-bit Baudot telegraph code and a matching 5-key chord keyboard was designed to be used with the operator forming the codes manually. The code is optimized for speed and low wear: chords were chosen so that the most common characters used the simplest chords. But telegraph operators were already using typewriters with QWERTY keyboards to \"copy\" received messages, and at the time it made more sense to build a typewriter that could generate the codes automatically, rather than making them learn to use a new input device.
Some early keypunch machines used a keyboard with 12 labeled keys to punch the correct holes in paper cards. The numbers 0 through 9 were represented by one punch; 26 letters were represented by combinations of two punches, and symbols were represented by combinations of two or three punches. Braille (a writing system for the blind) uses either 6 or 8 tactile \'points\' from which all letters and numbers are formed. When Louis Braille invented it, it was produced with a needle holing successively all needed points in a cardboard sheet. In 1892, Frank Haven Hall, superintendent of the Illinois Institute for the Education of the Blind, created the Hall Braille Writer, which was like a typewriter with 6 keys, one for each dot in a braille cell. The Perkins Brailler, first manufactured in 1951, uses a 6-key chord keyboard (plus a spacebar) to produce braille output, and has been very successful as a mass market affordable product. Braille, like Baudot, uses a number symbol and a shift symbol, which may be repeated for shift lock, to fit numbers and upper case into the 63 codes that 6 bits offer.
After World War II, with the arrival of electronics for reading chords and looking in tables of \"codes\", the postal sorting offices started to research chordic solutions to be able to employ people other than trained and expensive typists. In 1954, an important concept was discovered: chordic production is easier to master when the production is done at the release of the keys instead of when they are pressed.
Researchers at IBM investigated chord keyboards for both typewriters and computer data entry as early as 1959, with the idea that it might be faster than touch-typing if some chords were used to enter whole words or parts of words. A 1975 design by IBM Fellow Nat Rochester had 14 keys that were dimpled on the edges as well as the top, so one finger could press two adjacent keys for additional combinations. Their results were inconclusive, but research continued until at least 1978.
Doug Engelbart began experimenting with keysets to use with the mouse in the mid-1960s. In a famous 1968 demonstration, Engelbart introduced a computer human interface that included the QWERTY keyboard, a three button mouse, and a five key keyset. Engelbart used the keyset with his left hand and the mouse with his right to type text and enter commands. The mouse buttons marked selections and confirmed or aborted commands.
Users in Engelbart\'s Augmentation Research Center at SRI became proficient with the mouse and keyset. In the 1970s the funding Engelbart\'s group received from the Advanced Research Projects Agency (ARPA) was cut and many key members of Engelbart\'s team went to work for Xerox PARC where they continued to experiment with the mouse and keyset. Keychord sets were used at Xerox PARC in the early 1980s, along with mice, GUIs, on the Xerox Star and Alto workstations. A one-button version of the mouse was incorporated into the Apple Macintosh but Steve Jobs decided against incorporating the chorded keyset.
In the early 1980s, Philips Research labs at Redhill, Surrey did a brief study into small, cheap keyboards for entering text on a telephone. One solution used a grid of hexagonal keys with symbols inscribed into dimples in the keys that were either in the center of a key, across the boundary of two keys, or at the joining of three keys. Pressing down on one of the dimples would cause either one, two or three of the hexagonal buttons to be depressed at the same time, forming a chord that would be unique to that symbol. With this arrangement, a nine button keyboard with three rows of three hexagonal buttons could be fitted onto a telephone and could produce up to 33 different symbols. By choosing widely separated keys, one could employ one dimple as a \'shift\' key to allow both letters and numbers to be produced. With eleven keys in a 3/4/4 arrangement, 43 symbols could be arranged allowing for lowercase text, numbers and a modest number of punctuation symbols to be represented along with a \'shift\' function for accessing uppercase letters. While this had the advantage of being usable by untrained users via \'hunt and peck\' typing and requiring one less key switch than a conventional 12 button keypad, it had the disadvantage that some symbols required three times as much force to depress them as others which made it hard to achieve any speed with the device. That solution is still alive and proposed by Fastap and Unitap among others, and a commercial phone has been produced and promoted in Canada during 2006.
## Standards
Historically, the baudot and braille keyboards were standardized to some extent, but they are unable to replicate the full character set of a modern keyboard. Braille comes closest, as it has been extended to eight bits.
The only proposed modern standard, GKOS (or Global Keyboard Open Standard) can support most characters and functions found on a computer keyboard but has had little commercial development. There is, however, a GKOS keyboard application available for iPhone since May 8, 2010, for Android since October 3, 2010 and for MeeGo Harmattan since October 27, 2011.
## Stenography
Stenotype machines, sometimes used by court reporters, use a chording keyboard to represent sounds: on the standard keyboard, the U represents the sound and word, \'you\', and the three-key trigraph KAT represents the sound and word \'cat\'. The stenotype keyboard is explicitly ordered: in KAT, K, on the left, is the starting sound. P, S, and T, which are common starting sounds and also common ending sounds, are available on both sides of the keyboard: POP is a 3-key chord, using both P keys.
## Open-source designs {#open_source_designs}
Multiple open-source keyer/keyset designs are available, such as the pickey, a PS/2 device based on the PIC microcontroller; the spiffchorder, a USB device based on the Atmel AVR family of microcontrollers; the FeatherChorder, a BLE chorder based on the Adafruit Feather, an all-in-one board incorporating an Arduino-compatible microcontroller; and the GKOS keypad driver for Linux as well as the Gkos library for the Atmel/Arduino open-source board.
Plover is a free, open-source, cross-platform program intended to bring real-time stenographic technology not just to stenographers, but also to hobbyists using anything from professional Stenotype machines to low-cost NKRO gaming keyboards. It is available for Linux, Windows, and macOS.
Joy2chord is a chorded keyboard driver for Linux. With a configuration file, any joystick or gamepad can be turned into a chorded keyboard. This design philosophy was decided on to lower the cost of building devices, and in turn lower the entry barrier to becoming familiar with chorded keyboards. Macro keys, and multiple modes are also easily implemented with a user space driver.
## Commercial devices {#commercial_devices}
One minimal chordic keyboard example is Edgar Matias\' Half-Qwerty keyboard described in patent `{{patent|US|5288158}}`{=mediawiki} circa 1992 that produces the letters of the missing half when the user simultaneously presses the space bar along with the mirror key. INTERCHI \'93 published a study by Matias, MacKenzie and Buxton showing that people who have already learned to touch-type can quickly recover 50 to 70% of their two-handed typing speed. The loss contributes to the speed discussion above. It is implemented on two popular mobile phones, each provided with software disambiguation, which allows users to avoid using the space-bar.
\"Multiambic\" keyers for use with wearable computers were invented in Canada in the 1970s. Multiambic keyers are similar to chording keyboards but without the board, in that the keys are grouped in a cluster for being handheld, rather than for sitting on a flat surface.
Chording keyboards are also used as portable but two handed input devices for the visually impaired (either combined with a refreshable braille display or vocal synthesis). Such keyboards use a minimum of seven keys, where each key corresponds to an individual braille point, except one key which is used as a spacebar. In some applications, the spacebar is used to produce additional chords which enable the user to issue editing commands, such as moving the cursor, or deleting words. Note that the number of points used in braille computing is not 6, but 8, as this allows the user, among other things, to distinguish between small and capital letters, as well as identify the position of the cursor. As a result, most newer chorded keyboards for braille input include at least nine keys.
Touch screen chordic keyboards are available to smartphone users as an optional way of entering text. As the number of keys is low, the button areas can be made bigger and easier to hit on the small screen. The most common letters do not necessarily require chording as is the case with the GKOS keyboard optimised layouts (Android app) where the twelve most frequent characters only require single keys.
The DecaTxt one-handed Bluetooth Chord keyboard, by IN10DID, Inc. has ten keys, two at each finger and is able to replace all standard keystrokes with chords of four keys or less. It is small at 3.25\"x 2.25\" and weighs about 2 ounces, making it quite wearable strapped to either hand for use while walking. DecaTxt is generally considered as assistive technology since it works with a variety of issues such as limited vision, limb loss, shaking and poor motor skills.
The company CharaChorder commercially sells chorded entry devices. Their first commercially available device is the CharaChorder One, which features a split design with each having access to 9 switches that can be moved in five directions (up, down, left, right, and pressed) in contrast to typical keyboards. This device allows for both chorded entry as well as traditional character entry. The set of words that can be chorded can be dynamically changed by the user in real time, but by default includes the 300 most common words in the English language. This chorded entry feature allows for potentially extremely fast typing speeds, so much so the founder of the company has been banned from online typing competitions. Additionally, they create the Charachorder Lite with a more traditional keyboard design. The manufacturer claimed that users of the Charachorder One can reach speeds of 300 words per minute, while users of the Charachorder Lite can reach 250 words per minute.
### Historical
The WriteHander, a 12-key chord keyboard from NewO Company, appeared in 1978 issues of ROM Magazine, an early microcomputer applications magazine.
Another early commercial model was the six-button Microwriter, designed by Cy Endfield and Chris Rainey, and first sold in 1980. Microwriting is the system of chord keying and is based on a set of mnemonics. It was designed only for right-handed use.
In 1982 the Octima 8 keys cord keyboard was presented by Ergoplic Kebords Ltd an Israeli Startup that was founded by Israeli researcher with intensive experience in Man Machine Interface design. The keyboard had 8 keys one for each finger and additional 3 keys that enabled the production of numbers, punctuations and control functions. The keyboard was fully compatible with the IBM PC and AT keyboards and had an Apple IIe version as well. Its key combinations were based on a mnemonic system that enabled fast and easy touch type learning. Within a few hours the user could achieve a typing speed similar to hand writing speed. The unique design also gave a relief from hand stress (Carpal Tunnel Syndrome) and allowed longer typing sessions than traditional keyboards. It was multi-lingual supporting English, German, French and Hebrew.
The BAT is a 7-key hand-sized device from Infogrip, and has been sold since 1985. It provides one key for each finger and three for the thumb. It is proposed for the hand which does not hold the mouse, in an exact continuation of Engelbart\'s vision.
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Centaurus
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**Centaurus** (`{{IPAc-en|s|ɛ|n|ˈ|t|ɔːr|ə|s|,_|-|ˈ|t|ɑːr|-}}`{=mediawiki}) is a bright constellation in the southern sky. One of the largest constellations, Centaurus was included among the 48 constellations listed by the 2nd-century astronomer Ptolemy, and it remains one of the 88 modern constellations. In Greek mythology, Centaurus represents a centaur; a creature that is half human, half horse (another constellation named after a centaur is one from the zodiac: Sagittarius). Notable stars include Alpha Centauri, the nearest star system to the Solar System, its neighbour in the sky Beta Centauri, and HR 5171, one of the largest stars yet discovered. The constellation also contains Omega Centauri, the brightest globular cluster as visible from Earth and the largest identified in the Milky Way, possibly a remnant of a dwarf galaxy.
## Notable features {#notable_features}
thumb\|left\|upright=1.1\|Centaurus in the southwestern sky, shortly after sunset. right\|thumb\|upright=1.2\|The two bright stars are (left) Alpha Centauri and (right) Beta Centauri. The faint red star in the center of the red circle is Proxima Centauri. thumb\|right\|upright=1.4\|Centaurus in the *Firmamentum Sobiescianum* of Johannes Hevelius. `{{Abbreviation|N.B.|Nota bene (note well)}}`{=mediawiki} This image is reversed from what one sees looking at the sky --- it is as though one is looking at the \"celestial sphere\" from the outside.
### Stars
Centaurus contains several very bright stars. Its alpha and beta stars are used as \"pointer stars\" to help observers find the constellation Crux. Centaurus has 281 stars above magnitude 6.5, meaning that they are visible to the unaided eye, the most of any constellation. Alpha Centauri, the closest star system to the Sun, has a high proper motion; it will be a mere half-degree from Beta Centauri in approximately 4000 years.
Alpha Centauri is a triple star system composed of a binary system orbited by Proxima Centauri, currently the nearest star to the Sun. Traditionally called Rigil Kentaurus (from Arabic رجل قنطورس, meaning \"foot of the centaur\") or Toliman (from Arabic الظليمين meaning \"two male ostriches\"), the system has an overall magnitude of −0.28 and is 4.4 light-years from Earth. The primary and secondary are both yellow-hued stars; the first is of magnitude −0.01 and the second: 1.35. Proxima, the tertiary star, is a red dwarf of magnitude 11.0; it appears almost 2 degrees away from the close pairing of Alpha and has a period of approximately one million years. Also a flare star, Proxima has minutes-long outbursts where it brightens by over a magnitude. The Alpha couple revolve in 80-year periodicity and will next appear closest as seen from Earth\'s telescopes in 2037 and 2038, together as they appear to the naked eye they present the third-brightest \"star\" in the night sky.
One other first magnitude star Beta Centauri is in the constellation in a position beyond Proxima and toward the narrow axis of Crux, thus with Alpha forming a far-south limb of the constellation. Also called Hadar and Agena, it is a double star; the primary is a blue-hued giant star of magnitude 0.6, 525 light-years from Earth. The secondary is of magnitude 4.0 and has a modest separation, appearing only under intense magnification due to its distance.
The northerly star Theta Centauri, officially named Menkent, is an orange giant star of magnitude 2.06. It is the only bright star of Centaurus that is easily visible from mid-northern latitudes.
The next bright object is Gamma Centauri, a binary star which appears to the naked eye at magnitude 2.2. The primary and secondary are both blue-white hued stars of magnitude 2.9; their period is 84 years.
Centaurus also has many dimmer double stars and binary stars. 3 Centauri is a double star with a blue-white hued primary of magnitude 4.5 and a secondary of magnitude 6.0. The primary is 344 light-years away.
Centaurus is home to many variable stars. R Centauri is a Mira variable star with a minimum magnitude of 11.8 and a maximum magnitude of 5.3; it is about 1,250 light-years from Earth and has a period of 18 months. V810 Centauri is a semiregular variable.
BPM 37093 is a white dwarf star whose carbon atoms are thought to have formed a crystalline structure. Since diamond also consists of carbon arranged in a crystalline lattice (though of a different configuration), scientists have nicknamed this star \"Lucy\" after the Beatles song \"*Lucy in the Sky with Diamonds*.\"
PDS 70, (V1032 Centauri) a low mass T Tauri star is found in the constellation Centaurus. In July 2018 astronomers captured the first conclusive image of a protoplanetary disk containing a nascent exoplanet, named PDS 70b.
### Deep-sky objects {#deep_sky_objects}
ω Centauri (NGC 5139), despite being listed as the constellation\'s \"omega\" star, is in fact a naked-eye globular cluster, 17,000 light-years away with a diameter of 150 light-years. It is the largest and brightest globular cluster in the Milky Way; at ten times the size of the next-largest cluster, it has a magnitude of 3.7. It is also the most luminous globular cluster in the Milky Way, at over one million solar luminosities. Omega Centauri is classified as a Shapley class VIII cluster, which means that its center is loosely concentrated. It is also one of only two globular clusters to be given a stellar designation; in its case a Bayer letter. The other is 47 Tucanae (Xi Tucanae), which has a Flamsteed number. Omega Centauri contains several million stars, most of which are yellow dwarf stars, but also possesses red giants and blue-white stars; the stars have an average age of 12 billion years. This has prompted suspicion that Omega Centauri was the core of a dwarf galaxy that had been absorbed by the Milky Way. Omega Centauri was determined to be nonstellar in 1677 by the English astronomer Edmond Halley, though it was visible as a star to the ancients. Its status as a globular cluster was determined by James Dunlop in 1827. To the unaided eye, Omega Centauri appears fuzzy and is obviously non-circular; it is approximately half a degree in diameter, the same size as the full Moon.
Centaurus is also home to open clusters. NGC 3766 is an open cluster 6,300 light-years from Earth that is visible to the unaided eye. It contains approximately 100 stars, the brightest of which are 7th magnitude. NGC 5460 is another naked-eye open cluster, 2,300 light-years from Earth, that has an overall magnitude of 6 and contains approximately 40 stars.
There is one bright planetary nebula in Centaurus, NGC 3918, also known as the Blue Planetary. It has an overall magnitude of 8.0 and a central star of magnitude 11.0; it is 2600 light-years from Earth. The Blue Planetary was discovered by John Herschel and named for its color\'s similarity to Uranus, though the nebula is apparently three times larger than the planet.
Centaurus is rich in galaxies as well. NGC 4622 is a face-on spiral galaxy located 200 million light-years from Earth (redshift 0.0146). Its spiral arms wind in both directions, which makes it nearly impossible for astronomers to determine the rotation of the galaxy. Astronomers theorize that a collision with a smaller companion galaxy near the core of the main galaxy could have led to the unusual spiral structure. NGC 5253, a peculiar irregular galaxy, is located near the border with Hydra and M83, with which it likely had a close gravitational interaction 1--2 billion years ago. This may have sparked the galaxy\'s high rate of star formation, which continues today and contributes to its high surface brightness. NGC 5253 includes a large nebula and at least 12 large star clusters. In the eyepiece, it is a small galaxy of magnitude 10 with dimensions of 5 arcminutes by 2 arcminutes and a bright nucleus. NGC 4945 is a spiral galaxy seen edge-on from Earth, 13 million light-years away. It is visible with any amateur telescope, as well as binoculars under good conditions; it has been described as \"shaped like a candle flame\", being long and thin (16\' by 3\'). In the eyepiece of a large telescope, its southeastern dust lane becomes visible. Another galaxy is NGC 5102, found by star-hopping from Iota Centauri. In the eyepiece, it appears as an elliptical object 9 arcminutes by 2.5 arcminutes tilted on a southwest--northeast axis.
One of the closest active galaxies to Earth is the Centaurus A galaxy, NGC 5128, at 11 million light-years away (redshift 0.00183). It has a supermassive black hole at its core, which expels massive jets of matter that emit radio waves due to synchrotron radiation. Astronomers posit that its dust lanes, not common in elliptical galaxies, are due to a previous merger with another galaxy, probably a spiral galaxy. NGC 5128 appears in the optical spectrum as a fairly large elliptical galaxy with a prominent dust lane. Its overall magnitude is 7.0 and it has been seen under perfect conditions with the naked eye, making it one of the most distant objects visible to the unaided observer. In equatorial and southern latitudes, it is easily found by star hopping from Omega Centauri. In small telescopes, the dust lane is not visible; it begins to appear with about 4 inches of aperture under good conditions. In large amateur instruments, above about 12 inches in aperture, the dust lane\'s west-northwest to east-southeast direction is easily discerned. Another dim dust lane on the east side of the 12-arcminute-by-15-arcminute galaxy is also visible. ESO 270-17, also called the Fourcade-Figueroa Object, is a low-surface brightness object believed to be the remnants of a galaxy; it does not have a core and is very difficult to observe with an amateur telescope. It measures 7 arcminutes by 1 arcminute. It likely originated as a spiral galaxy and underwent a catastrophic gravitational interaction with Centaurus A around 500 million years ago, stopping its rotation and destroying its structure.
NGC 4650A is a polar-ring galaxy 136 million light-years from Earth (redshift 0.01). It has a central core made of older stars that resembles an elliptical galaxy, and an outer ring of young stars that orbits around the core. The plane of the outer ring is distorted, which suggests that NGC 4650A is the result of a galaxy collision about a billion years ago. This galaxy has also been cited in studies of dark matter, because the stars in the outer ring orbit too quickly for their collective mass. This suggests that the galaxy is surrounded by a dark matter halo, which provides the necessary mass.
One of the closest galaxy clusters to Earth is the Centaurus Cluster at c. 160 million light-years away, having redshift 0.0114. It has a cooler, denser central region of gas and a hotter, more diffuse outer region. The intracluster medium in the Centaurus Cluster has a high concentration of metals (elements heavier than helium) due to a large number of supernovae. This cluster also possesses a plume of gas whose origin is unknown.
## History
While Centaurus now has a high southern latitude, at the dawn of civilization it was an equatorial constellation. Precession has been slowly shifting it southward for millennia, and it is now close to its maximal southern declination. In a little over 7000 years it will be at maximum visibility for those in the northern hemisphere, visible at times in the year up to quite a high northern latitude. The figure of Centaurus can be traced back to a Babylonian constellation known as the Bison-man (MUL.GUD.ALIM). This being was depicted in two major forms: firstly, as a 4-legged bison with a human head, and secondly, as a being with a man\'s head and torso attached to the rear legs and tail of a bull or bison. It has been closely associated with the Sun god Utu-Shamash from very early times.
The Greeks depicted the constellation as a centaur and gave it its current name. It was mentioned by Eudoxus in the 4th century BC and Aratus in the 3rd century BC. In the 2nd century AD, Claudius Ptolemy catalogued 37 stars in Centaurus, including Alpha Centauri. Large as it is now, in earlier times it was even larger, as the constellation Lupus was treated as an asterism within Centaurus, portrayed in illustrations as an unspecified animal either in the centaur\'s grasp or impaled on its spear. The Southern Cross, which is now regarded as a separate constellation, was treated by the ancients as a mere asterism formed of the stars composing the centaur\'s legs. Additionally, what is now the minor constellation Circinus was treated as undefined stars under the centaur\'s front hooves.
According to the Roman poet Ovid (*Fasti* v.379), the constellation honors the centaur Chiron, who was tutor to many of the earlier Greek heroes including Heracles (Hercules), Theseus, and Jason, the leader of the Argonauts. It is not to be confused with the more warlike centaur represented by the zodiacal constellation Sagittarius. The legend associated with Chiron says that he was accidentally poisoned with an arrow shot by Hercules, and was subsequently placed in the heavens.
## Equivalents
In Chinese astronomy, the stars of Centaurus are found in three areas: the Azure Dragon of the East (東方青龍, *Dōng Fāng Qīng Lóng*), the Vermillion Bird of the South (南方朱雀, *Nán Fāng Zhū Què*), and the Southern Asterisms (近南極星區, *Jìnnánjíxīngōu*). Not all of the stars of Centaurus can be seen from China, and the unseen stars were classified among the Southern Asterisms by Xu Guangqi, based on his study of western star charts. However, most of the brightest stars of Centaurus, including α Centauri, θ Centauri (or Menkent), ε Centauri and η Centauri, can be seen in the Chinese sky.
Some Polynesian peoples considered the stars of Centaurus to be a constellation as well. On Pukapuka, Centaurus had two names: *Na Mata-o-te-tokolua* and *Na Lua-mata-o-Wua-ma-Velo*. In Tonga, the constellation was called by four names: *O-nga-tangata*, *Tautanga-ufi*, *Mamangi-Halahu*, and *Mau-kuo-mau*. Alpha and Beta Centauri were not named specifically by the people of Pukapuka or Tonga, but they were named by the people of Hawaii and the Tuamotus. In Hawaii, the name for Alpha Centauri was either *Melemele* or *Ka Maile-hope* and the name for Beta Centauri was either *Polapola* or *Ka Maile-mua*. In the Tuamotu islands, Alpha was called *Na Kuhi* and Beta was called *Tere*.
The Pointer (α Centauri and β Centauri) is one of the asterisms used by Bugis sailors for navigation, called *bintoéng balué*, meaning \"the widowed-before-marriage\". It is also called *bintoéng sallatang* meaning \"southern star\".
## Namesakes
Two United States Navy ships, `{{USS|Centaurus|AKA-17}}`{=mediawiki} and `{{USS|Centaurus|AK-264}}`{=mediawiki}, were named after Centaurus, the constellation.
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Impact crater
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An **impact crater** is a depression in the surface of a solid astronomical body formed by the hypervelocity impact of a smaller object. In contrast to volcanic craters, which result from explosion or internal collapse, impact craters typically have raised rims and floors that are lower in elevation than the surrounding terrain. Impact craters are typically circular, though they can be elliptical in shape or even irregular due to events such as landslides. Impact craters range in size from microscopic craters seen on lunar rocks returned by the Apollo Program to simple bowl-shaped depressions and vast, complex, multi-ringed impact basins. Meteor Crater is a well-known example of a small impact crater on Earth.
Impact craters are the dominant geographic features on many solid Solar System objects including the Moon, Mercury, Callisto, Ganymede, and most small moons and asteroids. On other planets and moons that experience more active surface geological processes, such as Earth, Venus, Europa, Io, Titan, and Triton, visible impact craters are less common because they become eroded, buried, or transformed by tectonic and volcanic processes over time. Where such processes have destroyed most of the original crater topography, the terms impact structure or astrobleme are more commonly used. In early literature, before the significance of impact cratering was widely recognised, the terms cryptoexplosion or cryptovolcanic structure were often used to describe what are now recognised as impact-related features on Earth.
The cratering records of very old surfaces, such as Mercury, the Moon, and the southern highlands of Mars, record a period of intense early bombardment in the inner Solar System around 3.9 billion years ago. The rate of crater production on Earth has since been considerably lower, but it is appreciable nonetheless. Earth experiences, on average, from one to three impacts large enough to produce a 20 km crater every million years. This indicates that there should be far more relatively young craters on the planet than have been discovered so far. The cratering rate in the inner solar system fluctuates as a consequence of collisions in the asteroid belt that create a family of fragments that are often sent cascading into the inner solar system. Formed in a collision 80 million years ago, the Baptistina family of asteroids is thought to have caused a large spike in the impact rate. The rate of impact cratering in the outer Solar System could be different from the inner Solar System.
Although Earth\'s active surface processes quickly destroy the impact record, about 190 terrestrial impact craters have been identified. These range in diameter from a few tens of meters up to about 300 km, and they range in age from recent times (e.g. the Sikhote-Alin craters in Russia whose creation was witnessed in 1947) to more than two billion years, though most are less than 500 million years old because geological processes tend to obliterate older craters. They are also selectively found in the stable interior regions of continents. Few undersea craters have been discovered because of the difficulty of surveying the sea floor, the rapid rate of change of the ocean bottom, and the subduction of the ocean floor into Earth\'s interior by processes of plate tectonics.
## History
Daniel M. Barringer, a mining engineer, was convinced already in 1903 that the crater he owned, Meteor Crater, was of cosmic origin. Most geologists at the time assumed it formed as the result of a volcanic steam eruption.
In the 1920s, the American geologist Walter H. Bucher studied a number of sites now recognized as impact craters in the United States. He concluded they had been created by some great explosive event, but believed that this force was probably volcanic in origin. However, in 1936, the geologists John D. Boon and Claude C. Albritton Jr. revisited Bucher\'s studies and concluded that the craters that he studied were probably formed by impacts.
Grove Karl Gilbert suggested in 1893 that the Moon\'s craters were formed by large asteroid impacts. Ralph Baldwin in 1949 wrote that the Moon\'s craters were mostly of impact origin. Around 1960, Gene Shoemaker revived the idea. According to David H. Levy, Shoemaker \"saw the craters on the Moon as logical impact sites that were formed not gradually, in eons, but explosively, in seconds.\" For his PhD degree at Princeton University (1960), under the guidance of Harry Hammond Hess, Shoemaker studied the impact dynamics of Meteor Crater. Shoemaker noted that Meteor Crater had the same form and structure as two explosion craters created from atomic bomb tests at the Nevada Test Site, notably Jangle U in 1951 and Teapot Ess in 1955. In 1960, Edward C. T. Chao and Shoemaker identified coesite (a form of silicon dioxide) at Meteor Crater, proving the crater was formed from an impact generating extremely high temperatures and pressures. They followed this discovery with the identification of coesite within suevite at Nördlinger Ries, proving its impact origin.
Armed with the knowledge of shock-metamorphic features, Carlyle S. Beals and colleagues at the Dominion Astrophysical Observatory in Victoria, British Columbia, Canada and Wolf von Engelhardt of the University of Tübingen in Germany began a methodical search for impact craters. By 1970, they had tentatively identified more than 50. Although their work was controversial, the American Apollo Moon landings, which were in progress at the time, provided supportive evidence by recognizing the rate of impact cratering on the Moon. Because the processes of erosion on the Moon are minimal, craters persist. Since the Earth could be expected to have roughly the same cratering rate as the Moon, it became clear that the Earth had suffered far more impacts than could be seen by counting evident craters.
## Crater formation {#crater_formation}
Impact cratering involves high velocity collisions between solid objects, typically much greater than the speed of sound in those objects. Such hyper-velocity impacts produce physical effects such as melting and vaporization that do not occur in familiar sub-sonic collisions. On Earth, ignoring the slowing effects of travel through the atmosphere, the lowest impact velocity with an object from space is equal to the gravitational escape velocity of about 11 km/s. The fastest impacts occur at about 72 km/s in the \"worst case\" scenario in which an object in a retrograde near-parabolic orbit hits Earth. The median impact velocity on Earth is about 20 km/s.
However, the slowing effects of travel through the atmosphere rapidly decelerate any potential impactor, especially in the lowest 12 kilometres where 90% of the Earth\'s atmospheric mass lies. Meteors of up to 7,000 kg lose all their cosmic velocity due to atmospheric drag at a certain altitude (retardation point), and start to accelerate again due to Earth\'s gravity until the body reaches its terminal velocity of 0.09 to 0.16 km/s. The larger the meteoroid (i.e. asteroids and comets) the more of its initial cosmic velocity it preserves. While an object of 9,000 kg maintains about 6% of its original velocity, one of 900,000 kg already preserves about 70%. Extremely large bodies (about 100,000 tonnes) are not slowed by the atmosphere at all, and impact with their initial cosmic velocity if no prior disintegration occurs.
Impacts at these high speeds produce shock waves in solid materials, and both impactor and the material impacted are rapidly compressed to high density. Following initial compression, the high-density, over-compressed region rapidly depressurizes, exploding violently, to set in train the sequence of events that produces the impact crater. Impact-crater formation is therefore more closely analogous to cratering by high explosives than by mechanical displacement. Indeed, the energy density of some material involved in the formation of impact craters is many times higher than that generated by high explosives. Since craters are caused by explosions, they are nearly always circular -- only very low-angle impacts cause significantly elliptical craters.
This describes impacts on solid surfaces. Impacts on porous surfaces, such as that of Hyperion, may produce internal compression without ejecta, punching a hole in the surface without filling in nearby craters. This may explain the \'sponge-like\' appearance of that moon.
It is convenient to divide the impact process conceptually into three distinct stages: (1) initial contact and compression, (2) excavation, (3) modification and collapse. In practice, there is overlap between the three processes with, for example, the excavation of the crater continuing in some regions while modification and collapse is already underway in others.
### Contact and compression {#contact_and_compression}
In the absence of atmosphere, the impact process begins when the impactor first touches the target surface. This contact accelerates the target and decelerates the impactor. Because the impactor is moving so rapidly, the rear of the object moves a significant distance during the short-but-finite time taken for the deceleration to propagate across the impactor. As a result, the impactor is compressed, its density rises, and the pressure within it increases dramatically. Peak pressures in large impacts exceed 1 T Pa to reach values more usually found deep in the interiors of planets, or generated artificially in nuclear explosions.
In physical terms, a shock wave originates from the point of contact. As this shock wave expands, it decelerates and compresses the impactor, and it accelerates and compresses the target. Stress levels within the shock wave far exceed the strength of solid materials; consequently, both the impactor and the target close to the impact site are irreversibly damaged. Many crystalline minerals can be transformed into higher-density phases by shock waves; for example, the common mineral quartz can be transformed into the higher-pressure forms coesite and stishovite. Many other shock-related changes take place within both impactor and target as the shock wave passes through, and some of these changes can be used as diagnostic tools to determine whether particular geological features were produced by impact cratering.
As the shock wave decays, the shocked region decompresses towards more usual pressures and densities. The damage produced by the shock wave raises the temperature of the material. In all but the smallest impacts this increase in temperature is sufficient to melt the impactor, and in larger impacts to vaporize most of it and to melt large volumes of the target. As well as being heated, the target near the impact is accelerated by the shock wave, and it continues moving away from the impact behind the decaying shock wave.
### Excavation
Contact, compression, decompression, and the passage of the shock wave all occur within a few tenths of a second for a large impact. The subsequent excavation of the crater occurs more slowly, and during this stage the flow of material is largely subsonic. During excavation, the crater grows as the accelerated target material moves away from the point of impact. The target\'s motion is initially downwards and outwards, but it becomes outwards and upwards. The flow initially produces an approximately hemispherical cavity that continues to grow, eventually producing a paraboloid (bowl-shaped) crater in which the centre has been pushed down, a significant volume of material has been ejected, and a topographically elevated crater rim has been pushed up. When this cavity has reached its maximum size, it is called the transient cavity.
The depth of the transient cavity is typically a quarter to a third of its diameter. Ejecta thrown out of the crater do not include material excavated from the full depth of the transient cavity; typically the depth of maximum excavation is only about a third of the total depth. As a result, about one third of the volume of the transient crater is formed by the ejection of material, and the remaining two thirds is formed by the displacement of material downwards, outwards and upwards, to form the elevated rim. For impacts into highly porous materials, a significant crater volume may also be formed by the permanent compaction of the pore space. Such compaction craters may be important on many asteroids, comets and small moons.
In large impacts, as well as material displaced and ejected to form the crater, significant volumes of target material may be melted and vaporized together with the original impactor. Some of this impact melt rock may be ejected, but most of it remains within the transient crater, initially forming a layer of impact melt coating the interior of the transient cavity. In contrast, the hot dense vaporized material expands rapidly out of the growing cavity, carrying some solid and molten material within it as it does so. As this hot vapor cloud expands, it rises and cools much like the archetypal mushroom cloud generated by large nuclear explosions. In large impacts, the expanding vapor cloud may rise to many times the scale height of the atmosphere, effectively expanding into free space.
Most material ejected from the crater is deposited within a few crater radii, but a small fraction may travel large distances at high velocity, and in large impacts it may exceed escape velocity and leave the impacted planet or moon entirely. The majority of the fastest material is ejected from close to the center of impact, and the slowest material is ejected close to the rim at low velocities to form an overturned coherent flap of ejecta immediately outside the rim. As ejecta escapes from the growing crater, it forms an expanding curtain in the shape of an inverted cone. The trajectory of individual particles within the curtain is thought to be largely ballistic.
Small volumes of un-melted and relatively un-shocked material may be spalled at very high relative velocities from the surface of the target and from the rear of the impactor. Spalling provides a potential mechanism whereby material may be ejected into inter-planetary space largely undamaged, and whereby small volumes of the impactor may be preserved undamaged even in large impacts. Small volumes of high-speed material may also be generated early in the impact by jetting. This occurs when two surfaces converge rapidly and obliquely at a small angle, and high-temperature highly shocked material is expelled from the convergence zone with velocities that may be several times larger than the impact velocity.
### Modification and collapse {#modification_and_collapse}
In most circumstances, the transient cavity is not stable and collapses under gravity. In small craters, less than about 4 km diameter on Earth, there is some limited collapse of the crater rim coupled with debris sliding down the crater walls and drainage of impact melts into the deeper cavity. The resultant structure is called a simple crater, and it remains bowl-shaped and superficially similar to the transient crater. In simple craters, the original excavation cavity is overlain by a lens of collapse breccia, ejecta and melt rock, and a portion of the central crater floor may sometimes be flat.
Above a certain threshold size, which varies with planetary gravity, the collapse and modification of the transient cavity is much more extensive, and the resulting structure is called a complex crater. The collapse of the transient cavity is driven by gravity, and involves both the uplift of the central region and the inward collapse of the rim. The central uplift is not the result of elastic rebound, which is a process in which a material with elastic strength attempts to return to its original geometry; rather the collapse is a process in which a material with little or no strength attempts to return to a state of gravitational equilibrium.
Complex craters have uplifted centers, and they have typically broad flat shallow crater floors, and terraced walls. At the largest sizes, one or more exterior or interior rings may appear, and the structure may be labeled an impact basin rather than an impact crater. Complex-crater morphology on rocky planets appears to follow a regular sequence with increasing size: small complex craters with a central topographic peak are called central peak craters, for example Tycho; intermediate-sized craters, in which the central peak is replaced by a ring of peaks, are called peak-ring craters, for example Schrödinger; and the largest craters contain multiple concentric topographic rings, and are called multi-ringed basins, for example Orientale. On icy (as opposed to rocky) bodies, other morphological forms appear that may have central pits rather than central peaks, and at the largest sizes may contain many concentric rings. Valhalla on Callisto is an example of this type.
### Subsequent modification {#subsequent_modification}
Long after an impact event, a crater may be further modified by erosion, mass wasting processes, viscous relaxation, or erased entirely. These effects are most prominent on geologically and meteorologically active bodies such as Earth, Titan, Triton, and Io. However, heavily modified craters may be found on more primordial bodies such as Callisto, where many ancient craters flatten into bright ghost craters, or palimpsests.
## Identifying impact craters {#identifying_impact_craters}
Non-explosive volcanic craters can usually be distinguished from impact craters by their irregular shape and the association of volcanic flows and other volcanic materials. Impact craters produce melted rocks as well, but usually in smaller volumes with different characteristics.
The distinctive mark of an impact crater is the presence of rock that has undergone shock-metamorphic effects, such as shatter cones, melted rocks, and crystal deformations. The problem is that these materials tend to be deeply buried, at least for simple craters. They tend to be revealed in the uplifted center of a complex crater, however.
Impacts produce distinctive shock-metamorphic effects that allow impact sites to be distinctively identified. Such shock-metamorphic effects can include:
- A layer of shattered or \"brecciated\" rock under the floor of the crater. This layer is called a \"breccia lens\".
- Shatter cones, which are chevron-shaped impressions in rocks. Such cones are formed most easily in fine-grained rocks.
- High-temperature rock types, including laminated and welded blocks of sand, spherulites and tektites, or glassy spatters of molten rock. The impact origin of tektites has been questioned by some researchers; they have observed some volcanic features in tektites not found in impactites. Tektites are also drier (contain less water) than typical impactites. While rocks melted by the impact resemble volcanic rocks, they incorporate unmelted fragments of bedrock, form unusually large and unbroken fields, and have a much more mixed chemical composition than volcanic materials spewed up from within the Earth. They also may have relatively large amounts of trace elements that are associated with meteorites, such as nickel, platinum, iridium, and cobalt. Note: scientific literature has reported that some \"shock\" features, such as small shatter cones, which are often associated only with impact events, have been found also in terrestrial volcanic ejecta.
- Microscopic pressure deformations of minerals. These include fracture patterns in crystals of quartz and feldspar, and formation of high-pressure materials such as diamond, derived from graphite and other carbon compounds, or stishovite and coesite, varieties of shocked quartz.
- Buried craters, such as the Decorah crater, can be identified through drill coring, aerial electromagnetic resistivity imaging, and airborne gravity gradiometry.
## Economic importance {#economic_importance}
On Earth, impact craters have resulted in useful minerals. Some of the ores produced from impact related effects on Earth include ores of iron, uranium, gold, copper, and nickel. It is estimated that the value of materials mined from impact structures is five billion dollars/year just for North America. The eventual usefulness of impact craters depends on several factors, especially the nature of the materials that were impacted and when the materials were affected. In some cases, the deposits were already in place and the impact brought them to the surface. These are called \"progenetic economic deposits.\" Others were created during the actual impact. The great energy involved caused melting. Useful minerals formed as a result of this energy are classified as \"syngenetic deposits.\" The third type, called \"epigenetic deposits,\" is caused by the creation of a basin from the impact. Many of the minerals that our modern lives depend on are associated with impacts in the past. The Vredeford Dome in the center of the Witwatersrand Basin is the largest goldfield in the world, which has supplied about 40% of all the gold ever mined in an impact structure (though the gold did not come from the bolide). The asteroid that struck the region was 6 mi wide. The Sudbury Basin was caused by an impacting body over 6 mi in diameter. This basin is famous for its deposits of nickel, copper, and platinum group elements. An impact was involved in making the Carswell structure in Saskatchewan, Canada; it contains uranium deposits. Hydrocarbons are common around impact structures. Fifty percent of impact structures in North America in hydrocarbon-bearing sedimentary basins contain oil/gas fields.
## Lists of craters {#lists_of_craters}
### Impact craters on Earth {#impact_craters_on_earth}
On Earth, the recognition of impact craters is a branch of geology, and is related to planetary geology in the study of other worlds. Out of many proposed craters, relatively few are confirmed. The following twenty are a sample of articles of confirmed and well-documented impact sites.
See the Earth Impact Database, a website concerned with 190 (`{{as of|2019|07|lc=y}}`{=mediawiki}) scientifically confirmed impact craters on Earth.
### Some extraterrestrial craters {#some_extraterrestrial_craters}
- Caloris Basin (Mercury)
- Hellas Basin (Mars)
- Herschel crater (Mimas)
- Mare Orientale (Moon)
- Petrarch crater (Mercury)
- South Pole -- Aitken basin (Moon)
### Largest named craters in the Solar System {#largest_named_craters_in_the_solar_system}
1. North Polar Basin/Borealis Basin (disputed) -- Mars -- Diameter: 10,600 km
2. South Pole-Aitken basin -- Moon -- Diameter: 2,500 km
3. Hellas Basin -- Mars -- Diameter: 2,100 km
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1. Caloris Basin -- Mercury -- Diameter: 1,550 km
2. Sputnik Planitia -- Pluto -- Diameter: 1,300 km
3. Imbrium Basin -- Moon -- Diameter: 1,100 km
4. Isidis Planitia -- Mars -- Diameter: 1,100 km
5. Mare Tranquilitatis -- Moon -- Diameter: 870 km
6. Argyre Planitia -- Mars -- Diameter: 800 km
7. Rembrandt -- Mercury -- Diameter: 715 km
8. Serenitatis Basin -- Moon -- Diameter: 700 km
9. Mare Nubium -- Moon -- Diameter: 700 km
10. Beethoven -- Mercury -- Diameter: 625 km
11. Valhalla -- Callisto -- Diameter: 600 km, with rings to 4,000 km diameter
12. Hertzsprung -- Moon -- Diameter: 590 km
13. Turgis -- Iapetus -- Diameter: 580 km
14. Apollo -- Moon -- Diameter: 540 km
15. Engelier -- Iapetus -- Diameter: 504 km
16. Mamaldi -- Rhea -- Diameter: 480 km
17. Huygens -- Mars -- Diameter: 470 km
18. Schiaparelli -- Mars -- Diameter: 470 km
19. Rheasilvia -- 4 Vesta -- Diameter: 460 km
20. Gerin -- Iapetus -- Diameter: 445 km
21. Odysseus -- Tethys -- Diameter: 445 km
22. Korolev -- Moon -- Diameter: 430 km
23. Falsaron -- Iapetus -- Diameter: 424 km
24. Dostoevskij -- Mercury -- Diameter: 400 km
25. Menrva -- Titan -- Diameter: 392 km
26. Tolstoj -- Mercury -- Diameter: 390 km
27. Goethe -- Mercury -- Diameter: 380 km
28. Malprimis -- Iapetus -- Diameter: 377 km
29. Tirawa -- Rhea -- Diameter: 360 km
30. Orientale Basin -- Moon -- Diameter: 350 km, with rings to 930 km diameter
31. Evander -- Dione -- Diameter: 350 km
32. Epigeus -- Ganymede -- Diameter: 343 km
33. Gertrude -- Titania -- Diameter: 326 km
34. Telemus -- Tethys -- Diameter: 320 km
35. Asgard -- Callisto -- Diameter: 300 km, with rings to 1,400 km diameter
36. Vredefort impact structure -- Earth -- Diameter: 300 km
37. Burney -- Pluto -- Diameter: 296 km
There are approximately twelve more impact craters/basins larger than 300 km on the Moon, five on Mercury, and four on Mars. Large basins, some unnamed but mostly smaller than 300 km, can also be found on Saturn\'s moons Dione, Rhea and Iapetus.
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Charles Farrar Browne
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**Charles Farrar Browne** (April 26, 1834 -- March 6, 1867) was an American humor writer, better known under his *nom de plume*, **Artemus Ward**, which as a character, an illiterate rube with \"Yankee common sense\", Browne also played in public performances. He is considered to be America\'s first stand-up comedian. His birth name was Brown but he added the \"e\" after he became famous.
## Biography
Browne was born on 26 April 1834,
in Waterford, Maine to Caroline (née Farrar)
\"a descendant of the first Puritans\" and Levi Brown,
who \"operated a store in Waterford, engaged in farming and did some surveying\",
and was a justice of the peace.
He began his career at the age of fourteen, \"learned the printer\'s trade\"`{{cite news |title=ARTEMUS WARD.; An Old Friend's Reminiscences of the Genial American Humorist. |url=https://www.nytimes.com/1905/01/04/archives/artemus-ward-an-old-friends-reminiscences-of-the-genial-american.html |access-date=14 June 2025 |work=[[nytimes.com]] |date=Jan 4, 1905}}`{=mediawiki}
at *The Advertiser* in Norway, Maine, and later apprenticed in the printing office of *The Skowhegan Clarion*,
Skowhegan, Maine, then, as a compositor and occasional contributor to the daily and weekly journals. In 1858, in *The Plain Dealer* newspaper (Cleveland, Ohio), he published the first of the \"Artemus Ward\" series (\"a barely literate circus sideshow manager who toured the country and wrote about the people and events he saw.\"`{{cite news |title=Coastal History: Maine's Charles F. Browne, a.k.a. Artemus Ward, and the birth of stand-up |url=https://www.pressherald.com/2019/04/24/coastal-history-maines-charles-f-browne-a-k-a-artemus-ward-and-the-birth-of-stand-up/ |access-date=14 June 2025 |work=[[Portland Press Herald]] |date=24 April 2019}}`{=mediawiki}
\"loosely based on P.T. Barnum\"
), which, in collected form, achieved great popularity in both America and England.
Browne\'s companion at the *Plain Dealer*, George Hoyt, wrote:
> \"his desk was a rickety table which had been whittled and gashed until it looked as if it had been the victim of lightning. His chair was a fit companion thereto, a wabbling, unsteady affair, sometimes with four and sometimes with three legs. But Browne saw neither the table, nor the chair, nor any person who might be near, nothing, in fact, but the funny pictures which were tumbling out of his brain. When writing, his gaunt form looked ridiculous enough. One leg hung over the arm of his chair like a great hook, while he would write away, sometimes laughing to himself, and then slapping the table in the excess of his mirth.\"
In 1860, he became editor of the first *Vanity Fair*, a humorous New York weekly that failed in 1863. At about the same time, he began to appear as a lecturer who, by his droll and eccentric humor, attracted large audiences. Browne was also known as a member of the New York bohemian set which included leader Henry Clapp Jr., Walt Whitman, Fitz Hugh Ludlow, and actress Adah Isaacs Menken.
> Though his books were popular, it was his lecturing, delivered with deadpan expression, that brought him fame.
In 1863, Browne came to San Francisco to perform as Artemus Ward. An early expert at show business publicity, Browne sent his manager ahead by several weeks to buy advertising in the local papers and promote the show among prominent citizens for endorsements. On November 13, 1863, Browne stood before a packed crowd at Platt\'s Music Hall, in Waterford, Maine.
## Legacy
In Cleveland, where Browne started his comedy career, an elementary school is named after him, known as **Artemus Ward Elementary** on W. 140th Street. In the American Garden of the Cleveland Cultural Gardens in Rockefeller Park, a monument of him was erected, next to Mark Twain.
## Works
### Short stories {#short_stories}
- A Visit to Brigham Young
- Women\'s Rights
- One of Mr Ward\'s Business Letters
- On \"Forts\"
- Fourth of July Oration
- High-Handed Outrage at Utica
- Artemus Ward and the Prince of Wales
- Interview with Lincoln
- Letters to his Wife
### *Artemus Ward* books {#artemus_ward_books}
- [Artemus Ward His Book](https://babel.hathitrust.org/cgi/pt?id=miun.ack0410.0001.001) (1862) (full text online)
- [Artemus Ward His Travels](https://babel.hathitrust.org/cgi/pt?id=miun.abs0367.0001.001) (1865) (full text online)
- [Artemus Ward Among the Mormons](https://babel.hathitrust.org/cgi/pt?id=mdp.39015006946506) (1865) (full text online)
- [Artemus Ward in London](https://babel.hathitrust.org/cgi/pt?id=uc2.ark:/13960/t84j0k81v) (1867) (full text online)
- [Artemus Ward\'s Panorama](https://archive.org/details/artemuswardspan00hinggoog/page/n9) (1869) (full text online)
- [Artemus Ward\'s Lecture](https://babel.hathitrust.org/cgi/pt?id=dul1.ark:/13960/t3jw9c54p&view=1up&seq=9) (1869) (full text online)
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Chojnów
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Piast Castle \| image3 = Chojnów, wieża kościoła Świętych Apostołów Piotra i Pawła (3).jpg{{!}}Gothic Saints Peter and Paul Church \| image4 = Baszta-tkaczy-chojnow.jpg{{!}}Medieval Weavers Tower \| caption1 = Market Square \| caption2 = Piast Castle \| caption3 = Saints Peter and Paul Church \| caption4 = Weavers Tower }} \| image_flag = POL Chojnów flag.svg \| image_shield = POL Chojnów COA.svg \| pushpin_map = Poland \| pushpin_label_position = right \| subdivision_type = Country \| subdivision_name = `{{POL}}`{=mediawiki} \| subdivision_type1 = Voivodeship \| subdivision_name1 = `{{flag|Lower Silesian Voivodeship|name=Lower Silesian}}`{=mediawiki} \| subdivision_type2 = County \| subdivision_name2 = Legnica \| subdivision_type3 = Gmina \| subdivision_name3 = Chojnów (urban gmina) \| leader_title = Mayor \| leader_name = Jan Serkies \| established_title = Established \| established_date = 14th century \| established_title3 = Town rights \| established_date3 = 1333 \| area_total_km2 = 5.32 \| population_as_of = 31 December 2021 \| population_total = 13002 \| population_density_km2 = auto \| timezone = CET \| utc_offset = +1 \| timezone_DST = CEST \| utc_offset_DST = +2 \| coordinates = 51 16 N 15 56 E region:PL display=title,inline \| elevation_m = 170 \| postal_code_type = Postal code \| postal_code = 59-224, 59-225 \| area_code = +48 76 \| blank_name = Car plates \| blank_info = DLE \| website = `{{URL|chojnow.eu}}`{=mediawiki} }} **Chojnów** `{{IPAc-pl|AUD|Pl-Chojnów.ogg|'|h|o|j|n|u|f}}`{=mediawiki} (*Haynau*) is a small town in Legnica County, Lower Silesian Voivodeship, in south-western Poland.`{{TERYT}}`{=mediawiki} It is located on the Skora river, a tributary of the Kaczawa at an average altitude of 170 m above sea level. Chojnów is the administrative seat of the rural gmina called Gmina Chojnów, although the town is not part of its territory and forms a separate urban gmina. As of December 2021, the town has 13,002 inhabitants.
Chojnów is located 18 km west of Legnica, 26 km east from Bolesławiec and 18 km north of Złotoryja, 5 km from the A4 motorway. It has railroad connections to Bolesławiec and Legnica.
## Heraldry
The Chojnów coat of arms is a blue escutcheon featuring a white castle with three towers. To the right side of the central tower is a silver crescent moon and to its left side a golden sun. In the gate of the castle is a Silesian Eagle on a yellow background. Chojnów\'s motto is \"Friendly Town\".
## Geography
Chojnów is located in the Central-Western part of the Lower Silesia region. The Skora (Leather) River flows through the town in a westerly direction. The city of Chojnów is 5.32 km2 in area, including 41% agricultural land.
Chojnów has a connection with the major cities of the country (road and rail) and located 5 km south of Chojnów has the A4 Autostrada. To the South of the town is the surrounding Chojnowska Plain.
## History
The town is first mentioned in a Latin mediaeval document issued in Wrocław on February 26, 1253, stating, the Silesian Duke Henry III when the town is mentioned under the name Honowo. Possible the name of nearby Hainau Island. The name is of Polish origin, and in more modern records from the 19th century, the Polish name appears as *Hajnów*, while *Haynau* is the Germanized version of the original Polish name.
The settlement of *Haynow* was mentioned in a 1272 deed. It was already called a *civitas* in a 1288 document issued by the Piast duke Henry V of Legnica, and officially received town privileges in 1333 from Duke Bolesław III the Generous. It was part of the duchies of Wrocław, Głogów and Legnica of fragmented Poland and remained under the rule of the Piast dynasty until 1675. Its population was predominantly Polish. In 1292 the first castellan of Chojnów, Bronisław Budziwojowic, was mentioned. In the 14th and early 15th centuries Chojnów was granted various privileges, including staple right and gold mining right, thanks to which it flourished.
The town survived the Hussites, who burned almost the entire town center and castle, but it quickly helped recover its former glory. The largest boom Chojnów experienced was in the 16th century, however by the end of that century began to decline due to fires and epidemic, which claimed many victims in 1613. During the Thirty Years\' War (1618--1648), there was another outbreak in the city, it was occupied by the Austrians and Swedes and in 1642 it was also plundered by the Swedes. It remained part of the Piast-ruled Duchy of Legnica until its dissolution in 1675, when it was incorporated to Habsburg-ruled Bohemia. In the 18th century, cloth production developed and a clothmaking school was established in the town. One of two main routes connecting Warsaw and Dresden ran through the town in the 18th century and Kings Augustus II the Strong and Augustus III of Poland traveled that route numerous times. In 1740 the town was captured by Prussia and subsequently annexed in 1742. In 1804 it suffered a flood. During the Napoleonic wars there were more epidemics. In 1813 in Chojnów, Napoleon Bonaparte issued instructions regarding the reorganization of the 8th Polish Corps of Prince Józef Poniatowski. The event is commemorated by a plaque in the facade of the Piast Castle. A railway line was opened in the 19th century. Sewer, Gas lighting a Newspaper and a hospital soon followed as the towns economy improved.
The city was not spared in World War II, with 30% of the town being destroyed on February 10, 1945, when Soviet Red Army troops took the abandoned town. After World War II and the implementation of the Oder-Neisse line in 1945, the town passed to the Republic of Poland. It was repopulated by Poles, expelled from former eastern Poland annexed by the Soviet Union. In 1946 it was renamed *Chojnów*, a more modern version of the old Polish *Hajnów*. Also Greeks, refugees of the Greek Civil War, settled in Chojnów.
## Population
## Economy
Chojnów is an industrial and agricultural town. Among local products are: paper, agricultural machinery, chains, metal furniture for hospitals, equipment for the meat industry, beer, wine, leather clothing, and clothing for infants, children and adults.
## Sights and nature {#sights_and_nature}
Among the interesting monuments of Chojnów are the 13th-century castle of the Dukes of Legnica (currently used as a museum), two old churches, the *Baszta Tkaczy* (*Weavers\' Tower*) and preserved fragments of city walls.
The biggest green area in Chojnów is small forest *Park Piastowski* (*Piast\'s Park*), named after Piast dynasty. Wild animals that can be found in the Chojnów area are roe deer, foxes, rabbits and wild domestic animals, especially cats.
## Culture and sport {#culture_and_sport}
Every year in the first days of June, the *Days of Chojnów* (*Dni Chojnowa*) are celebrated. The Whole-Poland bike race *Masters* has been organized yearly in Chojnów for the past few years.
Chojnów has a Municipal sports and recreation center formed in 2008 holding various events, festivals, reviews, exhibitions, and competitions. The regional Museum is housed in the old Piast era castle. The collections include tiles, relics, and the castle garden. Next to the Museum there is a municipal library. In śródmiejskim Park, near the Town Hall is the amphitheatre.
The local government-run weekly newspaper is Gazeta Chojnowska, which has been published since 1992. It is published biweekly. Editions have a run of 900 copies and it is one of the oldest newspapers in Poland issued without interruption. The *Chojnów* is the official newspaper of Chojnów with copy run of 750 copies.
## Education
In Chojnów, there are two kindergartens, two elementary schools and two middle schools.
- Mary Konopnickiej is the smallest elementary school in Chojnów, and is located in the northern part of the city, close to the train station and founded in 1962.
- Janusz Korczak is the largest primary school in Chojnów in the southern part of the town.
- Middle School No. (Pope John Paul II), it is situated in the north-western part of the city next to the \"Small Church\".
- Gimnazjum nr 2 im. Nicolaus Copernicus is the largest high school in Chojnów.
- Liceum Ogólnokształcące im. Nicolaus Copernicus
## Religion
Chojnów is in the Catholic deanery of Chojnów and has two parishes, Immaculate Conception of the Blessed Virgin Mary and also the Holy Apostles Peter and Paul. Both parishes have active congregations. There are also two Congregations of Jehovah\'s witnesses.
## Notable people {#notable_people}
- Johann Wilhelm Ritter (1776--1810), chemist and physicist
- Georg Michaelis (1857--1936), politician, Chancellor of Germany (1917).
- Edith Jacobson (1897--1978), German psychoanalyst
- Oswald Lange (1912--2000), German--American aerospace engineer
- Horst Mahler (born 1936), German lawyer, former Red Army Faction militant, now Neo-Nazi activist
## Twin towns -- sister cities {#twin_towns_sister_cities}
Chojnów is twinned with:
- Commentry, France
- Egelsbach, Germany
- Mnichovo Hradiště, Czech Republic
## Gallery
Chojnow(js).jpg\|Entrance to the Piast Castle Chojnów, Ab-047.JPG\|Flower beds in Chojnów Chojnów, Wzgórze Chmielowe.jpg\|Park Piastowski Chojnów, Ratusz (2).jpg\|Town hall SM Chojnów kościół Niepokalanego Poczęcia NMP (5) ID 593383.jpg\|Immaculate Conception Church SM Chojnów Konarskiego4 (0).jpg\|Nicolaus Copernicus Gymnasium No. 2 Chojnów, Ab-057.JPG\|Monument to Polish soldiers killed in World War II and murdered in labour camps and exiled to Siberia Łabędzi Staw.jpg\|Swan\'s Pond (*Łabędzi Staw*) in winter Chojnów, Dworzec kolejowy (2).jpg\|Chojnów Railway Station Chojnow 055 most kolejowy.jpg\|Railway bridge
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Clock
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A **clock** or **chronometer** is a device that measures and displays time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month, and the year. Devices operating on several physical processes have been used over the millennia.
Some predecessors to the modern clock may be considered \"clocks\" that are based on movement in nature: A sundial shows the time by displaying the position of a shadow on a flat surface. There is a range of duration timers, a well-known example being the hourglass. Water clocks, along with sundials, are possibly the oldest time-measuring instruments. A major advance occurred with the invention of the verge escapement, which made possible the first mechanical clocks around 1300 in Europe, which kept time with oscillating timekeepers like balance wheels.
Traditionally, in horology (the study of timekeeping), the term *clock* was used for a striking clock, while a clock that did not strike the hours audibly was called a **timepiece**. This distinction is not generally made any longer. Watches and other timepieces that can be carried on one\'s person are usually not referred to as clocks. Spring-driven clocks appeared during the 15th century. During the 15th and 16th centuries, clockmaking flourished. The next development in accuracy occurred after 1656 with the invention of the pendulum clock by Christiaan Huygens. A major stimulus to improving the accuracy and reliability of clocks was the importance of precise time-keeping for navigation. The mechanism of a timepiece with a series of gears driven by a spring or weights is referred to as clockwork; the term is used by extension for a similar mechanism not used in a timepiece. The electric clock was patented in 1840, and electronic clocks were introduced in the 20th century, becoming widespread with the development of small battery-powered semiconductor devices.
The timekeeping element in every modern clock is a harmonic oscillator, a physical object (resonator) that vibrates or oscillates at a particular frequency. This object can be a pendulum, a balance wheel, a tuning fork, a quartz crystal, or the vibration of electrons in atoms as they emit microwaves, the last of which is so precise that it serves as the formal definition of the second.
Clocks have different ways of displaying the time. Analog clocks indicate time with a traditional clock face and moving hands. Digital clocks display a numeric representation of time. Two numbering systems are in use: 12-hour time notation and 24-hour notation. Most digital clocks use electronic mechanisms and LCD, LED, or VFD displays. For the blind and for use over telephones, speaking clocks state the time audibly in words. There are also clocks for the blind that have displays that can be read by touch.
## Etymology
The word *clock* derives from the medieval Latin word for \'bell\'---*clocca*---and has cognates in many European languages. Clocks spread to England from the Low Countries, so the English word came from the Middle Low German and Middle Dutch *Klocke*. The word is also derived from the Middle English *clokke*, Old North French *cloque*, or Middle Dutch *clocke*, all of which mean \'bell\'.
## History of time-measuring devices {#history_of_time_measuring_devices}
### Sundials
The apparent position of the Sun in the sky changes over the course of each day, reflecting the rotation of the Earth. Shadows cast by stationary objects move correspondingly, so their positions can be used to indicate the time of day. A sundial shows the time by displaying the position of a shadow on a (usually) flat surface that has markings that correspond to the hours. Sundials can be horizontal, vertical, or in other orientations. Sundials were widely used in ancient times. With knowledge of latitude, a well-constructed sundial can measure local solar time with reasonable accuracy, within a minute or two. Sundials continued to be used to monitor the performance of clocks until the 1830s, when the use of the telegraph and trains standardized time and time zones between cities.
### Devices that measure duration, elapsed time and intervals {#devices_that_measure_duration_elapsed_time_and_intervals}
Many devices can be used to mark the passage of time without respect to reference time (time of day, hours, minutes, etc.) and can be useful for measuring duration or intervals. Examples of such duration timers are candle clocks, incense clocks, and the hourglass. Both the candle clock and the incense clock work on the same principle, wherein the consumption of resources is more or less constant, allowing reasonably precise and repeatable estimates of time passages. In the hourglass, fine sand pouring through a tiny hole at a constant rate indicates an arbitrary, predetermined passage of time. The resource is not consumed, but re-used.
### Water clocks {#water_clocks}
Water clocks, along with sundials, are possibly the oldest time-measuring instruments, with the only exception being the day-counting tally stick. Given their great antiquity, where and when they first existed is not known and is perhaps unknowable. The bowl-shaped outflow is the simplest form of a water clock and is known to have existed in Babylon and Egypt around the 16th century BC. Other regions of the world, including India and China, also have early evidence of water clocks, but the earliest dates are less certain. Some authors, however, write about water clocks appearing as early as 4000 BC in these regions of the world.
The Macedonian astronomer Andronicus of Cyrrhus supervised the construction of the Tower of the Winds in Athens in the 1st century BC, which housed a large clepsydra inside as well as multiple prominent sundials outside, allowing it to function as a kind of early clocktower. The Greek and Roman civilizations advanced water clock design with improved accuracy. These advances were passed on through Byzantine and Islamic times, eventually making their way back to Europe. Independently, the Chinese developed their own advanced water clocks (*水鐘*) by 725 AD, passing their ideas on to Korea and Japan.
Some water clock designs were developed independently, and some knowledge was transferred through the spread of trade. Pre-modern societies do not have the same precise timekeeping requirements that exist in modern industrial societies, where every hour of work or rest is monitored and work may start or finish at any time regardless of external conditions. Instead, water clocks in ancient societies were used mainly for astrological reasons. These early water clocks were calibrated with a sundial. While never reaching the level of accuracy of a modern timepiece, the water clock was the most accurate and commonly used timekeeping device for millennia until it was replaced by the more accurate pendulum clock in 17th-century Europe.
Islamic civilization is credited with further advancing the accuracy of clocks through elaborate engineering. In 797 (or possibly 801), the Abbasid caliph of Baghdad, Harun al-Rashid, presented Charlemagne with an Asian elephant named Abul-Abbas together with a \"particularly elaborate example\" of a water clock. Pope Sylvester II introduced clocks to northern and western Europe around 1000 AD.
### Mechanical water clocks {#mechanical_water_clocks}
The first known geared clock was invented by the great mathematician, physicist, and engineer Archimedes during the 3rd century BC. Archimedes created his astronomical clock,`{{fact|reason=I can't find any record of this book, ISBN doesn't even seem to exist|date=April 2024}}`{=mediawiki} which was also a cuckoo clock with birds singing and moving every hour. It is the first carillon clock as it plays music simultaneously with a person blinking his eyes, surprised by the singing birds. The Archimedes clock works with a system of four weights, counterweights, and strings regulated by a system of floats in a water container with siphons that regulate the automatic continuation of the clock. The principles of this type of clock are described by the mathematician and physicist Hero, who says that some of them work with a chain that turns a gear in the mechanism. Another Greek clock probably constructed at the time of Alexander was in Gaza, as described by Procopius. The Gaza clock was probably a Meteoroskopeion, i.e., a building showing celestial phenomena and the time. It had a pointer for the time and some automations similar to the Archimedes clock. There were 12 doors opening one every hour, with Hercules performing his labors, the Lion at one o\'clock, etc., and at night a lamp becomes visible every hour, with 12 windows opening to show the time.
The Tang dynasty Buddhist monk Yi Xing along with government official Liang Lingzan made the escapement in 723 (or 725) to the workings of a water-powered armillary sphere and clock drive, which was the world\'s first clockwork escapement. The Song dynasty polymath and genius Su Song (1020--1101) incorporated it into his monumental innovation of the astronomical clock tower of Kaifeng in 1088.`{{Page needed|date=July 2011}}`{=mediawiki} His astronomical clock and rotating armillary sphere still relied on the use of either flowing water during the spring, summer, and autumn seasons or liquid mercury during the freezing temperatures of winter (i.e., hydraulics). In Su Song\'s waterwheel linkwork device, the action of the escapement\'s arrest and release was achieved by gravity exerted periodically as the continuous flow of liquid-filled containers of a limited size. In a single line of evolution, Su Song\'s clock therefore united the concepts of the clepsydra and the mechanical clock into one device run by mechanics and hydraulics. In his memorial, Su Song wrote about this concept:
> According to your servant\'s opinion there have been many systems and designs for astronomical instruments during past dynasties all differing from one another in minor respects. But the principle of the use of water-power for the driving mechanism has always been the same. The heavens move without ceasing but so also does water flow (and fall). Thus if the water is made to pour with perfect evenness, then the comparison of the rotary movements (of the heavens and the machine) will show no discrepancy or contradiction; for the unresting follows the unceasing.
Song was also strongly influenced by the earlier armillary sphere created by Zhang Sixun (976 AD), who also employed the escapement mechanism and used liquid mercury instead of water in the waterwheel of his astronomical clock tower. The mechanical clockworks for Su Song\'s astronomical tower featured a great driving-wheel that was 11 feet in diameter, carrying 36 scoops, into each of which water was poured at a uniform rate from the \"constant-level tank\". The main driving shaft of iron, with its cylindrical necks supported on iron crescent-shaped bearings, ended in a pinion, which engaged a gear wheel at the lower end of the main vertical transmission shaft. This great astronomical hydromechanical clock tower was about ten metres high (about 30 feet), featured a clock escapement, and was indirectly powered by a rotating wheel either with falling water or liquid mercury. A full-sized working replica of Su Song\'s clock exists in the Republic of China (Taiwan)\'s National Museum of Natural Science, Taichung city. This full-scale, fully functional replica, approximately 12 meters (39 feet) in height, was constructed from Su Song\'s original descriptions and mechanical drawings. The Chinese escapement spread west and was the source for Western escapement technology. In the 12th century, Al-Jazari, an engineer from Mesopotamia (lived 1136--1206) who worked for the Artuqid king of Diyar-Bakr, Nasir al-Din, made numerous clocks of all shapes and sizes. The most reputed clocks included the elephant, scribe, and castle clocks, some of which have been successfully reconstructed. As well as telling the time, these grand clocks were symbols of the status, grandeur, and wealth of the Urtuq State. Knowledge of these mercury escapements may have spread through Europe with translations of Arabic and Spanish texts.
### Fully mechanical {#fully_mechanical}
The word *horologia* (from the Greek *ὥρα*---\'hour\', and *λέγειν*---\'to tell\') was used to describe early mechanical clocks, but the use of this word (still used in several Romance languages) for all timekeepers conceals the true nature of the mechanisms. For example, there is a record that in 1176, Sens Cathedral in France installed an \'horologe\', but the mechanism used is unknown. According to Jocelyn de Brakelond, in 1198, during a fire at the abbey of St Edmundsbury (now Bury St Edmunds), the monks \"ran to the clock\" to fetch water, indicating that their water clock had a reservoir large enough to help extinguish the occasional fire. The word *clock* (via Medieval Latin *clocca* from Old Irish *clocc*, both meaning \'bell\'), which gradually supersedes \"horologe\", suggests that it was the sound of bells that also characterized the prototype mechanical clocks that appeared during the 13th century in Europe.
thumb\|upright=1.2\|A 17th-century weight-driven clock in Läckö Castle, Sweden
In Europe, between 1280 and 1320, there was an increase in the number of references to clocks and horologes in church records, and this probably indicates that a new type of clock mechanism had been devised. Existing clock mechanisms that used water power were being adapted to take their driving power from falling weights. This power was controlled by some form of oscillating mechanism, probably derived from existing bell-ringing or alarm devices. This controlled release of power -- the escapement -- marks the beginning of the true mechanical clock, which differed from the previously mentioned cogwheel clocks. The verge escapement mechanism appeared during the surge of true mechanical clock development, which did not need any kind of fluid power, like water or mercury, to work.
These mechanical clocks were intended for two main purposes: for signalling and notification (e.g., the timing of services and public events) and for modeling the Solar System. The former purpose is administrative; the latter arises naturally given the scholarly interests in astronomy, science, and astrology and how these subjects integrated with the religious philosophy of the time. The astrolabe was used both by astronomers and astrologers, and it was natural to apply a clockwork drive to the rotating plate to produce a working model of the solar system.
Simple clocks intended mainly for notification were installed in towers and did not always require faces or hands. They would have announced the canonical hours or intervals between set times of prayer. Canonical hours varied in length as the times of sunrise and sunset shifted. The more sophisticated astronomical clocks would have had moving dials or hands and would have shown the time in various time systems, including Italian hours, canonical hours, and time as measured by astronomers at the time. Both styles of clocks started acquiring extravagant features, such as automata.
In 1283, a large clock was installed at Dunstable Priory in Bedfordshire in southern England; its location above the rood screen suggests that it was not a water clock. In 1292, Canterbury Cathedral installed a \'great horloge\'. Over the next 30 years, there were mentions of clocks at a number of ecclesiastical institutions in England, Italy, and France. In 1322, a new clock was installed in Norwich, an expensive replacement for an earlier clock installed in 1273. This had a large (2 metre) astronomical dial with automata and bells. The costs of the installation included the full-time employment of two clockkeepers for two years.
### Astronomical
An elaborate water clock, the \'Cosmic Engine\', was invented by Su Song, a Chinese polymath, designed and constructed in China in 1092. This great astronomical hydromechanical clock tower was about ten metres high (about 30 feet) and was indirectly powered by a rotating wheel with falling water and liquid mercury, which turned an armillary sphere capable of calculating complex astronomical problems.
In Europe, there were the clocks constructed by Richard of Wallingford in Albans by 1336, and by Giovanni de Dondi in Padua from 1348 to 1364. They no longer exist, but detailed descriptions of their design and construction survive, and modern reproductions have been made. They illustrate how quickly the theory of the mechanical clock had been translated into practical constructions, and also that one of the many impulses to their development had been the desire of astronomers to investigate celestial phenomena.
The Astrarium of Giovanni Dondi dell\'Orologio was a complex astronomical clock built between 1348 and 1364 in Padua, Italy, by the doctor and clock-maker Giovanni Dondi dell\'Orologio. The Astrarium had seven faces and 107 moving gears; it showed the positions of the Sun, the Moon and the five planets then known, as well as religious feast days. The astrarium stood about 1 metre high, and consisted of a seven-sided brass or iron framework resting on 7 decorative paw-shaped feet. The lower section provided a 24-hour dial and a large calendar drum, showing the fixed feasts of the church, the movable feasts, and the position in the zodiac of the Moon\'s ascending node. The upper section contained 7 dials, each about 30 cm in diameter, showing the positional data for the Primum Mobile, Venus, Mercury, the Moon, Saturn, Jupiter, and Mars. Directly above the 24-hour dial is the dial of the Primum Mobile, so called because it reproduces the diurnal motion of the stars and the annual motion of the Sun against the background of stars. Each of the \'planetary\' dials used complex clockwork to produce reasonably accurate models of the planets\' motion. These agreed reasonably well both with Ptolemaic theory and with observations.
Wallingford\'s clock had a large astrolabe-type dial, showing the Sun, the Moon\'s age, phase, and node, a star map, and possibly the planets. In addition, it had a wheel of fortune and an indicator of the state of the tide at London Bridge. Bells rang every hour, the number of strokes indicating the time. Dondi\'s clock was a seven-sided construction, 1 metre high, with dials showing the time of day, including minutes, the motions of all the known planets, an automatic calendar of fixed and movable feasts, and an eclipse prediction hand rotating once every 18 years. It is not known how accurate or reliable these clocks would have been. They were probably adjusted manually every day to compensate for errors caused by wear and imprecise manufacture. Water clocks are sometimes still used, and can be examined in places such as ancient castles and museums. The Salisbury Cathedral clock, built in 1386, is considered to be the world\'s oldest surviving mechanical clock that strikes the hours.
### Spring-driven {#spring_driven}
Matthew Norman carriage clock with winding key.jpg\|Matthew Norman carriage clock with winding key 1908 Gilbert mantel clock decorated with Memento Mori decoupage.JPG\|Decorated William Gilbert mantel clock
Clockmakers developed their art in various ways. Building smaller clocks was a technical challenge, as was improving accuracy and reliability. Clocks could be impressive showpieces to demonstrate skilled craftsmanship, or less expensive, mass-produced items for domestic use. The escapement in particular was an important factor affecting the clock\'s accuracy, so many different mechanisms were tried.
Spring-driven clocks appeared during the 15th century, although they are often erroneously credited to Nuremberg watchmaker Peter Henlein (or Henle, or Hele) around 1511. The earliest existing spring driven clock is the chamber clock given to Phillip the Good, Duke of Burgundy, around 1430, now in the Germanisches Nationalmuseum. Spring power presented clockmakers with a new problem: how to keep the clock movement running at a constant rate as the spring ran down. This resulted in the invention of the *stackfreed* and the fusee in the 15th century, and many other innovations, down to the invention of the modern *going barrel* in 1760.
Early clock dials did not indicate minutes and seconds. A clock with a dial indicating minutes was illustrated in a 1475 manuscript by Paulus Almanus, and some 15th-century clocks in Germany indicated minutes and seconds. An early record of a seconds hand on a clock dates back to about 1560 on a clock now in the Fremersdorf collection.
During the 15th and 16th centuries, clockmaking flourished, particularly in the metalworking towns of Nuremberg and Augsburg, and in Blois, France. Some of the more basic table clocks have only one time-keeping hand, with the dial between the hour markers being divided into four equal parts making the clocks readable to the nearest 15 minutes. Other clocks were exhibitions of craftsmanship and skill, incorporating astronomical indicators and musical movements. The cross-beat escapement was invented in 1584 by Jost Bürgi, who also developed the remontoire. Bürgi\'s clocks were a great improvement in accuracy as they were correct to within a minute a day. These clocks helped the 16th-century astronomer Tycho Brahe to observe astronomical events with much greater precision than before.`{{how|date=November 2014}}`{=mediawiki}
### Pendulum
The next development in accuracy occurred after 1656 with the invention of the pendulum clock. Galileo had the idea to use a swinging bob to regulate the motion of a time-telling device earlier in the 17th century. Christiaan Huygens, however, is usually credited as the inventor. He determined the mathematical formula that related pendulum length to time (about 99.4 cm or 39.1 inches for the one second movement) and had the first pendulum-driven clock made. The first model clock was built in 1657 in the Hague, but it was in England that the idea was taken up. The longcase clock (also known as the *grandfather clock*) was created to house the pendulum and works by the English clockmaker William Clement in 1670 or 1671. It was also at this time that clock cases began to be made of wood and clock faces to use enamel as well as hand-painted ceramics.
In 1670, William Clement created the anchor escapement, an improvement over Huygens\' crown escapement. Clement also introduced the pendulum suspension spring in 1671. The concentric minute hand was added to the clock by Daniel Quare, a London clockmaker and others, and the second hand was first introduced.
### Hairspring
In 1675, Huygens and Robert Hooke invented the spiral balance spring, or the hairspring, designed to control the oscillating speed of the balance wheel. This crucial advance finally made accurate pocket watches possible. The great English clockmaker Thomas Tompion, was one of the first to use this mechanism successfully in his pocket watches, and he adopted the minute hand which, after a variety of designs were trialled, eventually stabilised into the modern-day configuration. The rack and snail striking mechanism for striking clocks, was introduced during the 17th century and had distinct advantages over the \'countwheel\' (or \'locking plate\') mechanism. During the 20th century there was a common misconception that Edward Barlow invented *rack and snail* striking. In fact, his invention was connected with a repeating mechanism employing the rack and snail. The repeating clock, that chimes the number of hours (or even minutes) on demand was invented by either Quare or Barlow in 1676. George Graham invented the deadbeat escapement for clocks in 1720.
### Marine chronometer {#marine_chronometer}
A major stimulus to improving the accuracy and reliability of clocks was the importance of precise time-keeping for navigation. The position of a ship at sea could be determined with reasonable accuracy if a navigator could refer to a clock that lost or gained less than about 10 seconds per day. This clock could not contain a pendulum, which would be virtually useless on a rocking ship. In 1714, the British government offered large financial rewards to the value of 20,000 pounds for anyone who could determine longitude accurately. John Harrison, who dedicated his life to improving the accuracy of his clocks, later received considerable sums under the Longitude Act.
In 1735, Harrison built his first chronometer, which he steadily improved on over the next thirty years before submitting it for examination. The clock had many innovations, including the use of bearings to reduce friction, weighted balances to compensate for the ship\'s pitch and roll in the sea and the use of two different metals to reduce the problem of expansion from heat. The chronometer was tested in 1761 by Harrison\'s son and by the end of 10 weeks the clock was in error by less than 5 seconds.
### Mass production {#mass_production}
The British had dominated watch manufacture for much of the 17th and 18th centuries, but maintained a system of production that was geared towards high quality products for the elite. Although there was an attempt to modernise clock manufacture with mass-production techniques and the application of duplicating tools and machinery by the British Watch Company in 1843, it was in the United States that this system took off. In 1816, Eli Terry and some other Connecticut clockmakers developed a way of mass-producing clocks by using interchangeable parts. Aaron Lufkin Dennison started a factory in 1851 in Massachusetts that also used interchangeable parts, and by 1861 was running a successful enterprise incorporated as the Waltham Watch Company.
### Early electric {#early_electric}
In 1815, the English scientist Francis Ronalds published the first electric clock powered by dry pile batteries. Alexander Bain, a Scottish clockmaker, patented the electric clock in 1840. The electric clock\'s mainspring is wound either with an electric motor or with an electromagnet and armature. In 1841, he first patented the electromagnetic pendulum. By the end of the nineteenth century, the advent of the dry cell battery made it feasible to use electric power in clocks. Spring or weight-driven clocks that use electricity, either alternating current (AC) or direct current (DC), to rewind the spring or raise the weight of a mechanical clock would be classified as an electromechanical clock. This classification would also apply to clocks that employ an electrical impulse to propel the pendulum. In electromechanical clocks, electricity serves no time-keeping function. These types of clocks were made as individual timepieces but are more commonly used in synchronized time installations in schools, businesses, factories, railroads and government facilities as a master clock and slave clocks.
Where an AC electrical supply of stable frequency is available, timekeeping can be maintained very reliably by using a synchronous motor, essentially counting the cycles. The supply current alternates with an accurate frequency of 50 hertz in many countries, and 60 hertz in others. While the frequency may vary slightly during the day as the load changes, generators are designed to maintain an accurate number of cycles over a day, so the clock may be a fraction of a second slow or fast at any time, but will be perfectly accurate over a long time. The rotor of the motor rotates at a speed that is related to the alternation frequency. Appropriate gearing converts this rotation speed to the correct ones for the hands of the analog clock. Time in these cases is measured in several ways, such as by counting the cycles of the AC supply, vibration of a tuning fork, the behaviour of quartz crystals, or the quantum vibrations of atoms. Electronic circuits divide these high-frequency oscillations into slower ones that drive the time display.
### Quartz
The piezoelectric properties of crystalline quartz were discovered by Jacques and Pierre Curie in 1880. The first crystal oscillator was invented in 1917 by Alexander M. Nicholson, after which the first quartz crystal oscillator was built by Walter G. Cady in 1921. In 1927 the first quartz clock was built by Warren Marrison and J.W. Horton at Bell Telephone Laboratories in Canada. The following decades saw the development of quartz clocks as precision time measurement devices in laboratory settings---the bulky and delicate counting electronics, built with vacuum tubes at the time, limited their practical use elsewhere. The National Bureau of Standards (now NIST) based the time standard of the United States on quartz clocks from late 1929 until the 1960s, when it changed to atomic clocks. In 1969, Seiko produced the world\'s first quartz wristwatch, the Astron. Their inherent accuracy and low cost of production resulted in the subsequent proliferation of quartz clocks and watches.
### Atomic
Currently, atomic clocks are the most accurate clocks in existence. They are considerably more accurate than quartz clocks as they can be accurate to within a few seconds over trillions of years. Atomic clocks were first theorized by Lord Kelvin in 1879. In the 1930s the development of magnetic resonance created practical method for doing this. A prototype ammonia maser device was built in 1949 at the U.S. National Bureau of Standards (NBS, now NIST). Although it was less accurate than existing quartz clocks, it served to demonstrate the concept. The first accurate atomic clock, a caesium standard based on a certain transition of the caesium-133 atom, was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. Calibration of the caesium standard atomic clock was carried out by the use of the astronomical time scale *ephemeris time* (ET). As of 2013, the most stable atomic clocks are ytterbium clocks, which are stable to within less than two parts in 1 quintillion (`{{val|2|e=-18}}`{=mediawiki}).
## Operation
The invention of the mechanical clock in the 13th century initiated a change in timekeeping methods from continuous processes, such as the motion of the gnomon\'s shadow on a sundial or the flow of liquid in a water clock, to periodic oscillatory processes, such as the swing of a pendulum or the vibration of a quartz crystal, which had the potential for more accuracy. All modern clocks use oscillation.
Although the mechanisms they use vary, all oscillating clocks, mechanical, electric, and atomic, work similarly and can be divided into analogous parts. They consist of an object that repeats the same motion over and over again, an *oscillator*, with a precisely constant time interval between each repetition, or \'beat\'. Attached to the oscillator is a *controller* device, which sustains the oscillator\'s motion by replacing the energy it loses to friction, and converts its oscillations into a series of pulses. The pulses are then counted by some type of *counter*, and the number of counts is converted into convenient units, usually seconds, minutes, hours, etc. Finally some kind of *indicator* displays the result in human readable form.
### Power source {#power_source}
### Oscillator
The timekeeping element in every modern clock is a harmonic oscillator, a physical object (resonator) that vibrates or oscillates repetitively at a precisely constant frequency.
- In mechanical clocks, this is either a pendulum or a balance wheel.
- In some early electronic clocks and watches such as the Accutron, they use a tuning fork.
- In quartz clocks and watches, it is a quartz crystal.
- In atomic clocks, it is the vibration of electrons in atoms as they emit microwaves.
- In early mechanical clocks before 1657, it was a crude balance wheel or foliot which was not a harmonic oscillator because it lacked a balance spring. As a result, they were very inaccurate, with errors of perhaps an hour a day.
The advantage of a harmonic oscillator over other forms of oscillator is that it employs resonance to vibrate at a precise natural resonant frequency or \"beat\" dependent only on its physical characteristics, and resists vibrating at other rates. The possible precision achievable by a harmonic oscillator is measured by a parameter called its Q, or quality factor, which increases (other things being equal) with its resonant frequency. This is why there has been a long-term trend toward higher frequency oscillators in clocks. Balance wheels and pendulums always include a means of adjusting the rate of the timepiece. Quartz timepieces sometimes include a rate screw that adjusts a capacitor for that purpose. Atomic clocks are primary standards, and their rate cannot be adjusted.
#### Synchronized or slave clocks {#synchronized_or_slave_clocks}
Some clocks rely for their accuracy on an external oscillator; that is, they are automatically synchronized to a more accurate clock:
- Slave clocks, used in large institutions and schools from the 1860s to the 1970s, kept time with a pendulum, but were wired to a master clock in the building, and periodically received a signal to synchronize them with the master, often on the hour. Later versions without pendulums were triggered by a pulse from the master clock and certain sequences used to force rapid synchronization following a power failure.
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- Synchronous electric clocks do not have an internal oscillator, but count cycles of the 50 or 60 Hz oscillation of the AC power line, which is synchronized by the utility to a precision oscillator. The counting may be done electronically, usually in clocks with digital displays, or, in analog clocks, the AC may drive a synchronous motor which rotates an exact fraction of a revolution for every cycle of the line voltage, and drives the gear train. Although changes in the grid line frequency due to load variations may cause the clock to temporarily gain or lose several seconds during the course of a day, the total number of cycles per 24 hours is maintained extremely accurately by the utility company, so that the clock keeps time accurately over long periods.
- Computer real-time clocks keep time with a quartz crystal, but can be periodically (usually weekly) synchronized over the Internet to atomic clocks (UTC), using the Network Time Protocol (NTP).
- Radio clocks keep time with a quartz crystal, but are periodically synchronized to time signals transmitted from dedicated standard time radio stations or satellite navigation signals, which are set by atomic clocks.
### Controller
This has the dual function of keeping the oscillator running by giving it \'pushes\' to replace the energy lost to friction, and converting its vibrations into a series of pulses that serve to measure the time.
- In mechanical clocks, this is the escapement, which gives precise pushes to the swinging pendulum or balance wheel, and releases one gear tooth of the *escape wheel* at each swing, allowing all the clock\'s wheels to move forward a fixed amount with each swing.
- In electronic clocks this is an electronic oscillator circuit that gives the vibrating quartz crystal or tuning fork tiny \'pushes\', and generates a series of electrical pulses, one for each vibration of the crystal, which is called the clock signal.
- In atomic clocks the controller is an evacuated microwave cavity attached to a microwave oscillator controlled by a microprocessor. A thin gas of caesium atoms is released into the cavity where they are exposed to microwaves. A laser measures how many atoms have absorbed the microwaves, and an electronic feedback control system called a phase-locked loop tunes the microwave oscillator until it is at the frequency that causes the atoms to vibrate and absorb the microwaves. Then the microwave signal is divided by digital counters to become the clock signal.
In mechanical clocks, the low Q of the balance wheel or pendulum oscillator made them very sensitive to the disturbing effect of the impulses of the escapement, so the escapement had a great effect on the accuracy of the clock, and many escapement designs were tried. The higher Q of resonators in electronic clocks makes them relatively insensitive to the disturbing effects of the drive power, so the driving oscillator circuit is a much less critical component.
### Counter chain {#counter_chain}
This counts the pulses and adds them up to get traditional time units of seconds, minutes, hours, etc. It usually has a provision for *setting* the clock by manually entering the correct time into the counter.
- In mechanical clocks this is done mechanically by a gear train, known as the wheel train. The gear train scales the rotation speed to give a shaft rotating once per hour to which the minute hand of the clock is attached, a shaft rotating once per 12 hours to which the hour hand of the clock is attached, and in some clocks a shaft rotating once per minute, to which the second hand is attached. The gear train also has a second function; to transmit mechanical power from the power source to run the oscillator. There is a friction coupling called the \'cannon pinion\' between the gears driving the hands and the rest of the clock, allowing the hands to be turned to set the time.
- In digital clocks a series of integrated circuit counters or dividers add the pulses up digitally, using binary logic. Often pushbuttons on the case allow the hour and minute counters to be incremented and decremented to set the time.
### Indicator
This displays the count of seconds, minutes, hours, etc. in a human readable form.
- The earliest mechanical clocks in the 13th century did not have a visual indicator and signalled the time audibly by striking bells. Many clocks to this day are striking clocks which strike the hour.
- Analog clocks display time with an analog clock face, which consists of a dial with the numbers 1 through 12 or 24, the hours in the day, around the outside. The hours are indicated with an hour hand, which makes one or two revolutions in a day, while the minutes are indicated by a minute hand, which makes one revolution per hour. In mechanical clocks a gear train drives the hands; in electronic clocks the circuit produces pulses every second which drive a stepper motor and gear train, which move the hands.
- Digital clocks display the time in periodically changing digits on a digital display. A common misconception is that a digital clock is more accurate than an analog wall clock, but the indicator type is separate and apart from the accuracy of the timing source.
- Talking clocks and the speaking clock services provided by telephone companies speak the time audibly, using either recorded or digitally synthesized voices.
## Types
Clocks can be classified by the type of time display, as well as by the method of timekeeping.
### Time display methods {#time_display_methods}
#### Analog
Analog clocks usually use a clock face which indicates time using rotating pointers called \"hands\" on a fixed numbered dial or dials. The standard clock face, known universally throughout the world, has a short \"hour hand\" which indicates the hour on a circular dial of 12 hours, making two revolutions per day, and a longer \"minute hand\" which indicates the minutes in the current hour on the same dial, which is also divided into 60 minutes. It may also have a \"second hand\" which indicates the seconds in the current minute. The only other widely used clock face today is the 24 hour analog dial, because of the use of 24 hour time in military organizations and timetables. Before the modern clock face was standardized during the Industrial Revolution, many other face designs were used throughout the years, including dials divided into 6, 8, 10, and 24 hours. During the French Revolution the French government tried to introduce a 10-hour clock, as part of their decimal-based metric system of measurement, but it did not achieve widespread use. An Italian 6 hour clock was developed in the 18th century, presumably to save power (a clock or watch striking 24 times uses more power).
Another type of analog clock is the sundial, which tracks the sun continuously, registering the time by the shadow position of its gnomon. Because the sun does not adjust to daylight saving time, users must add an hour during that time. Corrections must also be made for the equation of time, and for the difference between the longitudes of the sundial and of the central meridian of the time zone that is being used (i.e. 15 degrees east of the prime meridian for each hour that the time zone is ahead of GMT). Sundials use some or part of the 24 hour analog dial. There also exist clocks which use a digital display despite having an analog mechanism---these are commonly referred to as flip clocks. Alternative systems have been proposed. For example, the \"Twelv\" clock indicates the current hour using one of twelve colors, and indicates the minute by showing a proportion of a circular disk, similar to a moon phase.
#### Digital
Kanazawa Station Water Clock.jpg\|Digital clock displaying time by controlling valves on the fountain Digital-clock-radio-basic hf.jpg\|Simplistic digital clock radio Analog clock with digital display.png\|Diagram of a mechanical digital display of a flip clock Cifra 5 digital flip clock designed by Gino Valle (1957).jpg\|Cifra 5 digital flip clock (1957) SAMSUNG Galaxy S22 Ultra BLACK.jpg\|A digital clock on a Samsung Galaxy smartphone
Digital clocks display a numeric representation of time. Two numeric display formats are commonly used on digital clocks:
- the 24-hour notation with hours ranging 00--23;
- the 12-hour notation with AM/PM indicator, with hours indicated as 12AM, followed by 1AM--11AM, followed by 12PM, followed by 1PM--11PM (a notation mostly used in domestic environments).
Most digital clocks use electronic mechanisms and LCD, LED, or VFD displays; many other display technologies are used as well (cathode-ray tubes, nixie tubes, etc.). After a reset, battery change or power failure, these clocks without a backup battery or capacitor either start counting from 12:00, or stay at 12:00, often with blinking digits indicating that the time needs to be set. Some newer clocks will reset themselves based on radio or Internet time servers that are tuned to national atomic clocks. Since the introduction of digital clocks in the 1960s, there has been a notable decline in the use of analog clocks.
Some clocks, called \'flip clocks\', have digital displays that work mechanically. The digits are painted on sheets of material which are mounted like the pages of a book. Once a minute, a page is turned over to reveal the next digit. These displays are usually easier to read in brightly lit conditions than LCDs or LEDs. Also, they do not go back to 12:00 after a power interruption. Flip clocks generally do not have electronic mechanisms. Usually, they are driven by AC-synchronous motors.
#### Hybrid (analog-digital) {#hybrid_analog_digital}
Clocks with analog quadrants, with a digital component, usually minutes and hours displayed analogously and seconds displayed in digital mode.
#### Auditory
For convenience, distance, telephony or blindness, auditory clocks present the time as sounds. The sound is either spoken natural language, (e.g. \"The time is twelve thirty-five\"), or as auditory codes (e.g. number of sequential bell rings on the hour represents the number of the hour like the bell, Big Ben). Most telecommunication companies also provide a speaking clock service as well.
#### Word
Word clocks are clocks that display the time visually using sentences. E.g.: \"It\'s about three o\'clock.\" These clocks can be implemented in hardware or software.
#### Projection
Some clocks, usually digital ones, include an optical projector that shines a magnified image of the time display onto a screen or onto a surface such as an indoor ceiling or wall. The digits are large enough to be easily read, without using glasses, by persons with moderately imperfect vision, so the clocks are convenient for use in their bedrooms. Usually, the timekeeping circuitry has a battery as a backup source for an uninterrupted power supply to keep the clock on time, while the projection light only works when the unit is connected to an A.C. supply. Completely battery-powered portable versions resembling flashlights are also available.
#### Tactile
Auditory and projection clocks can be used by people who are blind or have limited vision. There are also clocks for the blind that have displays that can be read by using the sense of touch. Some of these are similar to normal analog displays, but are constructed so the hands can be felt without damaging them. Another type is essentially digital, and uses devices that use a code such as Braille to show the digits so that they can be felt with the fingertips.
#### Multi-display {#multi_display}
Some clocks have several displays driven by a single mechanism, and some others have several completely separate mechanisms in a single case. Clocks in public places often have several faces visible from different directions, so that the clock can be read from anywhere in the vicinity; all the faces show the same time. Other clocks show the current time in several time-zones. Watches that are intended to be carried by travellers often have two displays, one for the local time and the other for the time at home, which is useful for making pre-arranged phone calls. Some equation clocks have two displays, one showing mean time and the other solar time, as would be shown by a sundial. Some clocks have both analog and digital displays. Clocks with Braille displays usually also have conventional digits so they can be read by sighted people.
## Purposes
Clocks are in homes, offices and many other places; smaller ones (watches) are carried on the wrist or in a pocket; larger ones are in public places, e.g. a railway station or church. A small clock is often shown in a corner of computer displays, mobile phones and many MP3 players.
The primary purpose of a clock is to *display* the time. Clocks may also have the facility to make a loud alert signal at a specified time, typically to waken a sleeper at a preset time; they are referred to as *alarm clocks*. The alarm may start at a low volume and become louder, or have the facility to be switched off for a few minutes then resume. Alarm clocks with visible indicators are sometimes used to indicate to children too young to read the time that the time for sleep has finished; they are sometimes called *training clocks*.
A clock mechanism may be used to *control* a device according to time, e.g. a central heating system, a VCR, or a time bomb (see: digital counter). Such mechanisms are usually called timers. Clock mechanisms are also used to drive devices such as solar trackers and astronomical telescopes, which have to turn at accurately controlled speeds to counteract the rotation of the Earth.
Most digital computers depend on an internal signal at constant frequency to synchronize processing; this is referred to as a clock signal. (A few research projects are developing CPUs based on asynchronous circuits.) Some equipment, including computers, also maintains time and date for use as required; this is referred to as time-of-day clock, and is distinct from the system clock signal, although possibly based on counting its cycles.
### Time standards {#time_standards}
For some scientific work timing of the utmost accuracy is essential. It is also necessary to have a standard of the maximum accuracy against which working clocks can be calibrated. An ideal clock would give the time to unlimited accuracy, but this is not realisable. Many physical processes, in particular including some transitions between atomic energy levels, occur at exceedingly stable frequency; counting cycles of such a process can give a very accurate and consistent time---clocks which work this way are usually called atomic clocks. Such clocks are typically large, very expensive, require a controlled environment, and are far more accurate than required for most purposes; they are typically used in a standards laboratory.
### Navigation
Until advances in the late twentieth century, navigation depended on the ability to measure latitude and longitude. Latitude can be determined through celestial navigation; the measurement of longitude requires accurate knowledge of time. This need was a major motivation for the development of accurate mechanical clocks. John Harrison created the first highly accurate marine chronometer in the mid-18th century. The Noon gun in Cape Town still fires an accurate signal to allow ships to check their chronometers. Many buildings near major ports used to have (some still do) a large ball mounted on a tower or mast arranged to drop at a pre-determined time, for the same purpose. While satellite navigation systems such as GPS require unprecedentedly accurate knowledge of time, this is supplied by equipment on the satellites; vehicles no longer need timekeeping equipment.
### Sports and games {#sports_and_games}
Clocks can be used to measure varying periods of time in games and sports. Stopwatches can be used to time the performance of track athletes. Chess clocks are used to limit the board game players\' time to make a move. In various sports, *`{{Vanchor|Game clock|text=game clocks}}`{=mediawiki}* measure the duration the game or subdivisions of the game, while other clocks may be used for tracking different durations; these include play clocks, shot clocks, and pitch clocks.
## Culture
### Folklore and superstition {#folklore_and_superstition}
In the United Kingdom, clocks are associated with various beliefs, many involving death or bad luck. In legends, clocks have reportedly stopped of their own accord upon a nearby person\'s death, especially those of monarchs. The clock in the House of Lords supposedly stopped at \"nearly\" the hour of George III\'s death in 1820, the one at Balmoral Castle stopped during the hour of Queen Victoria\'s death, and similar legends are related about clocks associated with William IV and Elizabeth I. Many superstitions exist about clocks. One stopping before a person has died may foretell coming death. Similarly, if a clock strikes during a church hymn or a marriage ceremony, death or calamity is prefigured for the parishioners or a spouse, respectively. Death or ill events are foreshadowed if a clock strikes the wrong time. It may also be unlucky to have a clock face a fire or to speak while a clock is striking.
In Chinese culture, giving a clock (`{{zh|t=送鐘|s=送钟|first=t|p=sòng zhōng}}`{=mediawiki}) is often taboo, especially to the elderly, as it is a homophone of the act of attending another\'s funeral (`{{zh|t={{linktext|送終}}|s={{linktext|送终}}|first=t|p=sòngzhōng}}`{=mediawiki}).
## Specific types {#specific_types}
+-----------------------------+--------------------------+--------------------------------+
| By mechanism | By function | By style |
+-----------------------------+--------------------------+--------------------------------+
| - Astronomical clock | - 10-hour clock | - American clock |
| - Atomic clock | - Alarm clock | - Automaton clock |
| - Candle clock | - Binary clock | - Balloon clock |
| - Congreve clock | - Braille watch | - Banjo clock |
| - Conical pendulum clock | - Chronometer watch | - Bracket clock |
| - Digital clock | - Cuckoo clock | - Carriage clock |
| - Electric clock | - Duodecimal clock | - Cartel clock |
| - Flip clock | - Equation clock | - Cat clock |
| - Flying pendulum clock | - Game clock | - Chariot clock |
| - Hourglass | - Japanese clock | - Clock tower |
| - Incense clock | - Master clock | - Cuckoo clock |
| - Lamport clock | - Musical clock | - Doll\'s head clock |
| - Mechanical watch | - Railroad chronometer | - Floral clock |
| - Observatory chronometer | - Slave clock | - French Empire mantel clock |
| - Oil-lamp clock | - Speaking clock | - Grandfather clock |
| - Pendulum clock | - Stopwatch | - Mora clock |
| - Projection clock | - Striking clock | - Lantern clock |
| - Pulsar clock | - Talking clock | - Corpus Clock |
| - Quantum clock | - Tide clock | - Lighthouse clock |
| - Quartz clock | - Time ball | - Mantel clock |
| - Radio clock | - Time clock | - Skeleton clock |
| - Rolling ball clock | - World clock | - Turret clock |
| - Spring drive watch | | - Watch |
| - Steam clock | | |
| - Sundial | | |
| - Torsion pendulum clock | | |
| - Atmos clock | | |
| - Water clock | | |
+-----------------------------+--------------------------+--------------------------------+
## Awards
- (GPHG)
-
| 2025-06-20T00:00:00 |
6,456 |
Charles Edward Jones
|
**Charles Edward** \"**Chuck**\" **Jones** (November 8, 1952 -- September 11, 2001) was a United States Air Force officer, an aeronautical engineer, computer programmer, and an astronaut in the USAF Manned Spaceflight Engineer Program. He was killed during the September 11 attacks, aboard American Airlines Flight 11.
## Life
Charles Edward Jones was born November 8, 1952, in Clinton, Indiana. He graduated from Wichita East High School in 1970, earned a Bachelor of Science degree in Astronautical Engineering from the United States Air Force Academy in 1974, and received a Master of Science degree in astronautics from Massachusetts Institute of Technology in 1980. He entered the USAF Manned Spaceflight Engineer Program in 1982, and was scheduled to fly on mission STS-71-B in December 1986, but the mission was canceled after the *Challenger* disaster in January 1986. He left the Manned Spaceflight Engineer program in 1987.
He later worked for Defense Intelligence Agency, Bolling Air Force Base in Washington, D.C., and was Systems Program Director for Intelligence and Information Systems, Hanscom Air Force Base, Massachusetts. Jones later was the manager of space programs for BAE Systems.
Jones was killed at the age of 48 in the attacks of September 11, 2001, aboard American Airlines Flight 11. Jones was flying that day on a routine business trip for BAE Systems, and had been living as a retired U.S. Air Force colonel in Bedford, Massachusetts, at the time of his death. He was survived by his wife Jeanette.
At the National 9/11 Memorial, Jones is memorialized at the North Pool, on Panel N-74.
thumb\|upright=1.0\|left\|Jones\' name is located on Panel N-74 of the National September 11 Memorial\'s North Pool, along with those of other passengers of Flight 11.
## Military decorations {#military_decorations}
His awards include:
--
--
+------------------------------------+
| Parachutist Badge |
+------------------------------------+
| Master Air and Space Missile Badge |
+------------------------------------+
| Defense Superior Service Medal |
+------------------------------------+
| Air Force Commendation Medal |
+------------------------------------+
| Joint Meritorious Unit Award |
+------------------------------------+
| Air Force Longevity Service Award\ |
| with silver leaf cluster |
+------------------------------------+
| |
+------------------------------------+
- Senior Missile Badge
| 2025-06-20T00:00:00 |
6,458 |
Ceramic
|
A **ceramic** is any of the various hard, brittle, heat-resistant, and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain, and brick.
The earliest ceramics made by humans were fired clay bricks used for building house walls and other structures. Other pottery objects such as pots, vessels, vases and figurines were made from clay, either by itself or mixed with other materials like silica, hardened by sintering in fire. Later, ceramics were glazed and fired to create smooth, colored surfaces, decreasing porosity through the use of glassy, amorphous ceramic coatings on top of the crystalline ceramic substrates. Ceramics now include domestic, industrial, and building products, as well as a wide range of materials developed for use in advanced ceramic engineering, such as semiconductors.
The word *ceramic* comes from the Ancient Greek word `{{wikt-lang|grc|κεραμικός}}`{=mediawiki} (`{{grc-transl|κεραμικός}}`{=mediawiki}), meaning \"of or for pottery\" (`{{etymology||''{{wikt-lang|grc|κέραμος}}'' ({{grc-transl|κέραμος}})|potter's clay, tile, pottery}}`{=mediawiki}). The earliest known mention of the root *ceram-* is the Mycenaean Greek `{{nowrap|{{Transliteration|gmy|ke-ra-me-we}}}}`{=mediawiki}, workers of ceramic, written in Linear B syllabic script. The word *ceramic* can be used as an adjective to describe a material, product, or process, or it may be used as a noun, either singular or, more commonly, as the plural noun *ceramics*.
## Materials
thumb\|upright=1.35\|right\|Silicon nitride rocket thruster. Left: Mounted in test stand. Right: Being tested with H~2~/O~2~ propellants. Ceramic material is an inorganic, metallic oxide, nitride, or carbide material. Some elements, such as carbon or silicon, may be considered ceramics. Ceramic materials are brittle, hard, strong in compression, and weak in shearing and tension. They withstand the chemical erosion that occurs in other materials subjected to acidic or caustic environments. Ceramics generally can withstand very high temperatures, ranging from 1,000 °C to 1,600 °C (1,800 °F to 3,000 °F).
thumb\|upright=1.2\|A low magnification SEM micrograph of an advanced ceramic material. The properties of ceramics make fracturing an important inspection method. The crystallinity of ceramic materials varies widely. Most often, fired ceramics are either vitrified or semi-vitrified, as is the case with earthenware, stoneware, and porcelain. Varying crystallinity and electron composition in the ionic and covalent bonds cause most ceramic materials to be good thermal and electrical insulators (researched in ceramic engineering). With such a large range of possible options for the composition/structure of a ceramic (nearly all of the elements, nearly all types of bonding, and all levels of crystallinity), the breadth of the subject is vast, and identifiable attributes (hardness, toughness, electrical conductivity) are difficult to specify for the group as a whole. General properties such as high melting temperature, high hardness, poor conductivity, high moduli of elasticity, chemical resistance, and low ductility are the norm, with known exceptions to each of these rules (piezoelectric ceramics, low glass transition temperature ceramics, superconductive ceramics).
Composites such as fiberglass and carbon fiber, while containing ceramic materials, are not considered to be part of the ceramic family.
Highly oriented crystalline ceramic materials are not amenable to a great range of processing. Methods for dealing with them tend to fall into one of two categories: either making the ceramic in the desired shape by reaction *in situ* or \"forming\" powders into the desired shape and then sintering to form a solid body. Ceramic forming techniques include shaping by hand (sometimes including a rotation process called \"throwing\"), slip casting, tape casting (used for making very thin ceramic capacitors), injection molding, dry pressing, and other variations.
Many ceramics experts do not consider materials with an amorphous (noncrystalline) character (i.e., glass) to be ceramics, even though glassmaking involves several steps of the ceramic process and its mechanical properties are similar to those of ceramic materials. However, heat treatments can convert glass into a semi-crystalline material known as glass-ceramic.
Traditional ceramic raw materials include clay minerals such as kaolinite, whereas more recent materials include aluminium oxide, more commonly known as alumina. Modern ceramic materials, which are classified as advanced ceramics, include silicon carbide and tungsten carbide. Both are valued for their abrasion resistance and are therefore used in applications such as the wear plates of crushing equipment in mining operations. Advanced ceramics are also used in the medical, electrical, electronics, and armor industries.
## History
thumb\|upright=0.55 \|Earliest known ceramics are the Gravettian figurines that date to 29,000--25,000 BC. Human beings appear to have been making their own ceramics for at least 26,000 years, subjecting clay and silica to intense heat to fuse and form ceramic materials. The earliest found so far were in southern central Europe and were sculpted figures, not dishes. The earliest known pottery was made by mixing animal products with clay and firing it at up to 800 °C. While pottery fragments have been found up to 19,000 years old, it was not until about 10,000 years later that regular pottery became common. An early people that spread across much of Europe is named after its use of pottery: the Corded Ware culture. These early Indo-European peoples decorated their pottery by wrapping it with rope while it was still wet. When the ceramics were fired, the rope burned off but left a decorative pattern of complex grooves on the surface.
The invention of the wheel eventually led to the production of smoother, more even pottery using the wheel-forming (throwing) technique, like the pottery wheel. Early ceramics were porous, absorbing water easily. It became useful for more items with the discovery of glazing techniques, which involved coating pottery with silicon, bone ash, or other materials that could melt and reform into a glassy surface, making a vessel less pervious to water.
### Archaeology
Ceramic artifacts have an important role in archaeology for understanding the culture, technology, and behavior of peoples of the past. They are among the most common artifacts to be found at an archaeological site, generally in the form of small fragments of broken pottery called sherds. The processing of collected sherds can be consistent with two main types of analysis: technical and traditional.
The traditional analysis involves sorting ceramic artifacts, sherds, and larger fragments into specific types based on style, composition, manufacturing, and morphology. By creating these typologies, it is possible to distinguish between different cultural styles, the purpose of the ceramic, and the technological state of the people, among other conclusions. Besides, by looking at stylistic changes in ceramics over time, it is possible to separate (seriate) the ceramics into distinct diagnostic groups (assemblages). A comparison of ceramic artifacts with known dated assemblages allows for a chronological assignment of these pieces.
The technical approach to ceramic analysis involves a finer examination of the composition of ceramic artifacts and sherds to determine the source of the material and, through this, the possible manufacturing site. Key criteria are the composition of the clay and the temper used in the manufacture of the article under study: the temper is a material added to the clay during the initial production stage and is used to aid the subsequent drying process. Types of temper include shell pieces, granite fragments, and ground sherd pieces called \'grog\'. Temper is usually identified by microscopic examination of the tempered material. Clay identification is determined by a process of refiring the ceramic and assigning a color to it using Munsell Soil Color notation. By estimating both the clay and temper compositions and locating a region where both are known to occur, an assignment of the material source can be made. Based on the source assignment of the artifact, further investigations can be made into the site of manufacture.
## Properties
The physical properties of any ceramic substance are a direct result of its crystalline structure and chemical composition. Solid-state chemistry reveals the fundamental connection between microstructure and properties, such as localized density variations, grain size distribution, type of porosity, and second-phase content, which can all be correlated with ceramic properties such as mechanical strength σ by the Hall-Petch equation, hardness, toughness, dielectric constant, and the optical properties exhibited by transparent materials.
Ceramography is the art and science of preparation, examination, and evaluation of ceramic microstructures. Evaluation and characterization of ceramic microstructures are often implemented on similar spatial scales to that used commonly in the emerging field of nanotechnology: from nanometers to tens of micrometers (µm). This is typically somewhere between the minimum wavelength of visible light and the resolution limit of the naked eye.
The microstructure includes most grains, secondary phases, grain boundaries, pores, micro-cracks, structural defects, and hardness micro indentions. Most bulk mechanical, optical, thermal, electrical, and magnetic properties are significantly affected by the observed microstructure. The fabrication method and process conditions are generally indicated by the microstructure. The root cause of many ceramic failures is evident in the cleaved and polished microstructure. Physical properties which constitute the field of materials science and engineering include the following:
### Mechanical properties {#mechanical_properties}
Mechanical properties are important in structural and building materials as well as textile fabrics. In modern materials science, fracture mechanics is an important tool in improving the mechanical performance of materials and components. It applies the physics of stress and strain, in particular the theories of elasticity and plasticity, to the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical failure of bodies. Fractography is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real-life failures.
Ceramic materials are usually ionic or covalent bonded materials. A material held together by either type of bond will tend to fracture before any plastic deformation takes place, which results in poor toughness and brittle behavior in these materials. Additionally, because these materials tend to be porous, pores and other microscopic imperfections act as stress concentrators, decreasing the toughness further, and reducing the tensile strength. These combine to give catastrophic failures, as opposed to the more ductile failure modes of metals.
These materials do show plastic deformation. However, because of the rigid structure of crystalline material, there are very few available slip systems for dislocations to move, and so they deform very slowly.
To overcome the brittle behavior, ceramic material development has introduced the class of ceramic matrix composite materials, in which ceramic fibers are embedded and with specific coatings are forming fiber bridges across any crack. This mechanism substantially increases the fracture toughness of such ceramics. Ceramic disc brakes are an example of using a ceramic matrix composite material manufactured with a specific process.
Scientists are working on developing ceramic materials that can withstand significant deformation without breaking. A first such material that can deform in room temperature was found in 2024.
#### Toughening Mechanisms {#toughening_mechanisms}
Many strategies are employed to improve the toughness of ceramics to prevent fracture. This includes crack deflection, microcrack toughening, crack bridging, incorporation of ductile particles, and transformation toughening.
Crack deflection is a toughening mechanism that involves deflecting cracks away from more rapid crack propagation paths, preventing catastrophic sudden failure. Cracks may be deflected using microstructures such as whiskers, as in the use of silicon carbide whiskers to reinforce molybdenum disilicide ceramic material in a 1987 paper. Crack deflecting second phases may also take the form of platelets, particles, or fibers.
Microcrack toughening involves nucleation (creation) of microcracks near a macroscopic crack tip where the crack propagates, which lowers the stress experienced by the tip and therefore the urgency of crack propagation. To improve toughness, second phase particles can be incorporated into ceramic such that they are subject to microcracking, which relieves stress to prevent fracture.
Crack bridging occurs when a strong discontinuous reinforcing phase applies a force behind the propagating tip of the crack that discourages further cracking. These second phase bridges essentially pin the crack to discourage its extension. Crack bridging can be used to improve toughness via the incorporation of second phase whiskers in the ceramic, as well as other shapes, to bridge cracks.
Ductile particle ceramic matrix composites are composed of ductile particles such as metals distributed in a ceramic matrix. These particles boost toughness by deforming plastically to absorb energy, and by bridging advancing cracks. To be most effective, the particles should be isolated from each other. The most studied iterations of these composites consist of an alumina matrix, and nickel, iron, molybdenum, copper, or silver metal particles.
Transformation toughening occurs when a material undergoes stress-induced phase transformation. Some ceramics are capable of undergoing stress-induced martensitic transformation, which involves an energy barrier that must be overcome by absorbing energy. Martensitic transformations are diffusionless shear transformations involving the transition between an \"austenite\" or \"parent\" phase that is stable at higher temperatures and a \"martensitic\" phase that is stable at lower temperatures. Because the transformation absorbs energy, stress-induced martensitic transformations can hinder crack progression and increases toughness. A key example of this phenomenon is zirconia, whose martensitic transformation involves a crystal structure transformation from a tetragonal crystal structure (the austenite phase) to a monoclinic structure. The volume increase associated with transformation from tetragonal to monoclinic also relieves tensile stress at the crack, tip, further discouraging cracking and increasing toughness. When zirconia particles in a ceramic matrix undergo transformation during fabrication due to cooling , the stress fields around the particles lead to nucleation and extension of microcracks, which can also improve toughness of the material. These stress fields, as well as the particles themselves, can also contribute to crack deflection.
#### Ice-templating for enhanced mechanical properties {#ice_templating_for_enhanced_mechanical_properties}
If a ceramic is subjected to substantial mechanical loading, it can undergo a process called ice-templating, which allows some control of the microstructure of the ceramic product and therefore some control of the mechanical properties. Ceramic engineers use this technique to tune the mechanical properties to their desired application. Specifically, the strength is increased when this technique is employed. Ice templating allows the creation of macroscopic pores in a unidirectional arrangement. The applications of this oxide strengthening technique are important for solid oxide fuel cells and water filtration devices.
To process a sample through ice templating, an aqueous colloidal suspension is prepared to contain the dissolved ceramic powder evenly dispersed throughout the colloid,`{{clarify|reason=is the powder in suspension or actually dissolved?|date=December 2019}}`{=mediawiki} for example yttria-stabilized zirconia (YSZ). The solution is then cooled from the bottom to the top on a platform that allows for unidirectional cooling. This forces ice crystals to grow in compliance with the unidirectional cooling, and these ice crystals force the dissolved YSZ particles to the solidification front`{{clarify|date=June 2023}}`{=mediawiki} of the solid-liquid interphase boundary, resulting in pure ice crystals lined up unidirectionally alongside concentrated pockets of colloidal particles. The sample is then heated and at the same the pressure is reduced enough to force the ice crystals to sublime and the YSZ pockets begin to anneal together to form macroscopically aligned ceramic microstructures. The sample is then further sintered to complete the evaporation of the residual water and the final consolidation of the ceramic microstructure.
During ice-templating, a few variables can be controlled to influence the pore size and morphology of the microstructure. These important variables are the initial solids loading of the colloid, the cooling rate, the sintering temperature and duration, and the use of certain additives which can influence the microstructural morphology during the process. A good understanding of these parameters is essential to understanding the relationships between processing, microstructure, and mechanical properties of anisotropically porous materials.
### Electrical properties {#electrical_properties}
#### Semiconductors
Some ceramics are semiconductors. Most of these are transition metal oxides that are II-VI semiconductors, such as zinc oxide. While there are prospects of mass-producing blue light-emitting diodes (LED) from zinc oxide, ceramicists are most interested in the electrical properties that show grain boundary effects. One of the most widely used of these is the varistor. These are devices that exhibit the property that resistance drops sharply at a certain threshold voltage. Once the voltage across the device reaches the threshold, there is a breakdown of the electrical structure`{{clarification needed|date=November 2021}}`{=mediawiki} in the vicinity of the grain boundaries, which results in its electrical resistance dropping from several megohms down to a few hundred ohms. The major advantage of these is that they can dissipate a lot of energy, and they self-reset; after the voltage across the device drops below the threshold, its resistance returns to being high. This makes them ideal for surge-protection applications; as there is control over the threshold voltage and energy tolerance, they find use in all sorts of applications. The best demonstration of their ability can be found in electrical substations, where they are employed to protect the infrastructure from lightning strikes. They have rapid response, are low maintenance, and do not appreciably degrade from use, making them virtually ideal devices for this application. Semiconducting ceramics are also employed as gas sensors. When various gases are passed over a polycrystalline ceramic, its electrical resistance changes. With tuning to the possible gas mixtures, very inexpensive devices can be produced.
#### Superconductivity
Under some conditions, such as extremely low temperatures, some ceramics exhibit high-temperature superconductivity (in superconductivity, \"high temperature\" means above 30 K). The reason for this is not understood, but there are two major families of superconducting ceramics.
#### Ferroelectricity and supersets {#ferroelectricity_and_supersets}
Piezoelectricity, a link between electrical and mechanical response, is exhibited by a large number of ceramic materials, including the quartz used to measure time in watches and other electronics. Such devices use both properties of piezoelectrics, using electricity to produce a mechanical motion (powering the device) and then using this mechanical motion to produce electricity (generating a signal). The unit of time measured is the natural interval required for electricity to be converted into mechanical energy and back again.
The piezoelectric effect is generally stronger in materials that also exhibit pyroelectricity, and all pyroelectric materials are also piezoelectric. These materials can be used to inter-convert between thermal, mechanical, or electrical energy; for instance, after synthesis in a furnace, a pyroelectric crystal allowed to cool under no applied stress generally builds up a static charge of thousands of volts. Such materials are used in motion sensors, where the tiny rise in temperature from a warm body entering the room is enough to produce a measurable voltage in the crystal.
In turn, pyroelectricity is seen most strongly in materials that also display the ferroelectric effect, in which a stable electric dipole can be oriented or reversed by applying an electrostatic field. Pyroelectricity is also a necessary consequence of ferroelectricity. This can be used to store information in ferroelectric capacitors, elements of ferroelectric RAM.
The most common such materials are lead zirconate titanate and barium titanate. Aside from the uses mentioned above, their strong piezoelectric response is exploited in the design of high-frequency loudspeakers, transducers for sonar, and actuators for atomic force and scanning tunneling microscopes.
#### Positive thermal coefficient {#positive_thermal_coefficient}
Temperature increases can cause grain boundaries to suddenly become insulating in some semiconducting ceramic materials, mostly mixtures of heavy metal titanates. The critical transition temperature can be adjusted over a wide range by variations in chemistry. In such materials, current will pass through the material until joule heating brings it to the transition temperature, at which point the circuit will be broken and current flow will cease. Such ceramics are used as self-controlled heating elements in, for example, the rear-window defrost circuits of automobiles.
At the transition temperature, the material\'s dielectric response becomes theoretically infinite. While a lack of temperature control would rule out any practical use of the material near its critical temperature, the dielectric effect remains exceptionally strong even at much higher temperatures. Titanates with critical temperatures far below room temperature have become synonymous with \"ceramic\" in the context of ceramic capacitors for just this reason.
### Optical properties {#optical_properties}
Optically transparent materials focus on the response of a material to incoming light waves of a range of wavelengths. Frequency selective optical filters can be utilized to alter or enhance the brightness and contrast of a digital image. Guided lightwave transmission via frequency selective waveguides involves the emerging field of fiber optics and the ability of certain glassy compositions as a transmission medium for a range of frequencies simultaneously (multi-mode optical fiber) with little or no interference between competing wavelengths or frequencies. This resonant mode of energy and data transmission via electromagnetic (light) wave propagation, though low powered, is virtually lossless. Optical waveguides are used as components in Integrated optical circuits (e.g. light-emitting diodes, LEDs) or as the transmission medium in local and long haul optical communication systems. Also of value to the emerging materials scientist is the sensitivity of materials to radiation in the thermal infrared (IR) portion of the electromagnetic spectrum. This heat-seeking ability is responsible for such diverse optical phenomena as night-vision and IR luminescence.
Thus, there is an increasing need in the military sector for high-strength, robust materials which have the capability to transmit light (electromagnetic waves) in the visible (0.4 -- 0.7 micrometers) and mid-infrared (1 -- 5 micrometers) regions of the spectrum. These materials are needed for applications requiring transparent armor, including next-generation high-speed missiles and pods, as well as protection against improvised explosive devices (IED).
In the 1960s, scientists at General Electric (GE) discovered that under the right manufacturing conditions, some ceramics, especially aluminium oxide (alumina), could be made translucent. These translucent materials were transparent enough to be used for containing the electrical plasma generated in high-pressure sodium street lamps. During the past two decades, additional types of transparent ceramics have been developed for applications such as nose cones for heat-seeking missiles, windows for fighter aircraft, and scintillation counters for computed tomography scanners. Other ceramic materials, generally requiring greater purity in their make-up than those above, include forms of several chemical compounds, including:
1. Barium titanate**:** (often mixed with strontium titanate) displays ferroelectricity, meaning that its mechanical, electrical, and thermal responses are coupled to one another and also history-dependent. It is widely used in electromechanical transducers, ceramic capacitors, and data storage elements. Grain boundary conditions can create PTC effects in heating elements.
2. Sialon (silicon aluminium oxynitride) has high strength; resistance to thermal shock, chemical and wear resistance, and low density. These ceramics are used in non-ferrous molten metal handling, weld pins, and the chemical industry.
3. Silicon carbide (SiC) is used as a susceptor in microwave furnaces, a commonly used abrasive, and as a refractory material.
4. Silicon nitride (Si~3~N~4~) is used as an abrasive powder.
5. Steatite (magnesium silicates) is used as an electrical insulator.
6. Titanium carbide Used in space shuttle re-entry shields and scratchproof watches.
7. Uranium oxide (UO~2~), used as fuel in nuclear reactors.
8. Yttrium barium copper oxide (YBa~2~Cu~3~O~7−x~), a high-temperature superconductor.
9. Zinc oxide (ZnO), which is a semiconductor, and used in the construction of varistors.
10. Zirconium dioxide (zirconia), which in pure form undergoes many phase changes between room temperature and practical sintering temperatures, can be chemically \"stabilized\" in several different forms. Its high oxygen ion conductivity recommends it for use in fuel cells and automotive oxygen sensors. In another variant, metastable structures can impart transformation toughening for mechanical applications; most ceramic knife blades are made of this material. Partially stabilised zirconia (PSZ) is much less brittle than other ceramics and is used for metal forming tools, valves and liners, abrasive slurries, kitchen knives and bearings subject to severe abrasion.
## Products
### By usage {#by_usage}
For convenience, ceramic products are usually divided into four main types; these are shown below with some examples:
1. Structural, including bricks, pipes, floor and roof tiles, vitrified tile
2. Refractories, such as kiln linings, gas fire radiants, steel and glass making crucibles
3. Whitewares, including tableware, cookware, wall tiles, pottery products and sanitary ware
4. Technical, also known as engineering, advanced, special, and fine ceramics. Such items include:
- gas burner nozzles
- ballistic protection, vehicle armor
- nuclear fuel uranium oxide pellets
- biomedical implants
- coatings of jet engine turbine blades
- ceramic matrix composite gas turbine parts
- reinforced carbon--carbon ceramic disc brakes
- missile nose cones
- bearings
- thermal insulation tiles used on the Space Shuttle orbiter
### Ceramics made with clay {#ceramics_made_with_clay}
Frequently, the raw materials of modern ceramics do not include clays. Those that do have been classified as:
1. Earthenware, fired at lower temperatures than other types
2. Stoneware, vitreous or semi-vitreous
3. Porcelain, which contains a high content of kaolin
4. Bone china
### Classification
Ceramics can also be classified into three distinct material categories:
1. Oxides**:** alumina, beryllia, ceria, zirconia
2. Non-oxides**:** carbide, boride, nitride, silicide
3. Composite materials**:** particulate reinforced, fiber reinforced, combinations of oxides and non-oxides.
Each one of these classes can be developed into unique material properties.
## Applications
1. Knife blades**:** the blade of a ceramic knife will stay sharp for much longer than that of a steel knife, although it is more brittle and susceptible to breakage.
2. Carbon-ceramic brake disks for vehicles: highly resistant to brake fade at high temperatures.
3. Advanced composite ceramic and metal matrices have been designed for most modern armoured fighting vehicles because they offer superior penetrating resistance against shaped charge (HEAT rounds) and kinetic energy penetrators.
4. Ceramics such as alumina and boron carbide have been used as plates in ballistic armored vests to repel high-velocity rifle fire. Such plates are known commonly as small arms protective inserts, or SAPIs. Similar low-weight material is used to protect the cockpits of some military aircraft.
5. Ceramic ball bearings can be used in place of steel. Their greater hardness results in lower susceptibility to wear. Ceramic bearings typically last triple the lifetime of steel bearings. They deform less than steel under load, resulting in less contact with the bearing retainer walls and lower friction. In very high-speed applications, heat from friction causes more problems for metal bearings than ceramic bearings. Ceramics are chemically resistant to corrosion and are preferred for environments where steel bearings would rust. In some applications their electricity-insulating properties are advantageous. Drawbacks to ceramic bearings include significantly higher cost, susceptibility to damage under shock loads, and the potential to wear steel parts due to ceramics\' greater hardness.
6. In the early 1980s Toyota researched production of an adiabatic engine using ceramic components in the hot gas area. The use of ceramics would have allowed temperatures exceeding 1650 °C. Advantages would include lighter materials and a smaller cooling system (or no cooling system at all), leading to major weight reduction. The expected increase of fuel efficiency (due to higher operating temperatures, demonstrated in Carnot\'s theorem) could not be verified experimentally. It was found that heat transfer on the hot ceramic cylinder wall was greater than the heat transfer to a cooler metal wall. This is because the cooler gas film on a metal surface acts as a thermal insulator. Thus, despite the desirable properties of ceramics, prohibitive production costs and limited advantages have prevented widespread ceramic engine component adoption. In addition, small imperfections in ceramic material along with low fracture toughness can lead to cracking and potentially dangerous equipment failure. Such engines are possible experimentally, but mass production is not feasible with current technology.
7. Experiments with ceramic parts for gas turbine engines are being conducted. Currently, even blades made of advanced metal alloys used in the engines\' hot section require cooling and careful monitoring of operating temperatures. Turbine engines made with ceramics could operate more efficiently, providing for greater range and payload.
8. Recent advances have been made in ceramics which include bioceramics such as dental implants and synthetic bones. Hydroxyapatite, the major mineral component of bone, has been made synthetically from several biological and chemical components and can be formed into ceramic materials. Orthopedic implants coated with these materials bond readily to bone and other tissues in the body without rejection or inflammatory reaction. They are of great interest for gene delivery and tissue engineering scaffolding. Most hydroxyapatite ceramics are quite porous and lack mechanical strength and are therefore used solely to coat metal orthopedic devices to aid in forming a bond to bone or as bone fillers. They are also used as fillers for orthopedic plastic screws to aid in reducing inflammation and increase the absorption of these plastic materials. Work is being done to make strong, fully dense nanocrystalline hydroxyapatite ceramic materials for orthopedic weight bearing devices, replacing foreign metal and plastic orthopedic materials with a synthetic but naturally occurring bone mineral. Ultimately, these ceramic materials may be used as bone replacement, or with the incorporation of protein collagens, the manufacture of synthetic bones.
9. Applications for actinide-containing ceramic materials include nuclear fuels for burning excess plutonium (Pu), or a chemically inert source of alpha radiation in power supplies for uncrewed space vehicles or microelectronic devices. Use and disposal of radioactive actinides require immobilization in a durable host material. Long half-life radionuclides such as actinide are immobilized using chemically durable crystalline materials based on polycrystalline ceramics and large single crystals.
10. High-tech ceramics are used for producing watch cases. The material is valued by watchmakers for its light weight, scratch resistance, durability, and smooth touch. IWC is one of the brands that pioneered the use of ceramic in watchmaking.
11. Ceramics are used in the design of mobile phone bodies due to their high hardness, resistance to scratches, and ability to dissipate heat. Ceramic\'s thermal management properties help in maintaining optimal device temperatures during heavy use enhancing performance. Additionally, ceramic materials can support wireless charging and offer better signal transmission compared to metals, which can interfere with antennas. Companies like Apple and Samsung have incorporated ceramic in their devices.
12. Ceramics made of silicon carbide are used in pump and valve components because of their corrosion resistance characteristics. It is also used in nuclear reactors as fuel cladding materials due to their ability to withstand radiation and thermal stress. Other uses of Silicon carbide ceramics include paper manufacturing, ballistics, chemical production, and as pipe system components.
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Canon law
|
**Canon law** (from *κανών*, *kanon*, a \'straight measuring rod, ruler\') is a set of ordinances and regulations made by ecclesiastical authority (church leadership) for the government of a Christian organization or church and its members.
Canon law includes the internal ecclesiastical law, or operational policy, governing the Catholic Church (both the Latin Church and the Eastern Catholic Churches), the Eastern Orthodox and Oriental Orthodox churches, and the individual national churches within the Anglican Communion. The way that such church law is legislated, interpreted and at times adjudicated varies widely among these four bodies of churches. In all three traditions, a canon was originally a rule adopted by a church council; these canons formed the foundation of canon law.
## Etymology
Greek *kanon* / *κανών*, Arabic *\[\[qaanoon\]\]* / *قانون*, Hebrew *kaneh* / *קָנֶה*, \'straight\'; a rule, code, standard, or measure; the root meaning in all these languages is \'reed\'; see also the Romance-language ancestors of the English word *cane*.
In the fourth century, the First Council of Nicaea (325) calls canons the disciplinary measures of the church: the term canon, κανὠν, means in Greek, a rule. There is a very early distinction between the rules enacted by the church and the legislative measures taken by the state called *leges*, Latin for laws.
## Apostolic Canons {#apostolic_canons}
The *Apostolic Canons* or *Ecclesiastical Canons of the Same Holy Apostles* is a collection of ancient ecclesiastical decrees (eighty-five in the Eastern, fifty in the Western Church) concerning the government and discipline of the Early Christian Church, incorporated with the Apostolic Constitutions which are part of the Ante-Nicene Fathers.
## Catholic Church {#catholic_church}
In the Catholic Church, canon law is the system of laws and legal principles made and enforced by the church\'s hierarchical authorities to regulate its external organization and government and to order and direct the activities of Catholics toward the mission of the church. It was the first modern Western legal system and is the oldest continuously functioning legal system in the West.
In the Latin Church, positive ecclesiastical laws, based directly or indirectly upon immutable divine law or natural law, derive formal authority in the case of universal laws from the supreme legislator (i.e., the Supreme Pontiff), who possesses the totality of legislative, executive, and judicial power in his person, while particular laws derive formal authority from a legislator inferior to the supreme legislator. The actual subject material of the canons is not just doctrinal or moral in nature, but all-encompassing of the human condition, and therefore extending beyond what is taken as revealed truth.
The Catholic Church also includes the main five rites (groups) of churches which are in full union with the Holy See and the Latin Church:
1. Alexandrian Rite Churches which include the Coptic Catholic Church, Eritrean Catholic Church, and Ethiopian Catholic Church.
2. West Syriac Rite which includes the Maronite Church, Syriac Catholic Church and the Syro-Malankara Catholic Church.
3. Armenian Rite Church which includes the Armenian Catholic Church.
4. Byzantine Rite Churches which include the Albanian Greek Catholic Church, Belarusian Greek Catholic Church, Bulgarian Greek Catholic Church, Greek Catholic Church of Croatia and Serbia, Greek Byzantine Catholic Church, Hungarian Greek Catholic Church, Italo-Albanian Catholic Church, Macedonian Greek Catholic Church, Melkite Greek Catholic Church, Romanian Greek Catholic Church, Russian Greek Catholic Church, Ruthenian Greek Catholic Church, Slovak Greek Catholic Church and Ukrainian Greek Catholic Church.
5. East Syriac Rite Churches which includes the Chaldean Catholic Church and Syro-Malabar Church.
All of these church groups are in full communion with the Supreme Pontiff and are subject to the *Code of Canons of the Eastern Churches*.
### History, sources of law, and codifications {#history_sources_of_law_and_codifications}
thumb\|left\|upright=1.35\|Image of pages from the *Decretum* of Burchard of Worms, an 11th-century book of canon law *Main article: Legal history of the Catholic Church, Philosophy, theology, and fundamental theory of Catholic canon law*
The Catholic Church has what is claimed to be the oldest continuously functioning internal legal system in Western Europe, much later than Roman law but predating the evolution of modern European civil law traditions.
The history of Latin canon law can be divided into four periods: the *jus antiquum*, the *jus novum*, the *jus novissimum* and the *Code of Canon Law*. In relation to the Code, history can be divided into the *jus vetus* (all law before the Code) and the *jus novum* (the law of the Code, or *jus codicis*).
The canon law of the Eastern Catholic Churches, which had developed some different disciplines and practices, underwent its own process of codification, resulting in the Code of Canons of the Eastern Churches promulgated in 1990 by Pope John Paul II.
### Catholic canon law as legal system {#catholic_canon_law_as_legal_system}
Roman Catholic canon law is a fully developed legal system, with all the necessary elements: courts, lawyers, judges, a fully articulated legal code, principles of legal interpretation, and coercive penalties, though it lacks civilly-binding force in most secular jurisdictions. One example where conflict between secular and canon law occurred was in the English legal system, as well as systems, such as the U.S., that derived from it. Here criminals could apply for the benefit of clergy. Being in holy orders, or fraudulently claiming to be, meant that criminals could opt to be tried by ecclesiastical rather than secular courts. The ecclesiastical courts were generally more lenient. Under the Tudors, the scope of clerical benefit was steadily reduced by Henry VII, Henry VIII, and Elizabeth I. The papacy disputed secular authority over priests\' criminal offenses. The benefit of clergy was systematically removed from English legal systems over the next 200 years, although it still occurred in South Carolina in 1855. In English Law, the use of this mechanism, which by that point was a legal fiction used for first offenders, was abolished by the Criminal Law Act 1827.
The academic degrees in Catholic canon law are the J.C.B. (*Juris Canonici Baccalaureatus*, Bachelor of Canon Law, normally taken as a graduate degree), J.C.L. (*Juris Canonici Licentiatus*, Licentiate of Canon Law) and the J.C.D. (*Juris Canonici Doctor*, Doctor of Canon Law). Because of its specialized nature, advanced degrees in civil law or theology are normal prerequisites for the study of canon law.
Much of Catholic canon law\'s legislative style was adapted from the Roman Code of Justinian. As a result, Roman ecclesiastical courts tend to follow the Roman Law style of continental Europe with some variation, featuring collegiate panels of judges and an investigative form of proceeding, called \"inquisitorial\", from the Latin \"inquirere\", to enquire. This is in contrast to the adversarial form of proceeding found in the common law system of English and U.S. law, which features such things as juries and single judges.
The institutions and practices of Catholic canon law paralleled the legal development of much of Europe, and consequently, both modern civil law and common law bear the influences of canon law. As Edson Luiz Sampel, a Brazilian expert in Catholic canon law, says, canon law is contained in the genesis of various institutes of civil law, such as the law in continental Europe and Latin American countries. Indirectly, canon law has significant influence in contemporary society.
Catholic Canonical jurisprudential theory generally follows the principles of Aristotelian-Thomistic legal philosophy. While the term \"law\" is never explicitly defined in the Catholic Code of Canon Law, the *Catechism of the Catholic Church* cites Aquinas in defining law as \"an ordinance of reason for the common good, promulgated by the one who is in charge of the community\" and reformulates it as \"a rule of conduct enacted by competent authority for the sake of the common good\".
### Code for the Eastern Churches {#code_for_the_eastern_churches}
The law of the Eastern Catholic Churches in full communion with the Roman papacy was in much the same state as that of the Latin Church before 1917; much more diversity in legislation existed in the various Eastern Catholic Churches. Each had its own special law, in which custom still played an important part. One major difference in Eastern Europe however, specifically in the Eastern Orthodox Christian churches, was in regards to divorce. Divorce started to slowly be allowed in specific instances such as adultery being committed, abuse, abandonment, impotence, and barrenness being the primary justifications for divorce. Eventually, the church began to allow remarriage to occur (for both spouses) post-divorce. In 1929 Pius XI informed the Eastern Churches of his intention to work out a Code for the whole of the Eastern Church. The publication of these Codes for the Eastern Churches regarding the law of persons was made between 1949 through 1958 but finalized nearly 30 years later.
The first Code of Canon Law (1917) was exclusively for the Latin Church, with application to the Eastern Churches only \"in cases which pertain to their very nature\". After the Second Vatican Council (1962 - 1965), the Vatican produced the *Code of Canons of the Eastern Churches* which became the first code of Eastern Catholic Canon Law.
## Eastern Orthodox Church {#eastern_orthodox_church}
The Eastern Orthodox Church, principally through the work of 18th-century Athonite monastic scholar Nicodemus the Hagiorite, has compiled canons and commentaries upon them in a work known as the *Pēdálion* (*Πηδάλιον*, \'Rudder\'), so named because it is meant to \"steer\" the church in her discipline. The dogmatic determinations of the Councils are to be applied rigorously since they are considered to be essential for the church\'s unity and the faithful preservation of the Gospel.
## Anglican Communion {#anglican_communion}
In the Church of England, the ecclesiastical courts that formerly decided many matters such as disputes relating to marriage, divorce, wills, and defamation, still have jurisdiction of certain church-related matters (e.g. discipline of clergy, alteration of church property, and issues related to churchyards). Their separate status dates back to the 12th century when the Normans split them off from the mixed secular/religious county and local courts used by the Saxons. In contrast to the other courts of England, the law used in ecclesiastical matters is at least partially a civil law system, not common law, although heavily governed by parliamentary statutes. Since the Reformation, ecclesiastical courts in England have been royal courts. The teaching of canon law at the Universities of Oxford and Cambridge was abrogated by Henry VIII; thereafter practitioners in the ecclesiastical courts were trained in civil law, receiving a Doctor of Civil Law (D.C.L.) degree from Oxford, or a Doctor of Laws (LL.D.) degree from Cambridge. Such lawyers (called \"doctors\" and \"civilians\") were centered at \"Doctors Commons\", a few streets south of St Paul\'s Cathedral in London, where they monopolized probate, matrimonial, and admiralty cases until their jurisdiction was removed to the common law courts in the mid-19th century.
Other churches in the Anglican Communion around the world (e.g., the Episcopal Church in the United States and the Anglican Church of Canada) still function under their own private systems of canon law.
In 2002 a Legal Advisors Consultation meeting at Canterbury concluded:
> \(1\) There are principles of canon law common to the churches within the Anglican Communion; (2) Their existence can be factually established; (3) Each province or church contributes through its own legal system to the principles of canon law common within the Communion; (4) these principles have strong persuasive authority and are fundamental to the self-understanding of each of the member churches; (5) These principles have a living force, and contain within themselves the possibility for further development; and (6) The existence of the principles both demonstrates and promotes unity in the Communion.
## Presbyterian and Reformed churches {#presbyterian_and_reformed_churches}
In Presbyterian and Reformed churches, canon law is known as \"practice and procedure\" or \"church order\", and includes the church\'s laws respecting its government, discipline, legal practice, and worship.
Roman canon law had been criticized by the Presbyterians as early as 1572 in the Admonition to Parliament. The protest centered on the standard defense that canon law could be retained so long as it did not contradict the civil law. According to Polly Ha, the Reformed church government refuted this, claiming that the bishops had been enforcing canon law for 1500 years.
## Lutheranism
The Book of Concord is the historic doctrinal statement of the Lutheran Church, consisting of ten credal documents recognized as authoritative in Lutheranism since the 16th century. However, the Book of Concord is a confessional document (stating orthodox belief) rather than a book of ecclesiastical rules or discipline, like canon law. Each Lutheran national church establishes its own system of church order and discipline, though these are referred to as \"canons\".
## United Methodist Church {#united_methodist_church}
The Book of Discipline contains the laws, rules, policies, and guidelines for The United Methodist Church. Its latest edition was published in 2024.
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Computational complexity
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In computer science, the **computational complexity** or simply **complexity** of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem.
The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an upper bound on the complexity of the problem solved by this algorithm. Moreover, for designing efficient algorithms, it is often fundamental to compare the complexity of a specific algorithm to the complexity of the problem to be solved. Also, in most cases, the only thing that is known about the complexity of a problem is that it is lower than the complexity of the most efficient known algorithms. Therefore, there is a large overlap between analysis of algorithms and complexity theory.
As the amount of resources required to run an algorithm generally varies with the size of the input, the complexity is typically expressed as a function `{{math|''n'' → ''f''(''n'')}}`{=mediawiki}, where `{{math|''n''}}`{=mediawiki} is the size of the input and `{{math|''f''(''n'')}}`{=mediawiki} is either the worst-case complexity (the maximum of the amount of resources that are needed over all inputs of size `{{math|''n''}}`{=mediawiki}) or the average-case complexity (the average of the amount of resources over all inputs of size `{{math|''n''}}`{=mediawiki}). Time complexity is generally expressed as the number of required elementary operations on an input of size `{{math|''n''}}`{=mediawiki}, where elementary operations are assumed to take a constant amount of time on a given computer and change only by a constant factor when run on a different computer. Space complexity is generally expressed as the amount of memory required by an algorithm on an input of size `{{math|''n''}}`{=mediawiki}.
## Complexity as a function of input size {#complexity_as_a_function_of_input_size}
It is impossible to count the number of steps of an algorithm on all possible inputs. As the complexity generally increases with the size of the input, the complexity is typically expressed as a function of the size `{{math|''n''}}`{=mediawiki} (in bits) of the input, and therefore, the complexity is a function of `{{math|''n''}}`{=mediawiki}. However, the complexity of an algorithm may vary dramatically for different inputs of the same size. Therefore, several complexity functions are commonly used.
The worst-case complexity is the maximum of the complexity over all inputs of size `{{mvar|n}}`{=mediawiki}, and the average-case complexity is the average of the complexity over all inputs of size `{{mvar|n}}`{=mediawiki} (this makes sense, as the number of possible inputs of a given size is finite). Generally, when \"complexity\" is used without being further specified, this is the worst-case time complexity that is considered.
## Asymptotic complexity {#asymptotic_complexity}
It is generally difficult to compute precisely the worst-case and the average-case complexity. In addition, these exact values provide little practical application, as any change of computer or of model of computation would change the complexity somewhat. Moreover, the resource use is not critical for small values of `{{mvar|n}}`{=mediawiki}, and this makes that, for small `{{mvar|n}}`{=mediawiki}, the ease of implementation is generally more interesting than a low complexity.
For these reasons, one generally focuses on the behavior of the complexity for large `{{mvar|n}}`{=mediawiki}, that is on its asymptotic behavior when `{{mvar|n}}`{=mediawiki} tends to the infinity. Therefore, the complexity is generally expressed by using big O notation.
For example, the usual algorithm for integer multiplication has a complexity of $O(n^2),$ this means that there is a constant $c_u$ such that the multiplication of two integers of at most `{{mvar|n}}`{=mediawiki} digits may be done in a time less than $c_un^2.$ This bound is *sharp* in the sense that the worst-case complexity and the average-case complexity are $\Omega(n^2),$ which means that there is a constant $c_l$ such that these complexities are larger than $c_ln^2.$ The radix does not appear in these complexity, as changing of radix changes only the constants $c_u$ and $c_l.$
## Models of computation {#models_of_computation}
The evaluation of the complexity relies on the choice of a model of computation, which consists in defining the basic operations that are done in a unit of time. When the model of computation is not explicitly specified, it is generally implicitely assumed as being a multitape Turing machine, since several more realistic models of computation, such as random-access machines are asymptotically equivalent for most problems. It is only for very specific and difficult problems, such as integer multiplication in time $O(n\log n),$ that the explicit definition of the model of computation is required for proofs.
### Deterministic models {#deterministic_models}
A deterministic model of computation is a model of computation such that the successive states of the machine and the operations to be performed are completely determined by the preceding state. Historically, the first deterministic models were recursive functions, lambda calculus, and Turing machines. The model of random-access machines (also called RAM-machines) is also widely used, as a closer counterpart to real computers.
When the model of computation is not specified, it is generally assumed to be a multitape Turing machine. For most algorithms, the time complexity is the same on multitape Turing machines as on RAM-machines, although some care may be needed in how data is stored in memory to get this equivalence.
### Non-deterministic computation {#non_deterministic_computation}
In a non-deterministic model of computation, such as non-deterministic Turing machines, some choices may be done at some steps of the computation. In complexity theory, one considers all possible choices simultaneously, and the non-deterministic time complexity is the time needed, when the best choices are always done. In other words, one considers that the computation is done simultaneously on as many (identical) processors as needed, and the non-deterministic computation time is the time spent by the first processor that finishes the computation. This parallelism is partly amenable to quantum computing via superposed entangled states in running specific quantum algorithms, like e.g. Shor\'s factorization of yet only small integers (`{{as of|2018|03|lc=yes}}`{=mediawiki}: 21 = 3 × 7).
Even when such a computation model is not realistic yet, it has theoretical importance, mostly related to the P = NP problem, which questions the identity of the complexity classes formed by taking \"polynomial time\" and \"non-deterministic polynomial time\" as least upper bounds. Simulating an NP-algorithm on a deterministic computer usually takes \"exponential time\". A problem is in the complexity class NP, if it may be solved in polynomial time on a non-deterministic machine. A problem is NP-complete if, roughly speaking, it is in NP and is not easier than any other NP problem. Many combinatorial problems, such as the Knapsack problem, the travelling salesman problem, and the Boolean satisfiability problem are NP-complete. For all these problems, the best known algorithm has exponential complexity. If any one of these problems could be solved in polynomial time on a deterministic machine, then all NP problems could also be solved in polynomial time, and one would have P = NP. `{{As of|2017}}`{=mediawiki} it is generally conjectured that `{{nowrap|P ≠ NP,}}`{=mediawiki} with the practical implication that the worst cases of NP problems are intrinsically difficult to solve, i.e., take longer than any reasonable time span (decades!) for interesting lengths of input.
### Parallel and distributed computation {#parallel_and_distributed_computation}
Parallel and distributed computing consist of splitting computation on several processors, which work simultaneously. The difference between the different model lies mainly in the way of transmitting information between processors. Typically, in parallel computing the data transmission between processors is very fast, while, in distributed computing, the data transmission is done through a network and is therefore much slower.
The time needed for a computation on `{{mvar|N}}`{=mediawiki} processors is at least the quotient by `{{mvar|N}}`{=mediawiki} of the time needed by a single processor. In fact this theoretically optimal bound can never be reached, because some subtasks cannot be parallelized, and some processors may have to wait a result from another processor.
The main complexity problem is thus to design algorithms such that the product of the computation time by the number of processors is as close as possible to the time needed for the same computation on a single processor.
### Quantum computing {#quantum_computing}
A quantum computer is a computer whose model of computation is based on quantum mechanics. The Church--Turing thesis applies to quantum computers; that is, every problem that can be solved by a quantum computer can also be solved by a Turing machine. However, some problems may theoretically be solved with a much lower time complexity using a quantum computer rather than a classical computer. This is, for the moment, purely theoretical, as no one knows how to build an efficient quantum computer.
Quantum complexity theory has been developed to study the complexity classes of problems solved using quantum computers. It is used in post-quantum cryptography, which consists of designing cryptographic protocols that are resistant to attacks by quantum computers.
## Problem complexity (lower bounds) {#problem_complexity_lower_bounds}
The complexity of a problem is the infimum of the complexities of the algorithms that may solve the problem, including unknown algorithms. Thus the complexity of a problem is not greater than the complexity of any algorithm that solves the problems.
It follows that every complexity of an algorithm, that is expressed with big O notation, is also an upper bound on the complexity of the corresponding problem.
On the other hand, it is generally hard to obtain nontrivial lower bounds for problem complexity, and there are few methods for obtaining such lower bounds.
For solving most problems, it is required to read all input data, which, normally, needs a time proportional to the size of the data. Thus, such problems have a complexity that is at least linear, that is, using big omega notation, a complexity $\Omega(n).$
The solution of some problems, typically in computer algebra and computational algebraic geometry, may be very large. In such a case, the complexity is lower bounded by the maximal size of the output, since the output must be written. For example, a system of `{{mvar|n}}`{=mediawiki} polynomial equations of degree `{{mvar|d}}`{=mediawiki} in `{{mvar|n}}`{=mediawiki} indeterminates may have up to $d^n$ complex solutions, if the number of solutions is finite (this is Bézout\'s theorem). As these solutions must be written down, the complexity of this problem is $\Omega(d^n).$ For this problem, an algorithm of complexity $d^{O(n)}$ is known, which may thus be considered as asymptotically quasi-optimal.
A nonlinear lower bound of $\Omega(n\log n)$ is known for the number of comparisons needed for a sorting algorithm. Thus the best sorting algorithms are optimal, as their complexity is $O(n\log n).$ This lower bound results from the fact that there are `{{math|''n''!}}`{=mediawiki} ways of ordering `{{mvar|n}}`{=mediawiki} objects. As each comparison splits in two parts this set of `{{math|''n''!}}`{=mediawiki} orders, the number of `{{mvar|N}}`{=mediawiki} of comparisons that are needed for distinguishing all orders must verify $2^N>n!,$ which implies $N =\Omega(n\log n),$ by Stirling\'s formula.
A standard method for getting lower bounds of complexity consists of *reducing* a problem to another problem. More precisely, suppose that one may encode a problem `{{mvar|A}}`{=mediawiki} of size `{{mvar|n}}`{=mediawiki} into a subproblem of size `{{math|''f''(''n'')}}`{=mediawiki} of a problem `{{mvar|B}}`{=mediawiki}, and that the complexity of `{{mvar|A}}`{=mediawiki} is $\Omega(g(n)).$ Without loss of generality, one may suppose that the function `{{mvar|f}}`{=mediawiki} increases with `{{mvar|n}}`{=mediawiki} and has an inverse function `{{mvar|h}}`{=mediawiki}. Then the complexity of the problem `{{mvar|B}}`{=mediawiki} is $\Omega(g(h(n))).$ This is the method that is used to prove that, if P ≠ NP (an unsolved conjecture), the complexity of every NP-complete problem is $\Omega(n^k),$ for every positive integer `{{mvar|k}}`{=mediawiki}.
## Use in algorithm design {#use_in_algorithm_design}
Evaluating the complexity of an algorithm is an important part of algorithm design, as this gives useful information on the performance that may be expected.
It is a common misconception that the evaluation of the complexity of algorithms will become less important as a result of Moore\'s law, which posits the exponential growth of the power of modern computers. This is wrong because this power increase allows working with large input data (big data). For example, when one wants to sort alphabetically a list of a few hundreds of entries, such as the bibliography of a book, any algorithm should work well in less than a second. On the other hand, for a list of a million of entries (the phone numbers of a large town, for example), the elementary algorithms that require $O(n^2)$ comparisons would have to do a trillion of comparisons, which would need around three hours at the speed of 10 million of comparisons per second. On the other hand, the quicksort and merge sort require only $n\log_2 n$ comparisons (as average-case complexity for the former, as worst-case complexity for the latter). For `{{math|1=''n'' = 1,000,000}}`{=mediawiki}, this gives approximately 30,000,000 comparisons, which would only take 3 seconds at 10 million comparisons per second.
Thus the evaluation of the complexity may allow eliminating many inefficient algorithms before any implementation. This may also be used for tuning complex algorithms without testing all variants. By determining the most costly steps of a complex algorithm, the study of complexity allows also focusing on these steps the effort for improving the efficiency of an implementation.
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Coercion
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**Coercion** involves compelling a party to act in an involuntary manner through the use of threats, including threats to use force against that party. It involves a set of forceful actions which violate the free will of an individual in order to induce a desired response. These actions may include extortion, blackmail, or even torture and sexual assault. Common-law systems codify the act of violating a law while under coercion as a duress crime.
Coercion used as leverage may force victims to act in a way contrary to their own interests. Coercion can involve not only the infliction of bodily harm, but also psychological abuse (the latter intended to enhance the perceived credibility of the threat). The threat of further harm may also lead to the acquiescence of the person being coerced. The concepts of coercion and persuasion are similar, but various factors distinguish the two. These include the intent, the willingness to cause harm, the result of the interaction, and the options available to the coerced party.
Political authors such as John Rawls, Thomas Nagel, and Ronald Dworkin contend whether governments are inherently coercive. In 1919, Max Weber (1864--1920), building on the view of Ihering (1818--1892), defined a state as \"a human community that (successfully) claims a monopoly on the legitimate use of physical force\". Morris argues that the state can operate through incentives rather than coercion. Healthcare systems may use informal coercion to make a patient adhere to a doctor\'s treatment plan. Under certain circumstances, medical staff may use physical coercion to treat a patient involuntarily., a practice which raises ethical concerns. Such practices has also been shown to cause moral distress among healthcare staff, especially when staff attitudes toward coercive measures are negative. To minimize the need for coercion in psychiatric care, various models such as *Safewards* and *Six Core Strategies* have been implemented with promising results.
## Overview
The purpose of coercion is to substitute one\'s aims with weaker ones that the aggressor wants the victim to have. For this reason, many social philosophers have considered coercion as the polar opposite to freedom. Various forms of coercion are distinguished: first on the basis of the *kind of injury* threatened, second according to its *aims* and *scope*, and finally according to its *effects*, from which its legal, social, and ethical implications mostly depend.
### Physical
Physical coercion is the most commonly considered form of coercion, where the content of the conditional threat is the use of force against a victim, their relatives or property. An often used example is \"putting a gun to someone\'s head\" (*at gunpoint*) or putting a \"knife under the throat\" (*at knifepoint* or cut-throat) to compel action under the threat that non-compliance may result in the attacker harming or even killing the victim. These are so common that they are also used as metaphors for other forms of coercion.
Armed forces in many countries use firing squads to maintain discipline and intimidate the masses, or opposition, into submission or silent compliance. However, there also are nonphysical forms of coercion, where the threatened injury does not immediately imply the use of force. Byman and Waxman (2000) define coercion as \"the use of threatened force, including the limited use of actual force to back up the threat, to induce an adversary to behave differently than it otherwise would.\" Coercion does not in many cases amount to destruction of property or life since compliance is the goal.
#### Pain compliance {#pain_compliance}
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Cosmological argument
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In the philosophy of religion, a **cosmological argument** is an argument for the existence of God based upon observational and factual statements concerning the universe (or some general category of its natural contents) typically in the context of causation, change, contingency or finitude. In referring to reason and observation alone for its premises, and precluding revelation, this category of argument falls within the domain of natural theology. A cosmological argument can also sometimes be referred to as an **argument from universal causation**, an **argument from first cause**, the **causal argument** or the **prime mover argument**.
The concept of causation is a principal underpinning idea in all cosmological arguments, particularly in affirming the necessity for a First Cause. The latter is typically determined in philosophical analysis to be God, as identified within classical conceptions of theism.
The origins of the argument date back to at least Aristotle, developed subsequently within the scholarly traditions of Neoplatonism and early Christianity, and later under medieval Islamic scholasticism through the 9th to 12th centuries. It would eventually be re-introduced to Christian theology in the 13th century by Thomas Aquinas. In the 18th century, it would become associated with the principle of sufficient reason formulated by Gottfried Leibniz and Samuel Clarke, itself an exposition of the Parmenidean causal principle that \"nothing comes from nothing\".
Contemporary defenders of cosmological arguments include William Lane Craig, Robert Koons, John Lennox, Stephen Meyer, and Alexander Pruss.
## History
### Classical philosophy {#classical_philosophy}
Plato (c. 427--347 BC) and Aristotle (c. 384--322 BC) both posited first cause arguments, though each had certain notable caveats. In *The Laws* (Book X), Plato posited that all movement in the world and the Cosmos was \"imparted motion\". This required a \"self-originated motion\" to set it in motion and to maintain it. In *Timaeus*, Plato posited a \"demiurge\" of supreme wisdom and intelligence as the creator of the Cosmos.
Aristotle argued *against* the idea of a first cause, often confused with the idea of a \"prime mover\" or \"unmoved mover\" (*πρῶτον κινοῦν ἀκίνητον* or *primus motor*) in his *Physics* and *Metaphysics*. Aristotle argued in *favor* of the idea of several unmoved movers, one powering each celestial sphere, which he believed lived beyond the sphere of the fixed stars, and explained why motion in the universe (which he believed was eternal) had continued for an infinite period of time. Aristotle argued the atomist\'s assertion of a non-eternal universe would require a first uncaused cause -- in his terminology, an efficient first cause -- an idea he considered a nonsensical flaw in the reasoning of the atomists.
Like Plato, Aristotle believed in an eternal cosmos with no beginning and no end (which in turn follows Parmenides\' famous statement that \"nothing comes from nothing\"). In what he called \"first philosophy\" or metaphysics, Aristotle *did* intend a theological correspondence between the prime mover and a deity; functionally, however, he provided an explanation for the apparent motion of the \"fixed stars\" (now understood as the daily rotation of the Earth). According to his theses, immaterial unmoved movers are eternal unchangeable beings that constantly think about thinking, but being immaterial, they are incapable of interacting with the cosmos and have no knowledge of what transpires therein. From an \"aspiration or desire\", the celestial spheres, *imitate* that purely intellectual activity as best they can, by uniform circular motion. The unmoved movers *inspiring* the planetary spheres are no different in kind from the prime mover, they merely suffer a dependency of relation to the prime mover. Correspondingly, the motions of the planets are subordinate to the motion inspired by the prime mover in the sphere of fixed stars. Aristotle\'s natural theology admitted no creation or capriciousness from the immortal pantheon, but maintained a defense against dangerous charges of impiety.
### Late antiquity to the Islamic Golden Age {#late_antiquity_to_the_islamic_golden_age}
Plotinus, a third-century Platonist, taught that the One transcendent absolute caused the universe to exist simply as a consequence of its existence (*creatio ex deo*). His disciple Proclus stated, \"The One is God\". In the 6th century, Syriac Christian neo-Platonist John Philoponus (c. 490 -- c. 570) examined the contradiction between Greek pagan adherences to the concept of a past-eternal world and Aristotelian rejection of the existence of actual infinities. Thereupon, he formulated arguments in defense of temporal finitism, which underpinned his arguments for the existence of God. Philosopher Steven M. Duncan notes that Philoponus\'s ideas eventually received their fullest articulation \"at the hands of Muslim and Jewish exponents of *kalam*\", or medieval Islamic scholasticism.
In the 11th century, Islamic philosopher Avicenna (c. 980 -- 1037) inquired into the question of being, in which he distinguished between essence (*māhiyya*) and existence (*wuǧūd*). He argued that the fact of existence could not be inferred from or accounted for by the essence of existing things, and that form and matter by themselves could not originate and interact with the movement of the universe or the progressive actualization of existing things. Thus, he reasoned that existence must be due to an agent cause that necessitates, imparts, gives, or adds existence to an essence. To do so, the cause must coexist with its effect and be an existing thing.
### Medieval Christian theology {#medieval_christian_theology}
Thomas Aquinas (c. 1225 -- 1274) adapted and enhanced the argument he found in his reading of Aristotle, Avicenna (the Proof of the Truthful) and Maimonides to formulate one of the most influential versions of the cosmological argument. His conception of the first cause was the idea that the universe must be caused by something that is itself uncaused, which he claimed is \'that which we call God\':
Importantly, Aquinas\'s Five Ways, given the second question of his *Summa Theologica*, are not the entirety of Aquinas\'s demonstration that the Christian God exists. The Five Ways form only the beginning of Aquinas\'s Treatise on the Divine Nature.
## General principles {#general_principles}
### The infinite regress {#the_infinite_regress}
A *regress* is a series of related elements, arranged in some type of sequence of succession, examined in backwards succession (regression) from a fixed point of reference. Depending on the type of regress, this retrograde examination may take the form of recursive analysis, in which the elements in a series are studied as products of prior, often simpler, elements. If there is no \'last member\' in a regress (i.e. no \'first member\' in the series) it becomes an infinite regress, continuing in perpetuity. In the context of the cosmological argument the term \'regress\' usually refers to *causal regress*, in which the series is a chain of cause and effect, with each element in the series arising from causal activity of the prior member. Some variants of the argument may also refer to *temporal regress*, wherein the elements are past events (discrete units of time) arranged in a temporal sequence.
An infinite regress argument attempts to establish the falsity of a proposition by showing that it entails an infinite regress that is vicious. The cosmological argument is a type of *positive* infinite regress argument given that it defends a proposition (in this case, the existence of a first cause) by arguing that its negation would lead to a vicious regress. An infinite regress may be vicious due to various reasons:
- Impossibility: Thought experiments such as Hilbert\'s Hotel are cited to demonstrate the metaphysical impossibility of actual infinities existing in reality. Accordingly, it may be argued that an infinite causal or temporal regress cannot occur in the real world.
- Implausibility: The regress contradicts empirical evidence (e.g. for the finitude of the past) or basic principles such as Occam\'s razor.
- Explanatory failure: A failure of explanatory goals resulting in an infinite regress of explanations. This may arise in the case of logical fallacies such as begging the question or from an attempt to investigate causes concerning origins or fundamental principles.
### Accidental and essential ordering of causes {#accidental_and_essential_ordering_of_causes}
Aquinas refers to the distinction found in Aristotle\'s *Physics* (8.5) that a series of causes may either be accidental or essential, though the designation of this terminology would follow later under John Duns Scotus at the turn of the 14th century.
In an accidentally ordered series of causes, earlier members need not continue exerting causal activity (having done so to propagate the chain) for the series to continue. For example, in a generational line, ancestors need no longer exist for their offspring to continue the sequence of descent. In an essential series, prior members must maintain causal interrelationship for the series to continue: If a hand grips a stick that moves a rock along the ground, the rock would stop motion once the hand or stick ceases to exist.
Based upon this distinction Frederick Copleston (1907--1994) characterises two types of causation: Causes *in fieri*, which cause an effect\'s *becoming*, or coming into existence, and causes *in esse*, which causally sustain an effect, in *being*, once it exists.
Two specific properties of an essentially ordered series have significance in the context of the cosmological argument:
- A first cause is essential: Later members exercise no independent causal power in continuing the series. In the example illustrated above, the rock derives its causal power essentially from the stick, which derives its causal power essentially from the hand.
- All members in the causal series must exist simultaneously in time, or timelessly.
Thomistic philosopher, R. P. Phillips comments on the characteristics of essential ordering:
: \"Each member of the series of causes possesses being solely by virtue of the actual present operation of a superior cause \... Life is dependent *inter alia* on a certain atmospheric pressure, this again on the continual operation of physical forces, whose being and operation depends on the position of the earth in the solar system, which itself must endure relatively unchanged, a state of being which can only be continuously produced by a definite---if unknown---constitution of the material universe. This constitution, however, cannot be its own cause \... We are thus irresistibly led to posit a first efficient cause which, while itself uncaused, shall impart causality to a whole series.\"
## Versions of the argument {#versions_of_the_argument}
### Aquinas\'s argument from contingency {#aquinass_argument_from_contingency}
In the scholastic era, Aquinas formulated the \"argument from contingency\", following Aristotle, in claiming that there must be something to explain the existence of the universe. Since the universe could, under different circumstances, conceivably *not* exist (i.e. it is contingent) its existence must have a cause. This cause cannot be embodied in another contingent thing, but something that exists by necessity (i.e. that *must* exist in order for anything else to exist). It is a form of argument from universal causation, therefore compatible with the conception of a universe that has no beginning in time. In other words, according to Aquinas, even if the universe has always existed, it still owes its continuing existence to an uncaused cause, he states: \"\... and this we understand to be God.\"
Aquinas\'s argument from contingency is formulated as the Third Way (Q2, A3) in the *Summa Theologica*. It may be expressed as follows:
1. There exist contingent things, for which non-existence is possible.
2. It is impossible for contingent things to always exist, so at some time they did not exist.
3. Therefore, if all things are contingent, then nothing would exist now.
4. There exists something rather than nothing.
He concludes thereupon that contingent beings are an insufficient explanation for the existence of other contingent beings. Furthermore, that there must exist a *necessary* being, whose non-existence is impossible, to explain the origination of all contingent beings.
5. Therefore, there exists a necessary being.
6. It is possible that a necessary being has a cause of its necessity in another necessary being.
7. The derivation of necessity between beings cannot regress to infinity (being an essentially ordered causal series).
8. Therefore, there exists a being that is necessary of itself, from which all necessity derives.
9. That being is whom everyone calls God.
### Leibnizian cosmological argument {#leibnizian_cosmological_argument}
In 1714, German philosopher Gottfried Leibniz presented a variation of the cosmological argument based upon the principle of sufficient reason. He writes: \"There can be found no fact that is true or existent, or any true proposition, without there being a sufficient reason for its being so and not otherwise, although we cannot know these reasons in most cases.\" Stating his argument succinctly:
: \"Why is there something rather than nothing? The sufficient reason \... is found in a substance which \... is a necessary being bearing the reason for its existence within itself.\"
Alexander Pruss formulates the argument as follows:
1. Every contingent fact has an explanation.
2. There is a contingent fact that includes all other contingent facts.
3. Therefore, there is an explanation of this fact.
4. This explanation must involve a necessary being.
5. This necessary being is God.
Premise 1 expresses the principle of sufficient reason. In premise 2, Leibniz proposes the existence of a logical conjunction of all contingent facts, referred to in later literature as the *Big Conjunctive Contingent Fact* (BCCF), representing the sum total of contingent reality. Premise 3 applies the principle of sufficient reason to the BCCF, given that it too, as a contingency, has a sufficient explanation. It follows, in statement 4, that the explanation of the BCCF must be necessary, not contingent, given that the BCCF incorporates all contingent facts. Statement 5 proposes that the necessary being explaining the totality of contingent facts is God.
Philosophers Joshua Rasmussen and T. Ryan Byerly have argued in defence of the inference from statement 4 to statement 5.
### Duns Scotus\'s metaphysical argument {#duns_scotuss_metaphysical_argument}
At the turn of the 14th century, medieval Christian theologian John Duns Scotus (1265/66--1308) formulated a metaphysical argument for the existence of God inspired by Aquinas\'s argument of the unmoved mover. Like other philosophers and theologians, Scotus believed that his statement for God\'s existence could be considered distinct to that of Aquinas. The form of the argument can be summarised as follows:
1. An effect cannot be produced by itself.
2. An effect cannot be produced by nothing.
3. A circle of causes is impossible.
4. Therefore, an effect must be produced by something else.
5. An accidentally ordered causal series cannot exist without an essentially ordered series.
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1. Each member in an accidentally ordered series (except a possible first) exists via causal activity of a prior member.
2. That causal activity is exercised by virtue of a certain form.
3. Therefore, that form is required by each member to effect causation.
4. The form itself is not a member of the series.
5. Therefore \[c,d\], accidentally ordered causes cannot exist without higher-order (essentially ordered) causes.
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```
6. An essentially ordered causal series cannot regress to infinity.
7. Therefore \[4,5,6\], there exists a first agent.
Scotus affirms, in premise 5, that an accidentally ordered series of causes is impossible without higher-order laws and processes that govern the basic principles of accidental causation, which he characterises as essentially ordered causes.
Premise 6 continues, in accordance with Aquinas\'s discourses on the Second Way and Third Way, that an essentially ordered series of causes cannot be an infinite regress. On this, Scotus posits that, if it is merely possible that a first agent exists, then it is necessarily true that a first agent exists, given that the non-existence of a first agent entails the impossibility of its own existence (by virtue of being a first cause in the chain). He argues further that it is *not impossible* for a being to exist that is causeless by virtue of ontological perfection.
With the formulation of this argument, Scotus establishes the first component of his \'triple primacy\': The characterisation of a being that is first in efficient causality, final causality and pre-eminence, or maximal excellence, which he ascribes to God.
### Kalam cosmological argument {#kalam_cosmological_argument}
The Kalam cosmological argument\'s central thesis is the impossibility of an infinite temporal regress of events (or past-infinite universe). Though a modern formulation that defends the finitude of the past through philosophical and scientific arguments, many of the argument\'s ideas originate in the writings of early Christian theologian John Philoponus (490--570 AD), developed within the proceedings of medieval Islamic scholasticism through the 9th to 12th centuries, eventually returning to Christian theological scholarship in the 13th century.
These ideas were revitalised for modern discourse by philosopher and theologian William Lane Craig through publications such as *The Kalām Cosmological Argument* (1979) and the *Blackwell Companion to Natural Theology* (2009). The form of the argument popularised by Craig is expressed in two parts, as an initial deductive syllogism followed by further philosophical analysis.
#### Initial syllogism {#initial_syllogism}
1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
#### Conceptual analysis of the conclusion {#conceptual_analysis_of_the_conclusion}
Craig argues that the cause of the universe necessarily embodies specific properties in creating the universe *ex nihilo* and in effecting creation from a timeless state (implying free agency). Based upon this analysis, he appends a further premise and conclusion:
4. If the universe has a cause, then an uncaused, personal Creator of the universe exists who *sans (without)* the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
5. Therefore, an uncaused, personal Creator of the universe exists, who *sans* the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
For scientific evidence of the finitude of the past, Craig refers to the Borde-Guth-Vilenkin theorem, which posits a past boundary to cosmic inflation, and the general consensus on the standard model of cosmology, which refers to the origin of the universe in the Big Bang.
For philosophical evidence, he cites Hilbert\'s paradox of the grand hotel and Bertrand Russell\'s Tristram Shandy paradox to prove (respectively) the impossibility of actual infinites existing in reality and of forming an actual infinite by successive addition. He concludes that past events, in comprising a series of events that are instantiated in reality and formed by successive addition, cannot extend to an infinite past.
Craig remarks upon the theological implications that follow from the conclusion of the argument:
: \"\... our whole universe was caused to exist by something beyond it and greater than it. For it is no secret that one of the most important conceptions of what theists mean by \'God\' is Creator of heaven and earth.\"
## Criticism and discourse {#criticism_and_discourse}
### \"What caused the first cause?\" {#what_caused_the_first_cause}
Objections to the cosmological argument may question why a first cause is unique in that it does not require any causes. Critics contend that the concept of a first cause qualifies as special pleading, or that arguing for the first cause\'s exemption raises the question of why there should be a first cause at all. Defenders maintain that this question is addressed by various formulations of the cosmological argument, emphasizing that none of its major iterations rests on the premise that everything requires a cause.
Andrew Loke refers to the Kalam cosmological argument, in which the causal premise (\"whatever begins to exist has a cause\") stipulates that only things which *begin to exist* require a cause. William Lane Craig asserts that---even if one posits a plurality of causes for the existence of the universe---a first uncaused cause is necessary, otherwise an infinite regress of causes would arise, which he argues is impossible. Similarly, Edward Feser proposes, in accordance with Aquinas\'s discourses on the Second Way, that an essentially ordered series of causes cannot regress to infinity, even if it may be theoretically possible for accidentally ordered causes to do so.
Various arguments have been presented to demonstrate the metaphysical impossibility of an actually infinite regress occurring in the real world, referring to thought experiments such as Hilbert\'s Hotel, the tale of Tristram Shandy, and variations.
### \"Does the universe need a cause?\" {#does_the_universe_need_a_cause}
Craig maintains that the causal principle is predicated in the metaphysical intuition that *nothing comes from nothing.* If such intuitions are false, he argues it would be inexplicable why anything and everything does not randomly come into existence without a cause. Yet, not all philosophers subscribe to the view of causality as *a priori* in justification. David Hume contends that the principle is rooted in experience, therefore within the category of *a posteriori* knowledge and subject to the problem of induction.
Whereas J. L. Mackie argues that cause and effect cannot be extrapolated to the origins of the universe based upon our inductive experiences and intellectual preferences, Craig proposes that causal laws are unrestricted metaphysical truths that are \"not contingent upon the properties, causal powers, and dispositions of the natural kinds of substances which happen to exist\".
### Identifying the first cause {#identifying_the_first_cause}
Secular philosophers such as Michael Martin argue that a cosmological argument may establish the existence of a first cause, but falls short of identifying that cause as personal, or as God as defined within classical or other specific conceptions of theism.
Defenders of the argument note that most formulations, such as by Aquinas, Duns Scotus and Craig, employ conceptual analysis to establish the identity of the cause. In Aquinas\'s *Summa Theologica*, the *Prima Pars* (First Part) is devoted predominantly to establishing the attributes of the cause, such as uniqueness, perfection and intelligence. In Scotus\'s *Ordinatio*, his metaphysical argument is the first component of the \'triple primacy\' through which he characterises the first cause as a being with the attributes of maximal excellence.
### Timeless origin of the universe {#timeless_origin_of_the_universe}
In the topic of cosmic origins and the standard model of cosmology, the initial singularity of the Big Bang is postulated to be the point at which space and time, as well as all matter and energy, came into existence. J. Richard Gott and James E. Gunn assert that the question of \"What was there before the Universe?\" makes no sense and that the concept of *before* becomes meaningless when considering a timeless state. They add that questioning what occurred before the Big Bang is akin to questioning what is north of the North Pole.
Craig refers to Kant\'s postulate that a cause can be simultaneous with its effect, denoting that this is true of the moment of creation when time itself came into being. He affirms that the history of 20th century cosmology belies the proposition that researchers have no strong intuition to pursue a causal explanation of the origin of time and the universe. Accordingly, physicists have sought to examine the causal origins of the Big Bang by conjecturing such scenarios as the collision of membranes. Feser also notes that versions of the cosmological argument presented by classical philosophers do not require a commitment to the Big Bang, or even to a cosmic origin.
### The Hume-Edwards principle {#the_hume_edwards_principle}
William L. Rowe characterises the Hume-Edwards principle, referring to arguments presented by David Hume, and later Paul Edwards, in their criticisms of the cosmological argument:
The principle stipulates that a causal series---even one that regresses to infinity---requires no explanatory causes beyond those that are members within that series. If every member of a series has a causal explanation within the sequence, the series in itself is explanatorily complete. Thus, it rejects arguments, such as by Duns Scotus, for the existence of higher-order, efficient causes that govern the basic principles of material causation. Notably, it contradicts Hume\'s own *Dialogues Concerning Natural Religion*, in which the character Demea reflects that, even if a succession of causes is infinite, the very existence of the chain still requires a cause.
### Causal loop arguments {#causal_loop_arguments}
Some objections to the cosmological argument refer to the possibility of loops in the structure of cause and effect that would avoid the need for a first cause. Gott and Li refer to the curvature of spacetime and closed timelike curves as possible mechanisms by which the universe may bring about its own existence. Richard Hanley contends that causal loops are neither logically nor physically impossible, remarking: \"\[In timed systems\] the only possibly objectionable feature that all causal loops share is that coincidence is required to explain them.\"
Andrew Loke argues that there is insufficient evidence to postulate a causal loop of the type that would avoid a first cause. He proposes that such a mechanism would suffer from the problem of vicious circularity, rendering it metaphysically impossible.
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Cow tipping
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Cow Tipping (*Beavis and Butt-Head* episode)}} `{{good article}}`{=mediawiki} `{{pp-semi-indef|small=yes}}`{=mediawiki} `{{Use mdy dates|date=May 2018}}`{=mediawiki} `{{Use American English|date=May 2018}}`{=mediawiki} right\|thumb\|upright=1.5\|alt=Photograph of a cow lying on its side\|Cows routinely lie down to sleep.
**Cow tipping** is the purported activity of sneaking up on any unsuspecting or sleeping upright cow and pushing it over for entertainment. The practice of cow tipping is generally considered an urban legend and stories of such feats viewed as tall tales. The implication that rural citizens seek such entertainment due to lack of alternatives is viewed as a stereotype. The concept of cow tipping apparently developed in the 1970s, though tales of animals that cannot rise if they fall has historical antecedents dating to the Roman Empire.
Cows routinely lie down and can easily regain their footing unless sick or injured. Scientific studies have been conducted to determine if cow tipping is theoretically possible, with varying conclusions. All agree that cows are large animals that are difficult to surprise and will generally resist attempts to be tipped. Estimates suggest a force of between 3000 and is needed, and that at least four and possibly as many as fourteen people would be required to achieve this. In real-life situations where cattle have to be laid on the ground, or \"cast\", such as for branding, hoof care or veterinary treatment, either rope restraints are required or specialized mechanical equipment is used that confines the cow and then tips it over. On rare occasions, cattle can lie down or fall down in proximity to a ditch or hill that restricts their normal ability to rise without help. Cow tipping has many references in popular culture and is also used as a figure of speech.
## Scientific study {#scientific_study}
Some versions of the urban legend suggest that because cows sleep standing up, it is possible to approach them and push them over without the animals reacting. However, cows only sleep lightly while standing up, and they are easily awakened. They lie down to sleep deeply. Furthermore, numerous sources have questioned the practice\'s feasibility, since most cows weigh over 450 kg and easily resist any lesser force.
A 2005 study led by Margo Lillie, a zoologist at the University of British Columbia, and her student Tracy Boechler, concluded that tipping a cow would require a force of nearly 3000 N and is therefore impossible to accomplish by a single person. Her calculations found that it would require more than four people to apply enough force to push over a cow, based on an estimate that a single person could exert 660 N of force. However, since a cow can brace itself, Lillie and Boechler suggested that five or six people would, most likely, be needed. Further, cattle are well aware of their surroundings and are very difficult to surprise, due to excellent senses of both smell and hearing. Lillie and Boechler\'s analysis found that if a cow did not move, the principles of static physics suggest that two people might be able to tip a cow if its centre of mass were pushed over its hooves before the cow could react. However, cows are not rigid or unresponsive, and the faster humans have to move, the less force they can exert. Thus Lillie and Boechler concluded that it is unlikely that cows can actually be tipped over in this way. Lillie stated, \"It just makes the physics of it all, in my opinion, impossible.\"
Although biologist Steven Vogel agrees that it would take a force of about 3,000 newtons to push over a standing cow, he thinks that the study by Lillie and Boechler overestimates the pushing ability of an individual human. Using data from Cotterell and Kamminga, who estimated that humans exert a pushing force of 280 newtons, Vogel suggests that someone applying force at the requisite height to topple a cow might generate a maximum push of no more than 300 newtons. By this calculation, at least 10 people would be needed to tip over a non-reacting cow. However, this combined force requirement, he says, might not be the greatest impediment to such a prank. Standing cows are not asleep and, like other animals, have ever-vigilant reflexes. \"If the cow does no more than modestly widen its stance without an overall shift of its center of gravity\", he says, \"about 4,000 newtons or 14 pushers would be needed---quite a challenge to deploy without angering the cow.\"
## Historical origins {#historical_origins}
The belief that certain animals cannot rise if pushed over has historical antecedents. Julius Caesar recorded a belief that a European elk had no knee joints and could not get up if it fell. Pliny said the same about the hind legs of an animal he called the achlis, which Pliny\'s 19th-century translators Bostock and Riley said was merely another name for the elk. They noted that Pliny\'s belief about the jointless back legs of the achlis (elk) was false.
In 1255, Louis IX of France gave an elephant to Henry III of England for his menagerie in the Tower of London. A drawing by the historian Matthew Paris for his *Chronica Majora* can be seen in his bestiary at Parker Library of Corpus Christi College, Cambridge. An accompanying text cites elephant lore suggesting that elephants did not have knees and were unable to get up if they fell.
Journalist Jake Steelhammer believes the American urban myth of cow tipping originated in the 1970s. It \"stampeded into the \'80s\", he says, \"when movies like *Tommy Boy* and *Heathers* featured cow tipping expeditions.\" Stories about cow tipping tend to be second-hand, he says, told by someone who does not claim to have tipped a cow but who knows someone else who says they did.
## Veterinary and husbandry practices {#veterinary_and_husbandry_practices}
Cattle may need to be deliberately thrown or tipped over for certain types of husbandry practices and medical treatment. When done for medical purposes, this is often called \"casting\", and when performed without mechanical assistance requires the attachment of 30 to of rope around the body and legs of the animal. After the rope is secured by non-slip bowline knots, it is pulled to the rear until the animal is off-balance. Once the cow is forced to lie down in sternal recumbency (on its chest), it can be rolled onto its side and its legs tied to prevent kicking.
A calf table or calf cradle, also called a \"tipping table\" or a \"throw down\", is a relatively modern invention designed to be used on calves that are being branded. A calf is run into a chute, confined, and then tipped by the equipment onto its side for easier branding and castration.
Hydraulic tilt tables for adult cattle have existed since the 1970s and are designed to lift and tip cattle onto their sides to enable veterinary care, particularly of the animals\' genitalia, and for hoof maintenance. (Unlike horses, cows generally do not cooperate with a farrier when standing.) A Canadian veterinarian explained, \"Using the table is much safer and easier than trying to get underneath to examine the animal\", and noted that cows tipped over on a padded table usually stop struggling and become calm fairly quickly. One design, developed at the Western College of Veterinary Medicine in Saskatoon, Saskatchewan, included \"cow comfort\" as a unique aspect of care using this type of apparatus.
### Involuntary recumbency {#involuntary_recumbency}
Cows may inadvertently tip themselves. Due to their bulk and relatively short legs, cattle cannot roll over. Those that lie down and roll to their sides with their feet pointing uphill may become stuck and unable to rise without assistance, with potentially fatal results. In such cases, two humans can roll or flip a cow onto its other side, so that its feet are aimed downhill, thus allowing it to rise on its own. In one documented case of \"real-life cow tipping\", a pregnant cow rolled into a gully in New Hampshire and became trapped in an inverted state until rescued by volunteer fire fighters. The owner of the cow commented that he had seen this happen \"once or twice\" before.
Trauma or illness may also result in a cow unable to rise to its feet. Such animals are sometimes called \"downers.\" Sometimes this occurs as a result of muscle and nerve damage from calving or a disease such as mastitis. Leg injuries, muscle tears, or a massive infection of some sort may also be causes. Downer cows are encouraged to get to their feet and have a much greater chance of recovery if they do. If unable to rise, some have survived---with medical care---as long as 14 days and were ultimately able to get back on their feet. Appropriate medical treatment for a downer cow to prevent further injury includes rolling from one side to the other every three hours, careful and frequent feeding of small amounts of fodder, and access to clean water.
### Death
Dead animals may appear to have been tipped over, but this is actually the process of rigor mortis, which stiffens the muscles of the carcass, beginning six to eight hours after death and lasting for one to two days. It is particularly noticeable in the limbs, which stick out straight. Post-mortem bloat also occurs because of gas formation inside the body. The process may result in cattle carcasses that wind up on their back with all four feet in the air.
## In popular culture {#in_popular_culture}
Assorted individuals have claimed to have performed cow tipping, often while under the influence of alcohol. These claims, to date, cannot be reliably verified, with Jake Swearingen of *Modern Farmer* noting in 2013 that YouTube, a popular source of videos of challenges and stunts, \"fails to deliver one single actual cow-tipping video\".
Pranksters have sometimes pushed over artificial cows. Along Chicago\'s Michigan Avenue in 1999, two \"apparently drunk\" men felled six fiberglass cows that were part of a Cows on Parade public art exhibit. Four other vandals removed a \"Wow cow\" sculpture from its lifeguard chair at Oak Street Beach and abandoned it in a pedestrian underpass. A year later, New York City anchored its CowParade art cows, including \"A Streetcow Named Desire\", to concrete bases \"to prevent the udder disrespect of cow-tippers and thieves.\"
Cow tipping has been featured in films from the 1980s and later, such as *Heathers* (1988), *Tommy Boy* (1995), *Barnyard* (2006), and *I Love You, Beth Cooper* (2009). It was also used in the title of a 1992 documentary film by Randy Redroad, *Cow Tipping---The Militant Indian Waiter*.
Variants of cow tipping have also been seen in popular media such as the film *Cars* (2006), which features a vehicular variant called tractor-tipping, and the video game *Fallout: New Vegas*, which allows the character to sneak up on and tip over a Brahmin, the game\'s two-headed cow-like animal. The board game *Battle Cattle* is based on the practice, with heavily armed cows having \"Tipping Defense Numbers.\"
In the Little Willies song \"Lou Reed\" from their 2006 self-titled debut album, Norah Jones sings about a fictional event during which musician Lou Reed tips cows in Texas. In another medium, *The Big Bang Theory*, a television show, uses cow tipping lore as an element to establish the nature of a rural character, Penny.
The term *cow tipping* is sometimes used as a figure of speech for pushing over something big. In *A Giant Cow-Tipping by Savages*, author John Weir Close uses the term to describe contemporary mergers and acquisitions. \"Tipping sacred cows\" has been used as a deliberate mixed metaphor in titles of books on Christian ministry and business management.
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Cassandra
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**Cassandra** or **Kassandra** (`{{IPAc-en|k|ə|'|s|æ|n|d|r|ə}}`{=mediawiki}; *Κασσάνδρα*, `{{IPA|el|kas:ándra|pron}}`{=mediawiki}, sometimes referred to as **Alexandra**; *Ἀλεξάνδρα*) in Greek mythology was a Trojan priestess dedicated to the god Apollo and fated by him to utter true prophecies but never to be believed. In modern usage her name is employed as a rhetorical device to indicate a person whose accurate prophecies, generally of impending disaster, are not believed.
Cassandra was a daughter of King Priam and Queen Hecuba of Troy. Her elder brother was Hector, the hero of the Greek-Trojan War. The older and most common versions of the myth state that she was admired by the god Apollo, who sought to win her love by means of the gift of seeing the future. According to Aeschylus, she promised him her favours, but after receiving the gift, she went back on her word. As the enraged Apollo could not revoke a divine power, he added to it the curse that nobody would believe her prophecies. In other sources, such as Hyginus and Pseudo-Apollodorus, Cassandra broke no promise to Apollo, but rather the power of foresight was given to her as an enticement to enter into a romantic engagement, the curse being added only when it failed to produce the result desired by the god.
Later versions on the contrary describe her falling asleep in a temple, where snakes licked (or whispered into) her ears which enabled her to hear the future.
## Etymology
Hjalmar Frisk (*Griechisches Etymologisches Wörterbuch*, Heidelberg, 1960--1970) notes \"unexplained etymology\", citing \"various hypotheses\" found in Wilhelm Schulze, Edgar Howard Sturtevant, J. Davreux, and Albert Carnoy. R. S. P. Beekes cites García Ramón\'s derivation of the name from the Proto-Indo-European root \**(s)kend-* \"raise\". The Online Etymology Dictionary states \"though the second element looks like a fem. form of Greek *andros* \"of man, male human being.\" Watkins suggests PIE *\*(s)kand-* \"to shine\" as source of second element. The name also has been connected to *kekasmai* \"to surpass, excel.\"
## Description
Cassandra was described by the chronicler Malalas in his account of the *Chronography* as \"shortish, round-faced, white, mannish figure, good nose, good eyes, dark pupils, blondish, curly, good neck, bulky breasts, small feet, calm, noble, priestly, an accurate prophet foreseeing everything, practicing hard, virgin\". Meanwhile, in the account of Dares the Phrygian, she was illustrated as \". . .of moderate stature, round-mouthed, and auburn-haired. Her eyes flashed. She knew the future.\"
## Biography
Cassandra was one of the many children born to the king and queen of Troy, Priam and Hecuba. She is the fraternal twin sister of Helenus, as well as the sister to Hector and Paris. One of the oldest and most common versions of her myth states that Cassandra was admired for her beauty and intelligence by the god Apollo, who sought to win her with the gift to see the future. According to Aeschylus, Cassandra promised Apollo favors, but, after receiving the gift, went back on her word and refused Apollo. Since the enraged Apollo could not revoke a divine power, he added a curse that nobody would believe Cassandra\'s prophecies.
## Mythology
Cassandra appears in texts written by Homer, Virgil, Aeschylus and Euripides. Each author depicts her prophetic powers differently.
In Homer\'s work, Cassandra is mentioned a total of four times \"as a virgin daughter of Priam, as bewailing Hector\'s death, as chosen by Agamemnon as his slave mistress after the sack of Troy, and is killed by Clytemnestra over Agamemnon\'s corpse after Clytemnestra murders him on his return home.\"
In Virgil\'s work, Cassandra appears in book two of his epic poem titled *Aeneid*, with her powers of prophecy restored. In Book 2 of the Aeneid, unlike Homer, Virgil presents Cassandra as having fallen into a mantic state and her prophecies reflect it. Likewise Seneca the Younger, in his play *Agamemnon*, has her prophesy why Agamemnon deserves his recorded death:
> *Quid me vocatis sospitem solam e meis, umbrae meorum? te sequor, tota pater Troia sepulte; frater, auxilium Phrygum terrorque Danaum, non ego antiquum decus video aut calentes ratibus ambustis manus, sed lacera membra et saucios vinclo gravi illos lacertos. te sequor... (Ag. 741--747)*\
> \
> *Why do you call me, the lone survivor of my family, My shades? I follow you, father buried with all of Troy; Brother, bulwark of Trojans, terrorizer of Greeks, I do not see your beauty of old or hands warmed by burnt ships, But your lacerated limbs and those famous shoulders savaged By heavy chains. I follow you\...*
Later on in Seneca\'s work, this behavior is reflected in acts 4 and 5 as \"Her mantic vision in act 4 will be supplemented by a further (in)sight into what is going on inside the palace in act 5 when she becomes a quasi-messenger and provides a meticulous account of Agamemnon\'s murder in the bath: \'I see and I am there and I enjoy it, no false vision deceives my eyes: let\'s watch\' (*video et intersum et fruor, / imago visus dubia non fallit meos: / spectemus*.)\"
### Gift of prophecy {#gift_of_prophecy}
Cassandra was given the gift of prophecy, but was also cursed by the god Apollo so that her true prophecies would not be believed. Many versions of the myth relate that she incurred the god\'s wrath by refusing him sexual favours after promising herself to him in exchange for the power of prophecy. In Aeschylus\' *Agamemnon*, she bemoans her relationship with Apollo:
> Apollo, Apollo! God of all ways, but only Death\'s to me, Once and again, O thou, Destroyer named, Thou hast destroyed me, thou, my love of old!
And she acknowledges her fault:
> I consented \[marriage\] to Loxias \[Apollo\] but broke my word. \... Ever since that fault I could persuade no one of anything.
Latin author Hyginus in Fabulae says: `{{blockquote|Cassandra, daughter of the king and queen, in the temple of Apollo, exhausted from practising, is said to have fallen asleep; whom, when Apollo wished to embrace her, she did not afford the opportunity of her body. On account of which thing, when she prophesied true things, she was not believed.}}`{=mediawiki}
Louise Bogan, an American poet, writes that another way Cassandra, as well as her twin brother Helenus, had earned their prophetic powers: \"*she and her brother Helenus were left overnight in the temple of the Thymbraean Apollo. No reason has been advanced for this night in the temple; perhaps it was a ritual routinely performed by everyone. When their parents looked in on them the next morning, the children were entwined with serpents, which flicked their tongues into the children\'s ears. This enabled Cassandra and Helenus to divine the future.*\" It would not be until Cassandra is much older that Apollo appears in the same temple and tried to seduce Cassandra, who rejects his advances, and curses her by making her prophecies not be believed.
Her cursed gift from Apollo became an endless pain and frustration to her. She was seen as a liar and a madwoman by her family and by the Trojan people. Because of this, her father, Priam, had locked her away in a chamber and guarded her like the madwoman she was believed to be. Though Cassandra made many predictions that went unbelieved, the one prophecy that was believed was that of Paris being her abandoned brother.
### Cassandra and the Fall of Troy {#cassandra_and_the_fall_of_troy}
#### Before the fall of Troy {#before_the_fall_of_troy}
Before the fall of Troy took place, Cassandra foresaw that if Paris went to Sparta and brought Helen back as his wife, the arrival of Helen would spark the downfall and destruction of Troy during the Trojan War. Despite the prophecy and ignoring Cassandra\'s warning, Paris still went to Sparta and returned with Helen. While the people of Troy rejoiced, Cassandra, angry with Helen\'s arrival, furiously snatched away Helen\'s golden veil and tore at her hair.
In Virgil\'s epic poem, the Aeneid, Cassandra warned the Trojans about the Greeks hiding inside the Trojan Horse, Agamemnon\'s death, her own demise at the hands of Aegisthus and Clytemnestra, her mother Hecuba\'s fate, Odysseus\'s ten-year wanderings before returning to his home, and the murder of Aegisthus and Clytemnestra by the latter\'s children Electra and Orestes. Cassandra predicted that her cousin Aeneas would escape during the fall of Troy and found a new nation in Rome.
#### During the fall of Troy {#during_the_fall_of_troy}
Coroebus and Othronus came to the aid of Troy during the Trojan War out of love for Cassandra and in exchange for her hand in marriage, but both were killed. According to one account, Priam offered Cassandra to Telephus\'s son Eurypylus, in order to induce Eurypylus to fight on the side of the Trojans. Cassandra was also the first to see the body of her brother Hector being brought back to the city.In *The Fall of Troy*, told by Quintus Smyrnaeus, Cassandra attempted to warn the Trojan people that Greek warriors were hiding in the Trojan Horse while they were celebrating their victory over the Greeks with feasting. Disbelieving Cassandra, the Trojans resorted to calling her names and hurling insults at her. Attempting to prove herself right, Cassandra took an axe in one hand and a burning torch in the other, and ran towards the Trojan Horse, intent on destroying the Greeks herself, but the Trojans stopped her. The Greeks hiding inside the Horse were relieved, but alarmed by how clearly she had divined their plan. At the fall of Troy, Cassandra sought shelter in the temple of Athena. There she embraced the wooden statue of Athena in supplication for her protection, but was abducted and brutally raped by Ajax the Lesser. Cassandra clung so tightly to the statue of the goddess that Ajax knocked it from its stand as he dragged her away. The actions of Ajax were a sacrilege because Cassandra was a supplicant at the sanctuary under the protection of the goddess Athena, and Ajax further defiled the temple by raping Cassandra.
In Apollodorus chapter 6, section 6, Ajax\'s death comes at the hands of both Athena and Poseidon: \"Athena threw a thunderbolt at the ship of Ajax; and when the ship went to pieces he made his way safe to a rock, and declared that he was saved in spite of the intention of Athena. But Poseidon smote the rock with his trident and split it, and Ajax fell into the sea and perished; and his body, being washed up, was buried by Thetis in Myconos\".
In some versions, Cassandra intentionally left a chest behind in Troy, with a curse on whichever Greek opened it first. Inside the chest was an image of Dionysus, made by Hephaestus and presented to the Trojans by Zeus. It was given to the Greek leader Eurypylus as a part of his share of the victory spoils of Troy. When he opened the chest and saw the image of the god, he went mad.
#### The aftermath of Troy and Cassandra\'s death {#the_aftermath_of_troy_and_cassandras_death}
Once Troy had fallen, Cassandra was taken as a *pallake* (concubine) by King Agamemnon of Mycenae. While he was away at war, Agamemnon\'s wife, Clytemnestra, had taken Aegisthus as her lover. Cassandra and Agamemnon were later killed by either Clytemnestra or Aegisthus. Various sources state that Cassandra and Agamemnon had twin boys, Teledamus and Pelops, who were murdered by Aegisthus.
The final resting place of Cassandra is either in Amyclae or Mycenae. Statues of Cassandra exist both in Amyclae and across the Peloponnese peninsula from Mycenae to Leuctra. In Mycenae, German business man and pioneer archeologist Heinrich Schliemann discovered in Grave Circle A the graves of Cassandra and Agamemnon and telegraphed back to King George I of Greece:
> *With great joy I announce to Your Majesty that I have discovered the tombs which the tradition proclaimed by Pausanias indicates to be the graves of Agamemnon, Cassandra, Eurymedon and their companions, all slain at a banquet by Clytemnestra and her lover Aegisthos.*
However, it was later discovered that the graves predated the Trojan War by at least 300 years.
## *Agamemnon* by Aeschylus {#agamemnon_by_aeschylus}
The play *Agamemnon* from Aeschylus\'s trilogy *Oresteia* depicts the king treading the scarlet cloth laid down for him, and walking offstage to his death. After the chorus\'s ode of foreboding, time is suspended in Cassandra\'s \"mad scene\". She has been onstage, silent and ignored. Her madness that is unleashed now is not the physical torment of other characters in Greek tragedy, such as in Euripides\' *Heracles* or Sophocles\' *Ajax*.
According to author Seth Schein, two further familiar descriptions of her madness are that of Heracles in *The Women of Trachis* or Io in *Prometheus Bound*. He specifies that her madness is not the type that uses language to descriptive physical agony or other physical symptoms. Instead, she speaks, disconnectedly and transcendent, in the grip of her psychic possession by Apollo, witnessing past and future events. Schein says, \"She evokes the same awe, horror and pity as do schizophrenics\". Cassandra is one of those \"who often combine deep, true insight with utter helplessness, and who retreat into madness.\"
Eduard Fraenkel remarked on the powerful contrasts between declaimed and sung dialogue in this scene. The frightened and respectful chorus are unable to comprehend her. She goes to her inevitable offstage murder by Clytemnestra with full knowledge of what is to befall her.
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Couplet
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In poetry, a **couplet** (`{{IPAc-en|ˈ|k|ʌ|p|l|ə|t}}`{=mediawiki} `{{respell|CUP|lət}}`{=mediawiki}) or **distich** (`{{IPAc-en|ˈ|d|ɪ|s|t|ɪ|k}}`{=mediawiki} `{{respell|DISS|tick}}`{=mediawiki}) is a pair of successive lines that rhyme and have the same metre. A couplet may be formal (closed) or run-on (open). In a formal (closed) couplet, each of the two lines is end-stopped, implying that there is a grammatical pause at the end of a line of verse. In a run-on (open) couplet, the meaning of the first line continues to the second.
## Background
The word \"couplet\" comes from the French word meaning \"two pieces of iron riveted or hinged together\". The term \"couplet\" was first used to describe successive lines of verse in Sir P. Sidney\'s *Arcadia*in 1590: \"In singing some short coplets, whereto the one halfe beginning, the other halfe should answere.\"
While couplets traditionally rhyme, not all do. Poems may use white space to mark out couplets if they do not rhyme. Couplets in iambic pentameter are called *heroic couplets*. John Dryden in the 17th century and Alexander Pope in the 18th century were both well known for their writing in heroic couplets. The Poetic epigram is also in the couplet form. Couplets can also appear as part of more complex rhyme schemes, such as sonnets.
Rhyming couplets are one of the simplest rhyme schemes in poetry. Because the rhyme comes so quickly, it tends to call attention to itself. Good rhyming couplets tend to \"explode\" as both the rhyme and the idea come to a quick close in two lines. Here are some examples of rhyming couplets where the sense as well as the sound \"rhymes\":
:
: True wit is nature to advantage dress\'d;
: What oft was thought, but ne\'er so well express\'d.
: --- Alexander Pope
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: Whether or not we find what we are seeking
: Is idle, biologically speaking.
: --- Edna St. Vincent Millay (at the end of a sonnet)
On the other hand, because rhyming couplets have such a predictable rhyme scheme, they can feel artificial and plodding. Here is a Pope parody of the predictable rhymes of his era:
:
: Where-e\'er you find \"the cooling western breeze,\"
: In the next line, it \"whispers through the trees;\"
: If crystal streams \"with pleasing murmurs creep,\"
: The reader\'s threatened (not in vain) with \"sleep.\"
## In English poetry {#in_english_poetry}
Regular rhyme was not originally a feature of English poetry: Old English verse came in metrically paired units somewhat analogous to couplets, but constructed according to alliterative verse principles. The rhyming couplet entered English verse in the early Middle English period through the imitation of medieval Latin and Old French models. The earliest surviving examples are a metrical paraphrase of the Lord\'s Prayer in short-line couplets, and the *Poema Morale* in septenary (or \"heptameter\") couplets, both dating from the twelfth century.
Rhyming couplets were often used in Middle English and early modern English poetry. Chaucer\'s *Canterbury Tales*, for instance, is predominantly written in rhyming couplets, and Chaucer also incorporated a concluding couplet into his rhyme royal stanza. Similarly, Shakespearean sonnets often employ rhyming couplets at the end to emphasize the theme. Take one of Shakespeare\'s most famous sonnets, Sonnet 18, for example (the rhyming couplet is shown in italics):
:
: Shall I compare thee to a summer\'s day?
: Thou art more lovely and more temperate:
: Rough winds do shake the darling buds of May,
: And summer\'s lease hath all too short a date:
: Sometimes too hot the eye of heaven shines,
: And often is his gold complexion dimm\'d;
: And every fair from fair sometime declines,
: By chance or nature\'s changing course untrimm\'d;
: But thy eternal summer shall not fade
: Nor lose possession of that fair thou owest;
: Nor shall Death brag thou wander\'st in his shade,
: When in eternal lines to time thou growest:
: *So long as men can breathe or eyes can see,*
: *So long lives this and this gives life to thee.*
In the late seventeenth century and early eighteenth-century English rhyming couplets achieved the zenith of their prestige in English verse, in the popularity of heroic couplets. The heroic couplet was used by famous poets for ambitious translations of revered Classical texts, for instance, in John Dryden\'s translation of the *Aeneid* and in Alexander Pope\'s translation of the *Iliad*.
Though poets still sometimes write in couplets, the form fell somewhat from favour in English in the twentieth century; contemporary poets writing in English sometimes prefer unrhymed couplets, distinguished by layout rather than by matching sounds.
## In Chinese poetry {#in_chinese_poetry}
Couplets called duilian may be seen on doorways in Chinese communities worldwide. Duilian displayed as part of the Chinese New Year festival, on the first morning of the New Year, are called chunlian (春聯; 春联). These are usually purchased at a market a few days before and glued to the doorframe. The text of the couplets is often traditional and contains hopes for prosperity. Other chunlian reflect more recent concerns. For example, the CCTV New Year\'s Gala usually promotes couplets reflecting current political themes in mainland China.
Some duilian may consist of two lines of four characters each. Duilian are read from top to bottom where the first line starts from the right.
## In Tamil poetry {#in_tamil_poetry}
Tamil literature contains some of the notable examples of ancient couplet poetry. The Tamil language has a rich and refined grammar for couplet poetry, and distichs in Tamil poetry follow the venpa metre. One of the most notable examples of Tamil couplet poetry is the ancient Tamil moral text of the Tirukkural, which contains a total of 1330 couplets written in the kural venpa metre from which the title of the work was derived centuries later. Each Kural couplet is made of exactly 7 words---4 in the first line and 3 in the second. The first word may rhyme with the fourth or the fifth word. Below is an example of a couplet:
:
: . (Tirukkural, verse 205)
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: *Transliteration*: Ilan endru theeyavai seyyarkka seyyin
: Ilanaagum matrum peyartthu
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:
: *Translation*: Make not thy poverty a plea for ill;
: Thine evil deeds will make thee poorer still. (Pope, 1886)
## In Hindustani poetry {#in_hindustani_poetry}
In Hindi, a couplet is called a *doha*, while in Urdu, it is called a *sher*.
Couplets were the most common form of poetry between the 12th and 18th Centuries, in Hidustani. Famous poets include Kabir, Tulsidas and Rahim Khan-i-Khanan.
Kabir (also known as Kabirdas) is thought to be one of the greatest composers of Hindustani couplets.
## Distich
The American poet J. V. Cunningham was noted for many distichs included in the various forms of epigrams included in his poetry collections, as exampled here:
Deep summer, and time passes. Sorrow wastes\
To a new sorrow. While Time heals time hastes
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Charles Williams (British writer)
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**Charles Walter Stansby Williams** (20 September 1886 -- 15 May 1945) was an English poet, novelist, playwright, theologian and literary critic. Most of his life was spent in London, where he was born, but in 1939 he moved to Oxford with the university press for which he worked until his death.
## Early life and education {#early_life_and_education}
Charles Williams was born in London in 1886, the only son of (Richard) Walter Stansby Williams (1848--1929) and Mary (née Wall). His father Walter was a journalist and foreign business correspondent for an importing firm, writing in French and German, who was a \'regular and valued\' contributor of verse, stories and articles to many popular magazines. His mother Mary, the sister of the ecclesiologist and historian J. Charles Wall, was a former milliner (hatmaker), of Islington. He had one sister, Edith, born in 1889. The Williams family lived in \'shabby-genteel\' circumstances, owing to Walter\'s increasing blindness and the decline of the firm by which he was employed, in Holloway. In 1894 the family moved to St Albans in Hertfordshire, where Williams lived until his marriage in 1917.
Educated at St Albans School, Williams was awarded a scholarship to University College London, but he left in 1904 without attempting to gain a degree due to an inability to pay tuition fees.
Williams began work in 1904 in a Methodist bookroom. He was employed by the Oxford University Press (OUP) as a proofreading assistant in 1908 and quickly climbed to the position of editor. He continued to work at the OUP in various positions of increasing responsibility until his death in 1945. One of his greatest editorial achievements was the publication of the first major English-language edition of the works of Søren Kierkegaard. His work was part of the literature event in the art competition at the 1924 Summer Olympics.
Although chiefly remembered as a novelist, Williams also published poetry, works of literary criticism, theology, drama, history, biography, and a voluminous number of book reviews. Some of his best-known novels are *War in Heaven* (1930), *Descent into Hell* (1937), and *All Hallows\' Eve* (1945). T. S. Eliot, who wrote an introduction for the last of these, described Williams\'s novels as \"supernatural thrillers\" because they explore the sacramental intersection of the physical with the spiritual while also examining the ways in which power, even spiritual power, can corrupt as well as sanctify.
All of Williams\'s fantasies, unlike those of J. R. R. Tolkien and most of those of C. S. Lewis, are set in the contemporary world. Williams has been described by Colin Manlove as one of the three main writers of \"Christian fantasy\" in the twentieth century (the other two being C. S. Lewis and T. F. Powys). Some writers of fantasy novels with contemporary settings, notably Tim Powers, cite Williams as their inspiration.
W. H. Auden, one of Williams\'s greatest admirers, reportedly re-read Williams\'s extraordinary and highly unconventional history of the church, *The Descent of the Dove* (1939), every year. Williams\'s study of Dante entitled *The Figure of Beatrice* (1944) was very highly regarded at its time of publication and continues to be consulted by Dante scholars today. His work inspired Dorothy L. Sayers to undertake her translation of *The Divine Comedy*. Williams, however, regarded his most important work to be his extremely dense and complex Arthurian poetry, of which two books were published, *Taliessin through Logres* (1938) and *The Region of the Summer Stars* (1944), and more remained unfinished at his death. Some of Williams\'s essays were collected and published posthumously in *Image of the City and Other Essays* (1958), edited by Anne Ridler.
Williams gathered many followers and disciples during his lifetime. He was, for a period, a member of the Salvator Mundi Temple of the Fellowship of the Rosy Cross. He met fellow Anglican Evelyn Underhill in 1937 and later wrote the introduction to her published *Letters* in 1943.
When World War II broke out in 1939, Oxford University Press moved its offices from London to Oxford. Williams was reluctant to leave his beloved city, and his wife Florence refused to go. From the nearly 700 letters he wrote to his wife during the war years, a generous selection has been published -- \"primarily... love letters,\" the editor calls them.
The move to Oxford did allow him to participate regularly in Lewis\'s literary society, the Inklings. In this setting Williams read (and improved) his final published novel, *All Hallows\' Eve.* He heard J. R. R. Tolkien read aloud to the group some of his early drafts of *The Lord of the Rings*. In addition to meeting in Lewis\'s rooms at Oxford, they regularly met at The Eagle and Child pub in Oxford. During this time Williams gave lectures at Oxford on John Milton, William Wordsworth, and other authors, and received an honorary M.A. degree.
Williams is buried in Holywell Cemetery in Oxford. His headstone bears the word \"poet\" followed by the words \"Under the Mercy\", a phrase often used by Williams himself.
## Personal life {#personal_life}
In 1917 Williams married his first sweetheart, Florence Conway, following a long courtship during which he presented her with a sonnet sequence that would later become his first published book of poetry, *The Silver Stair*. Their son Michael was born in 1922.
Williams was an unswerving and devoted member of the Church of England, reputedly with a tolerance of the scepticism of others and a firm belief in the necessity of a \"doubting Thomas\" in any apostolic body.
Although Williams attracted the attention and admiration of some of the most notable writers of his day, including T. S. Eliot and W. H. Auden, his greatest admirer was probably C. S. Lewis, whose novel *That Hideous Strength* (1945) has been regarded as partially inspired by his acquaintance with both the man and his novels and poems. Williams came to know Lewis after reading Lewis\'s then-recently published study *The Allegory of Love*; he was so impressed he jotted down a letter of congratulation and dropped it in the mail. Coincidentally, Lewis had just finished reading Williams\'s novel *The Place of the Lion* and had written a similar note of congratulation. The letters crossed in the mail and led to an enduring and fruitful friendship.
Lewis wrote the Preface to *Essays presented to Charles Williams*, originally intended as a festschrift for Williams, but published after his death. Essays were contributed by Lewis, Sayers, Tolkien, Owen Barfield, Gervase Mathew and Warren Lewis.
## Theology
Williams developed the concept of co-inherence and gave rare consideration to the theology of romantic love. Falling in love for Williams was a form of mystical envisioning in which one saw the beloved as he or she was seen through the eyes of God. Co-inherence was a term used in Patristic theology to describe the relationship between the human and divine natures of Jesus Christ and the relationship between the persons of the blessed Trinity. Williams extended the term to include the ideal relationship between the individual parts of God\'s creation, including human beings. It is our mutual indwelling: Christ in us and we in Christ, interdependent. It is also the web of interrelationships, social and economic and ecological, by which the social fabric and the natural world function. But especially for Williams, co-inherence is a way of talking about the Body of Christ and the communion of saints. He proposed founding an order, to be called the Companions of the Co-inherence, who would practice substitution and exchange, living in love-in-God, truly bearing one another\'s burdens, being willing to sacrifice and to forgive, living from and for one another in Christ. According to Gunnar Urang, co-inherence is the focus of all Williams\'s novels.
## Works
### Fiction
- 1930: *War in Heaven* (London: Victor Gollancz) -- The Holy Grail surfaces in an obscure country parish and becomes variously a sacramental object to protect or a vessel of power to exploit.
- 1930: *Many Dimensions* (London: Victor Gollancz) -- An evil antiquarian illegally purchases the fabled Stone of Suleiman (Williams uses this Muslim form rather than the more familiar King Solomon) from its Islamic guardian and returns to England to discover not only that the Stone can multiply itself infinitely without diminishing the original, but that it also allows its possessor to transcend the barriers of space and time.
- \"Et in Sempiternum Pereant,\" a short story first published in *The London Mercury*, December 1935, in which Lord Arglay (protagonist in *Many Dimensions*) has his life put at risk encountering a ghost on the path to damnation. Later included in *The Oxford Book of English Ghost Stories* (London: Oxford University Press, 1986)
- 1931: *The Place of the Lion* (London: Mundanus) -- Platonic archetypes begin to appear around an English country town, wreaking havoc and drawing to the surface the spiritual strengths and flaws of individual characters.
- 1932: *The Greater Trumps* (London: Victor Gollancz) -- The original Tarot deck is used to unlock enormous metaphysical powers by allowing the possessors to see across space and time, create matter, and raise powerful natural storms.
- 1933: *Shadows of Ecstasy* (London: Victor Gollancz) -- A humanistic adept has discovered that by focusing his energies inward he can extend his life almost indefinitely. He undertakes an experiment using African lore to die and resurrect his own body thereby assuring his immortality. His followers begin a revolutionary movement to supplant European civilisation. The first of Williams\'s novels to be written, though not the first published.
- 1937: *Descent into Hell* (London: Faber & Faber) -- Generally thought to be Williams\'s best novel, *Descent* deals with various forms of selfishness, and how the cycle of sin brings about the necessity for redemptive acts. In it, an academic becomes so far removed from the world that he fetishises a woman to the extent that his perversion takes the form of a succubus. Other characters include a doppelgänger, the ghost of a suicidal Victorian labourer, and a playwright modelled in some ways on the author. Illustrates Williams\'s belief in the replacement of sin and substitutional love.
- 1945: *All Hallows\' Eve* (London: Faber & Faber) -- Follows the fortunes of two women after death and their interactions with those they knew before, contrasting the results of action based either on selfishness or an accepting love.
- 1970--72: *The Noises That Weren\'t There*. Unfinished. First three chapters published in *Mythlore* 6 (Autumn 1970), 7 (Winter 1971) and 8 (Winter 1972).
### Plays
- c\. 1912: *The Chapel of the Thorn* (edited by Sørina Higgins; Berkeley: Apocryphile Press, 2014)
- 1930: *A Myth of Shakespeare* (London: Oxford University Press)
- 1930: *A Myth of Francis Bacon* (Published in the *Charles Williams Society Newsletter*, 11, 12, and 14)
- 1929--31: *Three Plays* (London: Oxford University Press)
- *The Rite of the Passion* (1929)
- *The Chaste Wanton* (1930)
- *The Witch* (1931)
- 1963: *Collected Plays by Charles Williams* (edited by John Heath-Stubbs; London: Oxford University Press)
- *Thomas Cranmer of Canterbury* (1936). Canterbury Festival play, following T. S. Eliot\'s *Murder in the Cathedral* in the preceding (inaugural) year.
- *Seed of Adam* (1937)
- *Judgement at Chelmsford* (1939)
- *The Death of Good Fortune* (1939)
- *The House by the Stable* (1939)
- *Terror of Light* (1940)
- *Grab and Grace* (1941)
- *The Three Temptations* (1942)
- *House of the Octopus* (1945)
- 2000: *The Masques of Amen House* (edited by David Bratman. Mythopoeic Press).
- *The Masque of the Manuscript* (1927)
- *The Masque of Perusal* (1929)
- *The Masque of the Termination of Copyright* (1930)
### Poetry
- 1912: *The Silver Stair* (London: Herbert and Daniel)
- 1917: *Poems of Conformity* (London: Oxford University Press)
- 1920: *Divorce* (London: Oxford University Press)
- 1924: *Windows of Night* (London: Oxford University Press)
- 1930: *Heroes and Kings* (London: Sylvan Press)
- 1954: *Taliessin through Logres* (1938) and *The Region of the Summer Stars* (1944) (London: Oxford University Press)
- 1991: *Charles Williams*, ed. David Llewellyn Dodds (Woodbridge and Cambridge, UK: Boydell & Brewer: Arthurian Poets series). Part II, Uncollected and unpublished poems (pp. 149--281).
### Theology {#theology_1}
- 1938: *He Came Down from Heaven* (London: Heinemann).
- 1939: *The Descent of the Dove: A Short History of the Holy Spirit in the Church* (London: Longmans, Green)
- 1941: *Witchcraft* (London: Faber & Faber)
- 1942: *The Forgiveness of Sins* (London: G. Bles)
- 1958: *The Image of the City and Other Essays* (edited by Anne Ridler; London: Oxford University Press). Parts II through V
- 1990: *Outlines of Romantic Theology* (Grand Rapids, Mich.: Eerdmans)
### Literary criticism {#literary_criticism}
- 1930: *Poetry at Present* (Oxford: Clarendon Press).
- 1932: *The English Poetic Mind* (Oxford: Clarendon Press).
- 1933: *Reason and Beauty in the Poetic Mind* (Oxford: Clarendon Press)
- 1940: *Introduction to Milton* (based on a lecture at Oxford University), in *The English Poems of John Milton* (Oxford University Press)
- 1941: *Religion and Love in Dante: The Theology of Romantic Love* (Dacre Press, Westminster).
- 1943: *The Figure of Beatrice* (London: Faber & Faber)
- 1948: *The Figure of Arthur* (unfinished), in *Arthurian Torso*, ed. C. S. Lewis (London: Oxford University Press)
- 1958: *The Image of the City and Other Essays* (edited by Anne Ridler; London: Oxford University Press). Parts I and VI
- 2003: *The Detective Fiction Reviews of Charles Williams* (edited by Jared C. Lobdell; McFarland)
- 2017: *The Celian Moment and Other Essays* (edited by Stephen Barber; Oxford: The Greystones Press)
### Biography
- 1933: *Bacon* (London: Arthur Barker)
- 1933: *A Short Life of Shakespeare* (Oxford: Clarendon Press). Abridgment of the 2-volume work by Sir Edmund Chambers
- 1934: *James I* (London: Arthur Barker)
- 1935: *Rochester* (London: Arthur Barker)
- 1936: *Queen Elizabeth* (London: Duckworth)
- 1937: *Henry VII* (London: Arthur Barker)
- 1937: *Stories of Great Names* (London: Oxford University Press). Alexander, Julius Caesar, Charlemagne, Joan of Arc, Shakespeare, Voltaire, John Wesley
- 1946: *Flecker of Dean Close* (London: Canterbury Press)
### Other works {#other_works}
- 1931: Introduction, *Poems of Gerard Manley Hopkins* (Ed. Robert Bridges; 2nd ed.; London: Oxford University Press; `{{OCLC|162569501}}`{=mediawiki})
- 1936: *The Story of the Aeneid* (London: Oxford University Press; `{{OCLC|221046736}}`{=mediawiki})
- 1939: *The Passion of Christ* (Oxford University Press, New York, `{{oclc|5655518}}`{=mediawiki} London `{{oclc|752602153}}`{=mediawiki})
- 1940: Introduction, Søren Kierkegaard\'s *The Present Age* (trans. Dru and Lowrie; Oxford University Press; `{{OCLC|2193267}}`{=mediawiki})
- 1943: Introduction, *The Letters of Evelyn Underhill* (Longmans, Green and Co.)
- 1958: *The New Christian Year* (Oxford University Press `{{OCLC|7003710}}`{=mediawiki})
- 1989: *Letters to Lalage: The Letters of Charles Williams to Lois Lang-Sims* (Kent State University Press)
- 2002: *To Michal from Serge: Letters from Charles Williams to His Wife, Florence, 1939--1945* (edited by Roma King Jr.; Kent State University Press)
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Cessna
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**Cessna** (`{{IPAc-en|ˈ|s|ɛ|s|n|ə|}}`{=mediawiki}) is an American brand of general aviation aircraft owned by Textron Aviation since 2014, headquartered in Wichita, Kansas. Originally, it was a brand of the **Cessna Aircraft Company**, an American general aviation aircraft manufacturing corporation also headquartered in Wichita. The company produced small, piston-powered aircraft, as well as business jets. For much of the mid-to-late 20th century, Cessna was one of the highest-volume and most diverse producers of general aviation aircraft in the world. It was founded in 1927 by Clyde Cessna and Victor Roos and was purchased by General Dynamics in 1985, then by Textron in 1992. In March 2014, when Textron purchased the Beechcraft and Hawker Aircraft corporations, Cessna ceased operations as a subsidiary company, and joined the others as one of the three distinct brands produced by Textron Aviation.
Throughout its history, and especially in the years following World War II, Cessna became best known for producing small, high-wing, piston aircraft. Its most popular and iconic aircraft is the Cessna 172, delivered since 1956 (with a break from 1986 to 1996), with more sold than any other aircraft in history. Since the first model was delivered in 1972, the brand has also been well known for its Citation family of low-wing business jets which vary in size.
## History
### Origins
Clyde Cessna, a farmer in Rago, Kansas, built his own aircraft and flew it in June 1911. He was the first person to do so between the Mississippi River and the Rocky Mountains. Cessna started his wood-and-fabric aircraft ventures in Enid, Oklahoma, testing many of his early planes on the salt flats. When bankers in Enid refused to lend him more money to build his planes, he moved to Wichita.
Cessna Aircraft was formed when Clyde Cessna and Victor Roos became partners in the Cessna-Roos Aircraft Company in 1927. Roos resigned just one month into the partnership, selling back his interest to Cessna. Shortly afterward, Roos\'s name was dropped from the company name.
The Cessna DC-6 earned certification on the same day as the stock market crash of 1929, October 29, 1929.
In 1932, the Cessna Aircraft Company closed due to the Great Depression.
However, the Cessna CR-3 custom racer made its first flight in 1933. The plane won the 1933 American Air Race in Chicago and later set a new world speed record for engines smaller than 500 cubic inches by averaging 237 mph.
Cessna\'s nephews, brothers Dwane and Dwight Wallace, bought the company from Cessna in 1934. They reopened it and began the process of building it into what would become a global success.
The Cessna C-37 was introduced in 1937 as Cessna\'s first seaplane when equipped with Edo floats. In 1940, Cessna received their largest order to date, when they signed a contract with the U.S. Army for 33 specially equipped Cessna T-50s, their first twin engine plane. Later in 1940, the Royal Canadian Air Force placed an order for 180 T-50s.
### Postwar boom {#postwar_boom}
Cessna returned to commercial production in 1946, after the revocation of wartime production restrictions (L-48), with the release of the Model 120 and Model 140. The approach was to introduce a new line of all-metal aircraft that used production tools, dies and jigs, rather than the hand-built tube-and-fabric construction process used before the war.
The Model 140 was named by the US Flight Instructors Association as the \"Outstanding Plane of the Year\" in 1948.
Cessna\'s first helicopter, the Cessna CH-1, received FAA type certification in 1955.
Cessna introduced the Cessna 172 in 1956. It became the most produced airplane in history. During the post-World War II era, Cessna was known as one of the \"Big Three\" in general aviation aircraft manufacturing, along with Piper and Beechcraft.
In 1959, Cessna acquired Aircraft Radio Corporation (ARC), of Boonton, New Jersey, a leading manufacturer of aircraft radios. During these years, Cessna expanded the ARC product line, and rebranded ARC radios as \"Cessna\" radios, making them the \"factory option\" for avionics in new Cessnas. However, during this time, ARC radios suffered a severe decline in quality and popularity. Cessna kept ARC as a subsidiary until 1983, selling it to avionics-maker Sperry.
In 1960, Cessna acquired McCauley Industrial Corporation, of Ohio, a leading manufacturer of propellers for light aircraft. McCauley became the world\'s leading producer of general aviation aircraft propellers, largely through their installation on Cessna airplanes.
In 1960, Cessna affiliated itself with Reims Aviation of Reims, France. In 1963, Cessna produced its 50,000th airplane, a Cessna 172.
Cessna\'s first business jet, the Cessna Citation I, performed its maiden flight on September 15, 1969.
Cessna produced its 100,000th single-engine airplane in 1975.
In 1985, Cessna ceased to be an independent company. It was purchased by General Dynamics. Production of the Cessna Caravan began. General Dynamics in turn sold Cessna to Textron in 1992.
Late in 2007, Cessna purchased the bankrupt Columbia Aircraft company for US\$26.4M and would continue production of the Columbia 350 and 400 as the Cessna 350 and Cessna 400 at the Columbia factory in Bend, Oregon. However, production of both aircraft had ended by 2018.
### Chinese production controversy {#chinese_production_controversy}
On November 27, 2007, Cessna announced the then-new Cessna 162 would be built in China by Shenyang Aircraft Corporation, which is a subsidiary of the China Aviation Industry Corporation I (AVIC I), a Chinese government-owned consortium of aircraft manufacturers. Cessna reported that the decision was made to save money and because the company had no more plant capacity in the United States at the time. Cessna received much negative feedback for this decision, with complaints centering on the recent quality problems with Chinese production of other consumer products, China\'s human rights record, exporting of jobs and China\'s less than friendly political relationship with the United States. The customer backlash surprised Cessna and resulted in a company public relations campaign. In early 2009, the company attracted further criticism for continuing plans to build the 162 in China while laying off large numbers of workers in the United States. In the end, the Cessna 162 was not a commercial success and only a small number were delivered before production was cancelled.
### 2008--2010 economic crisis {#economic_crisis}
The company\'s business suffered notably during the late-2000s recession, laying off more than half its workforce between January 2009 and September 2010.
On November 4, 2008, Cessna\'s parent company, Textron, indicated that Citation production would be reduced from the original 2009 target of 535 \"due to continued softening in the global economic environment\" and that this would result in an undetermined number of lay-offs at Cessna.
On November 8, 2008, at the Aircraft Owners and Pilots Association (AOPA) Expo, CEO Jack Pelton indicated that sales of Cessna aircraft to individual buyers had fallen, but piston and turboprop sales to businesses had not. \"While the economic slowdown has created a difficult business environment, we are encouraged by brisk activity from new and existing propeller fleet operators placing almost 200 orders for 2009 production aircraft,\" Pelton stated.
Beginning in January 2009, a total of 665 jobs were cut at Cessna\'s Wichita and Bend, Oregon, plants. The Cessna factory at Independence, Kansas, which builds the Cessna piston-engined aircraft and the Cessna Mustang, did not see any layoffs, but one third of the workforce at the former Columbia Aircraft facility in Bend was laid off. This included 165 of the 460 employees who built the Cessna 350 and 400. The remaining 500 jobs were eliminated at the main Cessna Wichita plant.
In January 2009, the company laid off an additional 2,000 employees, bringing the total to 4,600. The job cuts included 120 at the Bend, Oregon, facility reducing the plant that built the Cessna 350 and 400 to fewer than half the number of workers that it had when Cessna bought it. Other cuts included 200 at the Independence, Kansas, plant that builds the single-engined Cessnas and the Mustang, reducing that facility to 1,300 workers.
On April 29, 2009, the company suspended the Citation Columbus program and closed the Bend, Oregon, facility. The Columbus program was finally cancelled in early July 2009. The company reported, \"Upon additional analysis of the business jet market related to this product offering, we decided to formally cancel further development of the Citation Columbus\". With the 350 and 400 production moving to Kansas, the company indicated that it would lay off 1,600 more workers, including the remaining 150 employees at the Bend plant and up to 700 workers from the Columbus program.
In early June 2009, Cessna laid off an additional 700 salaried employees, bringing the total number of lay-offs to 7,600, which was more than half the company\'s workers at the time.
The company closed its three Columbus, Georgia, manufacturing facilities between June 2010 and December 2011. The closures included the new 100000 sqft facility that was opened in August 2008 at a cost of US\$25M, plus the McCauley Propeller Systems plant. These closures resulted in total job losses of 600 in Georgia. Some of the work was relocated to Cessna\'s Independence, Kansas, or Mexican facilities.
Cessna\'s parent company, Textron, posted a loss of US\$8M in the first quarter of 2010, largely driven by continuing low sales at Cessna, which were down 44%. Half of Cessna\'s workforce remained laid-off and CEO Jack Pelton stated that he expected the recovery to be long and slow.
In September 2010, a further 700 employees were laid off, bringing the total to 8,000 jobs lost. CEO Jack Pelton indicated this round of layoffs was due to a \"stalled \[and\] lackluster economy\" and noted that while the number of orders cancelled for jets had been decreasing, new orders had not met expectations. Pelton added, \"our strategy is to defend and protect our current markets while investing in products and services to secure our future, but we can do this only if we succeed in restructuring our processes and reducing our costs.\"
### 2010s
On May 2, 2011, CEO Jack J. Pelton retired. The new CEO, Scott A. Ernest, started on May 31, 2011. Ernest joined Textron after 29 years at General Electric, where he had most recently served as vice president and general manager, global supply chain for GE Aviation. Ernest previously worked for Textron CEO Scott Donnelly when both worked at General Electric.
In September 2011, the Federal Aviation Administration (FAA) proposed a US\$2.4 million fine against the company for its failure to follow quality assurance requirements while producing fiberglass components at its plant in Chihuahua, Mexico. Excess humidity meant that the parts did not cure correctly and quality assurance did not detect the problems. The failure to follow procedures resulted in the delamination in flight of a 7 ft section of one Cessna 400\'s wing skin from the spar while the aircraft was being flown by an FAA test pilot. The aircraft was landed safely. The FAA also discovered 82 other aircraft parts that had been incorrectly made and not detected by the company\'s quality assurance. The investigation resulted in an emergency Airworthiness Directive that affected 13 Cessna 400s.
Since March 2012, Cessna has been pursuing building business jets in China as part of a joint venture with Aviation Industry Corporation of China (AVIC). The company stated that it intends to eventually build all aircraft models in China, saying \"The agreements together pave the way for a range of business jets, utility single-engine turboprops and single-engine piston aircraft to be manufactured and certified in China.\"
In late April 2012, the company added 150 workers in Wichita as a result of anticipated increased demand for aircraft production. Overall, they have cut more than 6000 jobs in the Wichita plant since 2009.
In March 2014, Cessna ceased operations as a company and instead became a brand of Textron Aviation.
## Marketing initiatives {#marketing_initiatives}
During the 1950s and 1960s, Cessna\'s marketing department followed the lead of Detroit automakers and came up with many unique marketing terms in an effort to differentiate its product line from their competitors.
Other manufacturers and the aviation press widely ridiculed and spoofed many of the marketing terms, but Cessna built and sold more aircraft than any other manufacturer during the boom years of the 1960s and 1970s.
Generally, the names of Cessna models do not follow a theme, but there is usually logic to the numbering: the 100 series are the light singles, the 200s are the heftier, the 300s are light to medium twins, the 400s have \"wide oval\" cabin-class accommodation and the 500s are jets. Many Cessna models have names starting with C for the sake of alliteration (e.g. Citation, Crusader, Chancellor).
### Company terminology {#company_terminology}
Cessna marketing terminology includes:
- **Para-Lift Flaps** -- Large Fowler flaps Cessna introduced on the 170B in 1952, replacing the narrow chord plain flaps then in use.
- **Land-O-Matic** -- In 1956, Cessna introduced sprung-steel tricycle landing gear on the 172. The marketing department chose \"Land-O-Matic\" to imply that these aircraft were much easier to land and take off than the preceding conventional landing gear equipped Cessna 170. They even went as far as to say pilots could do \"drive-up take-offs and drive-in landings\", implying that flying these aircraft was as easy as driving a car. In later years, some Cessna models had their steel sprung landing gear replaced with steel tube gear legs. The 206 retains the original spring steel landing gear today.
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- **Omni-Vision** -- The rear windows on some Cessna singles, starting with the 182 and 210 in 1962 and followed by the 172 and 150 in 1963 and 1964 respectively. The term was intended to make the pilot feel visibility was improved on the notably poor-visibility Cessna line. The introduction of the rear window caused in most models a loss of cruise speed due to the extra drag, while not adding any useful visibility.
- **Cushioned Power** -- The rubber mounts on the cowling of the 1967 model 150, in addition to the rubber mounts isolating the engine from the cabin.
- **Omni-Flash** -- The flashing beacon on the tip of the fin that could be seen all around.
- **Open-View** -- This referred to the removal of the top section of the control wheel in 1967 models. These had been rectangular, they now became \"ram\'s horn\" shaped, thus not blocking the instrument panel as much.
- **Quick-Scan** -- Cessna introduced a new instrument panel layout in the 1960s and this buzzword was to indicate Cessna\'s panels were ahead of the competition.
- **Nav-O-Matic** -- The name of the Cessna autopilot system, which implied the system was relatively simple.
- **Camber-Lift** -- A marketing name used to describe Cessna aircraft wings starting in 1972 when the aerodynamics designers at Cessna added a slightly drooped leading edge to the standard NACA 2412 airfoil used on most of the light aircraft fleet. Writer Joe Christy described the name as \"stupid\" and added \"Is there any other kind \[of lift\]?\"
- **Stabila-Tip** -- Cessna started commonly using wingtip fuel tanks, carefully shaped for aerodynamic effect rather than being tubular-shaped. Tip tanks do have an advantage of reducing free surface effect of fuel affecting the balance of the aircraft in rolling maneuvers.
## Aircraft
In October 2020, Textron Aviation was producing the following Cessna-branded models:
- Cessna 172 Skyhawk -- high-wing, single piston-engined, four-seat aircraft in production since 1956
- Cessna 182 Skylane -- high-wing, single piston-engined, four-seat aircraft in production since 1956
- Cessna 206 Stationair -- high-wing, single piston-engined, six-seat utility aircraft in production since 1962
- Cessna 208 Caravan -- high-wing single-turboprop utility aircraft in production since 1984
- Cessna 408 SkyCourier -- high-wing twin-turboprop utility aircraft in production since 2022
- Cessna Citation family -- twin-engined business jets
- Cessna Citation 525 M2/CJ series -- in production since 1991
- Cessna Citation 560XL Excel -- in production since 1996
- Cessna Citation 680 Sovereign -- out of production since 2021
- Cessna Citation 680A Latitude -- in production since 2014
- Cessna Citation 700 Longitude -- in production since 2019
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6,556 |
Coprime integers
|
In number theory, two integers `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are **coprime**, **relatively prime** or **mutually prime** if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides `{{mvar|a}}`{=mediawiki} does not divide `{{mvar|b}}`{=mediawiki}, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also `{{mvar|a}}`{=mediawiki} *is prime to* `{{mvar|b}}`{=mediawiki} or `{{mvar|a}}`{=mediawiki} *is coprime with* `{{mvar|b}}`{=mediawiki}.
The numbers 8 and 9 are coprime, despite the fact that neither---considered individually---is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition.
## Notation and testing {#notation_and_testing}
When the integers `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula `{{math|1=gcd(''a'', ''b'') = 1}}`{=mediawiki} or `{{math|1=(''a'', ''b'') = 1}}`{=mediawiki}. In their 1989 textbook *Concrete Mathematics*, Ronald Graham, Donald Knuth, and Oren Patashnik proposed an alternative notation $a\perp b$ to indicate that `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are relatively prime and that the term \"prime\" be used instead of coprime (as in `{{mvar|a}}`{=mediawiki} is *prime* to `{{mvar|b}}`{=mediawiki}).
A fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants such as binary GCD algorithm or Lehmer\'s GCD algorithm.
The number of integers coprime with a positive integer `{{mvar|n}}`{=mediawiki}, between 1 and `{{mvar|n}}`{=mediawiki}, is given by Euler\'s totient function, also known as Euler\'s phi function, `{{math|''φ''(''n'')}}`{=mediawiki}.
A set of integers can also be called coprime if its elements share no common positive factor except 1. A stronger condition on a set of integers is pairwise coprime, which means that `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime for every pair `{{math|(''a'', ''b'')}}`{=mediawiki} of different integers in the set. The set `{{math|{2, 3, 4} }}`{=mediawiki} is coprime, but it is not pairwise coprime since 2 and 4 are not relatively prime.
## Properties
The numbers 1 and −1 are the only integers coprime with every integer, and they are the only integers that are coprime with 0.
A number of conditions are equivalent to `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} being coprime:
- No prime number divides both `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki}.
- There exist integers `{{mvar|x, y}}`{=mediawiki} such that `{{math|1=''ax'' + ''by'' = 1}}`{=mediawiki} (see Bézout\'s identity).
- The integer `{{mvar|b}}`{=mediawiki} has a multiplicative inverse modulo `{{mvar|a}}`{=mediawiki}, meaning that there exists an integer `{{mvar|y}}`{=mediawiki} such that `{{math|''by'' ≡ 1 (mod ''a'')}}`{=mediawiki}. In ring-theoretic language, `{{mvar|b}}`{=mediawiki} is a unit in the ring `{{tmath|\Z/a\Z}}`{=mediawiki} of integers modulo `{{mvar|a}}`{=mediawiki}.
- Every pair of congruence relations for an unknown integer `{{mvar|x}}`{=mediawiki}, of the form `{{math|''x'' ≡ ''k'' (mod ''a'')}}`{=mediawiki} and `{{math|''x'' ≡ ''m'' (mod ''b'')}}`{=mediawiki}, has a solution (Chinese remainder theorem); in fact the solutions are described by a single congruence relation modulo `{{mvar|ab}}`{=mediawiki}.
- The least common multiple of `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} is equal to their product `{{mvar|ab}}`{=mediawiki}, i.e. `{{math|1=lcm(''a'', ''b'') = ''ab''}}`{=mediawiki}.
As a consequence of the third point, if `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime and `{{math|''br'' ≡ ''bs'' (mod ''a'')}}`{=mediawiki}, then `{{math|''r'' ≡ ''s'' (mod ''a'')}}`{=mediawiki}. That is, we may \"divide by `{{mvar|b}}`{=mediawiki}\" when working modulo `{{mvar|a}}`{=mediawiki}. Furthermore, if `{{math|''b''<sub>1</sub>, ''b''<sub>2</sub>}}`{=mediawiki} are both coprime with `{{mvar|a}}`{=mediawiki}, then so is their product `{{math|''b''<sub>1</sub>''b''<sub>2</sub>}}`{=mediawiki} (i.e., modulo `{{mvar|a}}`{=mediawiki} it is a product of invertible elements, and therefore invertible); this also follows from the first point by Euclid\'s lemma, which states that if a prime number `{{mvar|p}}`{=mediawiki} divides a product `{{mvar|bc}}`{=mediawiki}, then `{{mvar|p}}`{=mediawiki} divides at least one of the factors `{{mvar|b, c}}`{=mediawiki}.
As a consequence of the first point, if `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime, then so are any powers `{{mvar|a<sup>k</sup>}}`{=mediawiki} and `{{mvar|b<sup>m</sup>}}`{=mediawiki}.
If `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime and `{{mvar|a}}`{=mediawiki} divides the product `{{mvar|bc}}`{=mediawiki}, then `{{mvar|a}}`{=mediawiki} divides `{{mvar|c}}`{=mediawiki}. This can be viewed as a generalization of Euclid\'s lemma.
The two integers `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime if and only if the point with coordinates `{{math|(''a'', ''b'')}}`{=mediawiki} in a Cartesian coordinate system would be \"visible\" via an unobstructed line of sight from the origin `{{math|(0, 0)}}`{=mediawiki}, in the sense that there is no point with integer coordinates anywhere on the line segment between the origin and `{{math|(''a'', ''b'')}}`{=mediawiki}. (See figure 1.)
In a sense that can be made precise, the probability that two randomly chosen integers are coprime is `{{math|6/''π''<sup>2</sup>}}`{=mediawiki}, which is about 61% (see `{{slink||Probability of coprimality}}`{=mediawiki}, below).
Two natural numbers `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime if and only if the numbers `{{math|2<sup>''a''</sup> − 1}}`{=mediawiki} and `{{math|2<sup>''b''</sup> − 1}}`{=mediawiki} are coprime. As a generalization of this, following easily from the Euclidean algorithm in base `{{math|''n'' > 1}}`{=mediawiki}:
: $\gcd\left(n^a - 1, n^b - 1\right) = n^{\gcd(a, b)} - 1.$
## Coprimality in sets {#coprimality_in_sets}
A set of integers $S=\{a_1,a_2, \dots, a_n\}$ can also be called *coprime* or *setwise coprime* if the greatest common divisor of all the elements of the set is 1. For example, the integers 6, 10, 15 are coprime because 1 is the only positive integer that divides all of them.
If every pair in a set of integers is coprime, then the set is said to be *pairwise coprime* (or *pairwise relatively prime*, *mutually coprime* or *mutually relatively prime*). Pairwise coprimality is a stronger condition than setwise coprimality; every pairwise coprime finite set is also setwise coprime, but the reverse is not true. For example, the integers 4, 5, 6 are (setwise) coprime (because the only positive integer dividing *all* of them is 1), but they are not *pairwise* coprime (because `{{math|1=gcd(4, 6) = 2}}`{=mediawiki}).
The concept of pairwise coprimality is important as a hypothesis in many results in number theory, such as the Chinese remainder theorem.
It is possible for an infinite set of integers to be pairwise coprime. Notable examples include the set of all prime numbers, the set of elements in Sylvester\'s sequence, and the set of all Fermat numbers.
## Probability of coprimality {#probability_of_coprimality}
Given two randomly chosen integers `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki}, it is reasonable to ask how likely it is that `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime. In this determination, it is convenient to use the characterization that `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime if and only if no prime number divides both of them (see Fundamental theorem of arithmetic).
Informally, the probability that any number is divisible by a prime (or in fact any integer) `{{mvar|p}}`{=mediawiki} is `{{tmath|\tfrac{1}{p};}}`{=mediawiki} for example, every 7th integer is divisible by 7. Hence the probability that two numbers are both divisible by `{{mvar|p}}`{=mediawiki} is `{{tmath|\tfrac{1}{p^2},}}`{=mediawiki} and the probability that at least one of them is not is `{{tmath|1-\tfrac{1}{p^2}.}}`{=mediawiki} Any finite collection of divisibility events associated to distinct primes is mutually independent. For example, in the case of two events, a number is divisible by primes `{{mvar|p}}`{=mediawiki} and `{{mvar|q}}`{=mediawiki} if and only if it is divisible by `{{mvar|pq}}`{=mediawiki}; the latter event has probability `{{tmath|\tfrac{1}{pq}.}}`{=mediawiki} If one makes the heuristic assumption that such reasoning can be extended to infinitely many divisibility events, one is led to guess that the probability that two numbers are coprime is given by a product over all primes,
: $\prod_{\text{prime } p} \left(1-\frac{1}{p^2}\right) = \left( \prod_{\text{prime } p} \frac{1}{1-p^{-2}} \right)^{-1} = \frac{1}{\zeta(2)} = \frac{6}{\pi^2} \approx 0.607927102 \approx 61\%.$
Here `{{mvar|ζ}}`{=mediawiki} refers to the Riemann zeta function, the identity relating the product over primes to `{{math|''ζ''(2)}}`{=mediawiki} is an example of an Euler product, and the evaluation of `{{math|''ζ''(2)}}`{=mediawiki} as `{{math|''π''<sup>2</sup>/6}}`{=mediawiki} is the Basel problem, solved by Leonhard Euler in 1735.
There is no way to choose a positive integer at random so that each positive integer occurs with equal probability, but statements about \"randomly chosen integers\" such as the ones above can be formalized by using the notion of *natural density*. For each positive integer `{{mvar|N}}`{=mediawiki}, let `{{mvar|P{{sub|N}}}}`{=mediawiki} be the probability that two randomly chosen numbers in $\{1,2,\ldots,N\}$ are coprime. Although `{{mvar|P{{sub|N}}}}`{=mediawiki} will never equal `{{math|6/''π''<sup>2</sup>}}`{=mediawiki} exactly, with work one can show that in the limit as $N \to \infty,$ the probability `{{mvar|P{{sub|N}}}}`{=mediawiki} approaches `{{math|6/''π''<sup>2</sup>}}`{=mediawiki}.
More generally, the probability of `{{mvar|k}}`{=mediawiki} randomly chosen integers being setwise coprime is `{{tmath|\tfrac{1}{\zeta(k)}.}}`{=mediawiki}
## Generating all coprime pairs {#generating_all_coprime_pairs}
All pairs of positive coprime numbers `{{math|(''m'', ''n'')}}`{=mediawiki} (with `{{math|''m'' > ''n''}}`{=mediawiki}) can be arranged in two disjoint complete ternary trees, one tree starting from `{{math|(2, 1)}}`{=mediawiki} (for even--odd and odd--even pairs), and the other tree starting from `{{math|(3, 1)}}`{=mediawiki} (for odd--odd pairs). The children of each vertex `{{math|(''m'', ''n'')}}`{=mediawiki} are generated as follows:
- Branch 1: $(2m-n,m)$
- Branch 2: $(2m+n,m)$
- Branch 3: $(m+2n,n)$
This scheme is exhaustive and non-redundant with no invalid members. This can be proved by remarking that, if $(a,b)$ is a coprime pair with $a>b,$ then
- if $a>3b,$ then $(a,b)$ is a child of $(m,n)=(a-2b, b)$ along branch 3;
- if $2b<a<3b,$ then $(a,b)$ is a child of $(m,n)=(b, a-2b)$ along branch 2;
- if $b<a<2b,$ then $(a,b)$ is a child of $(m,n)=(b, 2b-a)$ along branch 1.
In all cases $(m,n)$ is a \"smaller\" coprime pair with $m>n.$ This process of \"computing the father\" can stop only if either $a=2b$ or $a=3b.$ In these cases, coprimality, implies that the pair is either $(2,1)$ or $(3,1).$
Another (much simpler) way to generate a tree of positive coprime pairs `{{math|(''m'', ''n'')}}`{=mediawiki} (with `{{math|''m'' > ''n''}}`{=mediawiki}) is by means of two generators $f:(m,n)\rightarrow(m+n,n)$ and $g:(m,n)\rightarrow(m+n,m)$, starting with the root $(2,1)$. The resulting binary tree, the Calkin--Wilf tree, is exhaustive and non-redundant, which can be seen as follows. Given a coprime pair one recursively applies $f^{-1}$ or $g^{-1}$ depending on which of them yields a positive coprime pair with `{{math|''m'' > ''n''}}`{=mediawiki}. Since only one does, the tree is non-redundant. Since by this procedure one is bound to arrive at the root, the tree is exhaustive.
## Applications
In machine design, an even, uniform gear wear is achieved by choosing the tooth counts of the two gears meshing together to be relatively prime. When a 1:1 gear ratio is desired, a gear relatively prime to the two equal-size gears may be inserted between them.
In pre-computer cryptography, some Vernam cipher machines combined several loops of key tape of different lengths. Many rotor machines combine rotors of different numbers of teeth. Such combinations work best when the entire set of lengths are pairwise coprime.
## Generalizations
This concept can be extended to other algebraic structures than `{{tmath|\Z;}}`{=mediawiki} for example, polynomials whose greatest common divisor is 1 are called coprime polynomials.
### Coprimality in ring ideals {#coprimality_in_ring_ideals}
Two ideals `{{mvar|A}}`{=mediawiki} and `{{mvar|B}}`{=mediawiki} in a commutative ring `{{mvar|R}}`{=mediawiki} are called coprime (or *comaximal*) if $A+B=R.$ This generalizes Bézout\'s identity: with this definition, two principal ideals (`{{mvar|a}}`{=mediawiki}) and (`{{mvar|b}}`{=mediawiki}) in the ring of integers `{{tmath|\Z}}`{=mediawiki} are coprime if and only if `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are coprime. If the ideals `{{mvar|A}}`{=mediawiki} and `{{mvar|B}}`{=mediawiki} of `{{mvar|R}}`{=mediawiki} are coprime, then $AB=A\cap B;$ furthermore, if `{{mvar|C}}`{=mediawiki} is a third ideal such that `{{mvar|A}}`{=mediawiki} contains `{{mvar|BC}}`{=mediawiki}, then `{{mvar|A}}`{=mediawiki} contains `{{mvar|C}}`{=mediawiki}. The Chinese remainder theorem can be generalized to any commutative ring, using coprime ideals.
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6,558 |
Cello
|
The **violoncello** (`{{IPAc-en|ˌ|v|aɪ|ə|l|ə|n|ˈ|tʃ|ɛ|l|oʊ|audio=LL-Q1860 (eng)-Flame, not lame-Cello.wav}}`{=mediawiki} `{{respell|VY|ə|lən|CHEL|oh}}`{=mediawiki}, `{{IPA|it|vjolonˈtʃɛllo}}`{=mediawiki}), commonly abbreviated as **cello** (`{{IPAc-en|ˈ|tʃ|ɛ|l|oʊ}}`{=mediawiki} `{{respell|CHEL|oh}}`{=mediawiki}), is a middle pitched bowed (sometimes plucked and occasionally hit) string instrument of the violin family. Its four strings are usually tuned in perfect fifths: from low to high, C~2~, G~2~, D~3~ and A~3~. The viola\'s four strings are each an octave higher. Music for the cello is generally written in the bass clef; the tenor clef and treble clef are used for higher-range passages.
Played by a *cellist* or *violoncellist*, it enjoys a large solo repertoire with and without accompaniment, as well as numerous concerti. As a solo instrument, the cello uses its whole range, from bass to soprano, and in chamber music, such as string quartets and the orchestra\'s string section, it often plays the bass part, where it may be reinforced an octave lower by the double basses. Figured bass music of the Baroque era typically assumes a cello, viola da gamba or bassoon as part of the basso continuo group alongside chordal instruments such as organ, harpsichord, lute, or theorbo. Cellos are found in many other ensembles, from modern Chinese orchestras to cello rock bands.
## Etymology
The name *cello* is derived from the ending of the Italian *violoncello*, which means \"little violone\". Violone (\"big viola\") was a large-sized member of viol (viola da gamba) family or the violin (viola da braccio) family. The term \"violone\" today usually refers to the lowest-pitched instrument of the viols, a family of stringed instruments that went out of fashion around the end of the 17th century in most countries except England and, especially, France, where they survived another half-century before the louder violin family came into greater favour in that country as well.
In modern symphony orchestras, it is the second largest stringed instrument (the double bass is the largest). Thus, the name \"violoncello\" contained both the augmentative \"*-one*\" (\"big\") and the diminutive \"*-cello*\" (\"little\"). By the turn of the 20th century, it had become common to shorten the name to \'cello, with the apostrophe indicating the missing stem. It is now customary to use \"cello\" without apostrophe as the full designation. *Viol* is derived from the root *viola*, which was derived from Medieval Latin *vitula*, meaning stringed instrument.
## General description {#general_description}
### Tuning
Cellos are tuned in fifths, starting with C~2~ (two octaves below middle C), followed by G~2~, D~3~, and then A~3~. It is tuned in the exact same intervals and strings as the viola, but an octave lower. Similar to the double bass, the cello has an endpin that rests on the floor to support the instrument\'s weight. The cello is most closely associated with European classical music. The instrument is a part of the standard orchestra, as part of the string section, and is the bass voice of the string quartet (although many composers give it a melodic role as well), as well as being part of many other chamber groups.
### Works
Among the most well-known Baroque works for the cello are Johann Sebastian Bach\'s six unaccompanied Suites. Other significant works include Sonatas and Concertos by Antonio Vivaldi, and solo sonatas by Francesco Geminiani and Giovanni Bononcini. Domenico Gabrielli was one of the first composers to treat the cello as a solo instrument. As a basso continuo instrument the cello may have been used in works by Francesca Caccini (1587--1641), Barbara Strozzi (1619--1677) with pieces such as *Il primo libro di madrigali, per 2--5 voci e basso continuo, op. 1* and Elisabeth Jacquet de La Guerre (1665--1729), who wrote six sonatas for violin and basso continuo. Francesco Supriani\'s *Principij da imparare a suonare il violoncello e con 12 Toccate a solo* (before 1753), an early manual for learning the cello, dates from this era. As the title of the work suggests, it contains 12 toccatas for solo cello, which along with Johann Sebastian Bach\'s Cello Suites, are some of the first works of that type.
From the Classical era, the two concertos by Joseph Haydn in C major and D major stand out, as do the five sonatas for cello and pianoforte of Ludwig van Beethoven, which span the important three periods of his compositional evolution. Other outstanding examples include the three Concerti by Carl Philipp Emanuel Bach, Capricci by dall\'Abaco, and Sonatas by Flackton, Boismortier, and Luigi Boccherini. A *Divertimento for Piano, Clarinet, Viola and Cello* is among the surviving works by Duchess Anna Amalia of Brunswick-Wolfenbüttel (1739--1807). Wolfgang Amadeus Mozart supposedly wrote a Cello Concerto in F major, K. 206a in 1775, but this has since been lost. His Sinfonia Concertante in A major, K. 320e includes a solo part for cello, along with the violin and viola, although this work is incomplete and only exists in fragments, therefore it is given an Anhang number (Anh. 104).
Well-known works of the Romantic era include the Robert Schumann Concerto, the Antonín Dvořák Concerto, the first Camille Saint-Saëns Concerto, as well as the two sonatas and the Double Concerto by Johannes Brahms. A review of compositions for cello in the Romantic era must include the German composer Fanny Mendelssohn (1805--1847), who wrote Fantasia in G Minor for cello and piano and a Capriccio in A-flat for cello.
Compositions from the late 19th and early 20th century include three cello sonatas (including the Cello Sonata in C Minor written in 1880) by Dame Ethel Smyth (1858--1944), Edward Elgar\'s Cello Concerto in E minor, Claude Debussy\'s Sonata for Cello and Piano, and unaccompanied cello sonatas by Zoltán Kodály and Paul Hindemith. Pieces including cello were written by American Music Center founder Marion Bauer (1882--1955) (two trio sonatas for flute, cello, and piano) and Ruth Crawford Seeger (1901--1953) (Diaphonic suite No. 2 for bassoon and cello).
The cello\'s versatility made it popular with many composers in this era, such as Sergei Prokofiev, Dmitri Shostakovich, Benjamin Britten, György Ligeti, Witold Lutoslawski and Henri Dutilleux. Polish composer Grażyna Bacewicz (1909--1969) was writing for cello in the mid 20th century with Concerto No. 1 for Cello and Orchestra (1951), Concerto No. 2 for Cello and Orchestra (1963) and in 1964 composed her Quartet for four cellos.
Today it is sometimes featured in pop and rock recordings, examples of which are noted later in this article. The cello has also appeared in major hip-hop and R & B performances, such as singers Rihanna and Ne-Yo\'s 2007 performance at the American Music Awards. The instrument has also been modified for Indian classical music by Nancy Lesh and Saskia Rao-de Haas.^\[5\]^
## History
The violin family, including cello-sized instruments, emerged c. 1500 as a family of instruments distinct from the viola da gamba family. The earliest depictions of the violin family, from Italy c. 1530, show three sizes of instruments, roughly corresponding to what we now call violins, violas, and cellos. Contrary to a popular misconception, the cello did not evolve from the viola da gamba, but existed alongside it for about two and a half centuries. The violin family is also known as the viola da braccio (meaning viola for the arm) family, a reference to the primary way the members of the family are held. This is to distinguish it from the viola da gamba (meaning viola for the leg) family, in which all the members are all held with the legs. The likely predecessors of the violin family include the lira da braccio and the rebec. The earliest surviving cellos are made by Andrea Amati, the first known member of the celebrated Amati family of luthiers.
The direct ancestor to the violoncello was the bass violin.^\[*unt.\ library*\]^ Monteverdi referred to the instrument as \"basso de viola da braccio\" in *Orfeo* (1607). Although the first bass violin, possibly invented as early as 1538, was most likely inspired by the viol, it was created to be used in consort with the violin. The bass violin was actually often referred to as a \"*violone*\", or \"large viola\", as were the viols of the same period. Instruments that share features with both the bass violin and the *viola da gamba* appear in Italian art of the early 16th century.
The invention of wire-wound strings (fine wire around a thin gut core), c. 1660 in Bologna, allowed for a finer bass sound than was possible with purely gut strings on such a short body. Bolognese makers exploited this new technology to create the cello, a somewhat smaller instrument suitable for solo repertoire due to both the timbre of the instrument and the fact that the smaller size made it easier to play virtuosic passages. This instrument had disadvantages as well, however. The cello\'s light sound was not as suitable for church and ensemble playing, so it had to be doubled by organ, theorbo, or violone.
Around 1700, Italian players popularized the cello in northern Europe, although the bass violin (basse de violon) continued to be used for another two decades in France. Many existing bass violins were literally cut down in size to convert them into cellos according to the smaller pattern developed by Stradivarius, who also made a number of old pattern large cellos (the \'Servais\'). The sizes, names, and tunings of the cello varied widely by geography and time. The size was not standardized until c. 1750.
Despite similarities to the viola da gamba, the cello is actually part of the viola da braccio family, meaning \"viol of the arm\", which includes, among others, the violin and viola. Though paintings like Bruegel\'s \"The Rustic Wedding\", and Jambe de Fer in his *Epitome Musical* suggest that the bass violin had alternate playing positions, these were short-lived and the more practical and ergonomic *a gamba* position eventually replaced them entirely.
Baroque-era cellos differed from the modern instrument in several ways. The neck has a different form and angle, which matches the baroque bass-bar and stringing. The fingerboard is usually shorter than that of the modern cello, as the highest notes are not often called for in baroque music. Modern cellos have an endpin at the bottom to support the instrument (and transmit some of the sound through the floor), while Baroque cellos are held only by the calves of the player. Modern bows curve in and are held at the frog; Baroque bows curve out and are held closer to the bow\'s point of balance. Modern strings are normally flatwound with a metal (or synthetic) core; Baroque strings are made of gut, with the G and C strings wire-wound. Modern cellos often have fine tuners connecting the strings to the tailpiece, which makes it much easier to tune the instrument, but such pins are rendered ineffective by the flexibility of the gut strings used on Baroque cellos. Overall, the modern instrument has much higher string tension than the Baroque cello, resulting in a louder, more projecting tone, with fewer overtones. In addition, the instrument was less standardized in size and number of strings; a smaller, five-string variant (the violoncello piccolo) was commonly used as a solo instrument and five-string instruments are occasionally specified in the Baroque repertoire. BWV 1012 (Bach\'s 6th Cello Suite) was written for 5-string cello. The additional high E string on the five-string cello is an octave below the same string on the Violin, so anything written for the violin can be played on the 5 string cello, sounding an octave lower than written.
Few educational works specifically devoted to the cello existed before the 18th century and those that do exist contain little value to the performer beyond simple accounts of instrumental technique. One of the earliest cello manuals is Michel Corrette\'s *Méthode, thèorique et pratique pour apprendre en peu de temps le violoncelle dans sa perfection* (Paris, 1741).
## Modern use {#modern_use}
### Orchestral
thumb\|left\|upright=0.9\|The cello section of the orchestra of the Munich University of Applied Sciences is shown here. Cellos are part of the standard symphony orchestra, which usually includes eight to twelve cellists. The cello section, in standard orchestral seating, is located on stage left (the audience\'s right) in the front, opposite the first violin section. However, some orchestras and conductors prefer switching the positioning of the viola and cello sections. The *principal* cellist is the section leader, determining bowings for the section in conjunction with other string principals, playing solos, and leading entrances (when the section begins to play its part). Principal players always sit closest to the audience.
The cellos are a critical part of orchestral music; all symphonic works involve the cello section, and many pieces require cello soli or solos. Much of the time, cellos provide part of the low-register harmony for the orchestra. Often, the cello section plays the melody for a brief period, before returning to the harmony role. There are also cello concertos, which are orchestral pieces that feature a solo cellist accompanied by an entire orchestra.
### Solo
There are numerous cello concertos -- where a solo cello is accompanied by an orchestra -- notably 25 by Vivaldi, 12 by Boccherini, at least three by Haydn, three by C. P. E. Bach, two by Saint-Saëns, two by Dvořák, and one each by Robert Schumann, Lalo, and Elgar. There were also some composers who, while not otherwise cellists,`{{Clarify|date=February 2020|reason=Does this mean that Vivaldi, Haydn, CPE Bach, Sait-Saëns, Dvořák, Schumann, Lalo, and Elgar were all, like Boccherini, cellists?}}`{=mediawiki} did write cello-specific repertoire, such as Nikolaus Kraft, who wrote six cello concertos. Beethoven\'s Triple Concerto for Cello, Violin and Piano and Brahms\' Double Concerto for Cello and Violin are also part of the concertante repertoire, although in both cases the cello shares solo duties with at least one other instrument. Moreover, several composers wrote large-scale pieces for cello and orchestra, which are concertos in all but name. Some familiar \"concertos\" are Richard Strauss\' tone poem *Don Quixote*, Tchaikovsky\'s *Variations on a Rococo Theme*, Bloch\'s *Schelomo* and Bruch\'s *Kol Nidrei*.
In the 20th century, the cello repertoire grew immensely. This was partly due to the influence of virtuoso cellist Mstislav Rostropovich, who inspired, commissioned, and premiered dozens of new works. Among these, Prokofiev\'s *Symphony-Concerto*, Britten\'s *Cello Symphony*, the concertos of Shostakovich and Lutosławski as well as Dutilleux\'s *Tout un monde lointain\...* have already become part of the standard repertoire. Other major composers who wrote concertante works for him include Messiaen, Jolivet, Berio, and Penderecki. In addition, Arnold, Barber, Glass, Hindemith, Honegger, Ligeti, Myaskovsky, Penderecki, Rodrigo, Villa-Lobos and Walton wrote major concertos for other cellists, notably for Gaspar Cassadó, Aldo Parisot, Gregor Piatigorsky, Siegfried Palm and Julian Lloyd Webber.
There are also many sonatas for cello and piano. Those written by Beethoven, Mendelssohn, Chopin, Brahms, Grieg, Rachmaninoff, Debussy, Fauré, Shostakovich, Prokofiev, Poulenc, Carter, and Britten are particularly well known.
Other important pieces for cello and piano include Schumann\'s five *Stücke im Volkston* and transcriptions like Schubert\'s *Arpeggione Sonata* (originally for arpeggione and piano), César Franck\'s Cello Sonata (originally a violin sonata, transcribed by Jules Delsart with the composer\'s approval), Stravinsky\'s *Suite italienne* (transcribed by the composer -- with Gregor Piatigorsky -- from his ballet *Pulcinella*) and Bartók\'s first rhapsody (also transcribed by the composer, originally for violin and piano).
There are pieces for cello solo, Johann Sebastian Bach\'s six Suites for Cello (which are among the best-known solo cello pieces), Kodály\'s Sonata for Solo Cello and Britten\'s three Cello Suites. Other notable examples include Hindemith\'s and Ysaÿe\'s Sonatas for Solo Cello, Dutilleux\'s *Trois Strophes sur le Nom de Sacher*, Berio\'s *Les Mots Sont Allés*, Cassadó\'s Suite for Solo Cello, Ligeti\'s Solo Sonata, Carter\'s two *Figment*s and Xenakis\' *Nomos Alpha* and *Kottos*.
There are also modern solo pieces written for cello, such as Julie-O by Mark Summer.
### Quartets and other ensembles {#quartets_and_other_ensembles}
The cello is a member of the traditional string quartet as well as string quintets, sextet or trios and other mixed ensembles. There are also pieces written for two, three, four, or more cellos; this type of ensemble is also called a \"cello choir\" and its sound is familiar from the introduction to Rossini\'s William Tell Overture as well as Zaccharia\'s prayer scene in Verdi\'s Nabucco. Tchaikovsky\'s 1812 Overture also starts with a cello ensemble, with four cellos playing the top lines and two violas playing the bass lines. As a self-sufficient ensemble, its most famous repertoire is Heitor Villa-Lobos\' first of his Bachianas Brasileiras for cello ensemble (the fifth is for soprano and 8 cellos). Other examples are Offenbach\'s cello duets, quartet, and sextet, Pärt\'s Fratres for eight cellos and Boulez\' *Messagesquisse* for seven cellos, or even Villa-Lobos\' rarely played *Fantasia Concertante* (1958) for 32 cellos. The 12 cellists of the Berlin Philharmonic Orchestra (or \"the Twelve\" as they have since taken to being called) specialize in this repertoire and have commissioned many works, including arrangements of well-known popular songs.
### Popular music, jazz, world music and neoclassical {#popular_music_jazz_world_music_and_neoclassical}
The cello is less common in popular music than in classical music. Several bands feature a cello in their standard line-up, including Hoppy Jones of the Ink Spots and Joe Kwon of the Avett Brothers. The more common use in pop and rock is to bring the instrument in for a particular song. In the 1960s, artists such as the Beatles and Cher used the cello in popular music, in songs such as The Beatles\' \"Yesterday\", \"Eleanor Rigby\" and \"Strawberry Fields Forever\", and Cher\'s \"Bang Bang (My Baby Shot Me Down)\". \"Good Vibrations\" by the Beach Boys includes the cello in its instrumental ensemble, which includes a number of instruments unusual for this sort of music. Bass guitarist Jack Bruce, who had originally studied music on a performance scholarship for cello, played a prominent cello part in \"As You Said\" on Cream\'s *Wheels of Fire* studio album (1968).
In the 1970s, the Electric Light Orchestra enjoyed great commercial success taking inspiration from so-called \"Beatlesque\" arrangements, adding the cello (and violin) to the standard rock combo line-up and in 1978 the UK-based rock band Colosseum II collaborated with cellist Julian Lloyd Webber on the recording *Variations*. Most notably, Pink Floyd included a cello solo in their 1970 epic instrumental \"Atom Heart Mother\". Bass guitarist Mike Rutherford of Genesis was originally a cellist and included some cello parts in their *Foxtrot* album.
Established non-traditional cello groups include Apocalyptica, a group of Finnish cellists best known for their versions of Metallica songs; Rasputina, a group of cellists committed to an intricate cello style intermingled with Gothic music; the Massive Violins, an ensemble of seven singing cellists known for their arrangements of rock, pop and classical hits; Von Cello, a cello-fronted rock power trio; Break of Reality, who mix elements of classical music with the more modern rock and metal genre; Cello Fury, a cello rock band that performs original rock/classical crossover music; and Jelloslave, a Minneapolis-based cello duo with two percussionists. These groups are examples of a style that has become known as cello rock. The crossover string quartet Bond also includes a cellist. Silenzium and Cellissimo Quartet are Russian (Novosibirsk) groups playing rock and metal and having more and more popularity in Siberia. Cold Fairyland from Shanghai, China is using a cello along with a pipa as the main solo instrument to create East meets West progressive (folk) rock.
More recent bands who have used the cello include Clean Bandit, Aerosmith, The Auteurs, Nirvana, Oasis, Ra Ra Riot, Smashing Pumpkins, James, Talk Talk, Phillip Phillips, OneRepublic, Electric Light Orchestra and the baroque rock band Arcade Fire. An Atlanta-based trio, King Richard\'s Sunday Best, also uses a cellist in their lineup. So-called \"chamber pop\" artists like Kronos Quartet, The Vitamin String Quartet and Margot and the Nuclear So and So\'s have also recently made cello common in modern alternative rock. Heavy metal band System of a Down has also made use of the cello\'s rich sound. The indie rock band The Stiletto Formal are known for using a cello as a major staple of their sound; similarly, the indie rock band Canada employs two cello players in their lineup. The orch-rock group The Polyphonic Spree, which has pioneered the use of stringed and symphonic instruments, employs the cello in creative ways for many of their \"psychedelic-esque\" melodies. The first-wave screamo band I Would Set Myself On Fire For You featured a cello as well as a viola to create a more folk-oriented sound. The band Panic! at the Disco uses a cello in their song \"Build God, Then We\'ll Talk\", with lead vocalist Brendon Urie recording the cello solo himself. The Lumineers added cellist Nela Pekarek to the band in 2010. Radiohead makes frequent use of cello in their music, notably for the songs \"Burn The Witch\" and \"Glass Eyes\" in 2016.
In jazz, bassists Oscar Pettiford and Harry Babasin were among the first to use the cello as a solo instrument; both tuned their instruments in fourths, an octave above the double bass. Fred Katz (who was not a bassist) was one of the first notable jazz cellists to use the instrument\'s standard tuning and arco technique. Contemporary jazz cellists include Abdul Wadud, Diedre Murray, Ron Carter, Dave Holland, David Darling, Lucio Amanti, Akua Dixon, Ernst Reijseger, Fred Lonberg-Holm, Tom Cora and Erik Friedlander. Modern musical theatre pieces like Jason Robert Brown\'s *The Last Five Years*, Duncan Sheik\'s *Spring Awakening*, Adam Guettel\'s *Floyd Collins*, and Ricky Ian Gordon\'s *My Life with Albertine* use small string ensembles (including solo cellos) to a prominent extent.
In Indian classical music, Saskia Rao-de Haas is a well-established soloist as well as playing duets with her sitarist husband, Pt. Shubhendra Rao. Other cellists performing Indian classical music are Nancy Lesh (Dhrupad) and Anup Biswas. Both Rao and Lesh play the cello sitting cross-legged on the floor.
The cello can also be used in bluegrass and folk music, with notable players including Ben Sollee of the Sparrow Quartet and the \"Cajun cellist\" Sean Grissom, as well as Vyvienne Long, who, in addition to her own projects, has played for those of Damien Rice. Cellists such as Natalie Haas, Abby Newton, and Liz Davis Maxfield have contributed significantly to the use of cello playing in Celtic folk music, often with the cello featured as a primary melodic instrument and employing the skills and techniques of traditional fiddle playing. Lindsay Mac is becoming well known for playing the cello like a guitar, with her cover of The Beatles\' \"Blackbird\".
Canadian electronic music producer Aaron Funk (Venetian Snares), in the piece Szamár Madár (on his 2005 album Rossz Csillag Alatt Született), extensively samples Edward Elgar\'s Cello Concerto in E minor, Op. 85.
## Construction
The cello is typically made from carved wood, although other materials such as carbon fiber or aluminum may be used. A traditional cello has a spruce top, with maple for the back, sides, and neck. Other woods, such as poplar or willow, are sometimes used for the back and sides. Less expensive cellos frequently have tops and backs made of laminated wood. Laminated cellos are widely used in elementary and secondary school orchestras and youth orchestras, because they are much more durable than carved wood cellos (i.e., they are less likely to crack if bumped or dropped) and they are much less expensive.
The top and back are traditionally hand-carved, though less expensive cellos are often machine-produced. The sides, or ribs, are made by heating the wood and bending it around forms. The cello body has a wide top bout, narrow middle formed by two C-bouts, and wide bottom bout, with the bridge and F holes just below the middle. The top and back of the cello have a decorative border inlay known as purfling. While purfling is attractive, it is also functional: if the instrument is struck, the purfling can prevent cracking of the wood. A crack may form at the rim of the instrument but spreads no further. Without purfling, cracks can spread up or down the top or back. Playing, traveling and the weather all affect the cello and can increase a crack if purfling is not in place.
The fingerboard and pegs on a cello are generally made from ebony, as it is strong and does not wear out easily.
### Alternative materials {#alternative_materials}
In the late 1920s and early 1930s, the Aluminum Company of America (Alcoa) as well as German luthier G.A. Pfretzschner produced an unknown number of aluminum cellos (in addition to aluminum double basses and violins). Cello manufacturer Luis & Clark constructs cellos from carbon fibre. Carbon fibre instruments are particularly suitable for outdoor playing because of the strength of the material and its resistance to humidity and temperature fluctuations. Luis & Clark has produced over 1000 cellos, some of which are owned by cellists such as Yo-Yo Ma and Josephine van Lier.
### Neck, fingerboard, pegbox, and scroll {#neck_fingerboard_pegbox_and_scroll}
Above the main body is the carved neck. The neck has a curved cross-section on its underside, which is where the player\'s thumb runs along the neck during playing. The neck leads to a pegbox and the scroll, which are all normally carved out of a single piece of wood, usually maple. The fingerboard is glued to the neck and extends over the body of the instrument. The fingerboard is given a curved shape, matching the curve on the bridge. Both the fingerboard and bridge need to be curved so that the performer can bow individual strings. If the cello were to have a flat fingerboard and bridge, as with a typical guitar, the performer would only be able to bow the leftmost and rightmost two strings or bow all the strings. The performer would not be able to play the inner two strings alone.
The nut is a raised piece of wood, fitted where the fingerboard meets the pegbox, in which the strings rest in shallow slots or grooves to keep them the correct distance apart. The pegbox houses four tapered tuning pegs, one for each string. The pegs are used to tune the cello by either tightening or loosening the string. The pegs are called \"friction pegs\", because they maintain their position by friction. The scroll is a traditional ornamental part of the cello and a feature of all other members of the violin family. Ebony is usually used for the tuning pegs, fingerboard, and nut, but other hardwoods, such as boxwood or rosewood, can be used. Black fittings on low-cost instruments are often made from inexpensive wood that has been blackened or \"ebonized\" to look like ebony, which is much harder and more expensive. Ebonized parts such as tuning pegs may crack or split, and the black surface of the fingerboard will eventually wear down to reveal the lighter wood underneath.
### Strings
Historically, cello strings had cores made out of catgut, which, despite its name, is made from sheep or goat intestines. Most modern strings used in the 2010s are wound with metallic materials like aluminum, titanium and chromium. Cellists may mix different types of strings on their instruments. The pitches of the open strings are C, G, D, and A (black note heads in the playing range figure above), unless alternative tuning (scordatura) is specified by the composer. Some composers (e.g. Ottorino Respighi in the final movement of *The Pines of Rome*) ask that the low C be tuned down to a B-flat so that the performer can play a different low note on the lowest open string.
### Tailpiece and endpin {#tailpiece_and_endpin}
The tailpiece and endpin are found in the lower part of the cello. The tailpiece is the part of the cello to which the \"ball ends\" of the strings are attached by passing them through holes. The tailpiece is attached to the bottom of the cello. The tailpiece is traditionally made of ebony or another hardwood, but can also be made of plastic or steel on lower-cost instruments. It attaches the strings to the lower end of the cello and can have one or more fine tuners. The fine tuners are used to make smaller adjustments to the pitch of the string. The fine tuners can increase the tension of each string (raising the pitch) or decrease the tension of the string (lowering the pitch). When the performer is putting on a new string, the fine tuner for that string is normally reset to a middle position, and then the peg is turned to bring the string up to pitch. The fine turners are used for subtle, minor adjustments to pitch, such as tuning a cello to the oboe\'s 440 Hz A note or tuning the cello to a piano.
The endpin or spike is made of wood, metal, or rigid carbon fiber and supports the cello in playing position. The endpin can be retracted into the hollow body of the instrument when the cello is being transported in its case. This makes the cello easier to move about. When the performer wishes to play the cello, the endpin is pulled out to lengthen it. The endpin is locked into the player\'s preferred length with a screw mechanism. The adjustable nature of endpins enables performers of different ages and body sizes to adjust the endpin length to suit them. In the Baroque period, the cello was held between the calves, as there was no endpin at that time. The endpin was \"introduced by Adrien Servais c. 1845 to give the instrument greater stability\". Modern endpins are retractable and adjustable; older ones were removed when not in use. (The word \"endpin\" sometimes also refers to the button of wood located at this place in all instruments in the violin family, but this is usually called \"tailpin\".) The sharp tip of the cello\'s endpin is sometimes capped with a rubber tip that protects the tip from dulling and prevents the cello from slipping on the floor. Many cellists use a rubber pad with a metal cup to keep the tip from slipping on the floor. A number of accessories exist to keep the endpin from slipping; these include ropes that attach to the chair leg and other devices.
### Bridge and f-holes {#bridge_and_f_holes}
The bridge holds the strings above the cello and transfers their vibrations to the top of the instrument and the soundpost inside (see below). The bridge is not glued but rather held in place by the tension of the strings. The bridge is usually positioned by the cross point of the \"f-hole\" (i.e., where the horizontal line occurs in the \"f\"). The f-holes, named for their shape, are located on either side of the bridge and allow air to move in and out of the instrument as part of the sound-production process. The f-holes also act as access points to the interior of the cello for repairs or maintenance. Sometimes a small length of rubber hose containing a water-soaked sponge, called a Dampit, is inserted through the f-holes and serves as a humidifier. This keeps the wood components of the cello from drying out.
### Internal features {#internal_features}
Internally, the cello has two important features: a bass bar, which is glued to the underside of the top of the instrument, and a round wooden sound post, a solid wooden cylinder which is wedged between the top and bottom plates. The bass bar, found under the bass foot of the bridge, serves to support the cello\'s top and distribute the vibrations from the strings to the body of the instrument. The soundpost, found under the treble side of the bridge, connects the back and front of the cello. Like the bridge, the soundpost is not glued but is kept in place by the tensions of the bridge and strings. Together, the bass bar and sound post transfer the strings\' vibrations to the top (front) of the instrument (and to a lesser extent the back), acting as a diaphragm to produce the instrument\'s sound.
### Glue
Cellos are constructed and repaired using hide glue, which is strong but reversible, allowing for disassembly when needed. Tops may be glued on with diluted glue since some repairs call for the removal of the top. Theoretically, hide glue is weaker than the body\'s wood, so as the top or back shrinks side-to-side, the glue holding it lets go and the plate does not crack. Cellists repairing cracks in their cello do not use regular wood glue, because it cannot be steamed open when a repair has to be made by a luthier.
### Bow
thumb\|right\|upright=0.7\|A cello French bow *sul ponticello* Traditionally, bows are made from pernambuco or brazilwood. Both come from the same species of tree (*Caesalpinia echinata*), but Pernambuco, used for higher-quality bows, is the heartwood of the tree and is darker in color than brazilwood (which is sometimes stained to compensate). Pernambuco is a heavy, resinous wood with great elasticity, which makes it an ideal wood for instrument bows. Horsehair is stretched out between the two ends of the bow. The taut horsehair is drawn over the strings, while being held roughly parallel to the bridge and perpendicular to the strings, to produce sound. A small knob is twisted to increase or decrease the tension of the horsehair. The tension on the bow is released when the instrument is not being used. The amount of tension a cellist puts on the bow hair depends on the preferences of the player, the style of music being played, and for students, the preferences of their teacher.
Bows are also made from other materials, such as carbon fibre---stronger than wood---and fiberglass (often used to make inexpensive, lower-quality student bows). An average cello bow is 73 cm long (shorter than a violin or viola bow) 3 cm high (from the frog to the stick) and 1.5 cm wide. The frog of a cello bow typically has a rounded corner like that of a viola bow, but is wider. A cello bow is roughly 10 g heavier than a viola bow, which in turn is roughly 10 g heavier than a violin bow.
Bow hair is traditionally horsehair, though synthetic hair, in varying colors, is also used. Prior to playing, the musician tightens the bow by turning a screw to pull the frog (the part of the bow under the hand) back and increase the tension of the hair. Rosin is applied by the player to make the hair sticky. Bows need to be re-haired periodically. Baroque-style (1600--1750) cello bows were much thicker and were formed with a larger outward arch than modern cello bows. The inward arch of a modern cello bow produces greater tension, which in turn produces a louder sound.
The cello bow has also been used to play electric guitars. Jimmy Page pioneered its application on tracks such as \"Dazed and Confused\". The post-rock Icelandic band Sigur Rós\'s lead singer often plays guitar using a cello bow.
In 1989, the German cellist Michael Bach began developing a curved bow, encouraged by John Cage, Dieter Schnebel, Mstislav Rostropovich and Luigi Colani: and since then many pieces have been composed especially for it. This curved bow (*BACH.Bow*) is a convex curved bow which, unlike the ordinary bow, renders possible polyphonic playing on the various strings of the instrument. The BACH.Bow is particularly well-suited to the solo repertoire for violin and cello by J. S. Bach; which requires both polyphonic and monophonic playing.
## Physics
### Physical aspects {#physical_aspects}
When a string is bowed or plucked, it vibrates and moves the air around it, producing sound waves. Because the string is quite thin, not much air is moved by the string itself, and consequently, if the string was not mounted on a hollow body, the sound would be weak. In acoustic stringed instruments such as the cello, this lack of volume is solved by mounting the vibrating string on a larger hollow wooden body. The vibrations are transmitted to the larger body, which can move more air and produce a louder sound. Different designs of the instrument produce variations in the instrument\'s vibrational patterns and thus change the character of the sound produced. A string\'s fundamental pitch can be adjusted by changing its stiffness, which depends on tension and length. Tightening a string stiffens it by increasing both the outward forces along its length and the net forces it experiences during a distortion. A cello can be tuned by adjusting the tension of its strings, by turning the tuning pegs mounted on its pegbox and tension adjusters (fine tuners) on the tailpiece.
A string\'s length also affects its fundamental pitch. Shortening a string stiffens it by increasing its curvature during a distortion and subjecting it to larger net forces. Shortening the string also reduces its mass, but does not alter the mass per unit length, and it is the latter ratio rather than the total mass which governs the frequency. The string vibrates in a standing wave whose speed of propagation is given by $\sqrt{\frac{T}{m}}$, where `{{mvar|T}}`{=mediawiki} is the tension and `{{mvar|m}}`{=mediawiki} is the mass per unit length; there is a node at either end of the vibrating length, and thus the vibrating length `{{mvar|l}}`{=mediawiki} is half a wavelength. Since the frequency of any wave is equal to the speed divided by the wavelength, we have $\mathrm{frequency} = \frac{1}{2l} \cdot \sqrt{\frac{T}{m}}$. (Some writers, including Muncaster (cited below), use the Greek letter `{{mvar|μ}}`{=mediawiki} in place of `{{mvar|m}}`{=mediawiki}.) Thus shortening a string increases the frequency, and thus the pitch. Because of this effect, you can raise and change the pitch of a string by pressing it against the fingerboard in the cello\'s neck and effectively shortening it. Likewise strings with less mass per unit length, if under the same tension, will have a higher frequency and thus higher pitch than more massive strings. This is a prime reason the different strings on all string instruments have different fundamental pitches, with the lightest strings having the highest pitches.
thumb\|upright=0.45\|Spectrogram of a D chord arpeggiated on the cello. Yellow bands at the same level indicate the same harmonics excited by the bowing of different notes. Notes played from left to right: D--F`{{music|#}}`{=mediawiki}--A--F`{{music|#}}`{=mediawiki}--D.
A played note of E or F`{{sharp}}`{=mediawiki} has a frequency that is often very close to the natural resonating frequency of the body of the instrument, and if the problem is not addressed this can set the body into near resonance. This may cause an unpleasant sudden amplification of this pitch, and additionally a loud beating sound results from the interference produced between these nearby frequencies; this is known as the \"wolf tone\" because it is an unpleasant growling sound. The wood resonance appears to be split into two frequencies by the driving force of the sounding string. These two periodic resonances beat with each other. This wolf tone must be eliminated or significantly reduced for the cello to play the nearby notes with a pleasant tone. This can be accomplished by modifying the cello front plate, attaching a wolf eliminator (a metal cylinder or a rubber cylinder encased in metal), or moving the soundpost.
When a string is bowed or plucked to produce a note, the fundamental note is accompanied by higher frequency overtones. Each sound has a particular recipe of frequencies that combine to make the total sound.
## Playing technique {#playing_technique}
Playing the cello is done while seated with the instrument supported on the floor by the endpin. The right hand bows (or sometimes plucks) the strings to sound the notes. The left-hand fingertips stop the strings along their length, determining the pitch of each fingered note. Stopping the string closer to the bridge results in a higher-pitched sound because the vibrating string length has been shortened. On the contrary, a string stopped closer to the tuning pegs produces a lower sound. In the *neck* positions (which use just less than half of the fingerboard, nearest the top of the instrument), the thumb rests on the back of the neck, some people use their thumb as a marker of their position; in *thumb position* (a general name for notes on the remainder of the fingerboard) the thumb usually rests alongside the fingers on the string. Then, the side of the thumb is used to play notes. The fingers are normally held curved with each knuckle bent, with the fingertips in contact with the string. If a finger is required on two (or more) strings at once to play perfect fifths (in double stops or chords), it is used flat. The contact point can move slightly away from the nail to the finger\'s pad in slower or more expressive playing, allowing a fuller vibrato.
Vibrato is a small oscillation in the pitch of a note, usually considered an expressive technique. The closer towards the bridge the note is, the smaller the oscillation needed to create the effect. Harmonics played on the cello fall into two classes; natural and artificial. Natural harmonics are produced by lightly touching (but not depressing) the string at certain places and then bowing (or, rarely, plucking) the string. For example, the halfway point of the string will produce a harmonic that is one octave above the unfingered (open) string. Natural harmonics only produce notes that are part of the harmonic series on a particular string. Artificial harmonics (also called false harmonics or stopped harmonics), in which the player depresses the string fully with one finger while touching the same string lightly with another finger, can produce any note above middle C. Glissando (Italian for \"sliding\") is an effect achieved by sliding the finger up or down the fingerboard without releasing the string. This causes the pitch to rise and fall smoothly, without separate, discernible steps.
In cello playing, the bow is much like the breath of a wind instrument player. Arguably, it is a major factor in the expressiveness of the playing. The right hand holds the bow and controls the duration and character of the notes. In general, the bow is drawn across the strings roughly halfway between the end of the fingerboard and the bridge, in a direction perpendicular to the strings; however, the player may wish to move the bow\'s point of contact higher or lower depending on the desired sound. The bow is held and manipulated with all five fingers of the right hand, with the thumb opposite the fingers and closer to the cellist\'s body. Tone production and volume of sound depend on a combination of several factors. The four most important ones are *weight* applied to the string, the *angle* of the bow on the string, bow *speed*, and the *point of contact* of the bow hair with the string (sometimes abbreviated WASP).
Double stops involve the playing of two notes simultaneously. Two strings are fingered at once, and the bow is drawn to sound them both. Often, in pizzicato playing, the string is plucked directly with the fingers or thumb of the right hand. However, the strings may be plucked with a finger of the left hand in certain advanced pieces, either so that the cellist can play bowed notes on another string along with pizzicato notes or because the speed of the piece would not allow the player sufficient time to pluck with the right hand. In musical notation, pizzicato is often abbreviated as \"pizz.\" The position of the hand in pizzicato is commonly slightly over the fingerboard and away from the bridge.
A player using the col legno technique strikes or rubs the strings with the wood of the bow rather than the hair. In spiccato playing, the bow still moves in a horizontal motion on the string but is allowed to bounce, generating a lighter, somewhat more percussive sound. In staccato, the player moves the bow a small distance and stops it on the string, making a short sound, the rest of the written duration being taken up by silence. Legato is a technique in which notes are smoothly connected without breaks. It is indicated by a slur (curved line) above or below -- depending on their position on the staff -- the notes of the passage that is to be played legato.
*Sul ponticello* (\"on the bridge\") refers to bowing closer to (or nearly on) the bridge, while *sul tasto* (\"on the fingerboard\") calls for bowing nearer to (or over) the end of the fingerboard. At its extreme, sul ponticello produces a harsh, shrill sound with emphasis on overtones and high harmonics. In contrast, sul tasto produces a more flute-like sound that emphasizes the note\'s fundamental frequency and produces softened overtones. Composers have used both techniques, particularly in an orchestral setting, for special sounds and effects.
## Sizes
Standard-sized cellos are referred to as \"full-size\" or \"`{{frac|4|4}}`{=mediawiki}\" but are also made in smaller (fractional) sizes, including `{{frac|15|16}}`{=mediawiki}, `{{frac|7|8}}`{=mediawiki}, `{{frac|3|4}}`{=mediawiki}, `{{frac|1|2}}`{=mediawiki}, `{{frac|1|4}}`{=mediawiki}, `{{frac|1|8}}`{=mediawiki}, `{{frac|1|10}}`{=mediawiki}, and `{{frac|1|16}}`{=mediawiki}. The fractions refer to volume rather than length, so a `{{frac|1|2}}`{=mediawiki} size cello is much longer than half the length of a full size. The smaller cellos are identical to standard cellos in construction, range, and usage, but are simply scaled-down for the benefit of children and shorter adults.
Cellos in sizes larger than `{{frac|4|4}}`{=mediawiki} do exist, and cellists with unusually large hands may require such a non-standard instrument. Cellos made before c. 1700 tended to be considerably larger than those made and commonly played today. Around 1680, changes in string-making technology made it possible to play lower-pitched notes on shorter strings. The cellos of Stradivari, for example, can be clearly divided into two models: the style made before 1702, characterized by larger instruments (of which only three exist in their original size and configuration), and the style made during and after 1707, when Stradivari began making smaller cellos. This later model is the design most commonly used by modern luthiers. The scale length of a `{{frac|4|4}}`{=mediawiki} cello is about 27+1/2 in. The new size offered fuller tonal projection and a greater range of expression. The instrument in this form was able to contribute to more pieces musically and offered the possibility of greater physical dexterity for the player to develop technique.
Approximate dimensions for `{{frac|4|4}}`{=mediawiki} size cello{{cite web url=<http://www.stevensoncases.co.uk/chart.htm> title=Table of \'cello measurements access-date=2007-10-26 last=Stevenson archive-url = <https://web.archive.org/web/20080104141444/http://www.stevensoncases.co.uk/chart.htm> \|archive-date = 2008-01-04}} Average size
---------------------------------------------------------------------------- ------------------------------------------------- ------------------------------------- ------------------------ ---------------- ------------------------------------------------------------------------------------------------------------------------------------ --------------
Approximate width horizontally from A peg to C peg ends
Back length excluding half-round where neck joins
Upper bouts (shoulders)
Lower bouts (hips)
Bridge height
Rib depth at shoulders including edges of front and back
Rib depth at hips including edges
Distance beneath fingerboard to surface of belly at neck join
Bridge to back total depth
Overall height excluding end pin
End pin unit and spike
## Accessories
thumb\|right\|upright=0.9\|Rosin is applied to bow hair to increase the friction of the bow on the strings. thumb\|upright=0.7\|A brass wolf tone eliminator typically placed on the G string (second string from the left) of a cello, between the bridge and the tailpiece. (The black rubber piece on the D string (third from the left) is a mute.)
There are many accessories for the cello.
- Cases are used to protect the cello and bow (or multiple bows).
- Rosin, made from resins tapped from conifers, is applied to the bow hair to increase the effectiveness of the friction, grip or bite, and allow proper sound production. Rosin may have additives to modify the friction such as beeswax, gold, silver or tin. Commonly, rosins are classified as either dark or light, referring to color.
- Endpin stops or straps (tradenames include Rock stop and Black Hole) keep the cello from sliding if the endpin does not have a rubber piece on the end, or if a floor is particularly slippery.
- Wolf tone eliminators are placed on cello strings between the tailpiece and the bridge to eliminate acoustic anomalies known as wolf tones or \"wolfs\".
- Mutes are used to change the sound of the cello by adding mass and stiffness to the bridge. They alter the overtone structure, modifying the timbre and reducing the overall volume of sound produced by the instrument.
- Metronomes provide a steady tempo by sounding out a certain number of beats per minute. This tool is often used to instill a sense of rhythm into a musician. It acts as a mirror for rhythmic stability, allowing the musician to analyze where they rush or drag a tempo.
- Fine tuners, located on the tailpiece, allow the cello to be tuned easily and with greater accuracy.
## Instrument makers {#instrument_makers}
Cellos are made by luthiers, specialists in building and repairing stringed instruments, ranging from guitars to violins. The following luthiers are notable for the cellos they have produced:
- Nicolò Amati and others in the Amati family
- Nicolò Gagliano
- Matteo Goffriller
- Giovanni Battista Guadagnini
- Andrea Guarneri
- Pietro Guarneri
- Charles Mennégand
- Domenico Montagnana
- Giovanni Battista Rogeri
- Francesco Ruggieri
- Stefano Scarampella
- Antonio Stradivari
- David Tecchler
- Carlo Giuseppe Testore
- Jean Baptiste Vuillaume
## Cellists
A person who plays the cello is called a *cellist*. For a list of notable cellists, see the list of cellists and :Category:Cellists.
## Famous instruments {#famous_instruments}
right\|thumbnail\|upright=0.7\|The Servais Stradivarius is preserved in the Smithsonian Institution\'s National Museum of American History
Specific instruments are famous (or become famous) for a variety of reasons. An instrument\'s notability may arise from its age, the fame of its maker, its physical appearance, its acoustic properties, and its use by notable performers. The most famous instruments are generally known for all of these things. The most highly prized instruments are now collector\'s items and are priced beyond the reach of most musicians. These instruments are typically owned by some kind of organization or investment group, which may loan the instrument to a notable performer. For example, the Davidov Stradivarius, which is currently in the possession of one of the most widely known living cellists, Yo-Yo Ma, is actually owned by the Vuitton Foundation.
Some notable cellos:
- the \"King\", by Andrea Amati, is one of the oldest known cellos, built between 1538 and 1560---it is in the collection of the National Music Museum in South Dakota.
- Servais Stradivarius is in the collection of the Smithsonian Institution, Washington DC.
- Batta-Piatigorsky Stradivarius, played by Gregor Piatigorsky.
- Davidov Stradivarius, played by Jacqueline du Pré, currently played by Yo-Yo Ma.
- Barjansky Stradivarius, played by Julian Lloyd Webber.
- Bonjour Stradivarius, played by Soo Bae.
- Paganini-Ladenburg Stradivarius, played by Clive Greensmith of the Tokyo String Quartet.
- Duport Stradivarius, formerly played by Mstislav Rostropovich.
- Piatti Stradivarius, 1720, played by Carlos Prieto
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Conditional proof
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A **conditional proof** is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.
## Overview
The assumed antecedent of a conditional proof is called the **conditional proof assumption** (**CPA**). Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows. The validity of a conditional proof does not require that the CPA be true, only that *if it were true* it would lead to the consequent.
Conditional proofs are of great importance in mathematics. Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others. It can be much easier to show a proposition\'s truth to follow from another proposition than to prove it independently.
A famous network of conditional proofs is the NP-complete class of complexity theory. There is a large number of interesting tasks (see *List of NP-complete problems*), and while it is not known if a polynomial-time solution exists for any of them, it is known that if such a solution exists for some of them, one exists for all of them. Similarly, the Riemann hypothesis has many consequences already proven.
## Symbolic logic {#symbolic_logic}
As an example of a conditional proof in symbolic logic, suppose we want to prove A → C (if A, then C) from the first two premises below:
----- ---------- -----------------------------------------------------------------------------
1\. A → B (\"If A, then B\")
2\. B → C (\"If B, then C\")
3\. A (conditional proof assumption, \"Suppose A is true\")
4\. B (follows from lines 1 and 3, modus ponens; \"If A then B; A, therefore B\")
5\. C (follows from lines 2 and 4, modus ponens; \"If B then C; B, therefore C\")
6\. A → C (follows from lines 3--5, conditional proof; \"If A, then C\")
----- ---------- -----------------------------------------------------------------------------
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Conjunction introduction
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**Conjunction introduction** (often abbreviated simply as **conjunction** and also called **and introduction** or **adjunction**) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition $P$ is true, and the proposition $Q$ is true, then the logical conjunction of the two propositions $P$ and $Q$ is true. For example, if it is true that \"it is raining\", and it is true that \"the cat is inside\", then it is true that \"it is raining and the cat is inside\". The rule can be stated:
$$\frac{P,Q}{\therefore P \land Q}$$
where the rule is that wherever an instance of \"$P$\" and \"$Q$\" appear on lines of a proof, a \"$P \land Q$\" can be placed on a subsequent line.
## Formal notation {#formal_notation}
The *conjunction introduction* rule may be written in sequent notation:
: $P, Q \vdash P \land Q$
where $P$ and $Q$ are propositions expressed in some formal system, and $\vdash$ is a metalogical symbol meaning that $P \land Q$ is a syntactic consequence if $P$ and $Q$ are each on lines of a proof in some logical system;
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English in the Commonwealth of Nations
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The use of the English language in current and former countries of the Commonwealth was largely inherited from British colonisation, with some exceptions. English forms part of the Commonwealth\'s common culture and serves as the medium of inter-Commonwealth relations.
***Commonwealth English*** refers to English as practised in the Commonwealth; the term is most often interchangeable with *British English*, but is also used to distinguish between British English and that in the rest of the Commonwealth. English in the Commonwealth is diverse, and many regions have developed their own local varieties of the language. The official status of English varies; in Bangladesh, it lacks any but is widely used, and likewise in Cyprus, it is not official but is used as the *\[\[lingua franca\]\]*.
Written English in current and former Commonwealth countries generally favours British English spelling as opposed to that of American English, with some exceptions, particularly in Canada, where there are strong influences from neighbouring American English.
## Native varieties {#native_varieties}
Southern Hemisphere native varieties of English began to develop during the 18th century, with the colonisation of Australasia and South Africa. Australian English and New Zealand English are closely related to each other and share some similarities with South African English. Nonetheless, South African English has unique influences from indigenous African languages, and Dutch influences inherited alongside the evolution of Afrikaans, while New Zealand English has a lot of influences from the Māori language.
Canadian English contains elements of British English and American English, as well as many Canadianisms and some French influences. It is the product of several waves of immigration and settlement, from Britain, Ireland, France, the United States, and around the world, over a period of more than two centuries. In many Commonwealth countries, there exists a relatively small native Anglophone minority amongst a larger population who speak English as a second language; Anglo-Indians speak English as their mother tongue, but it is not the first language of most Indians.
### Africa
In addition to South Africa, a number of Commonwealth countries in Africa have native varieties of English. A community of native English speakers exists in Zimbabwe; the country\'s dialect bears features of British English, South African English and other Southern Hemisphere varieties of Commonwealth English. Also in Southern Africa and with historical influence from South Africa, Namibia and Botswana have their own dialects, with smaller native English-speaking populations. The same is true of Kenya and Uganda in East Africa.
### Caribbean
Caribbean English is drawn from British English and West African languages. It is influenced by constant contact with English-based Creoles. There is considerable influence from Hindustani and other South Asian languages in countries with language Indian populations, including Trinidad and Tobago, and Guyana. Jamaican English and Barbadian English bear influences of Irish English.
## Non-native varieties {#non_native_varieties}
Second-language varieties of English in Africa and Asia have often undergone \"indigenisation\"; that is, each English-speaking community has developed (or is in the process of developing) its own standards of usage, often under the influence of local languages. These dialects are sometimes referred to as *New Englishes* (McArthur, p. 36); most of them inherited non-rhoticity from Southern British English.
### Africa {#africa_1}
Several dialects of West African English exist, with considerable regional variation, though there is a set of common tendencies of pronunciation. Nigerian and Ghanaian English are the varieties with the largest number of speakers; English also holds official or national status in Sierra Leone, Cameroon's Anglophone provinces, the Gambia, and Saint Helena, a British territory. It also holds official status in Liberia, which is not a Commonwealth country but rather has a history connected to the United States of America.
National varieties of English are also spoken in Kenya, Uganda, and Tanzania.
Prior to Togo\'s admission at the 2022 Commonwealth Heads of Government Meeting, Togolese Foreign Minister Robert Dussey said that he expected Commonwealth membership to provide opportunities for Togolese citizens to learn English, and remarked that the country sought closer ties with the Anglophone world.
### Asia
#### Hong Kong {#hong_kong}
Hong Kong ceased to be part of the Commonwealth by virtue of being a British territory in 1997. Nonetheless, the English language there still enjoys official status.
#### Indian subcontinent {#indian_subcontinent}
English was introduced to the subcontinent by the British Raj. India has the largest English-speaking population in the Commonwealth, although comparatively very few speakers of Indian English are first-language speakers. The same is true of English spoken in other parts of South Asia, including Pakistani English, Sri Lankan English, Bangladeshi English and Myanmar English; though Myanmar is not a Commonwealth country, English is the mother tongue of the Anglo-Burmese population. South Asian English is fairly homogeneous across the subcontinent, though there are some differences based on various regional factors.
#### Malay Archipelago {#malay_archipelago}
Southeast Asian English includes Singapore English, Malaysian English, and Brunei English as well as other varieties in non-Commonwealth countries; it is not only the result of British colonisation but also American colonisation (as in the case of the Philippines) and globalisation. It has interacted with diverse local ecologies, shaping its form, function and status in the region.
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Charles McCarry
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**Charles McCarry** (June 14, 1930 -- February 26, 2019) was an American writer, primarily of spy fiction, and a former undercover operative for the Central Intelligence Agency.
## Biography
McCarry\'s family came from The Berkshires area of western Massachusetts. He was born in Pittsfield, and lived in Virginia. He graduated from Dalton High School.
McCarry began his writing career in the United States Army as a correspondent for *Stars and Stripes*. He served from 1948 to 1951 and achieved the rank of sergeant. He received initial training at Fort Benning, Georgia, and was stationed in Germany for almost two years and at Camp Pickett, Virginia for about a year.
After his army service, he was a speechwriter in the early Administration of President Dwight D. Eisenhower. In 1958, at the invitation of Cord Meyer, he accepted a post with the CIA, for whom he traveled the globe as a deep cover operative. He took a leave of absence to work for the 1960 Nixon campaign, writing for vice-presidential candidate Henry Cabot Lodge. He left the CIA for the last time in 1967, becoming a writer of spy novels.
McCarry was also an editor-at-large for *National Geographic* and contributed pieces to *The New York Times*, *The Wall Street Journal*, *The Washington Post*, the *Saturday Evening Post*, and other national publications.
## Approach to writing {#approach_to_writing}
McCarry believed that \"the best novels are about ordinary things: love, betrayal, death, trust, loneliness, marriage, fatherhood.\" In 1988 McCarry described the themes of his novels to date as \"ordinary things -- love, death, betrayal and the American dream.\"
McCarry wrote that: \"After I resigned \[from the CIA\], intending to spend the rest of my life writing fiction and knowing what tricks the mind can play when the gates are thrown wide open, as they are by the act of writing, between the imagination and that part of the brain in which information is stored, I took the precaution of writing a closely remembered narrative of my clandestine experiences. After correcting the manuscript, I burned it. What I kept for my own use was the atmosphere of secret life: How it worked on the five senses and what it did to the heart and mind. All the rest went up in flames, setting me free henceforth to make it all up. In all important matters, such as the creation of characters and the invention of plots, with rare and minor exceptions, that is what I have done. And, as might be expected, when I have been weak enough to use something that really happened as an episode in a novel, it is that piece of scrap, buried in a landfill of the imaginary, readers invariably refuse to believe.\"
McCarry was an admirer of the work of Eric Ambler and W. Somerset Maugham, especially the latter\'s Ashenden stories. He was also an admirer of Richard Condon, author of *The Manchurian Candidate* (1959).
## Paul Christopher series {#paul_christopher_series}
Ten of McCarry\'s novels involve the life story of a fictional character named Paul Christopher, who grew up in pre-Nazi Germany, and later served in the Marines and became an operative for a U.S. government entity known as \"the Outfit\", meant to represent the Central Intelligence Agency.
These books are, in order of publication:
1. *The Miernik Dossier* (1973): Christopher investigates a possible Soviet spy in Geneva
2. *The Tears of Autumn* (1974): Christopher investigates the Kennedy Assassination
3. *The Secret Lovers* (1977): Christopher discovers a secret plot within the CIA
4. *The Better Angels* (1979): Christopher\'s cousins steal a Presidential election
5. *The Last Supper* (1983): introduction to Christopher\'s parents in pre-World War II Germany; Christopher is imprisoned in China
6. *The Bride of the Wilderness* (1988): historical novel concerning 17th-century Christopher ancestors
7. *Second Sight* (1991): released from a Chinese prison, Christopher meets a daughter he did not know he had
8. *Shelley\'s Heart* (1995): sequel to *The Better Angels*: Christopher\'s cousins cause a Presidential impeachment
9. *Old Boys* (2004): Christopher\'s old associates discover a plot involving terrorists and the fate of Christopher\'s mother
10. *Christopher\'s Ghosts* (2007): the story of Christopher\'s first love in pre-World War II Germany
Alternately, in chronological order of events depicted:
1. *Bride of the Wilderness* (Christopher\'s ancestors)
2. *Last Supper* \[in part\] (Christopher\'s parents)
3. *Christopher\'s Ghosts*
4. *The Miernik Dossier*
5. *Secret Lovers*
6. *The Tears of Autumn*
7. *Last Supper* \[in part\]
8. *The Better Angels*
9. *Second Sight* (Christopher is a peripheral character)
10. *Shelley\'s Heart*
11. *Old Boys* (Christopher is a peripheral character)
## Reception
*The Wall Street Journal* described McCarry in 2013 as \"the dean of American spy writers\". *The New Republic* magazine called him \"poet laureate of the CIA\"; and Otto Penzler described him as \"the greatest espionage writer that America has ever produced.\" Jonathan Yardley, Pulitzer Prize-winning critic for the *Washington Post*, calls him a \"\'serious\' novelist\" whose work may include \"the best novel ever written about life in high-stakes Washington, D.C.\" In 2004 P. J. O\'Rourke called him \"the best modern writer on the subject of intrigue.\"
## Adaptations
The film *Wrong is Right* (1982), starring Sean Connery, was loosely based on McCarry\'s novel, *The Better Angels* (1979).
## Other books and publications {#other_books_and_publications}
### Non-Paul Christopher novels {#non_paul_christopher_novels}
- *Lucky Bastard* (1999). A comic novel in which a likeable but amoral, devious, and oversexed politician (thought by many to evoke Bill Clinton, when in fact McCarry himself said he was thinking about John F Kennedy.) is controlled by a female eastern-bloc subversive.
- *Ark* (2011). Earth\'s wealthiest man attempts to save humanity from a coming apocalypse.
- *The Shanghai Factor* (2013). A rookie spy in China is drawn into the lonely, compartmentalized world of counterintelligence, and misunderstands everything that he and those around him are doing.
- *The Mulberry Bush* (2015). Explores the world of South America\'s elites and militant revolutionaries, and the role of lifelong personal passions and agendas in their work and that of intelligence operatives.
### Non-fiction {#non_fiction}
- *Citizen Nader* (1972)
- *Double Eagle: Ben Abruzzo, Maxie Anderson, Larry Newman* (1979)
- *The Great Southwest* (1980)
- *Isles of the Caribbean* (National Geographic Society, Washington, DC, 1980, co-author)
- *For the Record: From Wall Street to Washington* (1988, by Donald Regan with Charles McCarry)
- *Paths of Resistance: The Art and Craft of the Political Novel* (1989, with Isabel Allende, Marge Piercy, Robert Stone and Gore Vidal)
- *Inner Circles: How America Changed the World: a Memoir* (1992, by Alexander Haig with Charles McCarry)
- *Caveat: Realism, Reagan, and Foreign Policy* (1984, by Alexander Haig with Charles McCarry). Stories include: In March 1981, shortly after taking office, Ronald Reagan was shot; Secretary of State Haig appeared in the White House press room and announced, \"I am in charge here!\"
- *From the Field: A Collection of Writings from National Geographic* (1997, editor)
### Collections including McCarry\'s work {#collections_including_mccarrys_work}
- Harlan Coben, ed. *The Best American Mystery Stories: 2011* − includes \"The End of the String.\"
- Alan Furst, editor *The Book of Spies −* includes excerpt from *The Tears of Autumn*.
Otto Penzler, editor:
- *Agents of Treachery* − includes \"The End of the Sting.\"
- *The 50 Greatest Mysteries of All Time* − includes \"The Hand of Carlos\"
- *The Big Book of Espionage* − includes \"The Hand of Carlos\"
### Short stories (fiction) {#short_stories_fiction}
- \"The Saint Who Said No\", *Saturday Evening Post*, December 9, 1961
- \"The Hand of Carlos\", *Armchair Detective* (1992)
- \"The End of the String\"
### Magazine articles (non-fiction) {#magazine_articles_non_fiction}
- \"A \... Week on the Road With Ralph Nader\", *Life* magazine, January 21, 1972
- \"John Rennon's Excrusive Gloupie: On the load to briss with the Yoko nobody Onos\", *Esquire* magazine, December 1, 1970
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Cimbri
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The **Cimbri** (*Κίμβροι*, `{{translit|grc|Kímbroi}}`{=mediawiki}; *Cimbri*) were an ancient tribe in Europe. Ancient authors described them variously as a Celtic, Gaulish, Germanic, or even Cimmerian people. Several ancient sources indicate that they lived in Jutland, which in some classical texts was called the Cimbrian peninsula. There is no direct evidence for the language they spoke, though some scholars argue that it was a Germanic language, while others argue that it was Celtic.
Together with the Teutones and the Ambrones, they fought the Roman Republic between 113 and 101 BC during the Cimbrian War. The Cimbri were initially successful, particularly at the Battle of Arausio, in which a large Roman army was routed. They then raided large areas in Gaul and Hispania. In 101 BC, during an attempted invasion of the Italian peninsula, the Cimbri were decisively defeated at the Battle of Vercellae by Gaius Marius, and their king, Boiorix, was killed. Some of the surviving captives are reported to have been among the rebellious gladiators in the Third Servile War.
## Name
The origin of the name *Cimbri* is unknown. One etymology is *inhabitant*, from *tḱoi-m-* \"home\" (English *home*), itself a derivation from *tḱei-\]\]* \"live\" (*κτίζω*, *sinō*); then, the Germanic *\*himbra-* finds an exact cognate in Slavic *sębrъ* \"farmer\" (Croatian, Serbian *sebar*, Belarusian сябар *sjábar*).
The name has also been related to the word *kimme* meaning \"rim\", i.e., \"the people of the coast\". Finally, since Antiquity, the name has been related to that of the Cimmerians.
The name of the Danish region Himmerland (Old Danish *Himbersysel*) has been proposed to be a derivative of their name. According to such proposals, the word *Cimbri* with a *c* would be an older form before Grimm\'s law (PIE *k* \> Germanic *h*). Alternatively, Latin *c-* represents an attempt to render the unfamiliar Proto-Germanic *h* = `{{IPA|[x]}}`{=mediawiki} (Latin *h* was `{{IPA|[h]}}`{=mediawiki} but was becoming silent in common speech at the time), perhaps due to Celtic-speaking interpreters (a Celtic intermediary could also explain why one proposed etymology for the Teutons, Germanic *\*Þeuðanōz*, became Latin *Teutones*).
Because of the similarity of the names, the Cimbri have been at times associated with Cymry, the Welsh name for themselves. However, *Cymry* is derived from Brittonic *\*Kombrogi* (cf. Allobroges), meaning \"compatriots\", and is linguistically unrelated to Cimbri.
## History
### Origins
Scholars generally see the Cimbri as originating in Jutland, but archaeologists have found no clear indications of any mass migration from Jutland in the early Iron Age. The Gundestrup Cauldron, which was deposited in a bog in Himmerland in the 2nd or 1st century BC, shows that there was some sort of contact with southeastern Europe, but it is uncertain if this contact can be associated with the Cimbrian militia expeditions against Rome of the 1st Century BC. It is known that the peoples of Northern Europe and the British Isles participated in annual partial population seasonal Winter migrations southward to what is now central Iberia and southern France where goods and resources were traded and cross-culture marriages were arranged.
Advocates for a northern homeland point to Greek and Roman sources that associate the Cimbri with the Jutland peninsula. According to the *Res gestae* (ch. 26) of Augustus, the Cimbri were still found in the area around the turn of the 1st century AD:
The contemporary Greek geographer Strabo testified that the Cimbri still existed as a Germanic tribe, presumably in the \"Cimbric peninsula\" (since they are said to live by the North Sea and to have paid tribute to Augustus):
On the map of Ptolemy, the \"Kimbroi\" are placed on the northernmost part of the peninsula of Jutland, i.e., in the modern landscape of Himmerland south of Limfjorden (since Vendsyssel-Thy north of the fjord was at that time a group of islands).
### Migration
Some time before 100 BC many of the Cimbri, as well as the Teutons and Ambrones, migrated south-east. After several unsuccessful battles with the Boii and other Celtic tribes, they appeared c. 113 BC in Noricum, where they invaded the lands of one of Rome\'s allies, the Taurisci.
On the request of the Roman consul Gnaeus Papirius Carbo, sent to defend the Taurisci, they retreated, only to find themselves deceived and attacked at the Battle of Noreia, where they defeated the Romans. Only a storm, which separated the combatants, saved the Roman forces from complete annihilation.
### Invading Gaul {#invading_gaul}
Now the road to Italy was open, but they turned west towards Gaul. They came into frequent conflict with the Romans, who usually came out the losers. In 109 BC, they defeated a Roman army under the consul Marcus Junius Silanus, who was the commander of Gallia Narbonensis. In 107 BC they defeated another Roman army under the consul Gaius Cassius Longinus, who was killed at the Battle of Burdigala (modern day Bordeaux) against the Tigurini, who were allies of the Cimbri.
### Attacking the Roman Republic {#attacking_the_roman_republic}
It was not until 105 BC that they planned an attack on the Roman Republic itself. At the Rhône, the Cimbri clashed with the Roman armies. Discord between the Roman commanders, the proconsul Quintus Servilius Caepio and the consul Gnaeus Mallius Maximus, hindered Roman coordination and so the Cimbri succeeded in first defeating the legate Marcus Aurelius Scaurus and later inflicted a devastating defeat on Caepio and Maximus at the Battle of Arausio. The Romans lost as many as 80,000 men, according to Livy; Mommsen (in his *History of Rome*) thought that excluded auxiliary cavalry and non-combatants who brought the total loss closer to 112,000. Other estimates are much smaller, but by any account a large Roman army was routed.
Rome was in panic, and the *terror cimbricus* became proverbial. Everyone expected to soon see the *new Gauls* outside of the gates of Rome. Desperate measures were taken: contrary to the Roman constitution, Gaius Marius, who had defeated Jugurtha, was elected consul and supreme commander for five years in a row (104--100 BC).
### Defeat
In 104--103 BC, the Cimbri had turned to the Iberian Peninsula where they pillaged far and wide, until they were confronted by a coalition of Celtiberians. Defeated, the Cimbri returned to Gaul, where they joined their allies, the Teutons. During this time, C. Marius had the time to prepare and, in 102 BC, he was ready to meet the Teutons and the Ambrones at the Rhône. These two tribes intended to pass into Italy through the western passes, while the Cimbri and the Tigurines were to take the northern route across the Rhine and later across the Central Eastern Alps.
At the estuary of the Isère, the Teutons and the Ambrones met Marius, whose well-defended camp they did not manage to overrun. Instead, they pursued their route, and Marius followed them. At Aquae Sextiae, the Romans won two battles and took the Teuton king Teutobod prisoner.
The Cimbri had penetrated through the Alps into northern Italy. The consul Quintus Lutatius Catulus had not dared to fortify the passes, but instead he had retreated behind the river Po, and so the land was open to the invaders. The Cimbri did not hurry, and the victors of Aquae Sextiae had the time to arrive with reinforcements. At the Battle of Vercellae, at the confluence of the river Sesia with the Po, in 101 BC, the long voyage of the Cimbri also came to an end.
It was a devastating defeat. Two chieftains, Lugius and Boiorix, died on the field, while the other chieftains Caesorix and Claodicus were captured. The women killed both themselves and their children in order to avoid slavery. The Cimbri were annihilated, although some may have survived to return to the homeland where a population with this name was residing in northern Jutland in the 1st century AD, according to the sources quoted above. Some of the surviving captives may have had sons that joined Spartacus\'s cause, and been among the rebelling gladiators in the Third Servile War.
Justin\'s epitome of Trogus has Mithridates VI send emissaries to the Cimbri to request military aid during the Social War (91-88 BCE). Justin also states that the Cimbri were again in Italy at this time, i.e. over ten years later.
### Supposed descendants {#supposed_descendants}
According to Julius Caesar, the Belgian tribe of the Atuatuci \"was descended from the Cimbri and Teutoni, who, upon their march into our province and Italy, set down such of their stock and stuff as they could not drive or carry with them on the near (i.e. west) side of the Rhine, and left six thousand men of their company there as guard and garrison\" (*Gall.* 2.29, trans. Edwards). They founded the city of Atuatuca in the land of the Belgic Eburones, whom they dominated. Thus Ambiorix king of the Eburones paid tribute and gave his son and nephew as hostages to the Atuatuci (*Gall.* 6.27). In the first century AD, the Eburones were replaced or absorbed by the Germanic Tungri, and the city was known as Atuatuca Tungrorum, i.e. the modern city of Tongeren.
The population of modern-day Himmerland claims to be the heirs of the ancient Cimbri. The adventures of the Cimbri are described by the Danish Nobel Prize--winning author Johannes V. Jensen, himself born in Himmerland, in the novel *Cimbrernes Tog* (1922), included in the epic cycle *Den lange Rejse* (English *The Long Journey*, 1923). The so-called Cimbrian bull (\"Cimbrertyren\"), a sculpture by Anders Bundgaard, was erected on 14 April 1937 in a central town square in Aalborg, the capital of the region of North Jutland.
A German ethnic minority speaking the Cimbrian language, having settled in the mountains between Vicenza, Verona, and Trento in Italy (also known as Seven Communities), is also called the *Cimbri*. For hundreds of years this isolated population and its present 4,400 inhabitants have claimed to be the direct descendants of the Cimbri retreating to this area after the Roman victory over their tribe. However, it is more likely that Bavarians settled here in the Middle Ages. Most linguists remain committed to the hypothesis of a medieval (11th to 12th century AD) immigration to explain the presence of small German-speaking communities in the north of Italy. Some genetic studies seem to prove a Celtic, not Germanic, descent for most inhabitants in the region that is reinforced by Gaulish toponyms such as those ending with the suffix *-ago* \< Celtic *-\*ako(n)* (e.g. Asiago is clearly the same place name as the numerous variants -- Azay, Aisy, Azé, Ezy -- in France, all of which derive from *\*Asiacum* \< Gaulish *\*Asiāko(n)*). On the other hand, the original place names in the region, from the specifically localized language known as \'Cimbro\' are still in use alongside the more modern names today. These indicate a different origin (e.g., Asiago is known also by its original Cimbro name of *Sleghe*). The Cimbrian origin myth was popularized by humanists in the 14th century.
Despite these connections to southern Germany, belief in a Himmerland origin persisted well into modern times. On one occasion in 1709, for instance, Frederick IV of Denmark paid the region\'s inhabitants a visit and was greeted as their king. The population, which kept its independence during the time of the Venice Republic, was later severely devastated by World War I. As a result, many Cimbri have left this mountainous region of Italy, effectively forming a worldwide diaspora.
## Culture
### Religion
The Cimbri are depicted as ferocious warriors who did not fear death. The host was followed by women and children on carts. Aged women, priestesses, dressed in white sacrificed the prisoners of war and sprinkled their blood, the nature of which allowed them to see what was to come.
Strabo gives this vivid description of the Cimbric folklore:
If the Cimbri did in fact come from Jutland, evidence that they practiced ritualistic sacrifice may be found in the Haraldskær Woman discovered in Jutland in the year 1835. Noosemarks and skin piercing were evident and she had been thrown into a bog rather than buried or cremated. Furthermore, the Gundestrup cauldron, found in Himmerland, may be a sacrificial vessel like the one described in Strabo\'s text. In style, the work looks like Thracian silver work, while many of the engravings are Celtic objects.
### Language
A major problem in determining whether the Cimbri were speaking a Celtic language or a Germanic language is that, at that time, the Greeks and Romans tended to refer to all groups to the north of their sphere of influence as Gauls, Celts, or Germani rather indiscriminately, and not based upon languages. Caesar seems to be one of the first authors to distinguish the *Celtae* and *Germani*, and he had a political motive for doing so, because it was an argument in favour of his push to set the Rhine as a new Roman border. Yet, one cannot always trust Caesar and Tacitus when they ascribe individuals and tribes to one or the other category, although Caesar made clear distinctions between the two cultures. Some ancient sources categorize the Cimbri as a Germanic tribe, but some ancient authors include the Cimbri among the Celts.
There are few direct testimonies to the language of the Cimbri: referring to the Northern Ocean (the Baltic or the North Sea), Pliny the Elder states: \"Philemon says that it is called Morimarusa, i.e. the Dead Sea, by the Cimbri, until the promontory of Rubea, and after that Cronium.\" The contemporary Gaulish terms for \"sea\" and \"dead\" appear to have been *mori* and *\*maruo-*; compare their well-attested modern Insular Celtic cognates *muir* and *marbh* (Irish), *môr* and *marw* (Welsh), and *mor* and *marv* (Breton). The same word for \"sea\" is also known from Germanic, but with an *a* (\**mari-*), whereas a cognate of *marbh* is unknown in all dialects of Germanic. Yet, given that Pliny had not heard the word directly from a Cimbric speaker, it cannot be ruled out that the word he heard had been translated into Gaulish.
The known Cimbri chiefs have Celtic names, including Boiorix (which may mean \"King of the Boii\" or, more literally, \"King of Strikers\"), Gaesorix (which means \"Spear King\"), and Lugius (which may be named after the Celtic god Lugus). Other evidence to the language of the Cimbri is circumstantial: thus, we are told that the Romans enlisted Gaulish Celts to act as spies in the Cimbri camp before the final showdown with the Roman army in 101 BC.
Jean Markale wrote that the Cimbri were associated with the Helvetii, and more especially with the indisputably Celtic Tigurini. These associations may link to a common ancestry, recalled from two hundred years previous, but that is not certain. Henri Hubert states \"All these names are Celtic, and they cannot be anything else\". Some authors take a different perspective.
Countering the argument of a Celtic origin is the literary evidence that the Cimbri originally came from northern Jutland, an area with no Celtic placenames, instead only Germanic ones. This does not rule out Cimbric Gallicization during the period when they lived in Gaul. Boiorix, who may have had a Celtic if not a Celticized Germanic name, was king of the Cimbri after they moved away from their ancestral home of northern Jutland. Boiorix and his tribe lived around Celtic peoples during his era as J. B. Rives points out in his introduction to Tacitus\' *Germania*; furthermore, the name \"Boiorix\" can be seen as having either Proto-Germanic or Celtic roots.
## In fiction {#in_fiction}
The science fiction story \"Delenda Est\" by Poul Anderson depicts an alternate history in which Hannibal won the Second Punic War and destroyed Rome, but Carthage proved unable to rule Italy -- which fell into utter chaos. Thus, there was no one to stop the Cimbri two hundred years later. They filled the vacuum, conquered Italy, assimilated the local population to their own culture and by the equivalent of the 20th century had made of Italy a flourishing, technologically advanced kingdom speaking a Germanic language. He also wrote an unrelated historical novel \"The Golden Slave\", about a Cimbrian chieftain who is enslaved by the Romans after the Battle of Vercellae.
Cimbri is referenced in Italo Calvino\'s novel *If on a Winter\'s Night a Traveller* as a fictional country that warred with a similarly fictionalised version of Cimmeria, thus imposing its own written language onto the Cimmerians.
Jeff Hein\'s historical fiction series The Cimbrian War tells the story of the Cimbri and their migration across Iron-Age Europe.
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Constantin Brâncuși
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**Constantin Brâncuși** (`{{IPA|ro|konstanˈtin brɨŋˈkuʃʲ|lang|Ro-Constantin Brâncuși.ogg}}`{=mediawiki}; February 19, 1876 -- March 16, 1957) was a Romanian sculptor, painter, and photographer who made his career in France. Considered one of the most influential sculptors of the 20th century and a pioneer of modernism, Brâncuși is called the patriarch of modern sculpture. As a child, he displayed an aptitude for carving wooden farm tools. Formal studies took him first to Bucharest, then to Munich, then to the École des Beaux-Arts in Paris from 1905 to 1907. His art emphasizes clean geometrical lines that balance forms inherent in his materials with the symbolic allusions of representational art. Brâncuși sought inspiration in non-European cultures as a source of primitive exoticism, as did Paul Gauguin, Pablo Picasso, André Derain, and others. However, other influences emerge from Romanian folk art traceable through Byzantine and Dionysian traditions.
## Early years {#early_years}
Brâncuși grew up in the village of Hobița, Gorj, near Târgu Jiu, close to Romania\'s Carpathian Mountains, an area known for its rich tradition of folk crafts, particularly woodcarving. Geometric patterns of the region are seen in his later works such as the Endless Column created in 1918.
His parents Nicolae and Maria Brâncuși were poor peasants who earned a meagre living through back-breaking labor; from the age of seven, Constantin herded the family\'s flock of sheep. He showed talent for carving objects out of wood and often ran away from home to escape the bullying of his father and older brothers.
At the age of nine, Brâncuși left the village to work in the nearest large town. At the age of eleven, he went into the service of a grocer in Slatina; and then he became a domestic in a public house in Craiova, where he remained for several years. When he was 18, Brâncuși created a violin by hand with materials he found around his workplace. Impressed by Brâncuși\'s talent for carving, an industrialist enrolled him in the Craiova School of Arts and Crafts (*școala de arte și meserii*), where he pursued his love for woodworking, graduating with honors in 1898.
He then enrolled in the Bucharest School of Fine Arts, where he received academic training in sculpture. He worked hard and quickly distinguished himself as talented. One of his earliest surviving works, under the guidance of his anatomy teacher, Dimitrie Gerota, is a masterfully rendered écorché (statue of a man with skin removed to reveal the muscles underneath) which was exhibited at the Romanian Athenaeum in 1903. Though just an anatomical study, it foreshadowed the sculptor\'s later efforts to reveal essence rather than merely copy outward appearance.
## Working in Paris {#working_in_paris}
In 1903, Brâncuși traveled to Munich, and from there to Paris. In Paris, he was welcomed by the community of artists and intellectuals brimming with new ideas. He worked for two years in the workshop of Antonin Mercié of the École des Beaux-Arts and was invited to enter the workshop of Auguste Rodin. Even though he admired the eminent Rodin he left the Rodin studio after only two months, saying, \"Nothing can grow under big trees.\"
After leaving Rodin\'s workshop, Brâncuși began developing the revolutionary style for which he is known. His first commissioned work, *The Prayer*, was part of a gravestone memorial. It depicts a young woman crossing herself as she kneels, and marks the first step toward abstracted, non-literal representation, and shows his drive to depict \"not the outer form but the idea, the essence of things.\" He also began doing more carving, rather than the method popular with his contemporaries, that of modeling in clay or plaster which would be cast in metal, and by 1908 he worked almost exclusively by carving.
In the following few years, he made many versions of *Sleeping Muse* and *The Kiss*, further simplifying forms to geometrical and sparse objects.
His works became popular in France, Romania, and the United States. Collectors, notably John Quinn, bought his pieces, and reviewers praised his works. In 1913 Brâncuși\'s work was displayed at both the Salon des Indépendants and the first exhibition in the U.S. of modern art, the Armory Show.
In 1920, he developed a notorious reputation with the entry of *Princess X* in the Salon. The phallic appearance of this large, gleaming bronze piece scandalized the Salon and, despite Brâncuși\'s explanation that it was simply meant to represent the essence of womanhood, it was removed from the exhibition. *Princess X* was revealed to be Princess Marie Bonaparte, direct descendant of the younger brother of Napoleon Bonaparte. The sculpture has been interpreted by some as symbolizing her obsession with the penis and her lifelong quest to achieve vaginal orgasm, with the help of Sigmund Freud.
Around this time, Brâncuși began crafting the bases for his sculptures with much care and originality because he considered them important to the works themselves.
One of his major groups of sculptures involved the *Bird in Space* --- simple abstract shapes representing a bird in flight. The works are based on his earlier *Măiastra* series. In Romanian folklore the Măiastra is a beautiful golden bird who foretells the future and cures the blind. Over the following 20 years, Brâncuși made multiple versions of *Bird in Space* out of marble or bronze. Athena Tacha Spear\'s book, *Brâncuși\'s Birds,* (CAA monographs XXI, NYU Press, New York, 1969), first sorted out the 36 versions and their development, from the early *Măiastra*, to the *Golden Bird* of the late teens, to the *Bird in Space*, which emerged in the early 1920s and which Brâncuși developed throughout his life.
One of these versions caused a major controversy in 1926 when photographer Edward Steichen purchased it and shipped it to the United States. Customs officers did not accept the *Bird* as a work of art and assessed customs duty on its import as an industrial item. After protracted court proceedings, this assessment was overturned, thus confirming the Bird\'s status as a duty-exempt work of art. The verdict was somewhat influenced by the Judge Justice Waite\'s personal appreciation of the art calling it \'beautiful\', \'symmetrical\', and \'ornamental\'. The ruling also established the important principle that \"art\" does not have to involve a realistic representation of nature, and that it was legitimate for it to simply represent an abstract concept -- in this case \"flight\".
His work became increasingly popular in the U.S, where he visited several times during his life. Worldwide fame in 1933 brought him the commission of building a meditation temple, the Temple of Deliverance, in India for the Maharajah of Indore, Yeshwant Rao Holkar. Holkar had commissioned three \"L\'Oiseau dans l\'Espace\"---in bronze, black and white marble---previously, but when Brâncuși went to India in 1937 to complete the plans and begin construction, the Mahrajah was away and, supposedly, lost interest in the project which was to be an homage to his wife, the Maharani Margaret Holkar,`{{failed verification|date=July 2023}}`{=mediawiki} who had died when he returned. Of the three birds, the bronze one is in the collection of the Norton Simon Museum in Pasadena, California, and the two marble birds are currently in the permanent collection of the National Gallery of Australia in Canberra, Australia.
In 1938, he finished the World War I monument in Târgu-Jiu where he had spent much of his childhood. *Table of Silence*, *The Gate of the Kiss*, and *Endless Column* commemorate the courage and sacrifice of Romanians who in 1916 defended Târgu Jiu from the forces of the Central Powers. The restoration of this ensemble was spearheaded by the World Monuments Fund and was completed in 2004.
The Târgu Jiu ensemble marks the apex of his artistic career. In his remaining 19 years he created fewer than 15 pieces, mostly reworking earlier themes, and while his fame grew, he withdrew. Brâncuși received his first retrospective in 1955 at the Guggenheim Museum in New York. In 1955 *Life* magazine reported, \"Wearing white pajamas and a yellow gnome-like cap, Brâncuși today hobbles about his studio tenderly caring for and communing with the silent host of fish, birds, heads, and endless columns which he created.\"
Brâncuși was cared for in his later years by a Romanian refugee couple. He became a French citizen in 1952 in order to make the caregivers his heirs, and to bequeath his studio and its contents to the Musée National d\'Art Moderne in Paris. In 2021, for IRCAM and Centre Pompidou\'s Festival Manifeste, the intermedial large-scale installation *Infinite Light Columns / Constellations of The Future, tribute to Constantin Brancusi* by artists duo Arotin & Serghei has been installed on Renzo Piano\'s IRCAM Tower on Centre Pompidou Square, on the opposite site to Brancusi\'s Studio.
## Personal life {#personal_life}
Brâncuși dressed simply, reflective of his Romanian peasant background. His studio was reminiscent of the houses of the peasants from his native region: there was a big slab of rock as a table and a primitive fireplace, similar to those found in traditional houses in his native Oltenia, while the rest of the furniture was made by him out of wood. Brâncuși would cook his own food, traditional Romanian dishes, with which he would treat his guests.
Brâncuși held a large spectrum of interests, from science to music, and was known to play the violin. He would sing old Romanian folk songs, often expressing his feelings of homesickness. After the installment of communism, the artist never permanently returned to his native Romania, but did visit eight times.
His circle of friends included artists and intellectuals in Paris such as Amedeo Modigliani, Ezra Pound, Henri Pierre Roché, Guillaume Apollinaire, Louise Bourgeois, Pablo Picasso, Man Ray, Marcel Duchamp, Henri Rousseau, Peggy Guggenheim, Tristan Tzara, and Fernand Léger. He was an old friend of Romany Marie, who was also Romanian, and referred Isamu Noguchi to her café in Greenwich Village. Although surrounded by the Parisian avant-garde, Brâncuși never lost contact with Romania and had friends from the community of Romanian artists and intellectuals living in Paris, including Benjamin Fondane, George Enescu, Theodor Pallady, Camil Ressu, Nicolae Dărăscu, Panait Istrati, Traian Vuia, Eugène Ionesco, Emil Cioran, Natalia Dumitresco, and Paul Celan. Another Romanian scholar wrote on Brâncuși, Mircea Eliade.
Brâncuși held a particular interest in mythology, especially Romanian mythology, folk tales, and traditional art (which also had a strong influence on his works), but he became interested in African and Mediterranean art as well.
A talented handyman, he built his own phonograph and made most of his furniture, utensils, and doorways. His worldview valued \"differentiating the essential from the ephemeral,\" with Plato, Lao-Tzu, and Milarepa as influences. Reportedly, he had a copy of the first ever translation from the Tibetan into French of Jacques Bacot\'s Le poete tibetain Milarepa: ses crimes, ses épreuves, son Nirvana that he kept by his bedside. He identified closely with Milarepa\'s mountain existence since Brancusi himself came from the Carpathian Mountains of Romania and he often thought he was a reincarnation of Milarepa. He was a saint-like idealist and near ascetic, turning his workshop into a place where visitors noted the deep spiritual atmosphere. However, particularly through the 1910s and 1920s, he was known as a pleasure seeker and merrymaker in his bohemian circle. He enjoyed cigarettes, good wine, and the company of women. He had one child, John Moore, with the New Zealand pianist Vera Moore. He never acknowledged his son as his own.
## Death and legacy {#death_and_legacy}
Brâncuși died on March 16, 1957, aged 81. He was buried in the Cimetière du Montparnasse in Paris. Alexandre Istrati and Natalia Dumitresco were later buried in the same grave. This cemetery also displays statues that Brâncuși carved for deceased artists.
At his death, Brâncuși left 1200 photographs and 215 sculptures. He bequeathed part of his collection to the French state on condition that his workshop be rebuilt as it was on the day he died. This reconstruction of his studio, adjacent to the Pompidou Centre, is open to the public. Brâncuși\'s studio inspired Swedish architect Klas Anshelm\'s design of the Malmö Konsthall, which opened in 1975.
In September 1957, African American sculptor Richard Hunt traveled from Chicago to Paris to view Brancusi\'s studio. Hunt\'s visit left an enduring impression on the 22-year-old artist, not only because of the artistic influence of Brancusi and exploration of biomorphic abstraction in sculpture but also because of the way which Hunt chose to live the majority of his life. Like Brancusi, Hunt slept in his own studio surrounded by his art and the tools used in his practice for much of his life.
Brancusi\'s *Bird in Space* sculptures inspired the Modernist poet, Ezra Pound, specifically his late *Cantos* which were written in the mid-twentieth century. The literary critic Lucy Jeffery highlights ways in which Brancusi\'s sculptural form influenced Ezra Pound, analysing Pound\'s *Canto CXVII et seq., 815*. Through close textual analysis and with direct reference to Brancusi\'s comments on his own creative process, Jeffery highlights how Pound\'s and Brancusi\'s sculptural process and resulting style is one of ambiguity and tension between: levity and weight, simplicity and complexity, ease and struggle. As Jeffery remarks: \'Despite their drive towards an holistic artwork, neither Brancusi nor Pound could, to borrow \[Albert\] Boime\'s phrasing, \"emancipate\" their art from the material or social context to which it belonged.\' In the article, Jeffery contextualises Brancusi\'s work in relation to the sculptor Gaudier-Brzeska, photographer Man Ray, and writers such as Mina Loy, Samuel Beckett, and Peter Russell.
In 1962, Georg Olden used Brâncuși\'s *Bird in Space* as the inspiration behind his design of the Clio Award statuette.
In November 1971, Brâncuși Memorial House was established in his birth village Hobița, as a branch of the Gorj County Muzeum.
Brâncuși was elected posthumously to the Romanian Academy in 1990.
Google commemorated his 135th birthday with a Doodle in 2011 consisting of seven of his works.
Brâncuși\'s works are housed in museums around the world: in Romania at the National Museum of Art and Craiova Art Museum, in the US at the Museum of Modern Art (New York City) and the Philadelphia Museum of Art, the former holding the largest collection of Brâncuși sculptures in the United States.
Constantin Brâncuși University in Târgu Jiu and a metro station in Bucharest are named after him.
In 2015, the Romanian Parliament declared February 19 \"The Brâncuși Day\", a working holiday in Romania.
Director Mick Davis plans to make a biographical film about Brâncuși called *The Sculptor*, and British director Peter Greenaway said in 2017 that he is working on a film called *Walking to Paris*, a film which shows Brâncuși\'s journey from Bucharest to Paris.
## Art market {#art_market}
Brâncuși\'s piece *Madame L.R.* sold for €29.185 million (\$37.2 million) in 2009, setting a record price for a sculpture sold at auction.
In May 2018, *La Jeune Fille Sophistiquée* (*Portrait de Nancy Cunard*), a polished bronze on a carved marble base (1932), sold for US\$71 million (with fees) at Christie\'s New York, setting a world record auction price for the artist.
## Brâncuși on his own work {#brâncuși_on_his_own_work}
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\"*Il y a des imbéciles qui définissent mon œuvre comme abstraite, pourtant ce qu\'ils qualifient d\'abstrait est ce qu\'il y a de plus réaliste, ce qui est réel n\'est pas l\'apparence mais l\'idée, l\'essence des choses.*\" \"There are idiots who define my work as abstract; yet what they call abstract is what is most realistic. What is real is not the appearance, but the idea, the essence of things.\"
\"*Am șlefuit materia pentru a afla linia continuă. Și când am constatat că n‑o pot afla, m‑am oprit; parcă cineva nevăzut mi‑a dat peste mâini.*\" \"I ground matter to find the continuous line. And when I realized I could not find it, I stopped, as if an unseen someone had slapped my hands.\"
\"*Ca arta să fie liberă și universală, trebuie să creezi ca un zeu, să comanzi ca un rege și să execuți ca un sclav.*\" \"For art to be free and universal, you must create like a god, command like a king and execute like a slave.\"
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## Selected works {#selected_works}
Both *Bird in Space* and *Sleeping Muse I* are sculptures of animate objects; however, unlike ones from Ancient Greece or Rome, or those from the High Renaissance period, these works of art are more abstract in style.
*Bird in Space* is a series from the 1920s. One of these, constructed in 1925 using wood, stone, and marble (Richler 178) stands around 72 inches tall and consists of a narrow feather standing erect on a wooden base. Similar models, but made from materials such as bronze, were also produced by Brâncuși and placed in exhibitions.
*Sleeping Muse I* has different versions as well; one, from 1909 to 1910, is made of marble and measures 6 ¾ in. in height (Adams 549). This is a model of a head, without a body, with markings to show features such as hair, nose, lips, and closed eyes. In *A History of Western Art*, Adams says that the sculpture has \"an abstract, curvilinear quality and a smooth contour that create an impression of elegance\" (549). The qualities which produce the effect can particularly be seen in the shape of the eyes and in the set of the mouth.
## Other works {#other_works}
- *Bust of a boy* (1906)
- *The Prayer* (1907)
- *La Sagesse de la Terre* (1908)
- *Sleeping Muse* (1910), Metropolitan Museum of Art
- *Prometheus* (1911)
- *Mademoiselle Pogany* (1912), Philadelphia Museum of Art
- *Miss Pogany* (1913,) drawing, the Botarro Collection
- *The Kiss* (1916), Philadelphia Museum of Art
- *Princess X* (1916),
- *Madame L.R.* (1914--1918)
- *A Muse* (1917)
- *Chimera* (1918)
- *Eileen Lane* (1922), the Botarro Collection
- *Bird in Space* (1924), Philadelphia Museum of Art
- *Portrait of Nancy Cunard* (also called *Sophisticated Young Lady*) (1925--1927)
- *Le Poisson* (1926)
- *Portrait of James Joyce*, for *Tales Told of Shem and Shaun* (Black Sun Press, Paris, 1929)
- *Le Coq* (1935)
- Sculptural Ensemble of Constantin Brâncuși at Târgu Jiu (Endless Column) (1935)
- *Blonde Negress I* (1926), Toledo Museum of Art
- *White Negress II* (1928), Art Institute of Chicago
<File:'Fish>\' by Constantin Brâncusi, Tate Modern.JPG\|Brancusi *Fish* Tate Modern Collection
## In fiction {#in_fiction}
- Robert McAlmon\'s 1925 collection of short stories *Distinguished Air* includes one that revolves around an exhibition of *Princess X*. In 1930 the watercolour painter Charles Demuth painted *Distinguished Air*, based on this story.
- In Evelyn Waugh\'s 1945 novel *Brideshead Revisited*, Anthony Blanche remarks in relating a story to Charles Ryder that \"I have two sculptures by Brancusi and several pretty things\" \[sic\].
- In the 1988 movie *Short Circuit 2*, a man walking through an outdoor exhibition speculates that the stationary Johnny 5 robot, who is also admiring the exhibit, is \"an early Brâncuși.\"
- In the 1999 science fiction series *Total Recall 2070*, one episode (\"Astral Projections\") featured an artifact called the \"Brancusi Stone\" because it looks like one of Brâncuși\'s sculptures.
- In the 2000 film *Mission to Mars*, the \"Face on Mars\" is modeled after Brâncuși\'s *Sleeping Muse*.
Apeirogon by Colum McCann p212
| 2025-06-20T00:00:00 |
6,586 |
Claus Sluter
|
thumb\|upright=1.4\|David and Jeremiah from the *Well of Moses* **Claus Sluter** (1340s in Haarlem -- 1405 or 1406 in Dijon) was a Dutch sculptor, living in the Duchy of Burgundy from about 1380. He was the most important northern European sculptor of his age and is considered a pioneer of the \"northern realism\" of the Early Netherlandish painting that came into full flower with the work of Jan van Eyck and others in the next generation.
## Life
The name \"Claes de Slutere van Herlam\" is inscribed in the Register of the Corporation of Stonemasons and Sculptors of Brussels around the years 1379/1380. He then moved to the Burgundian capital of Dijon, where from 1385 to 1389 he was the assistant of Jean de Marville, court sculptor to Philip the Bold, Duke of Burgundy. From 1389 to his death he was court sculptor himself, with the rank of *valet de chambre*. He was succeeded by his nephew Claus de Werve.
## Work
Sluter\'s most significant work is the so-called *Well of Moses* (1395--1403), or the Great Cross. It was created for the Carthusian monastery of Champmol, which was founded by Philip the Bold right outside Dijon in 1383. For many years, the top portion was thought to have included (along with Christ on a cross), sculptures of the Virgin and John the Evangelist. However it was more likely just Christ, with Mary Magdalene kneeling at the foot of the cross. The cross, and whatever was on the terrace below, was destroyed at some point after 1736 and before 1789, probable because the roof of the building protecting the monument collapsed. Some fragments from the original Cross are preserved in the Musée Archéologique de Dijon. Life-sized figures representing Old Testament prophets and kings (Moses, David, Daniel, Jeremiah, Zachariah, and Isaiah) stand around the base, holding phylacteries and books inscribed with verses from their respective texts, which were interpreted in the Middle Ages as typological prefigurations of the sacrifice of Christ. The work\'s physical structure, in which the Old Testament figures support those of the New Dispensation, literalizes the typological iconography. The pedestal surmounts a hexagonal fountain. The entire monument is executed in limestone quarried from Tonnerre and Asnières.
upright=1.4\|thumb\|Monumental portal of the Chartreuse of Champmol at Dijon by Claus Sluter The portal of the former mortuary chapel of Champmol is positioned a few feet away from the Well of Moses. It consists of three sculptural groups by Sluter: a standing Madonna and Child at the trumeau; the duke and St. John, his patron saint, at the left jamb and the duchess and her patron saint, Catherine, at the right one. Sluter was also responsible for the main part of the work on Philip\'s tomb, which (restored and partly reconstructed) has been moved to the Museum of Fine Arts which is housed in the former ducal palace in Dijon.
Sluter was one of the sculptors of the pleurants, or mourners, which occupy niches below the tombs of Philip the Bold, his wife Margaret, and John the Fearless.
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Computer vision
|
**Computer vision** tasks include methods for acquiring, processing, analyzing, and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the form of decisions. \"Understanding\" in this context signifies the transformation of visual images (the input to the retina) into descriptions of the world that make sense to thought processes and can elicit appropriate action. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory.
The scientific discipline of computer vision is concerned with the theory behind artificial systems that extract information from images. Image data can take many forms, such as video sequences, views from multiple cameras, multi-dimensional data from a 3D scanner, 3D point clouds from LiDaR sensors, or medical scanning devices. The technological discipline of computer vision seeks to apply its theories and models to the construction of computer vision systems.
Subdisciplines of computer vision include scene reconstruction, object detection, event detection, activity recognition, video tracking, object recognition, 3D pose estimation, learning, indexing, motion estimation, visual servoing, 3D scene modeling, and image restoration.
## Definition
Computer vision is an interdisciplinary field that deals with how computers can be made to gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to automate tasks that the human visual system can do. \"Computer vision is concerned with the automatic extraction, analysis, and understanding of useful information from a single image or a sequence of images. It involves the development of a theoretical and algorithmic basis to achieve automatic visual understanding.\" As a scientific discipline, computer vision is concerned with the theory behind artificial systems that extract information from images. The image data can take many forms, such as video sequences, views from multiple cameras, or multi-dimensional data from a medical scanner. As a technological discipline, computer vision seeks to apply its theories and models for the construction of computer vision systems. Machine vision refers to a systems engineering discipline, especially in the context of factory automation. In more recent times, the terms computer vision and machine vision have converged to a greater degree.
## History
In the late 1960s, computer vision began at universities that were pioneering artificial intelligence. It was meant to mimic the human visual system as a stepping stone to endowing robots with intelligent behavior. In 1966, it was believed that this could be achieved through an undergraduate summer project, by attaching a camera to a computer and having it \"describe what it saw\".
What distinguished computer vision from the prevalent field of digital image processing at that time was a desire to extract three-dimensional structure from images with the goal of achieving full scene understanding. Studies in the 1970s formed the early foundations for many of the computer vision algorithms that exist today, including extraction of edges from images, labeling of lines, non-polyhedral and polyhedral modeling, representation of objects as interconnections of smaller structures, optical flow, and motion estimation.
The next decade saw studies based on more rigorous mathematical analysis and quantitative aspects of computer vision. These include the concept of scale-space, the inference of shape from various cues such as shading, texture and focus, and contour models known as snakes. Researchers also realized that many of these mathematical concepts could be treated within the same optimization framework as regularization and Markov random fields. By the 1990s, some of the previous research topics became more active than others. Research in projective 3-D reconstructions led to better understanding of camera calibration. With the advent of optimization methods for camera calibration, it was realized that a lot of the ideas were already explored in bundle adjustment theory from the field of photogrammetry. This led to methods for sparse 3-D reconstructions of scenes from multiple images. Progress was made on the dense stereo correspondence problem and further multi-view stereo techniques. At the same time, variations of graph cut were used to solve image segmentation. This decade also marked the first time statistical learning techniques were used in practice to recognize faces in images (see Eigenface). Toward the end of the 1990s, a significant change came about with the increased interaction between the fields of computer graphics and computer vision. This included image-based rendering, image morphing, view interpolation, panoramic image stitching and early light-field rendering.
Recent work has seen the resurgence of feature-based methods used in conjunction with machine learning techniques and complex optimization frameworks. The advancement of Deep Learning techniques has brought further life to the field of computer vision. The accuracy of deep learning algorithms on several benchmark computer vision data sets for tasks ranging from classification, segmentation and optical flow has surpassed prior methods.
## Related fields {#related_fields}
### Solid-state physics {#solid_state_physics}
Solid-state physics is another field that is closely related to computer vision. Most computer vision systems rely on image sensors, which detect electromagnetic radiation, which is typically in the form of either visible, infrared or ultraviolet light. The sensors are designed using quantum physics. The process by which light interacts with surfaces is explained using physics. Physics explains the behavior of optics which are a core part of most imaging systems. Sophisticated image sensors even require quantum mechanics to provide a complete understanding of the image formation process. Also, various measurement problems in physics can be addressed using computer vision, for example, motion in fluids.
### Neurobiology
Neurobiology has greatly influenced the development of computer vision algorithms. Over the last century, there has been an extensive study of eyes, neurons, and brain structures devoted to the processing of visual stimuli in both humans and various animals. This has led to a coarse yet convoluted description of how natural vision systems operate in order to solve certain vision-related tasks. These results have led to a sub-field within computer vision where artificial systems are designed to mimic the processing and behavior of biological systems at different levels of complexity. Also, some of the learning-based methods developed within computer vision (*e.g.* neural net and deep learning based image and feature analysis and classification) have their background in neurobiology. The Neocognitron, a neural network developed in the 1970s by Kunihiko Fukushima, is an early example of computer vision taking direct inspiration from neurobiology, specifically the primary visual cortex.
Some strands of computer vision research are closely related to the study of biological vision---indeed, just as many strands of AI research are closely tied with research into human intelligence and the use of stored knowledge to interpret, integrate, and utilize visual information. The field of biological vision studies and models the physiological processes behind visual perception in humans and other animals. Computer vision, on the other hand, develops and describes the algorithms implemented in software and hardware behind artificial vision systems. An interdisciplinary exchange between biological and computer vision has proven fruitful for both fields.
### Signal processing {#signal_processing}
Yet another field related to computer vision is signal processing. Many methods for processing one-variable signals, typically temporal signals, can be extended in a natural way to the processing of two-variable signals or multi-variable signals in computer vision. However, because of the specific nature of images, there are many methods developed within computer vision that have no counterpart in the processing of one-variable signals. Together with the multi-dimensionality of the signal, this defines a subfield in signal processing as a part of computer vision.
### Robotic navigation {#robotic_navigation}
Robot navigation sometimes deals with autonomous path planning or deliberation for robotic systems to navigate through an environment. A detailed understanding of these environments is required to navigate through them. Information about the environment could be provided by a computer vision system, acting as a vision sensor and providing high-level information about the environment and the robot
### Visual computing {#visual_computing}
### Other fields {#other_fields}
Besides the above-mentioned views on computer vision, many of the related research topics can also be studied from a purely mathematical point of view. For example, many methods in computer vision are based on statistics, optimization or geometry. Finally, a significant part of the field is devoted to the implementation aspect of computer vision; how existing methods can be realized in various combinations of software and hardware, or how these methods can be modified in order to gain processing speed without losing too much performance. Computer vision is also used in fashion eCommerce, inventory management, patent search, furniture, and the beauty industry.
### Distinctions
The fields most closely related to computer vision are image processing, image analysis and machine vision. There is a significant overlap in the range of techniques and applications that these cover. This implies that the basic techniques that are used and developed in these fields are similar, something which can be interpreted as there is only one field with different names. On the other hand, it appears to be necessary for research groups, scientific journals, conferences, and companies to present or market themselves as belonging specifically to one of these fields and, hence, various characterizations which distinguish each of the fields from the others have been presented. In image processing, the input and output are both images, whereas in computer vision, the input is an image or video, and the output could be an enhanced image, an analysis of the image\'s content, or even a system\'s behavior based on that analysis.
Computer graphics produces image data from 3D models, and computer vision often produces 3D models from image data. There is also a trend towards a combination of the two disciplines, *e.g.*, as explored in augmented reality.
The following characterizations appear relevant but should not be taken as universally accepted:
- Image processing and image analysis tend to focus on 2D images, how to transform one image to another, *e.g.*, by pixel-wise operations such as contrast enhancement, local operations such as edge extraction or noise removal, or geometrical transformations such as rotating the image. This characterization implies that image processing/analysis neither requires assumptions nor produces interpretations about the image content.
- Computer vision includes 3D analysis from 2D images. This analyzes the 3D scene projected onto one or several images, *e.g.*, how to reconstruct structure or other information about the 3D scene from one or several images. Computer vision often relies on more or less complex assumptions about the scene depicted in an image.
- Machine vision is the process of applying a range of technologies and methods to provide imaging-based automatic inspection, process control, and robot guidance in industrial applications. Machine vision tends to focus on applications, mainly in manufacturing, *e.g.*, vision-based robots and systems for vision-based inspection, measurement, or picking (such as bin picking). This implies that image sensor technologies and control theory often are integrated with the processing of image data to control a robot and that real-time processing is emphasized by means of efficient implementations in hardware and software. It also implies that external conditions such as lighting can be and are often more controlled in machine vision than they are in general computer vision, which can enable the use of different algorithms.
- There is also a field called imaging which primarily focuses on the process of producing images, but sometimes also deals with the processing and analysis of images. For example, medical imaging includes substantial work on the analysis of image data in medical applications. Progress in convolutional neural networks (CNNs) has improved the accurate detection of disease in medical images, particularly in cardiology, pathology, dermatology, and radiology.
- Finally, pattern recognition is a field that uses various methods to extract information from signals in general, mainly based on statistical approaches and artificial neural networks. A significant part of this field is devoted to applying these methods to image data.
Photogrammetry also overlaps with computer vision, e.g., stereophotogrammetry vs. computer stereo vision.
## Applications
Applications range from tasks such as industrial machine vision systems which, say, inspect bottles speeding by on a production line, to research into artificial intelligence and computers or robots that can comprehend the world around them. The computer vision and machine vision fields have significant overlap. Computer vision covers the core technology of automated image analysis which is used in many fields. Machine vision usually refers to a process of combining automated image analysis with other methods and technologies to provide automated inspection and robot guidance in industrial applications. In many computer-vision applications, computers are pre-programmed to solve a particular task, but methods based on learning are now becoming increasingly common. Examples of applications of computer vision include systems for:
- Automatic inspection, *e.g.*, in manufacturing applications;
- Assisting humans in identification tasks, e.g., a species identification system;
- Controlling processes, *e.g.*, an industrial robot;
- Detecting events, *e.g.*, for visual surveillance or people counting, e.g., in the restaurant industry;
- Interaction, *e.g.*, as the input to a device for computer-human interaction;
- monitoring agricultural crops, e.g. an open-source vision transformers model has been developed to help farmers automatically detect strawberry diseases with 98.4% accuracy.
- Modeling objects or environments, *e.g.*, medical image analysis or topographical modeling;
- Navigation, *e.g.*, by an autonomous vehicle or mobile robot;
- Organizing information, *e.g.*, for indexing databases of images and image sequences.
- Tracking surfaces or planes in 3D coordinates for allowing Augmented Reality experiences.
- Analyzing the condition of facilities in industry or construction.
- Automatic real-time lip-reading for devices and apps to assist people with disabilities.
For 2024, the leading areas of computer vision were industry (market size US\$5.22 billion), medicine (market size US\$2.6 billion), military (market size US\$996.2 million).
### Medicine
One of the most prominent application fields is medical computer vision, or medical image processing, characterized by the extraction of information from image data to diagnose a patient. An example of this is the detection of tumours, arteriosclerosis or other malign changes, and a variety of dental pathologies; measurements of organ dimensions, blood flow, etc. are another example. It also supports medical research by providing new information: *e.g.*, about the structure of the brain or the quality of medical treatments. Applications of computer vision in the medical area also include enhancement of images interpreted by humans---ultrasonic images or X-ray images, for example---to reduce the influence of noise.
### Machine vision {#machine_vision}
A second application area in computer vision is in industry, sometimes called machine vision, where information is extracted for the purpose of supporting a production process. One example is quality control where details or final products are being automatically inspected in order to find defects. One of the most prevalent fields for such inspection is the Wafer industry in which every single Wafer is being measured and inspected for inaccuracies or defects to prevent a computer chip from coming to market in an unusable manner. Another example is a measurement of the position and orientation of details to be picked up by a robot arm. Machine vision is also heavily used in the agricultural processes to remove undesirable foodstuff from bulk material, a process called optical sorting.
### Military
The obvious examples are the detection of enemy soldiers or vehicles and missile guidance. More advanced systems for missile guidance send the missile to an area rather than a specific target, and target selection is made when the missile reaches the area based on locally acquired image data. Modern military concepts, such as \"battlefield awareness\", imply that various sensors, including image sensors, provide a rich set of information about a combat scene that can be used to support strategic decisions. In this case, automatic processing of the data is used to reduce complexity and to fuse information from multiple sensors to increase reliability.
### Autonomous vehicles {#autonomous_vehicles}
One of the newer application areas is autonomous vehicles, which include submersibles, land-based vehicles (small robots with wheels, cars, or trucks), aerial vehicles, and unmanned aerial vehicles (UAV). The level of autonomy ranges from fully autonomous (unmanned) vehicles to vehicles where computer-vision-based systems support a driver or a pilot in various situations. Fully autonomous vehicles typically use computer vision for navigation, e.g., for knowing where they are or mapping their environment (SLAM), for detecting obstacles. It can also be used for detecting certain task-specific events, *e.g.*, a UAV looking for forest fires. Examples of supporting systems are obstacle warning systems in cars, cameras and LiDAR sensors in vehicles, and systems for autonomous landing of aircraft. Several car manufacturers have demonstrated systems for autonomous driving of cars. There are ample examples of military autonomous vehicles ranging from advanced missiles to UAVs for recon missions or missile guidance. Space exploration is already being made with autonomous vehicles using computer vision, *e.g.*, NASA\'s *Curiosity* and CNSA\'s *Yutu-2* rover.
### Tactile feedback {#tactile_feedback}
thumb\|upright=1.15\|Rubber artificial skin layer with the flexible structure for the shape estimation of micro-undulation surfaces thumb\|upright=1.15\|Above is a silicon mold with a camera inside containing many different point markers. When this sensor is pressed against the surface, the silicon deforms, and the position of the point markers shifts. A computer can then take this data and determine how exactly the mold is pressed against the surface. This can be used to calibrate robotic hands in order to make sure they can grasp objects effectively. Materials such as rubber and silicon are being used to create sensors that allow for applications such as detecting microundulations and calibrating robotic hands. Rubber can be used in order to create a mold that can be placed over a finger, inside of this mold would be multiple strain gauges. The finger mold and sensors could then be placed on top of a small sheet of rubber containing an array of rubber pins. A user can then wear the finger mold and trace a surface. A computer can then read the data from the strain gauges and measure if one or more of the pins are being pushed upward. If a pin is being pushed upward then the computer can recognize this as an imperfection in the surface. This sort of technology is useful in order to receive accurate data on imperfections on a very large surface. Another variation of this finger mold sensor are sensors that contain a camera suspended in silicon. The silicon forms a dome around the outside of the camera and embedded in the silicon are point markers that are equally spaced. These cameras can then be placed on devices such as robotic hands in order to allow the computer to receive highly accurate tactile data.
Other application areas include:
- Support of visual effects creation for cinema and broadcast, *e.g.*, camera tracking (match moving).
- Surveillance.
- Driver drowsiness detection
- Tracking and counting organisms in the biological sciences
## Typical tasks {#typical_tasks}
Each of the application areas described above employ a range of computer vision tasks; more or less well-defined measurement problems or processing problems, which can be solved using a variety of methods. Some examples of typical computer vision tasks are presented below.
Computer vision tasks include methods for acquiring, processing, analyzing and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, *e.g.*, in the forms of decisions. Understanding in this context means the transformation of visual images (the input of the retina) into descriptions of the world that can interface with other thought processes and elicit appropriate action. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory.
### Recognition
The classical problem in computer vision, image processing, and machine vision is that of determining whether or not the image data contains some specific object, feature, or activity. Different varieties of recognition problem are described in the literature.
- **Object recognition** (also called **object classification**)`{{spaced ndash}}`{=mediawiki}one or several pre-specified or learned objects or object classes can be recognized, usually together with their 2D positions in the image or 3D poses in the scene. Blippar, Google Goggles, and LikeThat provide stand-alone programs that illustrate this functionality.
- **Identification**`{{spaced ndash}}`{=mediawiki}an individual instance of an object is recognized. Examples include identification of a specific person\'s face or fingerprint, identification of handwritten digits, or the identification of a specific vehicle.
- **Detection**`{{spaced ndash}}`{=mediawiki}the image data are scanned for specific objects along with their locations. Examples include the detection of an obstacle in the car\'s field of view and possible abnormal cells or tissues in medical images or the detection of a vehicle in an automatic road toll system. Detection based on relatively simple and fast computations is sometimes used for finding smaller regions of interesting image data which can be further analyzed by more computationally demanding techniques to produce a correct interpretation.
Currently, the best algorithms for such tasks are based on convolutional neural networks. An illustration of their capabilities is given by the ImageNet Large Scale Visual Recognition Challenge; this is a benchmark in object classification and detection, with millions of images and 1000 object classes used in the competition. Performance of convolutional neural networks on the ImageNet tests is now close to that of humans. The best algorithms still struggle with objects that are small or thin, such as a small ant on the stem of a flower or a person holding a quill in their hand. They also have trouble with images that have been distorted with filters (an increasingly common phenomenon with modern digital cameras). By contrast, those kinds of images rarely trouble humans. Humans, however, tend to have trouble with other issues. For example, they are not good at classifying objects into fine-grained classes, such as the particular breed of dog or species of bird, whereas convolutional neural networks handle this with ease.
Several specialized tasks based on recognition exist, such as:
- **Content-based image retrieval**`{{spaced ndash}}`{=mediawiki}finding all images in a larger set of images which have a specific content. The content can be specified in different ways, for example in terms of similarity relative to a target image (give me all images similar to image X) by utilizing reverse image search techniques, or in terms of high-level search criteria given as text input (give me all images which contain many houses, are taken during winter and have no cars in them).
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- **Pose estimation**`{{spaced ndash}}`{=mediawiki}estimating the position or orientation of a specific object relative to the camera. An example application for this technique would be assisting a robot arm in retrieving objects from a conveyor belt in an assembly line situation or picking parts from a bin.
- **Optical character recognition** (OCR)`{{spaced ndash}}`{=mediawiki}identifying characters in images of printed or handwritten text, usually with a view to encoding the text in a format more amenable to editing or indexing (*e.g.* ASCII). A related task is reading of 2D codes such as data matrix and QR codes.
- **Facial recognition`{{spaced ndash}}`{=mediawiki}** a technology that enables the matching of faces in digital images or video frames to a face database, which is now widely used for mobile phone facelock, smart door locking, etc.
- Emotion recognition**`{{spaced ndash}}`{=mediawiki}**a subset of facial recognition, emotion recognition refers to the process of classifying human emotions. Psychologists caution, however, that internal emotions cannot be reliably detected from faces.
- **Shape Recognition Technology** (SRT) in people counter systems differentiating human beings (head and shoulder patterns) from objects.
- **Human activity recognition** - deals with recognizing the activity from a series of video frames, such as, if the person is picking up an object or walking.
### Motion analysis {#motion_analysis}
Several tasks relate to motion estimation, where an image sequence is processed to produce an estimate of the velocity either at each points in the image or in the 3D scene or even of the camera that produces the images. Examples of such tasks are:
- **Egomotion**`{{spaced ndash}}`{=mediawiki}determining the 3D rigid motion (rotation and translation) of the camera from an image sequence produced by the camera.
- **Tracking**`{{spaced ndash}}`{=mediawiki}following the movements of a (usually) smaller set of interest points or objects (*e.g.*, vehicles, objects, humans or other organisms) in the image sequence. This has vast industry applications as most high-running machinery can be monitored in this way.
- **Optical flow**`{{spaced ndash}}`{=mediawiki}to determine, for each point in the image, how that point is moving relative to the image plane, *i.e.*, its apparent motion. This motion is a result of both how the corresponding 3D point is moving in the scene and how the camera is moving relative to the scene.
### Scene reconstruction {#scene_reconstruction}
Given one or (typically) more images of a scene, or a video, scene reconstruction aims at computing a 3D model of the scene. In the simplest case, the model can be a set of 3D points. More sophisticated methods produce a complete 3D surface model. The advent of 3D imaging not requiring motion or scanning, and related processing algorithms is enabling rapid advances in this field. Grid-based 3D sensing can be used to acquire 3D images from multiple angles. Algorithms are now available to stitch multiple 3D images together into point clouds and 3D models.
### Image restoration {#image_restoration}
Image restoration comes into the picture when the original image is degraded or damaged due to some external factors like lens wrong positioning, transmission interference, low lighting or motion blurs, etc., which is referred to as noise. When the images are degraded or damaged, the information to be extracted from them also gets damaged. Therefore, we need to recover or restore the image as it was intended to be. The aim of image restoration is the removal of noise (sensor noise, motion blur, etc.) from images. The simplest possible approach for noise removal is various types of filters, such as low-pass filters or median filters. More sophisticated methods assume a model of how the local image structures look to distinguish them from noise. By first analyzing the image data in terms of the local image structures, such as lines or edges, and then controlling the filtering based on local information from the analysis step, a better level of noise removal is usually obtained compared to the simpler approaches.
An example in this field is inpainting.
## System methods {#system_methods}
The organization of a computer vision system is highly application-dependent. Some systems are stand-alone applications that solve a specific measurement or detection problem, while others constitute a sub-system of a larger design which, for example, also contains sub-systems for control of mechanical actuators, planning, information databases, man-machine interfaces, etc. The specific implementation of a computer vision system also depends on whether its functionality is pre-specified or if some part of it can be learned or modified during operation. Many functions are unique to the application. There are, however, typical functions that are found in many computer vision systems.
- **Image acquisition** -- A digital image is produced by one or several image sensors, which, besides various types of light-sensitive cameras, include range sensors, tomography devices, radar, ultra-sonic cameras, etc. Depending on the type of sensor, the resulting image data is an ordinary 2D image, a 3D volume, or an image sequence. The pixel values typically correspond to light intensity in one or several spectral bands (gray images or colour images) but can also be related to various physical measures, such as depth, absorption or reflectance of sonic or electromagnetic waves, or magnetic resonance imaging.
- **Pre-processing** -- Before a computer vision method can be applied to image data in order to extract some specific piece of information, it is usually necessary to process the data in order to ensure that it satisfies certain assumptions implied by the method. Examples are:
- Re-sampling to ensure that the image coordinate system is correct.
- Noise reduction to ensure that sensor noise does not introduce false information.
- Contrast enhancement to ensure that relevant information can be detected.
- Scale space representation to enhance image structures at locally appropriate scales.
- **Feature extraction** -- Image features at various levels of complexity are extracted from the image data. Typical examples of such features are:
- Lines, edges and ridges.
- Localized interest points such as corners, blobs or points.
: More complex features may be related to texture, shape, or motion.
- **Detection/segmentation** -- At some point in the processing, a decision is made about which image points or regions of the image are relevant for further processing. Examples are:
- Selection of a specific set of interest points.
- Segmentation of one or multiple image regions that contain a specific object of interest.
- Segmentation of image into nested scene architecture comprising foreground, object groups, single objects or salient object parts (also referred to as spatial-taxon scene hierarchy), while the visual salience is often implemented as spatial and temporal attention.
- Segmentation or co-segmentation of one or multiple videos into a series of per-frame foreground masks while maintaining its temporal semantic continuity.
- **High-level processing** -- At this step, the input is typically a small set of data, for example, a set of points or an image region, which is assumed to contain a specific object. The remaining processing deals with, for example:
- Verification that the data satisfies model-based and application-specific assumptions.
- Estimation of application-specific parameters, such as object pose or object size.
- Image recognition -- classifying a detected object into different categories.
- Image registration -- comparing and combining two different views of the same object.
- **Decision making** Making the final decision required for the application, for example:
- Pass/fail on automatic inspection applications.
- Match/no-match in recognition applications.
- Flag for further human review in medical, military, security and recognition applications.
### Image-understanding systems {#image_understanding_systems}
Image-understanding systems (IUS) include three levels of abstraction as follows: low level includes image primitives such as edges, texture elements, or regions; intermediate level includes boundaries, surfaces and volumes; and high level includes objects, scenes, or events. Many of these requirements are entirely topics for further research.
The representational requirements in the designing of IUS for these levels are: representation of prototypical concepts, concept organization, spatial knowledge, temporal knowledge, scaling, and description by comparison and differentiation.
While inference refers to the process of deriving new, not explicitly represented facts from currently known facts, control refers to the process that selects which of the many inference, search, and matching techniques should be applied at a particular stage of processing. Inference and control requirements for IUS are: search and hypothesis activation, matching and hypothesis testing, generation and use of expectations, change and focus of attention, certainty and strength of belief, inference and goal satisfaction.
## Hardware
There are many kinds of computer vision systems; however, all of them contain these basic elements: a power source, at least one image acquisition device (camera, ccd, etc.), a processor, and control and communication cables or some kind of wireless interconnection mechanism. In addition, a practical vision system contains software, as well as a display in order to monitor the system. Vision systems for inner spaces, as most industrial ones, contain an illumination system and may be placed in a controlled environment. Furthermore, a completed system includes many accessories, such as camera supports, cables, and connectors.
Most computer vision systems use visible-light cameras passively viewing a scene at frame rates of at most 60 frames per second (usually far slower).
A few computer vision systems use image-acquisition hardware with active illumination or something other than visible light or both, such as structured-light 3D scanners, thermographic cameras, hyperspectral imagers, radar imaging, lidar scanners, magnetic resonance images, side-scan sonar, synthetic aperture sonar, etc. Such hardware captures \"images\" that are then processed often using the same computer vision algorithms used to process visible-light images.
While traditional broadcast and consumer video systems operate at a rate of 30 frames per second, advances in digital signal processing and consumer graphics hardware has made high-speed image acquisition, processing, and display possible for real-time systems on the order of hundreds to thousands of frames per second. For applications in robotics, fast, real-time video systems are critically important and often can simplify the processing needed for certain algorithms. When combined with a high-speed projector, fast image acquisition allows 3D measurement and feature tracking to be realized.
Egocentric vision systems are composed of a wearable camera that automatically take pictures from a first-person perspective.
As of 2016, vision processing units are emerging as a new class of processors to complement CPUs and graphics processing units (GPUs) in this role.
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Cotangent space
|
In differential geometry, the **cotangent space** is a vector space associated with a point $x$ on a smooth (or differentiable) manifold $\mathcal M$; one can define a cotangent space for every point on a smooth manifold. Typically, the cotangent space, $T^*_x\!\mathcal M$ is defined as the dual space of the tangent space at *$x$*, $T_x\mathcal M$, although there are more direct definitions (see below). The elements of the cotangent space are called **cotangent vectors** or **tangent covectors**.
## Properties
All cotangent spaces at points on a connected manifold have the same dimension, equal to the dimension of the manifold. All the cotangent spaces of a manifold can be \"glued together\" (i.e. unioned and endowed with a topology) to form a new differentiable manifold of twice the dimension, the cotangent bundle of the manifold.
The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms. The introduction of a Riemannian metric or a symplectic form gives rise to a natural isomorphism between the tangent space and the cotangent space at a point, associating to any tangent covector a canonical tangent vector.
## Formal definitions {#formal_definitions}
### Definition as linear functionals {#definition_as_linear_functionals}
Let $\mathcal M$ be a smooth manifold and let $x$ be a point in $\mathcal M$. Let $T_x\mathcal M$ be the tangent space at $x$. Then the cotangent space at $x$ is defined as the dual space of `{{nowrap|<math>T_x\mathcal M</math>:}}`{=mediawiki}
$$T^*_x\!\mathcal M = (T_x \mathcal M)^*$$
Concretely, elements of the cotangent space are linear functionals on $T_x\mathcal M$. That is, every element $\alpha\in T^*_x\mathcal M$ is a linear map
$$\alpha:T_x\mathcal M \to F$$
where $F$ is the underlying field of the vector space being considered, for example, the field of real numbers. The elements of $T^*_x\!\mathcal M$ are called cotangent vectors.
### Alternative definition {#alternative_definition}
In some cases, one might like to have a direct definition of the cotangent space without reference to the tangent space. Such a definition can be formulated in terms of equivalence classes of smooth functions on $\mathcal M$. Informally, we will say that two smooth functions *f* and *g* are equivalent at a point $x$ if they have the same first-order behavior near $x$, analogous to their linear Taylor polynomials; two functions *f* and *g* have the same first order behavior near $x$ if and only if the derivative of the function *f* − *g* vanishes at $x$. The cotangent space will then consist of all the possible first-order behaviors of a function near $x$.
Let $\mathcal M$ be a smooth manifold and let $x$ be a point in $\mathcal M$. Let $I_x$be the ideal of all functions in $C^\infty\! (\mathcal M)$ vanishing at $x$, and let $I_x^2$ be the set of functions of the form $\sum_i f_i g_i$, where $f_i, g_i \in I_x$. Then $I_x$ and $I_x^2$ are both real vector spaces and the cotangent space can be defined as the quotient space $T^*_x\!\mathcal M = I_x/I^2_x$ by showing that the two spaces are isomorphic to each other.
This formulation is analogous to the construction of the cotangent space to define the Zariski tangent space in algebraic geometry. The construction also generalizes to locally ringed spaces.
## The differential of a function {#the_differential_of_a_function}
Let $M$ be a smooth manifold and let $f\in C^\infty(M)$ be a smooth function. The differential of $f$ at a point $x$ is the map
$$\mathrm d f_x(X_x) = X_x(f)$$ where $X_x$ is a tangent vector at $x$, thought of as a derivation. That is $X(f)=\mathcal{L}_Xf$ is the Lie derivative of $f$ in the direction $X$, and one has $\mathrm df(X)=X(f)$. Equivalently, we can think of tangent vectors as tangents to curves, and write
$$\mathrm d f_x(\gamma'(0))=(f\circ\gamma)'(0)$$ In either case, $\mathrm df_x$ is a linear map on $T_xM$ and hence it is a tangent covector at $x$.
We can then define the differential map $\mathrm d:C^\infty(M)\to T_x^*(M)$ at a point $x$ as the map which sends $f$ to $\mathrm df_x$. Properties of the differential map include:
1. $\mathrm d$ is a linear map: $\mathrm d(af+bg)=a\mathrm df + b\mathrm dg$ for constants $a$ and $b$,
2. $\mathrm d(fg)_x=f(x)\mathrm dg_x+g(x)\mathrm df_x$
The differential map provides the link between the two alternate definitions of the cotangent space given above. Since for all $f \in I^2_x$ there exist $g_i, h_i \in I_x$ such that $f=\sum_i g_i h_i$, we have,
$\begin{array}{rcl}
\mathrm d f_x & = & \sum_i \mathrm d (g_i h_i)_x \\
& = & \sum_i (g_i(x)\mathrm d(h_i)_x+\mathrm d(g_i)_x h_{i}(x)) \\
& = & \sum_i (0\mathrm d(h_i)_x+\mathrm d(g_i)_x 0) \\
& = & 0
\end{array}$
So that all function in $I^2_x$ have differential zero, it follows that for every two functions $f \in I^2_x$, $g \in I_x$, we have $\mathrm d (f+g)=\mathrm d (g)$. We can now construct an isomorphism between $T^*_x\!\mathcal M$ and $I_x/I^2_x$ by sending linear maps $\alpha$ to the corresponding cosets $\alpha + I^2_x$. Since there is a unique linear map for a given kernel and slope, this is an isomorphism, establishing the equivalence of the two definitions.
## The pullback of a smooth map {#the_pullback_of_a_smooth_map}
Just as every differentiable map $f:M\to N$ between manifolds induces a linear map (called the *pushforward* or *derivative*) between the tangent spaces
$$f_{*}^{}\colon T_x M \to T_{f(x)} N$$ every such map induces a linear map (called the *pullback*) between the cotangent spaces, only this time in the reverse direction:
$$f^{*}\colon T_{f(x)}^{*} N \to T_{x}^{*} M .$$ The pullback is naturally defined as the dual (or transpose) of the pushforward. Unraveling the definition, this means the following:
$$(f^{*}\theta)(X_x) = \theta(f_{*}^{}X_x) ,$$ where $\theta\in T_{f(x)}^*N$ and $X_x\in T_xM$. Note carefully where everything lives.
If we define tangent covectors in terms of equivalence classes of smooth maps vanishing at a point then the definition of the pullback is even more straightforward. Let $g$ be a smooth function on $N$ vanishing at $f(x)$. Then the pullback of the covector determined by $g$ (denoted $\mathrm d g$) is given by
$$f^{*}\mathrm dg = \mathrm d(g \circ f).$$ That is, it is the equivalence class of functions on $M$ vanishing at $x$ determined by $g\circ f$.
## Exterior powers {#exterior_powers}
The $k$-th exterior power of the cotangent space, denoted $\Lambda^k(T_x^*\mathcal{M})$, is another important object in differential and algebraic geometry. Vectors in the $k$-th exterior power, or more precisely sections of the $k$-th exterior power of the cotangent bundle, are called differential $k$-forms. They can be thought of as alternating, multilinear maps on $k$ tangent vectors. For this reason, tangent covectors are frequently called *one-forms*.
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6,621 |
Cnidaria
|
**Cnidaria** (`{{IPAc-en|n|ᵻ|ˈ|d|ɛər|i|ə|,_|n|aɪ|-}}`{=mediawiki} `{{respell|nih|DAIR|ee|ə|,_|ny|-}}`{=mediawiki}) is a phylum under kingdom Animalia containing over 11,000 species of aquatic invertebrates found both in freshwater and marine environments (predominantly the latter), including jellyfish, hydroids, sea anemones, corals and some of the smallest marine parasites. Their distinguishing features are an uncentralized nervous system distributed throughout a gelatinous body and the presence of cnidocytes or cnidoblasts, specialized cells with ejectable flagella used mainly for envenomation and capturing prey. Their bodies consist of mesoglea, a non-living, jelly-like substance, sandwiched between two layers of epithelium that are mostly one cell thick. Cnidarians are also some of the few animals that can reproduce both sexually and asexually.
Cnidarians mostly have two basic body forms: swimming medusae and sessile polyps, both of which are radially symmetrical with mouths surrounded by tentacles that bear cnidocytes, which are specialized stinging cells used to capture prey. Both forms have a single orifice and body cavity that are used for digestion and respiration. Many cnidarian species produce colonies that are single organisms composed of medusa-like or polyp-like zooids, or both (hence they are trimorphic). Cnidarians\' activities are coordinated by a decentralized nerve net and simple receptors. Cnidarians also have rhopalia, which are involved in gravity sensing and sometimes chemoreception. Several free-swimming species of Cubozoa and Scyphozoa possess balance-sensing statocysts, and some have simple eyes. Not all cnidarians reproduce sexually, but many species have complex life cycles of asexual polyp stages and sexual medusae stages. Some, however, omit either the polyp or the medusa stage, and the parasitic classes evolved to have neither form.
Cnidarians were formerly grouped with ctenophores, also known as comb jellies, in the phylum Coelenterata, but increasing awareness of their differences caused them to be placed in separate phyla. Most cnidarians are classified into four main groups: the almost wholly sessile Anthozoa (sea anemones, corals, sea pens); swimming Scyphozoa (jellyfish); Cubozoa (box jellies); and Hydrozoa (a diverse group that includes all the freshwater cnidarians as well as many marine forms, and which has both sessile members, such as *Hydra*, and colonial swimmers (such as the Portuguese man o\' war)). Staurozoa have recently been recognised as a class in their own right rather than a sub-group of Scyphozoa, and the highly derived parasitic Myxozoa and Polypodiozoa were firmly recognized as cnidarians only in 2007.
Most cnidarians prey on organisms ranging in size from plankton to animals several times larger than themselves, but many obtain much of their nutrition from symbiotic dinoflagellates, and a few are parasites. Many are preyed on by other animals including starfish, sea slugs, fish, turtles, and even other cnidarians. Many scleractinian corals---which form the structural foundation for coral reefs---possess polyps that are filled with symbiotic photo-synthetic zooxanthellae. While reef-forming corals are almost entirely restricted to warm and shallow marine waters, other cnidarians can be found at great depths, in polar regions, and in freshwater.
Cnidarians are a very ancient phylum, with fossils having been found in rocks formed about `{{ma|580}}`{=mediawiki} during the Ediacaran period, preceding the Cambrian Explosion. Other fossils show that corals may have been present shortly before `{{ma|490}}`{=mediawiki} and diversified a few million years later. Molecular clock analysis of mitochondrial genes suggests an even older age for the crown group of cnidarians, estimated around `{{ma|741}}`{=mediawiki}, almost 200 million years before the Cambrian period, as well as before any fossils. Recent phylogenetic analyses support monophyly of cnidarians, as well as the position of cnidarians as the sister group of bilaterians.
## Etymology
The term *cnidaria* derives from the Ancient Greek word *knídē* (κνίδη "nettle"), signifying the coiled thread reminiscent of cnidocytes.
## Distinguishing features {#distinguishing_features}
Cnidarians form a phylum of animals that are more complex than sponges, about as complex as ctenophores (comb jellies), and less complex than bilaterians, which include almost all other animals. Both cnidarians and ctenophores are more complex than sponges as they have: cells bound by inter-cell connections and carpet-like basement membranes; muscles; nervous systems; and **some** have sensory organs. Cnidarians are distinguished from all other animals by having cnidocytes that fire harpoon-like structures that are mainly used to capture prey. In some species, cnidocytes can also be used as anchors. Cnidarians are also distinguished by the fact that they have only one opening in their body for ingestion and excretion i.e. they do not have a separate mouth and anus.
Like sponges and ctenophores, cnidarians have two main layers of cells that sandwich a middle layer of jelly-like material, which is called the mesoglea in cnidarians; more complex animals have three main cell layers and no intermediate jelly-like layer. Hence, cnidarians and ctenophores have traditionally been labelled diploblastic, along with sponges. However, both cnidarians and ctenophores have a type of muscle that, in more complex animals, arises from the middle cell layer. As a result, some recent text books classify ctenophores as triploblastic, and it has been suggested that cnidarians evolved from triploblastic ancestors.
Sponges Cnidarians Ctenophores Bilateria
------------------------------------------------------------- ----------------------------------------------------------------------------- -------------------------------------------- ---------------------- -------------------
Cnidocytes No Yes No
Colloblasts No Yes No
Digestive and circulatory organs No Yes
Number of main cell layers Two, with jelly-like layer between them Two Two Three
Cells in each layer bound together cell-adhesion molecules, but no basement membranes except Homoscleromorpha. inter-cell connections; basement membranes
Sensory organs No Yes
Number of cells in middle \"jelly\" layer Many Few (Not applicable)
Cells in outer layers can move inwards and change functions Yes No (Not applicable)
Nervous system No Yes, simple Simple to complex
Muscles None Mostly epitheliomuscular Mostly myoepithelial Mostly myocytes
## Description
### Basic body forms {#basic_body_forms}
Most adult cnidarians appear as either free-swimming medusae or sessile polyps, and many hydrozoans species are known to alternate between the two forms.
Both are radially symmetrical, like a wheel and a tube respectively. Since these animals have no heads, their ends are described as \"oral\" (nearest the mouth) and \"aboral\" (furthest from the mouth).
Most have fringes of tentacles equipped with cnidocytes around their edges, and medusae generally have an inner ring of tentacles around the mouth. Some hydroids may consist of colonies of zooids that serve different purposes, such as defence, reproduction and catching prey. The mesoglea of polyps is usually thin and often soft, but that of medusae is usually thick and springy, so that it returns to its original shape after muscles around the edge have contracted to squeeze water out, enabling medusae to swim by a sort of jet propulsion.
### Skeletons
In medusae, the only supporting structure is the mesoglea. *Hydra* and most sea anemones close their mouths when they are not feeding, and the water in the digestive cavity then acts as a hydrostatic skeleton, rather like a water-filled balloon. Other polyps such as *Tubularia* use columns of water-filled cells for support. Sea pens stiffen the mesoglea with calcium carbonate spicules and tough fibrous proteins, rather like sponges.
In some colonial polyps, a chitinous epidermis gives support and some protection to the connecting sections and to the lower parts of individual polyps. A few polyps collect materials such as sand grains and shell fragments, which they attach to their outsides. Some colonial sea anemones stiffen the mesoglea with sediment particles.
A mineralized exoskeleton made of calcium carbonate is found in subphylum Anthozoa in the order Scleractinia (stony corals; class Hexacorallia) and the class Octocorallia, and in subphylum Medusozoa in three hydrozoan families in order Anthoathecata; Milleporidae, Stylasteridae and Hydractiniidae (the latter with a mix of calcified and uncalcified species).
### Main cell layers {#main_cell_layers}
Cnidaria are diploblastic animals; in other words, they have two main cell layers, while more complex animals are triploblasts having three main layers. The two main cell layers of cnidarians form epithelia that are mostly one cell thick, and are attached to a fibrous basement membrane, which they secrete. They also secrete the jelly-like mesoglea that separates the layers. The layer that faces outwards, known as the ectoderm (\"outside skin\"), generally contains the following types of cells:
- Epitheliomuscular cells whose bodies form part of the epithelium but whose bases extend to form muscle fibers in parallel rows. The fibers of the outward-facing cell layer generally run at right angles to the fibers of the inward-facing one. In Anthozoa (anemones, corals, etc.) and Scyphozoa (jellyfish), the mesoglea also contains some muscle cells.
- Cnidocytes, the harpoon-like \"nettle cells\" that give the phylum Cnidaria its name. These appear between or sometimes on top of the muscle cells.
- Nerve cells. Sensory cells appear between or sometimes on top of the muscle cells, and communicate via synapses (gaps across which chemical signals flow) with motor nerve cells, which lie mostly between the bases of the muscle cells. Some form a simple nerve net.
- Interstitial cells, which are unspecialized and can replace lost or damaged cells by transforming into the appropriate types. These are found between the bases of muscle cells.
In addition to epitheliomuscular, nerve and interstitial cells, the inward-facing gastroderm (\"stomach skin\") contains gland cells that secrete digestive enzymes. In some species it also contains low concentrations of cnidocytes, which are used to subdue prey that is still struggling.
The mesoglea contains small numbers of amoeba-like cells, and muscle cells in some species. However, the number of middle-layer cells and types are much lower than in sponges.
### Polymorphism
Polymorphism refers to the occurrence of structurally and functionally more than two different types of individuals within the same organism. It is a characteristic feature of cnidarians, particularly the polyp and medusa forms, or of zooids within colonial organisms like those in Hydrozoa. In Hydrozoans, colonial individuals arising from individual zooids will take on separate tasks. For example, in *Obelia* there are feeding individuals, the gastrozooids; the individuals capable of asexual reproduction only, the gonozooids, blastostyles and free-living or sexually reproducing individuals, the medusae.
### Cnidocytes
These \"nettle cells\" function as harpoons, since their payloads remain connected to the bodies of the cells by threads. Three types of cnidocytes are known:
- Nematocysts inject venom into prey, and usually have barbs to keep them embedded in the victims. Most species have nematocysts.
- Spirocysts do not penetrate the victim or inject venom, but entangle it by means of small sticky hairs on the thread.
- Ptychocysts are not used for prey capture --- instead the threads of discharged ptychocysts are used for building protective tubes in which their owners live. Ptychocysts are found only in the order Ceriantharia, tube anemones.
The main components of a cnidocyte are:
- A cilium (fine hair) which projects above the surface and acts as a trigger. Spirocysts do not have cilia.
- A tough capsule, the cnida, which houses the thread, its payload and a mixture of chemicals that may include venom or adhesives or both. (\"cnida\" is derived from the Greek word κνίδη, which means \"nettle\")
- A tube-like extension of the wall of the cnida that points into the cnida, like the finger of a rubber glove pushed inwards. When a cnidocyte fires, the finger pops out. If the cell is a venomous nematocyte, the \"finger\"\'s tip reveals a set of barbs that anchor it in the prey.
- The thread, which is an extension of the \"finger\" and coils round it until the cnidocyte fires. The thread is usually hollow and delivers chemicals from the cnida to the target.
- An operculum (lid) over the end of the cnida. The lid may be a single hinged flap or three flaps arranged like slices of pie.
- The cell body, which produces all the other parts.
It is difficult to study the firing mechanisms of cnidocytes as these structures are small but very complex. At least four hypotheses have been proposed:
- Rapid contraction of fibers round the cnida may increase its internal pressure.
- The thread may be like a coiled spring that extends rapidly when released.
- In the case of *Chironex* (the \"sea wasp\"), chemical changes in the cnida\'s contents may cause them to expand rapidly by polymerization.
- Chemical changes in the liquid in the cnida make it a much more concentrated solution, so that osmotic pressure forces water in very rapidly to dilute it. This mechanism has been observed in nematocysts of the class Hydrozoa, sometimes producing pressures as high as 140 atmospheres, similar to that of scuba air tanks, and fully extending the thread in as little as 2 milliseconds (0.002 second).
Cnidocytes can only fire once, and about 25% of a hydra\'s nematocysts are lost from its tentacles when capturing a brine shrimp. Used cnidocytes have to be replaced, which takes about 48 hours. To minimise wasteful firing, two types of stimulus are generally required to trigger cnidocytes: nearby sensory cells detect chemicals in the water, and their cilia respond to contact. This combination prevents them from firing at distant or non-living objects. Groups of cnidocytes are usually connected by nerves and, if one fires, the rest of the group requires a weaker minimum stimulus than the cells that fire first.
### Locomotion
Medusae swim by a form of jet propulsion: muscles, especially inside the rim of the bell, squeeze water out of the cavity inside the bell, and the springiness of the mesoglea powers the recovery stroke. Since the tissue layers are very thin, they provide too little power to swim against currents and just enough to control movement within currents.
Hydras and some sea anemones can move slowly over rocks and sea or stream beds by various means: creeping like snails, crawling like inchworms, or by somersaulting. A few can swim clumsily by waggling their bases.
### Nervous system and senses {#nervous_system_and_senses}
Cnidarians are generally thought to have no brains or even central nervous systems. However, they do have integrative areas of neural tissue that could be considered some form of centralization. Most of their bodies are innervated by decentralized nerve nets that control their swimming musculature and connect with sensory structures, though each clade has slightly different structures. These sensory structures, usually called rhopalia, can generate signals in response to various types of stimuli such as light, pressure, chemical changes, and much more. Medusa usually have several of them around the margin of the bell that work together to control the motor nerve net, that directly innervates the swimming muscles. Most cnidarians also have a parallel system. In scyphozoans, this takes the form of a diffuse nerve net, which has modulatory effects on the nervous system. As well as forming the \"signal cables\" between sensory neurons and motoneurons, intermediate neurons in the nerve net can also form ganglia that act as local coordination centers. Communication between nerve cells can occur by chemical synapses or gap junctions in hydrozoans, though gap junctions are not present in all groups. Cnidarians have many of the same neurotransmitters as bilaterians, including chemicals such as glutamate, GABA, and glycine. Serotonin, dopamine, noradrenaline, octopamine, histamine, and acetylcholine, on the other hand, are absent.
This structure ensures that the musculature is excited rapidly and simultaneously, and can be directly stimulated from any point on the body, and it also is better able to recover after injury.
Medusae and complex swimming colonies such as siphonophores and chondrophores sense tilt and acceleration by means of statocysts, chambers lined with hairs which detect the movements of internal mineral grains called statoliths. If the body tilts in the wrong direction, the animal rights itself by increasing the strength of the swimming movements on the side that is too low. Most species have ocelli (\"simple eyes\"), which can detect sources of light. However, the agile box jellyfish are unique among Medusae because they possess four kinds of true eyes that have retinas, corneas and lenses. Although the eyes probably do not form images, Cubozoa can clearly distinguish the direction from which light is coming as well as negotiate around solid-colored objects.
### Feeding and excretion {#feeding_and_excretion}
Cnidarians feed in several ways: predation, absorbing dissolved organic chemicals, filtering food particles out of the water, obtaining nutrients from symbiotic algae within their cells, and parasitism. Most obtain the majority of their food from predation but some, including the corals *Hetroxenia* and *Leptogorgia*, depend almost completely on their endosymbionts and on absorbing dissolved nutrients. Cnidaria give their symbiotic algae carbon dioxide, some nutrients, and protection against predators.
Predatory species use their cnidocytes to poison or entangle prey, and those with venomous nematocysts may start digestion by injecting digestive enzymes. The \"smell\" of fluids from wounded prey makes the tentacles fold inwards and wipe the prey off into the mouth. In medusae, the tentacles around the edge of the bell are often short and most of the prey capture is done by \"oral arms\", which are extensions of the edge of the mouth and are often frilled and sometimes branched to increase their surface area. These \"oral arms\" aid in cnidarians\' ability to move prey towards their mouth once it has been poisoned and entangled. Medusae often trap prey or suspended food particles by swimming upwards, spreading their tentacles and oral arms and then sinking. In species for which suspended food particles are important, the tentacles and oral arms often have rows of cilia whose beating creates currents that flow towards the mouth, and some produce nets of mucus to trap particles. Their digestion is both intra and extracellular.
Once the food is in the digestive cavity, gland cells in the gastroderm release enzymes that reduce the prey to slurry, usually within a few hours. This circulates through the digestive cavity and, in colonial cnidarians, through the connecting tunnels, so that gastroderm cells can absorb the nutrients. Absorption may take a few hours, and digestion within the cells may take a few days. The circulation of nutrients is driven by water currents produced by cilia in the gastroderm or by muscular movements or both, so that nutrients reach all parts of the digestive cavity. Nutrients reach the outer cell layer by diffusion or, for animals or zooids such as medusae which have thick mesogleas, are transported by mobile cells in the mesoglea.
Indigestible remains of prey are expelled through the mouth. The main waste product of cells\' internal processes is ammonia, which is removed by the external and internal water currents.
### Respiration
There are no respiratory organs, and both cell layers absorb oxygen from and expel carbon dioxide into the surrounding water. When the water in the digestive cavity becomes stale it must be replaced, and nutrients that have not been absorbed will be expelled with it. Some Anthozoa have ciliated grooves on their tentacles, allowing them to pump water out of and into the digestive cavity without opening the mouth. This improves respiration after feeding and allows these animals, which use the cavity as a hydrostatic skeleton, to control the water pressure in the cavity without expelling undigested food.
Cnidaria that carry photosynthetic symbionts may have the opposite problem, an excess of oxygen, which may prove toxic. The animals produce large quantities of antioxidants to neutralize the excess oxygen.
### Regeneration
All cnidarians can regenerate, allowing them to recover from injury and to reproduce asexually. Medusae have limited ability to regenerate, but polyps can do so from small pieces or even collections of separated cells. This enables corals to recover even after apparently being destroyed by predators.
## Reproduction
### Sexual
Cnidarian sexual reproduction often involves a complex life cycle with both polyp and medusa stages. For example, in Scyphozoa (jellyfish) and Cubozoa (box jellies), a larva swims until it finds a good site, and then becomes a polyp. This grows normally but then absorbs its tentacles and splits horizontally into a series of disks that become juvenile medusae, a process called strobilation. The juveniles swim off and slowly grow to maturity, while the polyp re-grows and may continue strobilating periodically. The adult medusae have gonads in the gastroderm, and these release ova and sperm into the water in the breeding season.
This phenomenon of succession of differently organized generations (one asexually reproducing, sessile polyp, followed by a free-swimming medusa or a sessile polyp that reproduces sexually) is sometimes called \"alternation of asexual and sexual phases\" or \"metagenesis\", but should not be confused with the alternation of generations as found in plants.
Shortened forms of this life cycle are common, for example some oceanic scyphozoans omit the polyp stage completely, and cubozoan polyps produce only one medusa. Hydrozoa have a variety of life cycles. Some have no polyp stages and some (e.g. *hydra*) have no medusae. In some species, the medusae remain attached to the polyp and are responsible for sexual reproduction; in extreme cases these reproductive zooids may not look much like medusae. Meanwhile, life cycle reversal, in which polyps are formed directly from medusae without the involvement of sexual reproduction process, was observed in both Hydrozoa (*Turritopsis dohrnii* and *Laodicea undulata*) and Scyphozoa (*Aurelia* sp.1). Anthozoa have no medusa stage at all and the polyps are responsible for sexual reproduction.
Spawning is generally driven by environmental factors such as changes in the water temperature, and their release is triggered by lighting conditions such as sunrise, sunset or the phase of the moon. Many species of Cnidaria may spawn simultaneously in the same location, so that there are too many ova and sperm for predators to eat more than a tiny percentage --- one famous example is the Great Barrier Reef, where at least 110 corals and a few non-cnidarian invertebrates produce enough gametes to turn the water cloudy. These mass spawnings may produce hybrids, some of which can settle and form polyps, but it is not known how long these can survive. In some species the ova release chemicals that attract sperm of the same species.
The fertilized eggs develop into larvae by dividing until there are enough cells to form a hollow sphere (blastula) and then a depression forms at one end (gastrulation) and eventually becomes the digestive cavity. However, in cnidarians the depression forms at the end further from the yolk (at the animal pole), while in bilaterians it forms at the other end (vegetal pole). The larvae, called planulae, swim or crawl by means of cilia. They are cigar-shaped but slightly broader at the \"front\" end, which is the aboral, vegetal-pole end and eventually attaches to a substrate if the species has a polyp stage.
Anthozoan larvae either have large yolks or are capable of feeding on plankton, and some already have endosymbiotic algae that help to feed them. Since the parents are immobile, these feeding capabilities extend the larvae\'s range and avoid overcrowding of sites. Scyphozoan and hydrozoan larvae have little yolk and most lack endosymbiotic algae, and therefore have to settle quickly and metamorphose into polyps. Instead, these species rely on their medusae to extend their ranges.
### Asexual
All known cnidarians can reproduce asexually by various means, in addition to regenerating after being fragmented. Hydrozoan polyps only bud, while the medusae of some hydrozoans can divide down the middle. Scyphozoan polyps can both bud and split down the middle. In addition to both of these methods, Anthozoa can split horizontally just above the base. Asexual reproduction makes the daughter cnidarian a clone of the adult. The ability of cnidarians to asexually reproduce ensures a greater number of mature medusa that can mature to reproduce sexually.
### DNA repair {#dna_repair}
Two classical DNA repair pathways, nucleotide excision repair and base excision repair, are present in hydra, and these repair pathways facilitate unhindered reproduction. The identification of these pathways in hydra is based, in part, on the presence in the hydra genome of genes homologous to genes in other genetically well studied species that have been demonstrated to play key roles in these DNA repair pathways.
## Classification
Cnidarians were for a long time grouped with ctenophores in the phylum Coelenterata, but increasing awareness of their differences caused them to be placed in separate phyla. Modern cnidarians are generally classified into four main classes: sessile Anthozoa (sea anemones, corals, sea pens); swimming Scyphozoa (jellyfish) and Cubozoa (box jellies); and Hydrozoa, a diverse group that includes all the freshwater cnidarians as well as many marine forms, and has both sessile members such as *Hydra* and colonial swimmers such as the Portuguese Man o\' War. Staurozoa have recently been recognised as a class in their own right rather than a sub-group of Scyphozoa, and the parasitic Myxozoa and Polypodiozoa are now recognized as highly derived cnidarians rather than more closely related to the bilaterians.
Hydrozoa Scyphozoa Cubozoa Anthozoa Myxozoa
-------------------------------------- ------------------------ ----------- ------------- -------------------------------- ------------------------
Number of species 3,600 228 42 6,100 1300
Examples *Hydra*, siphonophores Jellyfish Box jellies Sea anemones, corals, sea pens *Myxobolus cerebralis*
Cells found in mesoglea No Yes Yes Yes
Nematocysts in exodermis No Yes Yes Yes
Medusa phase in life cycle In some species Yes Yes No
Number of medusae produced per polyp Many Many One (not applicable)
Stauromedusae, small sessile cnidarians with stalks and no medusa stage, have traditionally been classified as members of the Scyphozoa, but recent research suggests they should be regarded as a separate class, Staurozoa.
The Myxozoa, microscopic parasites, were first classified as protozoans. Research then found that *Polypodium hydriforme*, a non-myxozoan parasite *within* the egg cells of sturgeon, is closely related to the Myxozoa and suggested that both *Polypodium* and the Myxozoa were intermediate between cnidarians and bilaterian animals. More recent research demonstrates that the previous identification of bilaterian genes reflected contamination of the myxozoan samples by material from their host organism, and they are now firmly identified as heavily derived cnidarians, and more closely related to Hydrozoa and Scyphozoa than to Anthozoa.
Some researchers classify the extinct conulariids as cnidarians, while others propose that they form a completely separate phylum.
Current classification according to the World Register of Marine Species:
- class Anthozoa Ehrenberg, 1834
- subclass Ceriantharia Perrier, 1893 --- Tube-dwelling anemones
- subclass Hexacorallia Haeckel, 1896 --- stony corals
- subclass Octocorallia Haeckel, 1866 --- soft corals and sea fans
- class Cubozoa Werner, 1973 --- box jellies
- class Hydrozoa Owen, 1843 --- hydrozoans (fire corals, hydroids, hydroid jellyfishes, siphonophores\...)
- class Myxozoa Grassé, 1970 --- obligate parasites
- class Polypodiozoa Raikova, 1994 --- (uncertain status)
- class Scyphozoa Goette, 1887 --- \"true\" jellyfishes
- class Staurozoa Marques & Collins, 2004 --- stalked jellyfishes
Image:Cerianthus filiformis.jpg\|*Cerianthus filiformis* (Ceriantharia) Image:Haeckel Actiniae.jpg\|Sea anemones (Actiniaria, part of Hexacorallia) Image:Hertshoon.jpg\|Coral *Acropora muricata* (Scleractinia, part of Hexacorallia) Image:Gorgonia ventalina, Bahamas.jpg\|Sea fan *Gorgonia ventalina* (Alcyonacea, part of Octocorallia) Image:Carybdea branchi9.jpg\|Box jellyfish *Carybdea branchi* (Cubozoa) Image:Portuguese Man-O-War (Physalia physalis).jpg\|Siphonophore *Physalia physalis* (Hydrozoa) Image:Fdl17-9-grey.jpg\|*Myxobolus cerebralis* (Myxozoa) Image:Polypodium hydriforme.jpg\|*Polypodium hydriforme* (Polypodiozoa) Image:Phyllorhiza punctata macro II.jpg\|Jellyfish *Phyllorhiza punctata* (Scyphozoa) Image:Haliclystus antarcticus 1B.jpg\|Stalked jelly *Haliclystus antarcticus* (Staurozoa)
## Ecology
Many cnidarians are limited to shallow waters because they depend on endosymbiotic algae for much of their nutrients. The life cycles of most have polyp stages, which are limited to locations that offer stable substrates. Nevertheless, major cnidarian groups contain species that have escaped these limitations. Hydrozoans have a worldwide range: some, such as *Hydra*, live in freshwater; *Obelia* appears in the coastal waters of all the oceans; and *Liriope* can form large shoals near the surface in mid-ocean. Among anthozoans, a few scleractinian corals, sea pens and sea fans live in deep, cold waters, and some sea anemones inhabit polar seabeds while others live near hydrothermal vents over 10 km below sea-level. Reef-building corals are limited to tropical seas between 30°N and 30°S with a maximum depth of 46 m, temperatures between 20 and, high salinity, and low carbon dioxide levels. Stauromedusae, although usually classified as jellyfish, are stalked, sessile animals that live in cool to Arctic waters. Cnidarians range in size from a mere handful of cells for the parasitic myxozoans through *Hydra*\'s length of 5 -, to the lion\'s mane jellyfish, which may exceed 2 m in diameter and 75 m in length.
Prey of cnidarians ranges from plankton to animals several times larger than themselves. Some cnidarians are parasites, mainly on jellyfish but a few are major pests of fish. Others obtain most of their nourishment from endosymbiotic algae or dissolved nutrients. Predators of cnidarians include: sea slugs, flatworms and comb jellies, which can incorporate nematocysts into their own bodies for self-defense (nematocysts used by cnidarian predators are referred to as kleptocnidae); starfish, notably the crown of thorns starfish, which can devastate corals; butterfly fish and parrot fish, which eat corals; and marine turtles, which eat jellyfish. Some sea anemones and jellyfish have a symbiotic relationship with some fish; for example clownfish live among the tentacles of sea anemones, and each partner protects the other against predators.
Coral reefs form some of the world\'s most productive ecosystems. Common coral reef cnidarians include both anthozoans (hard corals, octocorals, anemones) and hydrozoans (fire corals, lace corals). The endosymbiotic algae of many cnidarian species are very effective primary producers, in other words converters of inorganic chemicals into organic ones that other organisms can use, and their coral hosts use these organic chemicals very efficiently. In addition, reefs provide complex and varied habitats that support a wide range of other organisms. Fringing reefs just below low-tide level also have a mutually beneficial relationship with mangrove forests at high-tide level and seagrass meadows in between: the reefs protect the mangroves and seagrass from strong currents and waves that would damage them or erode the sediments in which they are rooted, while the mangroves and seagrass protect the coral from large influxes of silt, fresh water and pollutants. This additional level of variety in the environment is beneficial to many types of coral reef animals, which for example may feed in the sea grass and use the reefs for protection or breeding.
## Evolutionary history {#evolutionary_history}
### Fossil record {#fossil_record}
The earliest widely accepted animal fossils are rather modern-looking cnidarians, possibly from around `{{ma|580}}`{=mediawiki}, although fossils from the Doushantuo Formation can only be dated approximately. The identification of some of these as embryos of animals has been contested, but other fossils from these rocks strongly resemble tubes and other mineralized structures made by corals. Their presence implies that the cnidarian and bilaterian lineages had already diverged. Although the Ediacaran fossil *Charnia* used to be classified as a jellyfish or sea pen, more recent study of growth patterns in *Charnia* and modern cnidarians has cast doubt on this hypothesis, leaving the Canadian polyp *Haootia* and the British *Auroralumina* as the only recognized cnidarian body fossils from the Ediacaran. *Auroralumina* is the earliest known animal predator. Few fossils of cnidarians without mineralized skeletons are known from more recent rocks, except in Lagerstätten that preserved soft-bodied animals.
A few mineralized fossils that resemble corals have been found in rocks from the Cambrian period, and corals diversified in the Early Ordovician. These corals, which were wiped out in the Permian--Triassic extinction event about `{{ma|252}}`{=mediawiki}, did not dominate reef construction since sponges and algae also played a major part. During the Mesozoic era, rudist bivalves were the main reef-builders, but they were wiped out in the Cretaceous--Paleogene extinction event `{{ma|66}}`{=mediawiki}, and since then the main reef-builders have been scleractinian corals.
Hydroconozoa is an extinct class of cnidarians, established by K.B. Korde in 1964 based on Lower Cambrian fossils from Tuva, USSR. These conical and cylindrical organisms, including genera like Hydroconus and Tuvaeconus, possessed external skeletons with features resembling both scyphozoans and tetracorals. Their unique skeletal structures suggest a distinct lineage within early cnidarian evolution.
### Phylogeny
It is difficult to reconstruct the early stages in the evolutionary \"family tree\" of animals using only morphology (their shapes and structures) because of the large differences between the major groups of animals. Hence, reconstructions now rely almost entirely on molecular phylogenetics, which groups organisms based on their biochemistry, most commonly by analyzing DNA or RNA sequences.
In 1866, it was proposed that Cnidaria and Ctenophora were more closely related to each other than to Bilateria and formed a group called Coelenterata (\"hollow guts\") because both rely on the flow of water in and out of a single cavity for feeding, excretion and respiration. In 1881, it was proposed that Ctenophora and Bilateria were more closely related to each other, since they shared features that Cnidaria lack, such as a middle layer of cells (mesoglea in Ctenophora, mesoderm in Bilateria) between the outer and inner layer found in other animals. However, more recent analyses indicate that these similarities were evolved independently in both lineages, instead of being present in their common ancestor. The current view is that Cnidaria and Bilateria are more closely related to each other than either is to Ctenophora. This grouping of Cnidaria and Bilateria has been labelled \"Planulozoa\", named so because the earliest Bilateria were probably similar to the planula larvae of Cnidaria.
In 2005, Katja Seipel and Volker Schmid suggested that cnidarians and ctenophores are simplified descendants of triploblastic animals, since ctenophores and the medusa stage of some cnidarians have striated muscle, which in bilaterians arises from the mesoderm. They did not commit themselves on whether bilaterians evolved from early cnidarians or from the hypothesized triploblastic ancestors of cnidarians.
Resolving the evolutionary relationships within Cnidaria has also been challenging, with almost every possible combination of clades being proposed. As time went on though, a semi-consensus has started to emerge. The enigmatic *Polypodium hydriforme* and subphylum Myxozoa have been firmly placed within the Cnidaria and have been shown to be closely related to the Medusozoa. In addition, these two groups have been found to likely be each other\'s closest relatives which, if true, would form the clade \"Endocnidozoa\". The relationships within the Medusozoa are currently probably the most contentious part of the tree. Traditionally, the class Scyphozoa also included Staurozoa and Cubozoa, but significant morphological differences eventually lead to the split of the three. The group containing them has since been named \"Acraspeda\". The relationships between these three and Hydrozoa have since and still are debated. A relationship between Scyphozoa and Cubozoa with Staurozoa as its sister has seen support in nearly all studies, but the position of the remaining class, Hydrozoa, is not understood. Several studies have found that Acraspeda is paraphyletic, with Hydrozoa being more closely related to Scyphozoa than to the other classes. At the same time, other studies have recovered Acraspeda as being monophyletic. The subphylum Anthozoa is argued to have either two or three classes, but the relationships between them is not disputed; the tube-dwelling anemones of the class Ceriantharia have consistently shown to be more closely related to the Hexacorallia than to the Octocorallia.
In molecular phylogenetics analyses from 2005 onwards, important groups of developmental genes show the same variety in cnidarians as in chordates. In fact cnidarians, and especially anthozoans (sea anemones and corals), retain some genes that are present in bacteria, protists, plants and fungi but not in bilaterians.
## Interaction with humans {#interaction_with_humans}
Jellyfish stings killed about 1,500 people in the 20th century, and cubozoans are particularly dangerous. On the other hand, some large jellyfish are considered a delicacy in East and Southeast Asia. Coral reefs have long been economically important as providers of fishing grounds, protectors of shore buildings against currents and tides, and more recently as centers of tourism. However, they are vulnerable to over-fishing, mining for construction materials, pollution, and damage caused by tourism.
Beaches protected from tides and storms by coral reefs are often the best places for housing in tropical countries. Reefs are an important food source for low-technology fishing, both on the reefs themselves and in the adjacent seas. However, despite their great productivity, reefs are vulnerable to over-fishing, because much of the organic carbon they produce is exhaled as carbon dioxide by organisms at the middle levels of the food chain and never reaches the larger species that are of interest to fishermen. Tourism centered on reefs provides much of the income of some tropical islands, attracting photographers, divers and sports fishermen. However, human activities damage reefs in several ways: mining for construction materials; pollution, including large influxes of fresh water from storm drains; commercial fishing, including the use of dynamite to stun fish and the capture of young fish for aquariums; and tourist damage caused by boat anchors and the cumulative effect of walking on the reefs. Coral, mainly from the Pacific Ocean has long been used in jewellery, and demand rose sharply in the 1980s.
Some large jellyfish species of the Rhizostomeae order are commonly consumed in Japan, Korea and Southeast Asia. In parts of the range, fishing industry is restricted to daylight hours and calm conditions in two short seasons, from March to May and August to November. The commercial value of jellyfish food products depends on the skill with which they are prepared, and \"Jellyfish Masters\" guard their trade secrets carefully. Jellyfish is very low in cholesterol and sugars, but cheap preparation can introduce undesirable amounts of heavy metals.
The \"sea wasp\" *Chironex fleckeri* has been described as the world\'s most venomous jellyfish and is held responsible for 67 deaths, although it is difficult to identify the animal as it is almost transparent. Most stingings by *C. fleckeri* cause only mild symptoms. Seven other box jellies can cause a set of symptoms called Irukandji syndrome, which takes about 30 minutes to develop, and from a few hours to two weeks to disappear. Hospital treatment is usually required, and there have been a few deaths.
A number of the parasitic myxozoans are commercially important pathogens in salmonid aquaculture. A Scyphozoa species -- *Pelagia noctiluca* -- and a Hydrozoa -- *Muggiaea atlantica* -- have caused repeated mass mortality in salmon farms over the years around Ireland. A loss valued at £1 million struck in November 2007, 20,000 died off Clare Island in 2013 and four fish farms collectively lost tens of thousands of salmon in September 2017.
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Children of Dune
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***Children of Dune*** is a 1976 science fiction novel by Frank Herbert, the third in his *Dune* series of six novels. Originally serialized in *Analog Science Fiction and Fact* in 1976, it was the last *Dune* novel to be serialized before book publication.
At the end of *Dune Messiah*, Paul Atreides walks into the desert, a blind man, leaving his sister Alia to rule the universe as regent for his twin children, Leto II and Ghanima. Awakened in the womb by the spice, the children are the heirs to Paul\'s prescient vision of the fate of the universe, a role that Alia desperately craves. House Corrino schemes to return to the throne, while the Bene Gesserit make common cause with the Tleilaxu and Spacing Guild to gain control of the spice and Paul\'s children.
Initially selling over 75,000 copies, it became the first hardcover best-seller in science fiction. The novel was critically well-received for its plot, action, and atmosphere and was nominated for the Hugo Award for Best Novel in 1977. *Dune Messiah* (1969) and *Children of Dune* were collectively adapted by the Sci-Fi Channel in 2003 into a miniseries titled *Frank Herbert\'s Children of Dune*.
## Plot
Nine years after Emperor Paul \"Muad\'Dib\" Atreides walked into the desert, the ecological transformation of Dune has reached the point where some Fremen are living without stillsuits in the less arid climate and have started to move out of the sietches and into villages and cities. As the old ways erode, more and more pilgrims arrive to experience the planet of Muad\'Dib. The imperial high council has lost its political might and is powerless to control the jihad.
Paul\'s young twin children, Leto II and Ghanima, have concluded that their aunt and guardian Alia has succumbed to Abomination---possession by her grandfather Baron Vladimir Harkonnen---and fear that a similar fate awaits them. They (and Alia) also realize that the terraforming of Dune will kill all the sandworms, thus destroying the source of the spice, but the Baron desires this outcome. Leto also fears that, like his father, he will become trapped by his prescience.
Meanwhile, a new religious figure called \"The Preacher\" has risen in the desert, rallying against the religious government\'s injustices and the changes among the Fremen. Some Fremen believe he is Paul Atreides. Princess Wensicia of the fallen House Corrino on Salusa Secundus plots to assassinate the twins and regain power for her House.
Lady Jessica returns to Arrakis and recognizes that her daughter is possessed, but finds no signs of Abomination in the twins. Leto arranges for Fremen leader Stilgar to protect Ghanima if there is an attempt on their lives. The Preacher journeys to Salusa Secundus to meet Wensicia\'s son Farad\'n, and in return pledges the Duncan Idaho ghola as an agent of House Corrino. Alia attempts to assassinate Jessica, who escapes into the desert with Duncan\'s help, precipitating a rebellion among the Fremen. The twins anticipate and survive the Corrino assassination plot, faking Leto\'s death.
Leto leaves to seek out Jacurutu, a mythical Fremen sietch and possible holdout of the Preacher, while Ghanima, changing her memory with self-hypnosis, reports (and believes) that her brother has been murdered. Duncan and Jessica flee to Salusa Secundus, where Jessica begins to mentor Farad\'n in the ways of the Bene Gesserit. He sidelines and publicly denounces his regent mother Wensicia over the assassination attempt, and allies with the Bene Gesserit, who promise to marry him to Ghanima and support his bid to become Emperor.
A band of Fremen outlaws capture Leto and force him to undergo the spice trance at the suggestion of Gurney Halleck, who has infiltrated the group on Jessica\'s orders. Leto\'s spice-induced visions show him a myriad of possible futures where humanity becomes extinct and only one where it survives. He names this future \"The Golden Path\" and resolves to bring it to fruition---something that his father, who had already glimpsed this future, refused to do. He escapes his captors and sacrifices his humanity in pursuit of the Golden Path by physically fusing with a school of sandtrout, the larval form of sandworms, in the process gaining superhuman strength and near-invulnerability. He travels across the desert destroying qanats to slow down the ecological transformation of Dune, and eventually confronts the Preacher, who is indeed Paul.
Duncan returns to Arrakis and provokes Stilgar into killing him so that Stilgar is forced to take Ghanima and go into hiding. Eventually though, Alia recaptures Ghanima and arranges her marriage to Farad\'n, planning to exploit the expected chaos when Ghanima kills him to avenge her brother\'s murder. Paul and Leto return to the capital, where Jessica and Farad\'n have arrived for his betrothal to Ghanima, to confront Alia. Upon arriving, Paul is publicly murdered by agents of Alia\'s government, to her horror. Leto reveals himself in a display of superhuman strength and triggers the return of Ghanima\'s genuine memories. He confronts Alia and offers to help her overcome her possession, but the Baron resists. Alia, while fighting the Baron\'s possession, manages to throw herself off a high balcony, killing both herself and the Baron.
Leto declares himself Emperor and asserts control over the Fremen. Farad\'n enlists in his service and delivers control of the Corrino armies and his Sardaukar. In describing the Golden Path to Farad\'n, Leto reveals that he will live for thousands of years due to the sandworm skin and genetics he is encased in. Leto marries Ghanima to consolidate power, but because his sandworm skin destroyed his ability to reproduce, he allows Farad\'n to be her true consort so the Atreides line can continue. Ghanima reflects that one twin had to follow the Path, but Leto was always the stronger.
## Publication history {#publication_history}
Parts of *Dune Messiah* and *Children of Dune* were written before *Dune* was completed. *Children of Dune* was originally serialized in *Analog Science Fiction and Fact* in 1976, and was the last *Dune* novel to be serialized before book publication. *Dune Messiah* and *Children of Dune* were published in one volume by the Science Fiction Book Club in 2002.
## Analysis
Herbert likened the initial trilogy of novels (*Dune*, *Dune Messiah*, and *Children of Dune*) to a fugue -- *Dune* was a heroic melody, *Dune Messiah* was its inversion, while *Children of Dune* expands the number of interplaying themes. Paul rises to power in *Dune* by seizing control of the single critical resource in the universe, melange. His enemies are dead or overthrown, and he is set to take the reins of power and bring a hard but enlightened peace to the universe. Herbert chose in the books that followed to undermine Paul\'s triumph with a string of failures and philosophical paradoxes.
## Critical reception {#critical_reception}
Initially selling over 75,000 copies, *Children of Dune* became the first hardcover best-seller in the science fiction field. The novel was critically well-received for its gripping plot, action, and atmosphere, and was nominated for the Hugo Award for Best Novel in 1977.
The *Los Angeles Times* called *Children of Dune* \"a major event\", and *Challenging Destiny* noted that \"Herbert adds enough new twists and turns to the ongoing saga that familiarity with the recurring elements brings pleasure.\" *Publishers Weekly* wrote, \"Ranging from palace intrigue and desert chases to religious speculation and confrontations with the supreme intelligence of the universe, there is something here for all science fiction fans.\" In a 1976 review, Spider Robinson found *Children of Dune* unsatisfying, faulting the ending as unconvincing and thematically overfamiliar. The novel is referred to in *A Thousand Plateaus* (1980) by Gilles Deleuze and Félix Guattari. David Pringle gave the novel a rating of two stars out of four and described the novel as \"dark and convoluted stuff.\"
## Adaptation
*Dune Messiah* (1969) and *Children of Dune* were collectively adapted by the Sci-Fi Channel in 2003 into a miniseries titled *Frank Herbert\'s Children of Dune*. The three-part, six-hour miniseries covers the bulk of the plot of *Dune Messiah* in the first installment, and adapts *Children of Dune* in the second and third parts.
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Chapterhouse: Dune
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***Chapterhouse: Dune*** is a 1985 science fiction novel by Frank Herbert, the last in his *Dune* series of six novels. It rose to No. 2 on *The New York Times* Best Seller list.
A direct follow-up to *Heretics of Dune*, the novel chronicles the continued struggles of the Bene Gesserit sisterhood against the violent Honored Matres, who are succeeding in their bid to seize control of the universe and destroy the factions and planets that oppose them.
*Chapterhouse: Dune* ends with a cliffhanger, and Herbert\'s subsequent death in 1986 left some overarching plotlines of the series unresolved. Two decades later, Herbert\'s son Brian Herbert, along with Kevin J. Anderson, published two sequels -- *Hunters of Dune* (2006) and *Sandworms of Dune* (2007) -- based in part on notes left behind by Frank Herbert for what he referred to as *Dune 7*, his own planned seventh novel in the *Dune* series.
## Plot
The Bene Gesserit find themselves the target of the Honored Matres, whose conquest of the Old Empire is almost complete. The Matres are seeking to assimilate the technology and superhuman skills of the Bene Gesserit, and exterminate the Sisterhood itself. Now in command of the Bene Gesserit, Mother Superior Darwi Odrade continues to develop her drastic, secret plan to overcome the Honored Matres. The Bene Gesserit are also terraforming the planet Chapterhouse to accommodate the all-important sandworms, as the planet Dune had been destroyed by the Matres.
Sheeana, in charge of the project, expects sandworms to appear soon. The Honored Matres have also destroyed the entire Bene Tleilax civilization, with Tleilaxu Master Scytale the only one of his kind left alive. In Bene Gesserit captivity, Scytale possesses the Tleilaxu secret of ghola production, which he has reluctantly traded for the Sisterhood\'s protection. The first ghola produced is that of their recently deceased military genius, Miles Teg. The Bene Gesserit have two other prisoners on Chapterhouse: the latest Duncan Idaho ghola, and his lover, former Honored Matre Murbella, whom they have accepted as a novice despite their suspicion that she intends to escape back to the Honored Matres.
Lampadas, a center for Bene Gesserit education, is destroyed by the Honored Matres. The planet\'s Chancellor, Reverend Mother Lucilla, manages to escape carrying the shared-minds of millions of Reverend Mothers. Lucilla is forced to land on Gammu where she seeks refuge with an underground group of Jews, known as \"Secret Israel\". The Rabbi gives Lucilla sanctuary, but to save his people from the Matres he must deliver her to them. Before doing so, he reveals Rebecca, a \"wild\" Reverend Mother who has gained her Other Memory without Bene Gesserit training.
Lucilla shares minds with Rebecca, who promises to take the memories of Lampadas safely back to the Sisterhood. Lucilla is then \"betrayed\", and taken before the Great Honored Matre Dama, who tries to persuade her to join the Honored Matres, preserving her life in exchange for Bene Gesserit secrets. The Honored Matres are particularly interested in learning to voluntarily modify their body chemistry, a skill that atrophied among the Bene Gesserit who went out into the Scattering and evolved into the Honored Matres. From this, Lucilla deduces that the greater enemy that the Matres are fleeing from is making extensive use of biological warfare. Lucilla refuses to share this knowledge with the Matres, and Dama ultimately kills her.
Back on Chapterhouse, Odrade confronts Duncan and forces him to admit that he is a Mentat, proving that he retains the memories of his many ghola lives. Meanwhile, Murbella collapses under the pressure of Bene Gesserit training, and realizes that she wants to be Bene Gesserit. Odrade believes that the Sisterhood made a mistake in fearing emotion, and that in order to evolve, they must learn to accept emotions. Murbella survives the spice agony and becomes a Reverend Mother. Odrade confronts Sheeana, discovering that Duncan and Sheeana have been allies for some time. Sheeana does not reveal that they have been considering the option of reawakening Teg\'s memory through imprinting, nor does Odrade discover that Sheeana has the keys to Duncan\'s no-ship prison.
Teg is awakened by Sheeana using imprinting techniques. Odrade appoints him again as Bashar of the military forces of the Sisterhood for the assault on the Honored Matres. Odrade announces to the Bene Gesserit that Teg will lead an attack against the Honored Matres. She also makes clear her intention to share her memories with Murbella and Sheeana, making them candidates to succeed her as Mother Superior if she dies. Odrade meets with the Great Honored Matre while the Bene Gesserit forces under Teg attack Gammu, and then Junction, with tremendous force. Teg uses his secret ability to see no-ships to secure control of the system, and victory for the Bene Gesserit seems inevitable. In the midst of this battle, Rebecca and the Jews take refuge with the Bene Gesserit fleet.
Dama\'s chief advisor Logno assassinates Dama with poison and assumes control of the Honored Matres. Too late, Odrade and Teg realize they have fallen into a trap, and the Honored Matres use a mysterious weapon, which kills without wounding, to turn defeat into victory, and capture Odrade. Murbella saves as much of the Bene Gesserit force as she can and they withdraw to Chapterhouse. Odrade, however, had planned for the possible failure of the Bene Gesserit attack and left Murbella instructions for a last desperate gamble. Murbella pilots a small craft down to the surface, announcing herself as an Honored Matre who, in the confusion, has managed to escape the Bene Gesserit with all their secrets. She arrives on the planet and is taken to the Great Honored Matre, and taunts her. Unable to control her anger, Logno attacks but is killed by Murbella.
Awed by her physical prowess, the remaining Honored Matres are forced to accept her as their new leader. Odrade is also killed in the melee and Murbella shares with Odrade to absorb her newest memories, as they had already shared prior to the battle. Murbella\'s ascension to leadership, and her bringing the Honored Matres to merge with the Bene Gesserit, is not accepted as victory by all the latter. Some flee Chapterhouse, notably Sheeana, who has a vision of her own, and arranges to have some of the new worms that have emerged in the Chapterhouse desert brought aboard the no-ship. Sheeana is joined by Duncan. The two escape in the giant no-ship, with Scytale, Teg and the Jews. Murbella recognizes their plan at the last minute, but is powerless to stop them. Two mysterious entities resembling an old married couple, Daniel and Marty, whom Duncan had seen in visions, wryly note the refugees\' escape.
## Reception
*Chapterhouse: Dune* debuted at No. 5 and rose to No. 2 on *The New York Times* Best Seller list. Gerald Jonas of *The New York Times* noted that \"Against all odds, the universe of *Dune* keeps getting richer in texture, more challenging in its moral dilemmas.\"
Dave Langford reviewed the novel for *White Dwarf* #65, and stated that \"The hyper-acute characters are impressive, the resolution thoughtful and humane. Though initially I gave up after *Children*, *Heretics* and *Chapter House* have partially Restored My Faith.\"
## Sequels
Two decades after Frank Herbert\'s death, his son Brian Herbert, along with Kevin J. Anderson, published two sequels -- *Hunters of Dune* (2006) and *Sandworms of Dune* (2007) -- based on notes left behind by Frank Herbert for what he referred to as *Dune 7*, his own planned seventh novel in the *Dune* series,`{{Herbert notes}}`{=mediawiki} while also continuing plot-lines from Brian Herbert\'s and Kevin J. Anderson\'s own *Dune* prequel novels.
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Cantor Fitzgerald
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**Cantor Fitzgerald, L.P.** is an American financial services firm that was founded in 1945. It specializes in institutional equity, fixed-income sales and trading, and serving the middle market with investment banking services, prime brokerage, and commercial real estate financing. It is also active in new businesses, including advisory and asset management services, gaming technology, and e-commerce. It has more than 5,000 institutional clients.
Cantor Fitzgerald is one of 24 primary dealers that are authorized to trade US government securities with the Federal Reserve Bank of New York.
Cantor Fitzgerald\'s 1,600 employees work in more than 30 locations, including financial centers in the Americas, Europe, Asia-Pacific, and the Middle East. Together with its affiliates, Cantor Fitzgerald operates in more than 60 offices in 20 countries and has more than 12,500 employees.
Before 2001, the company\'s headquarters were located between the 101st and 105th floors of the North Tower of the World Trade Center in New York City, just above the impact site of American Airlines Flight 11 during the September 11 attacks. 658 Cantor Fitzgerald employees who were present that day were killed, representing the largest loss of life among any single organization in the attacks.
## Early history {#early_history}
Cantor Fitzgerald was formed in 1945 by Bernard Gerald Cantor and John Fitzgerald as an investment bank and brokerage business.
In 1965, Cantor Fitzgerald began \"large block\" sales/trading of equities for institutional customers. It became the world\'s first electronic marketplace for US government securities in 1972, and in 1983 it was the first to offer worldwide screen brokerage services in US government securities, becoming in time the market\'s premier government securities dealer. It also became known for `{{clarification needed span|text=the quality of its institutional distribution business model.|reason=What exactly does this mean, in layman's terms, linked as best as it can be to pertinent Wikipedia articles.|date=April 2025}}`{=mediawiki}
In 1991, Howard Lutnick was named president and CEO of Cantor Fitzgerald; he became chairman of Cantor Fitzgerald, L.P., in 1996.
## September 11 attacks {#september_11_attacks}
Cantor Fitzgerald\'s corporate headquarters and New York City office, on the 101st to the 105th floors of 1 World Trade Center in Lower Manhattan (2 to 6 floors above the impact zone of American Airlines Flight 11), were destroyed during the September 11 attacks. At 8:46:46 a.m., eighteen seconds after the plane struck the tower, a Goldman Sachs server issued an alert saying that its trading system had gone offline because it could not connect with the server. Since all stairwells leading past the impact zone were destroyed by the initial crash or blocked with smoke, fire, or debris, every employee who reported for work that morning was killed in the attacks; 658 of its 960 New York employees were killed or missing, or 68.5% of its total workforce, which was considerably more than any of the other World Trade Center tenants, the New York City Police Department, the Port Authority Police Department, the New York City Fire Department, or the Department of Defense. Forty-six contractors, food service workers, and visitors in the Cantor Fitzgerald offices at the time were also killed. CEO Howard Lutnick was not present that day, but his younger brother, Gary, was among those killed. Lutnick vowed to keep the company alive, and the company was able to bring its trading markets back online within a week.
On September 19, Cantor Fitzgerald made a pledge to distribute 25% of the firm\'s profits for the next five years (that would otherwise have been distributed to its partners), and committed to paying for ten years of health care for the benefit of the families of its 658 former Cantor Fitzgerald, eSpeed, and TradeSpark employees. In 2006, the company had completed its promise, having paid a total of \$180 million (and an additional \$17 million from a relief fund run by Lutnick\'s sister, Edie).
Until the attacks, Cantor had handled about a quarter of the daily transactions in the multi-trillion dollar treasury security market. Cantor Fitzgerald subsequently rebuilt its infrastructure, partly through the efforts of its London office, and relocated its headquarters to Midtown Manhattan. The company\'s effort to regain its footing was the subject of Tom Barbash\'s 2003 book *On Top of the World: Cantor Fitzgerald, Howard Lutnick, and 9/11: A Story of Loss and Renewal* as well as a 2012 documentary, *Out of the Clear Blue Sky*.
On September 2, 2004, Cantor and other organizations filed a civil lawsuit against Saudi Arabia for allegedly providing money to the hijackers and al-Qaeda. It was later joined in the suit by the Port Authority of New York and New Jersey. Most of the claims against Saudi Arabia were dismissed on January 18, 2005.
In December 2013, Cantor Fitzgerald settled its lawsuit against American Airlines for \$135 million. Cantor Fitzgerald had been suing for loss of property and interruption of business by alleging the airline to have been negligent by allowing hijackers to board Flight 11.
## Recent history {#recent_history}
In 2003, the firm launched its fixed-income sales and trading group. Three years later, the Federal Reserve added Cantor Fitzgerald & Co. to its list of primary dealers. The firm later launched Cantor Prime Services in 2009. It was meant to be a provider of multi-asset, perimeter brokerage prime brokerage platforms to exploit its clearing, financing, and execution capabilities. A year after, Cantor Fitzgerald began building its real estate business with the launch of CCRE. Cantor\'s affiliate, BGC Partners, expanded into commercial real estate services in 2011 by its purchase of Newmark Knight Frank and the assets of Grubb & Ellis, to form Newmark Grubb Knight Frank.
On December 5, 2014, two Cantor Fitzgerald analysts were said to be in the top 25 analysts on TipRanks. Cantor Fitzgerald has a prolific special-purpose acquisition company underwriting practice, having led all banks in SPAC underwriting activity in both 2018 and 2019.
In March 2016, Sage Kelly, formerly of Jefferies & Co., joined the firm as senior managing director and head of its investment-banking division.
## Philanthropy
Former chairman and CEO Howard Lutnick\'s sister Edie wrote *An Unbroken Bond: The Untold Story of How the 658 Cantor Fitzgerald Families Faced the Tragedy of 9/11 and Beyond*. All proceeds from the book\'s sale benefit the Cantor Fitzgerald Relief Fund and the charities it assists.
The Cantor Fitzgerald Relief Fund provided \$10 million to families affected by Hurricane Sandy. Howard Lutnick and the Relief Fund \"adopted\" 19 elementary schools in impacted areas by distributing \$1,000 prepaid debit cards to each family from the schools. A total of \$10 million in funds was given to families affected by the storm.
Two days after the 2013 Moore tornado struck Moore, Oklahoma, killing 24 people and injuring hundreds, Lutnick pledged to donate \$2 million to families affected by the tornado. The donation was given to families in the form of \$1,000 debit cards.
Each year, on September 11, Cantor Fitzgerald and its affiliate, BGC Partners, donate 100% of their revenue to charitable causes on their annual Charity Day, which was initially established to raise money to assist the families of the Cantor employees who died in the World Trade Center attacks. Since its inception, Charity Day has raised \$192 million for charities globally.
## Subsidiaries and affiliates {#subsidiaries_and_affiliates}
The firm has many subsidiaries and affiliates, including:
- BGC Partners, named after fixed-income trading innovator and founder B. Gerald Cantor, is a global brokerage company that services the wholesale financial markets and commercial real estate marketplace in New York, London, and other financial centers. BGC Partners includes Newmark Grubb Knight Frank, the fourth-largest real estate service provider in the US.
- Cantor Ventures is the company\'s corporate venture capital and enterprise development arm. Led by Henrique De Castro, the group\'s current investments include delivery.com, Ritani, TopLine Game Labs, AdFin, Lucera, NewsWhip, and XIX Entertainment.
- Hollywood Stock Exchange, founded in 1996, is the world\'s virtual entertainment stock market.
- TopLine Game Labs is a technology company to create short-duration fantasy sports and entertainment-based social gaming. Headquartered in Los Angeles, TopLine Game Labs was, in 2013, building a platform-agnostic architecture to power game experiences for sports.
## Senior management {#senior_management}
### List of chairpersons {#list_of_chairpersons}
1. Bernie Cantor (1945--1996)
2. Howard Lutnick (1996--2025)
3. Brandon Lutnick (2025--present)
### List of CEOs {#list_of_ceos}
1. Bernie Cantor (1945--1991)
2. Howard Lutnick (1991--2025)
3. Pascal Bandelier, Sage Kelly, and Christian Wall (co-CEOs) (since February 2025)
### List of presidents {#list_of_presidents}
1. Anshu Jain (2017--2022)
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Lists of composers
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This is a list of lists of composers grouped by various criteria.
## Name
- List of composers by name
## Women
- List of female composers by name
- List of female composers by birth date
- List of Australian female composers
## Genre
- Anime composer
- List of Carnatic composers
- List of film score composers
- List of major opera composers
- List of composers of musicals
- List of musicals by composer: A to L, M to Z
- List of ragtime composers
- List of symphony composers
- List of acousmatic-music composers
- List of Spaghetti Western composers
- List of television theme music composers
## Western classical period {#western_classical_period}
- List of Medieval composers
- List of Renaissance composers
- List of Baroque composers
- List of Classical-era composers
- List of Romantic-era composers
- List of 20th-century classical composers
- List of 21st-century classical composers
## Nationality or ethnicity {#nationality_or_ethnicity}
- Chronological lists of classical composers by nationality
- List of composers by nationality
## Instrument
- List of composers for the classical guitar
- List of organ composers
- List of piano composers
- List of composers and their preferred lyricists
- List of string quartet composers
## Classification
- Chronological lists of classical composers
- List of Anglican church composers -- See also Religious music
- List of composers in the Mannheim school
- List of composers of African descent
- List of composers of Caribbean descent
- List of modernist composers
- List of Byzantine composers
- List of composers in literature
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Cuisine
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A **cuisine** is a style of cooking characterized by distinctive ingredients, techniques and dishes, and usually associated with a specific culture or geographic region. Regional food preparation techniques, customs and ingredients combine to enable dishes unique to a region.
## Etymology
Used in English since the late 18th century, the word cuisine---meaning manner or style of cooking---is borrowed from the French for \'style of cooking\' (literally \'kitchen\'), as originally derived from Latin *coquere*, \'to cook\'.
## Influences on cuisine {#influences_on_cuisine}
A cuisine is partly determined by ingredients that are available locally or through trade. Regional ingredients are developed and commonly contribute to a regional or national cuisine, such as Japanese rice in Japanese cuisine.
Religious food laws can also exercise an influence on cuisine, such as Indian cuisine and Hinduism that is mainly lacto-vegetarian (avoiding meat and eggs) due to sacred animal worship. Sikhism in Punjabi cuisine, Buddhism in East Asian cuisine, Christianity in European cuisine, Islam in Middle Eastern cuisine, and Judaism in Jewish and Israeli cuisine all exercise an influence on cuisine.
Some factors that have an influence on a region\'s cuisine include the area\'s climate, the trade among different countries, religious or sumptuary laws and culinary culture exchange. For example, a tropical diet may be based more on fruits and vegetables, while a polar diet might rely more on meat and fish.
The area\'s climate, in large measure, determines the native foods that are available. In addition, climate influences food preservation. For example, foods preserved for winter consumption by smoking, curing and pickling have remained significant in world cuisines for their altered gustatory properties.
The trade among different countries also largely affects a region\'s cuisine. Dating back to the ancient spice trade, seasonings such as cinnamon, cassia, cardamom, ginger and turmeric were important items of commerce in the earliest evolution of trade, and India was a global market for this. Cinnamon and cassia found their way to the Middle East at least 4,000 years ago.
Certain foods and food preparations are required or proscribed by the religiousness or sumptuary laws, such as Islamic dietary laws and Jewish dietary laws.
Culinary culture exchange is also an important factor for cuisine in many regions: Japan\'s first substantial and direct exposure to the West came with the arrival of European missionaries in the second half of the 16th century. At that time, the combination of Spanish and Portuguese game frying techniques with an East Asian method for cooking vegetables in oil, led to the development of *tempura*, the \"popular Japanese dish in which seafood and many different types of vegetables are coated with batter and deep fried\".
## History
Cuisine dates back to classical antiquity. As food began to require more planning, there was an emergence of meals that situated around culture.
## Evolution of cuisine {#evolution_of_cuisine}
Cuisines evolve continually, and new cuisines are created by innovation and cultural interaction. One recent example is fusion cuisine, which combines elements of various culinary traditions while not being categorized per any one cuisine style, and generally refers to the innovations in many contemporary restaurant cuisines since the 1970s. *Nouvelle cuisine* (\'New cuisine\') is an approach to cooking and food presentation in French cuisine that was popularized in the 1960s by the food critics Henri Gault, who invented the phrase, and his colleagues André Gayot and Christian Millau in a new restaurant guide, the Gault-Millau, or *Le Nouveau Guide*. Molecular cuisine, is a modern style of cooking which takes advantage of many technical innovations from the scientific disciplines (molecular cooking). The term was coined in 1999 by the French INRA chemist Hervé This because he wanted to distinguish it from the name Molecular gastronomy (a scientific activity) that was introduced by him and the late Oxford physicist Nicholas Kurti in 1988. It is also named as multi sensory cooking, modernist cuisine, culinary physics and experimental cuisine by some chefs. Besides, international trade brings new foodstuffs including ingredients to existing cuisines and leads to changes. The introduction of hot pepper to China from South America around the end of the 17th century, greatly influencing Sichuan cuisine, which combines the original taste (with use of Sichuan pepper) with the taste of newly introduced hot pepper and creates a unique mala (*麻辣*) flavor that\'s mouth-numbingly spicy and pungent.
## Global cuisine {#global_cuisine}
A global cuisine is a cuisine that is practiced around the world, and can be categorized according to the common use of major foodstuffs, including grains, produce and cooking fats.
## Regional diversity {#regional_diversity}
Regional cuisines can vary based on availability and usage of specific ingredients, local cooking traditions and practices, as well as overall cultural differences. Such factors can be more-or-less uniform across wide swaths of territory, or vary intensely within individual regions. For example, in Central and North South America, corn (maize), both fresh and dried, is a staple food, and is used in many different ways. In northern Europe, wheat, rye and fats of animal origin predominate, while in southern Europe olive oil is ubiquitous and rice is more prevalent. In Italy, the cuisine of the north, featuring butter and rice, stands in contrast to that of the south, with its wheat pasta and olive oil. In some parts of Greece, gyros is the staple, while in others this role is filled by bread. Throughout the Middle East and Mediterranean, common ingredients include lamb, olive oil, lemons, peppers and rice. The vegetarianism practiced in much of India has made pulses (crops harvested solely for the dry seed) such as chickpeas and lentils as important as wheat or rice. From India to Indonesia, the extensive use of spices is characteristic; coconuts and seafood are also used throughout the region both as foodstuffs and as seasonings.
### African cuisine {#african_cuisine}
African cuisines use a combination of locally available fruits, cereals and vegetables, as well as milk and meat products. In some parts of the continent, the traditional diet features a preponderance of milk, curd and whey products. In much of tropical Africa, however, cow\'s milk is rare and cannot be produced locally (owing to various diseases that affect livestock). The continent\'s diverse demographic makeup is reflected in the many different eating and drinking habits, dishes and preparation techniques of its manifold populations.
<File:Injera> with eight kinds of stew.jpg\|Typical Ethiopian and Eritrean cuisine: *Injera* (thin pancake-like bread) and several types of *wat* (stew) <File:Iftar.jpg%7CA> Ramadan dinner in Tanzania <File:Yassapoulet.JPG>\|Yassa is a popular dish throughout West Africa prepared with chicken or fish. Chicken yassa is pictured. <File:Spices1.jpg%7CSpices> at central market in Agadir, Morocco
### Asian cuisines {#asian_cuisines}
Due to Asia\'s vast size and extremely diverse geography and demographics, Asian cuisines are many and varied, and include East Asian cuisine, South Asian cuisine, Southeast Asian cuisine, Central Asian cuisine and West Asian cuisine. Ingredients common to East Asia and Southeast Asia (due to overseas Chinese influence) include rice, ginger, garlic, sesame seeds, chilies, dried onions, soy and tofu, with stir frying, steaming and deep frying being common cooking methods. While rice is common to most regional cuisines in Asia, different varieties are popular in the different regions: Basmati rice is popular in South Asia, Jasmine rice in Southeast Asia, and long-grain rice in China and short-grain rice in Japan and Korea. Curry is also a common ingredient found in South Asia, Southeast Asia and East Asia (notably Japanese curry); however, they are not popular in West Asian and Central Asian cuisines. Those curry dishes with origins in South Asia usually have a yogurt base, with origins in Southeast Asia a coconut milk base, and in East Asia a stewed meat and vegetable base. South Asian cuisine and Southeast Asian cuisine are often characterized by their extensive use of spices and herbs native to the tropical regions of Asia.
<File:CantoneseRestaurantSeafood.jpg%7CDue> to Guangdong\'s location on the southern coast of China, fresh live seafood is a specialty in Cantonese cuisine. Such markets selling seafood are found across East Asia. <File:Vegetarian> Curry.jpeg\|Traditional North Indian vegetarian thali with various curries from India. Various curry dishes are found across South Asia. <File:Thai> market food 01.jpg\|A market stall at Thanin market in Chiang Mai, Thailand, selling readily-made food. Market stalls selling food are found across Southeast Asia. <File:Tajik> dastarkhan meal.jpg\|A Tajik feast. A large feast is commonly associated with cultures of Central Asia. <File:Assyriancusiene.jpg%7CTypical> Assyrian cuisine; an example of a type of meal found in West Asia
### European cuisine {#european_cuisine}
European cuisine (alternatively, \"Western cuisine\") include the cuisines of Europe and other Western countries. European cuisine includes non-indigenous cuisines of North America, Australasia, Oceania and Latin America as well. The term is used by East Asians to contrast with East Asian styles of cooking. When used in English, the term may refer more specifically to cuisine *in* (Continental) Europe; in this context, a synonym is **Continental cuisine**.
<File:Sunday> roast - roast beef 1.jpg\|An English Sunday roast with roast beef, roast potatoes, vegetables and Yorkshire pudding <File:Traditional_pizza_from_Napoli.jpg%7CTraditional> pizza from Naples: originally Italian dish <File:German> sausages and cheese.jpg\|German sausages and cheese <File:-2020-09-14> Beef stroganoff, Trimingham.JPG\|Beef Stroganoff, a Russian dish
### Oceanian cuisine {#oceanian_cuisine}
Oceanian cuisines include Australian cuisine, New Zealand cuisine and cuisines from many other islands or island groups throughout Oceania. Australian cuisine consists of immigrant Anglo-Celtic derived cuisine, and Bushfood prepared and eaten by native Aboriginal Australian peoples, and various newer Asian influences. New Zealand cuisine also consists of European inspired dishes, such as Pavlova, and native Māori cuisine. Across Oceania, staples include the Kūmura and Taro, which was/is a staple from Papua New Guinea to the South Pacific. On most islands in the south pacific, fish are widely consumed because of the proximity to the ocean.
<File:Australian> bush tucker, Alice Springs.jpg\|*Bush Tucker* (bush foods) harvested at Alice Springs Desert Park in Australia <File:Hangi> prepare.jpg\|A Hāngī being prepared, a New Zealand Māori method of cooking food for special occasions using hot rocks buried in a pit oven <File:Pig> on the Samoan Umu.jpg\|Samoan *umu*, an oven of hot rocks above ground
### Cuisines of the Americas {#cuisines_of_the_americas}
The cuisines of the Americas are found across North and South America, and are based on the cuisines of the countries from which the immigrant people came from, primarily Europe. However, the traditional European cuisine has been adapted by the addition of many local and native ingredients, and many of their techniques have been added to traditional foods as well. Native American cuisine is prepared by indigenous populations across the continent, and its influences can be seen on multi-ethnic Latin American cuisine. Many staple foods have been seen to be eaten across the continent, such as corn (maize), beans and potatoes have their own respective native origins. The regional cuisines are North American cuisine, Mexican cuisine, Central American cuisine, South American cuisine and Caribbean cuisine.
<File:Bandeja> paisa 30062011.jpg\|Bandeja paisa from Peñól de Guatapé in Antioquia, Colombia <File:Coco> bread wrapped beef patty.jpg\|A Jamaican patty wrapped in coco bread <File:Buffalo> - Wings at Airport Anchor Bar.jpg\|Buffalo wings with blue cheese dressing, served with lager beer <File:001> Tacos de carnitas, carne asada y al pastor.jpg\|Tacos filled with several meat types, mainly beef, chicken and pork
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Codec
|
A **codec** is a computer hardware or software component that encodes or decodes a data stream or signal. *Codec* is a portmanteau of **coder/decoder**.
In electronic communications, an **endec** is a device that acts as both an encoder and a decoder on a signal or data stream, and hence is a type of codec. *Endec* is a portmanteau of **encoder/decoder**.
A coder or encoder encodes a data stream or a signal for transmission or storage, possibly in encrypted form, and the decoder function reverses the encoding for playback or editing. Codecs are used in videoconferencing, streaming media, and video editing applications.
## History
Originally, in the mid-20th century, a codec was a hardware device that coded analog signals into digital form using pulse-code modulation (PCM). Later, the term was also applied to software for converting between digital signal formats, including companding functions.
## Examples
An audio codec converts analog audio signals into digital signals for transmission or encodes them for storage. A receiving device converts the digital signals back to analog form using an audio decoder for playback. An example of this is the codecs used in the sound cards of personal computers. A video codec accomplishes the same task for video signals.
When implementing the Infrared Data Association (IrDA) protocol, an endec may be used between the UART and the optoelectronic systems.
## Compression
In addition to encoding a signal, a codec may also compress the data to reduce transmission bandwidth or storage space. Compression codecs are classified primarily into lossy codecs and lossless codecs.
Lossless codecs are often used for archiving data in compressed form while retaining all information present in the original stream. If preserving the original quality of the stream is more important than eliminating the correspondingly larger data sizes, lossless codecs are preferred. This is especially true if the data is to undergo further processing (for example, editing) in which case the repeated application of processing (encoding and decoding) on lossy codecs will degrade the quality of the resulting data such that it is no longer identifiable (visually, audibly, or both). Using more than one codec or encoding scheme successively can also degrade quality significantly. The decreasing cost of storage capacity and network bandwidth has a tendency to reduce the need for lossy codecs for some media.
Many popular codecs are lossy. They reduce quality in order to maximize compression. Often, this type of compression is virtually indistinguishable from the original uncompressed sound or images, depending on the codec and the settings used. The most widely used lossy data compression technique in digital media is based on the discrete cosine transform (DCT), used in compression standards such as JPEG images, H.26x and MPEG video, and MP3 and AAC audio. Smaller data sets ease the strain on relatively expensive storage sub-systems such as non-volatile memory and hard disk, as well as write-once-read-many formats such as CD-ROM, DVD, and Blu-ray Disc. Lower data rates also reduce cost and improve performance when the data is transmitted, e.g., over the internet.
## Media codecs {#media_codecs}
Two principal techniques are used in codecs, pulse-code modulation and delta modulation. Codecs are often designed to emphasize certain aspects of the media to be encoded. For example, a digital video (using a DV codec) of a sports event needs to encode motion well but not necessarily exact colors, while a video of an art exhibit needs to encode color and surface texture well.
Audio codecs for cell phones need to have very low latency between source encoding and playback. In contrast, audio codecs for recording or broadcasting can use high-latency audio compression techniques to achieve higher fidelity at a lower bit rate.
There are thousands of audio and video codecs, ranging in cost from free to hundreds of dollars or more. This variety of codecs can create compatibility and obsolescence issues. The impact is lessened for older formats, for which free or nearly-free codecs have existed for a long time. The older formats are often ill-suited to modern applications, however, such as playback on small portable devices. For example, raw uncompressed PCM audio (44.1 kHz, 16-bit stereo, as represented on an audio CD or in a .wav or .aiff file) has long been a standard across multiple platforms, but its transmission over networks is slow and expensive compared with more modern compressed formats, such as Opus and MP3.
Many multimedia data streams contain both audio and video, and often some metadata that permits synchronization of audio and video. Each of these three streams may be handled by different programs, processes, or hardware; but for the multimedia data streams to be useful in stored or transmitted form, they must be encapsulated together in a container format.
Lower bitrate codecs allow more users, but they also have more distortion. Beyond the initial increase in distortion, lower bit rate codecs also achieve their lower bit rates by using more complex algorithms that make certain assumptions, such as those about the media and the packet loss rate. Other codecs may not make those same assumptions. When a user with a low bitrate codec talks to a user with another codec, additional distortion is introduced by each transcoding.
Audio Video Interleave (AVI) is sometimes erroneously described as a codec, but AVI is actually a container format, while a codec is a software or hardware tool that encodes or decodes audio or video into or from some audio or video format. Audio and video encoded with many codecs might be put into an AVI container, although AVI is not an ISO standard. There are also other well-known container formats, such as Ogg, ASF, QuickTime, RealMedia, Matroska, and DivX Media Format. MPEG transport stream, MPEG program stream, MP4, and ISO base media file format are examples of container formats that are ISO standardized.
## Malware
**`{{vanchor|Fake codec|text=Fake codecs}}`{=mediawiki}** are used when an online user takes a type of codec and installs viruses and other malware into whatever data is being compressed and uses it as a disguise. This disguise appears as a codec download through a pop-up alert or ad. When a user goes to click or download that codec, the malware is then installed on the computer. Once a fake codec is installed it is often used to access private data, corrupt an entire computer system or to keep spreading the malware. One of the previous most used ways to spread malware was fake AV pages and with the rise of codec technology, both have been used in combination to take advantage of online users. This combination allows fake codecs to be automatically downloaded to a device through a website linked in a pop-up ad, virus/codec alerts or articles as well.
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Christopher Báthory
|
**Christopher Báthory** (*Báthory Kristóf*; 1530 -- 27 May 1581) was voivode of Transylvania from 1576 to 1581. He was a younger son of Stephen Báthory of Somlyó. Christopher\'s career began during the reign of Queen Isabella Jagiellon, who administered the eastern territories of the Kingdom of Hungary on behalf of her son, John Sigismund Zápolya, from 1556 to 1559. He was one of the commanders of John Sigismund\'s army in the early 1560s.
Christopher\'s brother, Stephen Báthory, who succeeded John Sigismund in 1571, made Christopher captain of Várad (now Oradea in Romania). After being elected King of Poland, Stephen Báthory adopted the title of Prince of Transylvania and made Christopher voivode in 1576. Christopher cooperated with Márton Berzeviczy, whom his brother appointed to supervise the administration of the Principality of Transylvania as the head of the Transylvanian chancellery at Kraków. Christopher ordered the imprisonment of Ferenc Dávid, a leading theologian of the Unitarian Church of Transylvania, who started to condemn the adoration of Jesus. He supported his brother\'s efforts to settle the Jesuits in Transylvania.
## Early life {#early_life}
Christopher was the third of the four sons of Stephen Báthory of Somlyó and Catherine Telegdi. His father was a supporter of John Zápolya, King of Hungary, who made him voivode of Transylvania in February 1530. Christopher was born in Báthorys\' castle at Szilágysomlyó (now Șimleu Silvaniei in Romania) in the same year. His father died in 1534.
His brother, Andrew, and their kinsman, Tamás Nádasdy, took charge of Christopher\'s education. Christopher visited England, France, Italy, Spain, and the Holy Roman Empire in his youth. He also served as a page in Emperor Charles V\'s court.
## Career
Christopher entered the service of John Zápolya\'s widow, Isabella Jagiellon, in the late 1550s. At the time, Isabella administered the eastern territories of the Kingdom of Hungary on behalf of her son, John Sigismund Zápolya. She wanted to persuade Henry II of France to withdraw his troops from three fortresses that the Ottomans had captured in Banat, so she sent Christopher to France to start negotiations in 1557.
John Sigismund took charge of the administration of his realm after his mother died on 15 November 1559. He retained his mother\'s advisors, including Christopher who became one of his most influential officials. After the rebellion of Melchior Balassa, Christopher persuaded John Sigismund to fight for his realm instead of fleeing to Poland in 1562. Christopher was one of the commanders of John Sigismund\'s troops during the ensuing war against the Habsburg rulers of the western territories of the Kingdom of Hungary, Ferdinand and Maximilian, who tried to reunite the kingdom under their rule. Christopher defeated Maximilian\'s commander, Lazarus von Schwendi, forcing him to lift the siege of Huszt (now Khust in Ukraine) in 1565.
After the death of John Sigismund, the Diet of Transylvania elected Christopher\'s younger brother, Stephen Báthory, voivode (or ruler) on 25 May 1571. Stephen made Christopher captain of Várad (now Oradea in Romania). The following year, the Ottoman Sultan, Selim II (who was the overlord of Transylvania), acknowledged the hereditary right of the Báthory family to rule the province.
## Reign
Stephen Báthory was elected King of Poland on 15 December 1575. He adopted the title of Prince of Transylvania and made Christopher voivode on 14 January 1576. An Ottoman delegation confirmed Christopher\'s appointment at the Diet in Gyulafehérvár (now Alba Iulia in Romania) in July. The sultan\'s charter (or *ahidnâme*) sent to Christopher emphasized that he should keep the peace along the frontiers. Stephen set up a separate chancellery in Kraków to keep an eye on the administration of Transylvania. The head of the new chancellery, Márton Berzeviczy, and Christopher cooperated closely.
Anti-Trinitarian preachers began to condemn the worshiping of Jesus in Partium and Székely Land in 1576, although the Diet had already forbade all doctrinal innovations. Ferenc Dávid, the most influential leader of the Unitarian Church of Transylvania, openly joined the dissenters in the autumn of 1578. Christopher invited Fausto Sozzini, a leading Anti-Trinitarian theologian, to Transylvania to convince Dávid that the new teaching was erroneous. Since Dávid refused to obey, Christopher held a Diet and the \"Three Nations\" (including the Unitarian delegates) ordered Dávid\'s imprisonment. Christopher also supported his brother\'s attempts to strengthen the position of the Roman Catholic Church in Transylvania. He granted estates to the Jesuits to promote the establishment of a college in Kolozsvár (now Cluj-Napoca in Romania) on 5 May 1579.
Christopher fell seriously ill after his second wife, Elisabeth Bocskai, died in early 1581. After a false rumor about Christopher\'s death reached Istanbul, Koca Sinan Pasha proposed Transylvania to Pál Márkházy whom Christopher had been forced into exile. Although Christopher\'s only surviving son Sigismund was still a minor, the Diet elected him as voivode before Christopher\'s death, because they wanted to prevent the appointment of Márkházy. Christopher died in Gyulafehérvár on 27 May 1581. He was buried in the Jesuits\' church in Gyulafehérvár, almost two years later, on 14 March 1583.
## Family
Christopher\'s first wife, Catherina Danicska, was a Polish noblewoman, but only the Hungarian form of her name is known. Their eldest son, Balthasar Báthory, moved to Kraków shortly after Stephen Báthory was crowned King of Poland; he drowned in the Vistula River in May 1577 at the age of 22. Christopher\'s and Catherina\'s second son, Nicholas, was born in 1567 and died in 1576.
Christopher\'s second wife, Elisabeth Bocskai, was a Calvinist noblewoman. Their first child, Cristina (or Griselda), was born in 1569. She was given in marriage to Jan Zamoyski, Chancellor of Poland, in 1583. Christopher\'s youngest son, Sigismund, was born in 1573.
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6,672 |
Caribbean cuisine
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**Caribbean cuisine** is a fusion of West African, Creole, Amerindian, European, Latin American, Indian/South Asian, Chinese, Javanese/Indonesian, North American, and Middle Eastern cuisines. These traditions were brought from many countries when they moved to the Caribbean. In addition, the population has created styles that are unique to the region.
## History
As a result of the colonization, the Caribbean is a fusion of multiple sources; British, Spanish, Dutch and French colonized the area and brought their respective cuisines that mixed with West African as well as Amerindian, Indian/South Asian, East Asian, Portuguese, and Arab, influences from enslaved, indentured and other laborers brought to work on the plantations.
In 1493, during the voyages of Christopher Columbus, the Spaniards introduced a variety of ingredients, including coconut, chickpeas, cilantro, eggplants, onions and garlic.
## Caribbean dishes {#caribbean_dishes}
Ingredients that are common in most islands\' dishes are rice, plantains, beans, cassava, cilantro, bell peppers, chickpeas, tomatoes, sweet potatoes, coconut, and any of various meats that are locally available like beef, poultry, pork, goat or fish. A characteristic seasoning for the region is a green herb-and-oil-based marinade called sofrito, which imparts a flavor profile which is quintessentially Caribbean in character. Ingredients may include garlic, onions, Scotch bonnet peppers, celery, green onions, and herbs like cilantro, Mexican mint, chives, marjoram, rosemary, tarragon and thyme. This green seasoning is used for a variety of dishes like curries, stews and roasted meats.
Traditional dishes are so important to regional culture that, for example, the local version of Caribbean goat stew has been chosen as the official national dish of Montserrat and is also one of the signature dishes of St. Kitts and Nevis. Another popular dish in the Anglophone Caribbean is called \"cook-up\", or pelau. Ackee and saltfish is another popular dish that is unique to Jamaica. Callaloo is a dish containing leafy vegetables such as spinach and sometimes okra amongst others, widely distributed in the Caribbean, with a distinctively mixed African and indigenous character.
The variety of dessert dishes in the area also reflects the mixed origins of the recipes. In some areas, black cake, a derivative of English Christmas pudding, may be served, especially on special occasions.
Over time, food from the Caribbean has evolved into a narrative technique through which their culture has been accentuated and promoted. However, by studying Caribbean culture through a literary lens there then runs the risk of generalizing exoticist ideas about food practices from the tropics. Some food theorists argue that this depiction of Caribbean food in various forms of media contributes to the inaccurate conceptions revolving around their culinary practices, which are much more grounded in unpleasant historical events. Therefore, it can be argued that the connection between the idea of the Caribbean being the ultimate paradise and Caribbean food being exotic is based on inaccurate information.
## By location {#by_location}
- Anguillian cuisine
- Antigua and Barbuda cuisine
- Aruban cuisine
- Bahamian cuisine
- Barbadian cuisine
- Cayman Islands cuisine
- Cuban cuisine
- Curaçaoan cuisine
- Dominica cuisine
- Dominican Republic cuisine
- Grenadan cuisine
- Guadeloupean cuisine
- Haitian cuisine
- Jamaican cuisine
- Martinique cuisine
- Montserratian cuisine
- Puerto Rican cuisine
- Saint Barthélemy cuisine
- Saint Kitts and Nevis cuisine
- Saint Lucian cuisine
- Trinidad and Tobago cuisine
- Turks and Caicos Islands cuisine
- Virgin Islands cuisine
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6,684 |
Communications in Afghanistan
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**Communications in Afghanistan** is under the control of the Ministry of Communications and Information Technology (MCIT). It has rapidly expanded after the Karzai administration was formed in late 2001, and has embarked on wireless companies, internet, radio stations and television channels.
The Afghan government signed a \$64.5 million agreement in 2006 with China\'s ZTE on the establishment of a countrywide optical fiber telecommunications network. The project began to improve telephone, internet, television and radio services throughout Afghanistan. About 90% of the country\'s population had access to communication services by the end of 2013.
Afghanistan uses its own space satellite called Afghansat 1. There are about 18 million mobile phone users in the country. Telecom companies include Afghan Telecom, Afghan Wireless, Etisalat, MTN, Roshan, Salaam. Around 20% of the population has access to the Internet.
## Internet
Afghanistan was given legal control of the \".af\" domain in 2003, and the Afghanistan Network Information Center (AFGNIC) was established to administer domain names. The country has 327,000 IP addresses and around 6,000 .af domains. Internet in Afghanistan is accessed by over 9 million users today. According to a 2020 estimate, over 7 million residents, which is roughly 18% of the population, had access to the internet. There are over a dozen different internet service providers in Afghanistan.
## Postal service {#postal_service}
In 1870, a central post office was established at Bala Hissar in Kabul and a post office in the capital of each province. The service was slowly being expanded over the years as more postal offices were established in each large city by 1918. Afghanistan became a member of the Universal Postal Union in 1928, and the postal administration elevated to the Ministry of Communication in 1934. Civil war caused a disruption in issuing official stamps during the 1980s--90s war but in 1999 postal service was operating again. Postal services to/from Kabul worked remarkably well all throughout the war years. Postal services to/from Herat resumed in 1997. The Afghan government has reported to the UPU several times about illegal stamps being issued and sold in 2003 and 2007.
Afghanistan Post has been reorganizing the postal service in 2000s with assistance from Pakistan Post. The Afghanistan Postal commission was formed to prepare a written policy for the development of the postal sector, which will form the basis of a new postal services law governing licensing of postal services providers. The project was expected to finish by 2008.
## Radio
Radio broadcasting in Afghanistan began in 1925 with Radio Kabul being the first station. The country currently has over 200 AM, FM and shortwave radio stations. They broadcast in Dari, Pashto, English, Uzbeki and a number of other languages.
## Satellite
In January 2014 the Afghan Ministry of Communications and Information Technology signed an agreement with Eutelsat for the use of satellite resources to enhance deployment of Afghanistan\'s national broadcasting and telecommunications infrastructure as well as its international connectivity. Afghansat 1 was officially launched in May 2014, with expected service for at least seven years in Afghanistan. The Afghan government plans to launch Afghansat 2 after the lease of Afghansat 1 ends.
## Telephone
According to 2013 statistics, there were 20,521,585 GSM mobile phone subscribers and 177,705 CDMA subscribers in Afghanistan. Mobile communications have improved because of the introduction of wireless carriers. The first was Afghan Wireless and the second Roshan, which began providing services to all major cities within Afghanistan. There are also a number of VSAT stations in major cities such as Kabul, Kandahar, Herat, Mazari Sharif, and Jalalabad, providing international and domestic voice/data connectivity. The international calling code for Afghanistan is +93. The following is a partial list of mobile phone companies in the country:
- Afghan Telecom (provides 4G services)
- Afghan Wireless (provides 4G services)
- Etisalat (provides 4G services)
- MTN Group (provides 4G services)
- Roshan (provides 4G services)
- Salaam Network (provides 3G services)
All the companies providing communication services are obligated to deliver 2.5% of their income to the communication development fund annually. According to the Ministry of Communication and Information Technology there are 4760 active towers throughout the country which covers 85% of the population. The Ministry of Communication and Information Technology plans to expand its services in remote parts of the country where the remaining 15% of the population will be covered with the installation of 700 new towers. According to WikiLeaks, phone calls in Afghanistan have been monitored by the National Security Agency.
## Television
There are over 106 television operators in Afghanistan and 320 television transmitters, many of which are based Kabul, while others are broadcast from other provinces. Selected foreign channels are also shown to the public in Afghanistan, but with the use of the internet, over 3,500 international TV channels may be accessed in Afghanistan.
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Christian of Oliva
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**Christian of Oliva** (*Chrystian z Oliwy*), also **Christian of Prussia** (*Christian von Preußen*) (died 4 December(?) 1245) was the first missionary bishop of Prussia.
## History
Christian was born about 1180 in the Duchy of Pomerania, possibly in the area of Chociwel (according to Johannes Voigt). Probably as a juvenile he joined the Cistercian Order at newly established Kołbacz (*Kolbatz*) Abbey and in 1209 entered Oliwa Abbey near Gdańsk, founded in 1178 by the Samboride dukes of Pomerelia. At this time the Piast duke Konrad I of Masovia with the consent of Pope Innocent III had started the first of several unsuccessful Prussian Crusades into the adjacent Chełmno Land and Christian acted as a missionary among the Prussians east of the Vistula River.
In 1209, Christian was commissioned by the Pope to be responsible for the Prussian missions between the Vistula and Neman Rivers and in 1212 he was appointed bishop. In 1215 he went to Rome in order to report to the Curia on the condition and prospects of his mission, and was consecrated first \"Bishop of Prussia\" at the Fourth Council of the Lateran. His seat as a bishop remained at Oliwa Abbey on the western side of the Vistula, whereas the pagan Prussian (later East Prussian) territory was on the eastern side of it.
The attempts by Konrad of Masovia to subdue the Prussian lands had picked long-term and intense border quarrels, whereby the Polish lands of Masovia, Cuyavia and even Greater Poland became subject to continuous Prussian raids. Bishop Christian asked the new Pope Honorius III for the consent to start another Crusade, however a first campaign in 1217 proved a failure and even the joint efforts by Duke Konrad with the Polish High Duke Leszek I the White and Duke Henry I the Bearded of Silesia in 1222/23 only led to the reconquest of Chełmno Land but did not stop the Prussian invasions. At least Christian was able to establish the Diocese of Chełmno east of the Vistula, adopting the episcopal rights from the Masovian Bishop of Płock, confirmed by both Duke Konrad and the Pope.
Duke Konrad of Masovia still was not capable to end the Prussian attacks on his territory and in 1226 began to conduct negotiations with the Teutonic Knights under Grand Master Hermann von Salza in order to strengthen his forces. As von Salza initially hesitated to offer his services, Christian created the military Order of Dobrzyń (*Fratres Milites Christi*) in 1228, however to little avail.
Meanwhile, von Salza had to abandon his hope to establish an Order\'s State in the Burzenland region of Transylvania, which had led to an éclat with King Andrew II of Hungary. He obtained a charter by Emperor Frederick II issued in the 1226 Golden Bull of Rimini, whereby Chełmno Land would be the unshared possession of the Teutonic Knights, which was confirmed by Duke Konrad of Masovia in the 1230 Treaty of Kruszwica. Christian ceded his possessions to the new State of the Teutonic Order and in turn was appointed Bishop of Chełmno the next year.
Bishop Christian continued his mission in Sambia (*Samland*), where from 1233 to 1239 he was held captive by pagan Prussians, and freed in trade for five other hostages who then in turn were released for a ransom of 800 Marks, granted to him by Pope Gregory IX. He had to deal with the constant cut-back of his autonomy by the Knights and asked the Roman Curia for mediation. In 1243, the Papal legate William of Modena divided the Prussian lands of the Order\'s State into four dioceses, whereby the bishops retained the secular rule over about on third of the diocesan territory:
- Bishopric of Chełmno (Chełmno Land, Ziemia Chełminska)
- Bishopric of Pomesania (Pomesania)
- Bishopric of Warmia (Ermland) (state)/ Diocese of Warmia (ecclesiastical ambit)
- Bishopric of Samland (Sambia)
all suffragan dioceses under the Archbishopric of Riga. Christian was supposed to choose one of them, but did not agree to the division. He possibly retired to the Cistercians Abbey in Sulejów, where he died before the conflict was solved.
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Cofinality
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In mathematics, especially in order theory, the **cofinality** cf(*A*) of a partially ordered set *A* is the least of the cardinalities of the cofinal subsets of *A*. Formally,
$$\operatorname{cf}(A) = \inf \{|B| : B \subseteq A, (\forall x \in A) (\exists y \in B) (x \leq y)\}$$
This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member. The cofinality of a partially ordered set *A* can alternatively be defined as the least ordinal *x* such that there is a function from *x* to *A* with cofinal image. This second definition makes sense without the axiom of choice. If the axiom of choice is assumed, as will be the case in the rest of this article, then the two definitions are equivalent.
Cofinality can be similarly defined for a directed set and is used to generalize the notion of a subsequence in a net.
## Examples
- The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal (and must be contained in every other cofinal subset).
- In particular, the cofinality of any nonzero finite ordinal, or indeed any finite directed set, is 1, since such sets have a greatest element.
- Every cofinal subset of a partially ordered set must contain all maximal elements of that set. Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements.
- In particular, let $A$ be a set of size $n,$ and consider the set of subsets of $A$ containing no more than $m$ elements. This is partially ordered under inclusion and the subsets with $m$ elements are maximal. Thus the cofinality of this poset is $n$ choose $m.$
- A subset of the natural numbers $\N$ is cofinal in $\N$ if and only if it is infinite, and therefore the cofinality of $\aleph_0$ is $\aleph_0.$ Thus $\aleph_0$ is a regular cardinal.
- The cofinality of the real numbers with their usual ordering is $\aleph_0,$ since $\N$ is cofinal in $\R.$ The usual ordering of $\R$ is not order isomorphic to $c,$ the cardinality of the real numbers, which has cofinality strictly greater than $\aleph_0.$ This demonstrates that the cofinality depends on the order; different orders on the same set may have different cofinality.
## Properties
If $A$ admits a totally ordered cofinal subset, then we can find a subset $B$ that is well-ordered and cofinal in $A.$ Any subset of $B$ is also well-ordered. Two cofinal subsets of $B$ with minimal cardinality (that is, their cardinality is the cofinality of $B$) need not be order isomorphic (for example if $B = \omega + \omega,$ then both $\omega + \omega$ and $\{\omega + n : n < \omega\}$ viewed as subsets of $B$ have the countable cardinality of the cofinality of $B$ but are not order isomorphic). But cofinal subsets of $B$ with minimal order type will be order isomorphic.
## Cofinality of ordinals and other well-ordered sets {#cofinality_of_ordinals_and_other_well_ordered_sets}
The **cofinality of an ordinal** $\alpha$ is the smallest ordinal $\delta$ that is the order type of a cofinal subset of $\alpha.$ The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set.
Thus for a limit ordinal $\alpha,$ there exists a $\delta$-indexed strictly increasing sequence with limit $\alpha.$ For example, the cofinality of $\omega^2$ is $\omega,$ because the sequence $\omega \cdot m$ (where $m$ ranges over the natural numbers) tends to $\omega^2;$ but, more generally, any countable limit ordinal has cofinality $\omega.$ An uncountable limit ordinal may have either cofinality $\omega$ as does $\omega_\omega$ or an uncountable cofinality.
The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal.
## Regular and singular ordinals {#regular_and_singular_ordinals}
A **regular ordinal** is an ordinal that is equal to its cofinality. A **singular ordinal** is any ordinal that is not regular.
Every regular ordinal is the initial ordinal of a cardinal. Any limit of regular ordinals is a limit of initial ordinals and thus is also initial but need not be regular. Assuming the axiom of choice, $\omega_{\alpha+1}$ is regular for each $\alpha.$ In this case, the ordinals $0, 1, \omega, \omega_1,$ and $\omega_2$ are regular, whereas $2, 3, \omega_\omega,$ and $\omega_{\omega \cdot 2}$ are initial ordinals that are not regular.
The cofinality of any ordinal $\alpha$ is a regular ordinal, that is, the cofinality of the cofinality of $\alpha$ is the same as the cofinality of $\alpha.$ So the cofinality operation is idempotent.
## Cofinality of cardinals {#cofinality_of_cardinals}
If $\kappa$ is an infinite cardinal number, then $\operatorname{cf}(\kappa)$ is the least cardinal such that there is an unbounded function from $\operatorname{cf}(\kappa)$ to $\kappa;$ $\operatorname{cf}(\kappa)$ is also the cardinality of the smallest set of strictly smaller cardinals whose sum is $\kappa;$ more precisely $\operatorname{cf}(\kappa) = \min \left\{ |I|\ :\ \kappa = \sum_{i \in I} \lambda_i\ \land \forall i \in I \colon \lambda_i < \kappa\right\}.$
That the set above is nonempty comes from the fact that $\kappa = \bigcup_{i \in \kappa} \{i\}$ that is, the disjoint union of $\kappa$ singleton sets. This implies immediately that $\operatorname{cf}(\kappa) \leq \kappa.$ The cofinality of any totally ordered set is regular, so $\operatorname{cf}(\kappa) = \operatorname{cf}(\operatorname{cf}(\kappa)).$
Using König\'s theorem, one can prove $\kappa < \kappa^{\operatorname{cf}(\kappa)}$ and $\kappa < \operatorname{cf}\left(2^\kappa\right)$ for any infinite cardinal $\kappa.$
The last inequality implies that the cofinality of the cardinality of the continuum must be uncountable. On the other hand, $\aleph_\omega = \bigcup_{n < \omega} \aleph_n,$ the ordinal number ω being the first infinite ordinal, so that the cofinality of $\aleph_\omega$ is card(ω) = $\aleph_0.$ (In particular, $\aleph_\omega$ is singular.) Therefore, $2^{\aleph_0} \neq \aleph_\omega.$
(Compare to the continuum hypothesis, which states $2^{\aleph_0} = \aleph_1.$)
Generalizing this argument, one can prove that for a limit ordinal $\delta$ $\operatorname{cf} (\aleph_\delta) = \operatorname{cf} (\delta).$
On the other hand, if the axiom of choice holds, then for a successor or zero ordinal $\delta$ $\operatorname{cf} (\aleph_\delta) = \aleph_\delta.$
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Citadel
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A **citadel** is the most fortified area of a town or city. It may be a castle, fortress, or fortified center. The term is a diminutive of *city*, meaning \"little city\", because it is a smaller part of the city of which it is the defensive core.
In a fortification with bastions, the citadel is the strongest part of the system, sometimes well inside the outer walls and bastions, but often forming part of the outer wall for the sake of economy. It is positioned to be the last line of defence, should the enemy breach the other components of the fortification system.
## History
### 3300--1300 BC
Some of the oldest known structures which have served as citadels were built by the Indus Valley civilisation, where citadels represented a centralised authority. Citadels in Indus Valley were almost 12 meters tall. The purpose of these structures, however, remains debated. Though the structures found in the ruins of Mohenjo-daro were walled, it is far from clear that these structures were defensive against enemy attacks. Rather, they may have been built to divert flood waters.
Several settlements in Anatolia, including the Assyrian cities of Kaneš in modern-day Kültepe, featured citadels. Kaneš\' citadel contained the city\'s palace, temples, and official buildings. The citadel of the Greek city of Mycenae was built atop a highly-defensible rectangular hill and was later surrounded by walls in order to increase its defensive capabilities.
### 800 BC -- 400 AD {#bc_400_ad}
In Ancient Greece, the Acropolis, which literally means \"high city\", placed on a commanding eminence, was important in the life of the people, serving as a lookout, a refuge, and a stronghold in peril, as well as containing military and food supplies, the shrine of the god and a royal palace. The most well known is the Acropolis of Athens, but nearly every Greek city-state had one -- the Acrocorinth is famed as a particularly strong fortress. In a much later period, when Greece was ruled by the Latin Empire, the same strong points were used by the new feudal rulers for much the same purpose.
In the first millennium BC, the Castro culture emerged in northwestern Portugal and Spain in the region extending from the Douro river up to the Minho, but soon expanding north along the coast, and east following the river valleys. It was an autochthonous evolution of Atlantic Bronze Age communities. In 2008, the origins of the Celts were attributed to this period by John T. Koch and supported by Barry Cunliffe. The Ave River Valley in Portugal was the core region of this culture, with a large number of small settlements (the *castros*), but also settlements known as citadels or oppida by the Roman conquerors. These had several rings of walls and the Roman conquest of the citadels of Abobriga, Lambriaca and Cinania around 138 BC was possible only by prolonged siege. Ruins of notable citadels still exist, and are known by archaeologists as Citânia de Briteiros, Citânia de Sanfins, Cividade de Terroso and Cividade de Bagunte.
#### 167--160 BC {#bc_1}
Rebels who took power in a city, but with the citadel still held by the former rulers, could by no means regard their tenure of power as secure. One such incident played an important part in the history of the Maccabean Revolt against the Seleucid Empire. The Hellenistic garrison of Jerusalem and local supporters of the Seleucids held out for many years in the Acra citadel, making Maccabean rule in the rest of Jerusalem precarious. When finally gaining possession of the place, the Maccabeans pointedly destroyed and razed the Acra, though they constructed another citadel for their own use in a different part of Jerusalem.
### 400--1600
At various periods, and particularly during the Middle Ages and the Renaissance, the citadel -- having its own fortifications, independent of the city walls -- was the last defence of a besieged army, often held after the town had been conquered. Locals and defending armies have often held out citadels long after the city had fallen. For example, in the 1543 Siege of Nice the Ottoman forces led by Barbarossa conquered and pillaged the town and took many captives, but the citadel held out.
In the Philippines, the Ivatan people of the northern islands of Batanes often built fortifications to protect themselves during times of war. They built their so-called *idjangs* on hills and elevated areas. These fortifications were likened to European castles because of their purpose. Usually, the only entrance to the castles would be via a rope ladder that would only be lowered for the villagers and could be kept away when invaders arrived.
### 1600 to the present {#to_the_present}
In times of war, the citadel in many cases afforded retreat to the people living in the areas around the town. However, citadels were often used also to protect a garrison or political power from the inhabitants of the town where it was located, being designed to ensure loyalty from the town that they defended. This was used, for example, during the Dutch Wars of 1664--1667, King Charles II of England constructed a Royal Citadel at Plymouth, an important channel port which needed to be defended from a possible naval attack. However, due to Plymouth\'s support for the Parliamentarians, in the then-recent English Civil War, the Plymouth Citadel was so designed that its guns could fire on the town as well as on the sea approaches.
Barcelona had a great citadel built in 1714 to intimidate the Catalans against repeating their mid-17th- and early-18th-century rebellions against the Spanish central government. In the 19th century, when the political climate had liberalized enough to permit it, the people of Barcelona had the citadel torn down, and replaced it with the city\'s main central park, the Parc de la Ciutadella. A similar example is the Citadella in Budapest, Hungary.
The attack on the Bastille in the French Revolution -- though afterwards remembered mainly for the release of the handful of prisoners incarcerated there -- was to considerable degree motivated by the structure\'s being a Royal citadel in the midst of revolutionary Paris.
Similarly, after Garibaldi\'s overthrow of Bourbon rule in Palermo, during the 1860 Unification of Italy, Palermo\'s Castellamare Citadel -- a symbol of the hated and oppressive former rule -- was ceremoniously demolished.
Following Belgium gaining its independence in 1830, a Dutch garrison under General David Hendrik Chassé held out in Antwerp Citadel between 1830 and 1832, while the city had already become part of independent Belgium.
The Siege of the Alcázar in the Spanish Civil War, in which the Nationalists held out against a much larger Republican force for two months until relieved, shows that in some cases a citadel can be effective even in modern warfare; a similar case is the Battle of Huế during the Vietnam War, where a North Vietnamese Army division held the citadel of Huế for 26 days against roughly their own numbers of much better-equipped US and South Vietnamese troops.
### Modern usage {#modern_usage}
The Citadelle of Québec (the construction was started in 1673 and completed in 1820) still survives as the largest citadel still in official military operation in North America. It is home to the Royal 22nd Regiment of the Canadian Army and forms part of the Ramparts of Quebec City dating back to 1620s.
Since the mid 20th century, citadels have commonly enclosed military command and control centres, rather than cities or strategic points of defence on the boundaries of a country. These modern citadels are built to protect the command centre from heavy attacks, such as aerial or nuclear bombardment. The military citadels under London in the UK, including the massive underground complex Pindar beneath the Ministry of Defence, are examples, as is the Cheyenne Mountain nuclear bunker in the US.
## Naval term {#naval_term}
On armoured warships, the heavily armoured section of the ship that protects the ammunition and machinery spaces is called the armoured citadel.
A modern naval interpretation refers to the heaviest protected part of the hull as \"the vitals\", and the citadel is the semi-armoured freeboard above the vitals. Generally, Anglo-American and German languages follow this while Russian sources/language refer to \"the vitals\" as цитадель \"citadel\". Likewise, Russian literature often refers to the turret of a tank as the \'tower\'.
The safe room on a ship is also called a citadel.
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Cerberus
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In Greek mythology, **Cerberus** (`{{IPAc-en|ˈ|s|ɜr|b|ər|ə|s|audio=LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-Cerberus.wav}}`{=mediawiki} or `{{IPAc-en|ˈ|k|ɜr|b|ər|ə|s}}`{=mediawiki}; *Κέρβερος* *Kérberos* `{{IPA|el|ˈkerberos|}}`{=mediawiki}), often referred to as the **hound of Hades**, is a multi-headed dog that guards the gates of the underworld to prevent the dead from leaving. He was the offspring of the monsters Echidna and Typhon, and was usually described as having three heads, a serpent for a tail, and snakes protruding from his body. Cerberus is primarily known for his capture by Heracles, the last of Heracles\' twelve labours.
## Etymology
The etymology of Cerberus\' name is uncertain. Ogden refers to attempts to establish an Indo-European etymology as \"not yet successful\". It has been claimed to be related to the Sanskrit word सर्वरा *sarvarā*, used as an epithet of one of the dogs of Yama, from a Proto-Indo-European word \**k̑érberos*, meaning \"spotted\". Lincoln (1991), among others, critiques this etymology. This etymology was also rejected by Manfred Mayrhofer, who proposed an Austro-Asiatic origin for the word, and by Beekes. Lincoln notes a similarity between Cerberus and the Norse mythological dog Garmr, relating both names to a Proto-Indo-European root *\*ger-* \"to growl\" (perhaps with the suffixes *-\*m/\*b* and *-\*r*). However, as Ogden observes, this analysis actually requires *Kerberos* and *Garmr* to be derived from two *different* Indo-European roots (\**ker-* and \**gher-* respectively), and so does not actually establish a relationship between the two names.
Though probably not Greek, Greek etymologies for Cerberus have been offered. An etymology given by Servius (the late-fourth-century commentator on Virgil)---but rejected by Ogden---derives Cerberus from the Greek word *creoboros* meaning \"flesh-devouring\". Another suggested etymology derives Cerberus from \"Ker berethrou\", meaning \"evil of the pit\".
## Descriptions
Descriptions of Cerberus vary, including the number of his heads. Cerberus was usually three-headed, though not always. Cerberus had several multi-headed relatives. His father was the multi snake-footed Typhon, and Cerberus was the brother of three other multi-headed monsters, the multi-snake-headed Lernaean Hydra; Orthrus, the two-headed dog that guarded the Cattle of Geryon; and the Chimera, who had three heads: that of a lion, a goat, and a snake. And, like these close relatives, Cerberus was, with only the rare iconographic exception, multi-headed.
In the earliest description of Cerberus, Hesiod\'s *Theogony* (c. 8th -- 7th century BC), Cerberus has fifty heads, while Pindar (c. 522 -- c. 443 BC) gave him one hundred heads. However, later writers almost universally give Cerberus three heads. An exception is the Latin poet Horace\'s Cerberus which has a single dog head, and one hundred snake heads. Perhaps trying to reconcile these competing traditions, Apollodorus\'s Cerberus has three dog heads and the heads of \"all sorts of snakes\" along his back, while the Byzantine poet John Tzetzes (who probably based his account on Apollodorus) gives Cerberus fifty heads, three of which were dog heads, the rest being the \"heads of other beasts of all sorts\".
In art Cerberus is most commonly depicted with two dog heads (visible), never more than three, but occasionally with only one. On one of the two earliest depictions (c. 590--580 BC), a Corinthian cup from Argos (see below), now lost, Cerberus was shown as a normal single-headed dog. The first appearance of a three-headed Cerberus occurs on a mid-sixth-century BC Laconian cup (see below).
Horace\'s many snake-headed Cerberus followed a long tradition of Cerberus being part snake. This is perhaps already implied as early as in Hesiod\'s *Theogony*, where Cerberus\' mother is the half-snake Echidna, and his father the snake-headed Typhon. In art, Cerberus is often shown as being part snake, for example the lost Corinthian cup showed snakes protruding from Cerberus\' body, while the mid sixth-century BC Laconian cup gives Cerberus a snake for a tail. In the literary record, the first certain indication of Cerberus\' serpentine nature comes from the rationalized account of Hecataeus of Miletus (fl. 500--494 BC), who makes Cerberus a large poisonous snake. Plato refers to Cerberus\' composite nature, and Euphorion of Chalcis (3rd century BC) describes Cerberus as having multiple snake tails, and presumably in connection to his serpentine nature, associates Cerberus with the creation of the poisonous aconite plant. Virgil has snakes writhe around Cerberus\' neck, Ovid\'s Cerberus has a venomous mouth, necks \"vile with snakes\", and \"hair inwoven with the threatening snake\", while Seneca gives Cerberus a mane consisting of snakes, and a single snake tail.
Cerberus was given various other traits. According to Euripides, Cerberus not only had three heads but three bodies, and according to Virgil he had multiple backs. Cerberus ate raw flesh (according to Hesiod), had eyes which flashed fire (according to Euphorion), a three-tongued mouth (according to Horace), and acute hearing (according to Seneca).
## Twelfth Labour of Heracles {#twelfth_labour_of_heracles}
Cerberus\' only mythology concerns his capture by Heracles. As early as Homer we learn that Heracles was sent by Eurystheus, the king of Tiryns, to bring back Cerberus from Hades the king of the underworld. According to Apollodorus, this was the twelfth and final labour imposed on Heracles. In a fragment from a lost play *Pirithous*, (attributed to either Euripides or Critias) Heracles says that, although Eurystheus commanded him to bring back Cerberus, it was not from any desire to see Cerberus, but only because Eurystheus thought that the task was impossible.
Heracles was aided in his mission by his being an initiate of the Eleusinian Mysteries. Euripides has his initiation being \"lucky\" for Heracles in capturing Cerberus. And both Diodorus Siculus and Apollodorus say that Heracles was initiated into the Mysteries, in preparation for his descent into the underworld. According to Diodorus, Heracles went to Athens, where Musaeus, the son of Orpheus, was in charge of the initiation rites, while according to Apollodorus, he went to Eumolpus at Eleusis.
Heracles also had the help of Hermes, the usual guide of the underworld, as well as Athena. In the *Odyssey*, Homer has Hermes and Athena as his guides. And Hermes and Athena are often shown with Heracles on vase paintings depicting Cerberus\' capture. By most accounts, Heracles made his descent into the underworld through an entrance at Tainaron, the most famous of the various Greek entrances to the underworld. The place is first mentioned in connection with the Cerberus story in the rationalized account of Hecataeus of Miletus (fl. 500--494 BC), and Euripides, Seneca, and Apolodorus, all have Heracles descend into the underworld there. However Xenophon reports that Heracles was said to have descended at the Acherusian Chersonese near Heraclea Pontica, on the Black Sea, a place more usually associated with Heracles\' exit from the underworld (see below). Heraclea, founded c. 560 BC, perhaps took its name from the association of its site with Heracles\' Cerberian exploit.
### Theseus and Pirithous {#theseus_and_pirithous}
While in the underworld, Heracles met the heroes Theseus and Pirithous, where the two companions were being held prisoner by Hades for attempting to carry off Hades\'s wife Persephone. Along with bringing back Cerberus, Heracles also managed (usually) to rescue Theseus, and in some versions Pirithous as well. According to Apollodorus, Heracles found Theseus and Pirithous near the gates of Hades, bound to the \"Chair of Forgetfulness, to which they grew and were held fast by coils of serpents\", and when they saw Heracles, \"they stretched out their hands as if they should be raised from the dead by his might\", and Heracles was able to free Theseus, but when he tried to raise up Pirithous, \"the earth quaked and he let go.\"
The earliest evidence for the involvement of Theseus and Pirithous in the Cerberus story, is found on a shield-band relief (c. 560 BC) from Olympia, where Theseus and Pirithous (named) are seated together on a chair, arms held out in supplication, while Heracles approaches, about to draw his sword. The earliest literary mention of the rescue occurs in Euripides, where Heracles saves Theseus (with no mention of Pirithous). In the lost play *Pirithous*, both heroes are rescued, while in the rationalized account of Philochorus, Heracles was able to rescue Theseus, but not Pirithous. In one place Diodorus says Heracles brought back both Theseus and Pirithous, by the favor of Persephone, while in another he says that Pirithous remained in Hades, or according to \"some writers of myth\" that neither Theseus, nor Pirithous returned. Both are rescued in the *Fabulae* of Hyginus.
### Capture
There are various versions of how Heracles accomplished Cerberus\' capture. According to Apollodorus, Heracles asked Hades for Cerberus, and Hades told Heracles he would allow him to take Cerberus only if he \"mastered him without the use of the weapons which he carried\", and so, using his lion-skin as a shield, Heracles squeezed Cerberus around the head until he submitted.
In some early sources Cerberus\' capture seems to involve Heracles fighting Hades. Homer (*Iliad* 5.395--397) has Hades injured by an arrow shot by Heracles. A scholium to the *Iliad* passage, explains that Hades had commanded that Heracles \"master Cerberus without shield or Iron\". Heracles did this, by (as in Apollodorus) using his lion-skin instead of his shield, and making stone points for his arrows, but when Hades still opposed him, Heracles shot Hades in anger. Consistent with the no iron requirement, on an early-sixth-century BC lost Corinthian cup, Heracles is shown attacking Hades with a stone, while the iconographic tradition, from c. 560 BC, often shows Heracles using his wooden club against Cerberus.
Euripides has Amphitryon ask Heracles: \"Did you conquer him in fight, or receive him from the goddess \[i.e. Persephone\]? To which Heracles answers: \"In fight\", and the *Pirithous* fragment says that Heracles \"overcame the beast by force\". However, according to Diodorus, Persephone welcomed Heracles \"like a brother\" and gave Cerberus \"in chains\" to Heracles. Aristophanes has Heracles seize Cerberus in a stranglehold and run off, while Seneca has Heracles again use his lion-skin as shield, and his wooden club, to subdue Cerberus, after which a quailing Hades and Persephone allow Heracles to lead a chained and submissive Cerberus away. Cerberus is often shown being chained, and Ovid tells that Heracles dragged the three headed Cerberus with chains of adamant.
### Exit from the underworld {#exit_from_the_underworld}
There were several locations which were said to be the place where Heracles brought up Cerberus from the underworld. The geographer Strabo (63/64 BC -- c. AD 24) reports that \"according to the myth writers\" Cerberus was brought up at Tainaron, the same place where Euripides has Heracles enter the underworld. Seneca has Heracles enter and exit at Tainaron. Apollodorus, although he has Heracles enter at Tainaron, has him exit at Troezen. The geographer Pausanias tells us that there was a temple at Troezen with \"altars to the gods said to rule under the earth\", where it was said that, in addition to Cerberus being \"dragged\" up by Heracles, Semele was supposed to have been brought up out of the underworld by Dionysus.
Another tradition had Cerberus brought up at Heraclea Pontica (the same place which Xenophon had earlier associated with Heracles\' descent) and the cause of the poisonous plant aconite which grew there in abundance. Herodorus of Heraclea and Euphorion said that when Heracles brought Cerberus up from the underworld at Heraclea, Cerberus \"vomited bile\" from which the aconite plant grew up. Ovid, also makes Cerberus the cause of the poisonous aconite, saying that on the \"shores of Scythia\", upon leaving the underworld, as Cerberus was being dragged by Heracles from a cave, dazzled by the unaccustomed daylight, Cerberus spewed out a \"poison-foam\", which made the aconite plants growing there poisonous. Seneca\'s Cerberus too, like Ovid\'s, reacts violently to his first sight of daylight. Enraged, the previously submissive Cerberus struggles furiously, and Heracles and Theseus must together drag Cerberus into the light.
Pausanias reports that according to local legend Cerberus was brought up through a chasm in the earth dedicated to Clymenus (Hades) next to the sanctuary of Chthonia at Hermione, and in Euripides\' *Heracles*, though Euripides does not say that Cerberus was brought out there, he has Cerberus kept for a while in the \"grove of Chthonia\" at Hermione. Pausanias also mentions that at Mount Laphystion in Boeotia, that there was a statue of Heracles Charops (\"with bright eyes\"), where the Boeotians said Heracles brought up Cerberus. Other locations which perhaps were also associated with Cerberus being brought out of the underworld include, Hierapolis, Thesprotia, and Emeia near Mycenae.
### Presented to Eurystheus, returned to Hades {#presented_to_eurystheus_returned_to_hades}
In some accounts, after bringing Cerberus up from the underworld, Heracles paraded the captured Cerberus through Greece. Euphorion has Heracles lead Cerberus through Midea in Argolis, as women and children watch in fear, and Diodorus Siculus says of Cerberus, that Heracles \"carried him away to the amazement of all and exhibited him to men.\" Seneca has Juno complain of Heracles \"highhandedly parading the black hound through Argive cities\" and Heracles greeted by laurel-wreathed crowds, \"singing\" his praises.
Then, according to Apollodorus, Heracles showed Cerberus to Eurystheus, as commanded, after which he returned Cerberus to the underworld. However, according to Hesychius of Alexandria, Cerberus escaped, presumably returning to the underworld on his own.
## Iconography
thumb\|upright=1.3\|One of the two earliest depictions of the capture of Cerberus (composed of the last five figures on the right) shows, from right to left: Cerberus, with a single dog head and snakes rising from his body, fleeing right, Hermes, with his characteristic hat (*petasos*) and caduceus, Heracles, with quiver on his back, stone in left hand, and bow in right, a goddess, standing in front of Hades\' throne, facing Heracles, and Hades, with scepter, fleeing left. Drawing of a lost Corinthian cup (c. 590--580 BC) from Argos.
The capture of Cerberus was a popular theme in ancient Greek and Roman art. The earliest depictions date from the beginning of the sixth century BC. One of the two earliest depictions, a Corinthian cup (c. 590--580 BC) from Argos (now lost), shows a naked Heracles, with quiver on his back and bow in his right hand, striding left, accompanied by Hermes. Heracles threatens Hades with a stone, who flees left, while a goddess, perhaps Persephone or possibly Athena, standing in front of Hades\' throne, prevents the attack. Cerberus, with a single canine head and snakes rising from his head and body, flees right. On the far right a column indicates the entrance to Hades\' palace. Many of the elements of this scene---Hermes, Athena, Hades, Persephone, and a column or portico---are common occurrences in later works. The other earliest depiction, a relief *pithos* fragment from Crete (c. 590--570 BC), is thought to show a single lion-headed Cerberus with a snake (open-mouthed) over his back being led to the right.
A mid-sixth-century BC Laconian cup by the Hunt Painter adds several new features to the scene which also become common in later works: three heads, a snake tail, Cerberus\' chain and Heracles\' club. Here Cerberus has three canine heads, is covered by a shaggy coat of snakes, and has a tail which ends in a snake head. He is being held on a chain leash by Heracles who holds his club raised over head.
In Greek art, the vast majority of depictions of Heracles and Cerberus occur on Attic vases. Although the lost Corinthian cup shows Cerberus with a single dog head, and the relief *pithos* fragment (c. 590--570 BC) apparently shows a single lion-headed Cerberus, in Attic vase painting Cerberus usually has two dog heads. In other art, as in the Laconian cup, Cerberus is usually three-headed. Occasionally in Roman art Cerberus is shown with a large central lion head and two smaller dog heads on either side.
As in the Corinthian and Laconian cups (and possibly the relief *pithos* fragment), Cerberus is often depicted as part snake. In Attic vase painting, Cerberus is usually shown with a snake for a tail or a tail which ends in the head of a snake. Snakes are also often shown rising from various parts of his body including snout, head, neck, back, ankles, and paws.
Two Attic amphoras from Vulci, one (c. 530--515 BC) by the Bucci Painter (Munich 1493), the other (c. 525--510 BC) by the Andokides painter (Louvre F204), in addition to the usual two heads and snake tail, show Cerberus with a mane down his necks and back, another typical Cerberian feature of Attic vase painting. Andokides\' amphora also has a small snake curling up from each of Cerberus\' two heads.
Besides this lion-like mane and the occasional lion-head mentioned above, Cerberus was sometimes shown with other leonine features. A pitcher (c. 530--500) shows Cerberus with mane and claws, while a first-century BC sardonyx cameo shows Cerberus with leonine body and paws. In addition, a limestone relief fragment from Taranto (c. 320--300 BC) shows Cerberus with three lion-like heads.
During the second quarter of the 5th century BC the capture of Cerberus disappears from Attic vase painting. After the early third century BC, the subject becomes rare everywhere until the Roman period. In Roman art the capture of Cerberus is usually shown together with other labors. Heracles and Cerberus are usually alone, with Heracles leading Cerberus.
## Cerberus rationalized {#cerberus_rationalized}
At least as early as the 6th century BC, some ancient writers attempted to explain away various fantastical features of Greek mythology; included in these are various rationalized accounts of the Cerberus story. The earliest such account (late 6th century BC) is that of Hecataeus of Miletus. In his account Cerberus was not a dog at all, but rather simply a large venomous snake, which lived on Tainaron. The serpent was called the \"hound of Hades\" only because anyone bitten by it died immediately, and it was this snake that Heracles brought to Eurystheus. The geographer Pausanias (who preserves for us Hecataeus\' version of the story) points out that, since Homer does not describe Cerberus, Hecataeus\' account does not necessarily conflict with Homer, since Homer\'s \"Hound of Hades\" may not in fact refer to an actual dog.
Other rationalized accounts make Cerberus out to be a normal dog. According to Palaephatus (4th century BC) Cerberus was one of the two dogs who guarded the cattle of Geryon, the other being Orthrus. Geryon lived in a city named Tricranium (in Greek *Tricarenia*, \"Three-Heads\"), from which name both Cerberus and Geryon came to be called \"three-headed\". Heracles killed Orthus, and drove away Geryon\'s cattle, with Cerberus following along behind. Molossus, a Mycenaen, offered to buy Cerberus from Eurystheus (presumably having received the dog, along with the cattle, from Heracles). But when Eurystheus refused, Molossus stole the dog and penned him up in a cave in Tainaron. Eurystheus commanded Heracles to find Cerberus and bring him back. After searching the entire Peloponnesus, Heracles found where it was said Cerberus was being held, went down into the cave, and brought up Cerberus, after which it was said: \"Heracles descended through the cave into Hades and brought up Cerberus.\"
In the rationalized account of Philochorus, in which Heracles rescues Theseus, Perithous is eaten by Cerberus. In this version of the story, Aidoneus (i.e., \"Hades\") is the mortal king of the Molossians, with a wife named Persephone, a daughter named Kore (another name for the goddess Persephone) and a large mortal dog named Cerberus, with whom all suitors of his daughter were required to fight. After having stolen Helen, to be Theseus\' wife, Theseus and Perithous, attempt to abduct Kore, for Perithous, but Aidoneus catches the two heroes, imprisons Theseus, and feeds Perithous to Cerberus. Later, while a guest of Aidoneus, Heracles asks Aidoneus to release Theseus, as a favor, which Aidoneus grants.
A 2nd-century AD Greek known as Heraclitus the paradoxographer (not to be confused with the 5th-century BC Greek philosopher Heraclitus)---claimed that Cerberus had two pups that were never away from their father, which made Cerberus appear to be three-headed.
## Cerberus allegorized {#cerberus_allegorized}
Servius, a medieval commentator on Virgil\'s *Aeneid*, derived Cerberus\' name from the Greek word *creoboros* meaning \"flesh-devouring\" (see above), and held that Cerberus symbolized the corpse-consuming earth, with Heracles\' triumph over Cerberus representing his victory over earthly desires. Later, the mythographer Fulgentius, allegorizes Cerberus\' three heads as representing the three origins of human strife: \"nature, cause, and accident\", and (drawing on the same flesh-devouring etymology as Servius) as symbolizing \"the three ages---infancy, youth, old age, at which death enters the world.\" The Byzantine historian and bishop Eusebius wrote that Cerberus was represented with three heads, because the positions of the sun above the earth are three---rising, midday, and setting.
The later Vatican Mythographers repeat and expand upon the traditions of Servius and Fulgentius. All three Vatican Mythographers repeat Servius\' derivation of Cerberus\' name from *creoboros*. The Second Vatican Mythographer repeats (nearly word for word) what Fulgentius had to say about Cerberus, while the Third Vatican Mythographer, in another very similar passage to Fugentius\', says (more specifically than Fugentius), that for \"the philosophers\" Cerberus represented hatred, his three heads symbolizing the three kinds of human hatred: natural, causal, and casual (i.e. accidental).
The Second and Third Vatican Mythographers, note that the three brothers Zeus, Poseidon and Hades each have tripartite insignia, associating Hades\' three-headed Cerberus, with Zeus\' three-forked thunderbolt, and Poseidon\'s three-pronged trident, while the Third Vatican Mythographer adds that \"some philosophers think of Cerberus as the tripartite earth: Asia, Africa, and Europe. This earth, swallowing up bodies, sends souls to Tartarus.\"
Virgil described Cerberus as \"ravenous\" (*fame rabida*), and a rapacious Cerberus became proverbial. Thus Cerberus came to symbolize avarice, and so, for example, in Dante\'s *Inferno,* Cerberus is placed in the Third Circle of Hell, guarding over the gluttons, where he \"rends the spirits, flays and quarters them,\" and Dante (perhaps echoing Servius\' association of Cerberus with earth) has his guide Virgil take up handfuls of earth and throw them into Cerberus\' \"rapacious gullets.\"
## Namesakes
In the constellation Cerberus introduced by Johannes Hevelius in 1687, Cerberus is drawn as a three-headed snake, held in Hercules\' hand (previously these stars had been depicted as a branch of the tree on which grew the Apples of the Hesperides).
In 1829, French naturalist Georges Cuvier gave the name *Cerberus* to a genus of Asian snakes, which are commonly called \"dog-faced water snakes\" in English.
In 1988 the Massachusetts Institute of Technology (MIT) developed Kerberos, a computer-network authentication protocol, named after Cerberus.
In 2023 European heatwaves, the most significant of which was named \"Cerberus Heatwave\", which brought the hottest temperatures ever recorded in Europe.
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Cardinal vowels
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**Cardinal vowels** are a set of reference vowels used by phoneticians in describing the sounds of languages. They are classified depending on the position of the tongue relative to the roof of the mouth, how far forward or back is the highest point of the tongue, and the position of the lips (rounded or unrounded).
A cardinal vowel is a vowel sound produced when the tongue is in an extreme position, either front or back, high or low. The current system was systematised by Daniel Jones in the early 20th century, though the idea goes back to earlier phoneticians, notably Ellis and Bell.
## Table of cardinal vowels {#table_of_cardinal_vowels}
Three of the cardinal vowels---`{{IPA|[i]}}`{=mediawiki}, `{{IPA|[ɑ]}}`{=mediawiki} and `{{IPA|[u]}}`{=mediawiki}---have articulatory definitions. The vowel `{{IPA|[i]}}`{=mediawiki} is produced with the tongue as far forward and as high in the mouth as is possible (without producing friction), with spread lips. The vowel `{{IPA|[u]}}`{=mediawiki} is produced with the tongue as far back and as high in the mouth as is possible, with protruded lips. This sound can be approximated by adopting the posture to whistle a very low note, or to blow out a candle. And `{{IPA|[ɑ]}}`{=mediawiki} is produced with the tongue as low and as far back in the mouth as possible.
The other vowels are \'auditorily equidistant\' between these three \'corner vowels\', at four degrees of aperture or \'height\': close (high tongue position), close-mid, open-mid, and open (low tongue position).
These degrees of aperture plus the front-back distinction define eight reference points on a mixture of articulatory and auditory criteria. These eight vowels are known as the eight \'primary cardinal vowels\', and vowels like these are common in the world\'s languages.
The lip positions can be reversed with the lip position for the corresponding vowel on the opposite side of the front-back dimension, so that e.g. Cardinal 1 can be produced with rounding somewhat similar to that of Cardinal 8; these are known as \'secondary cardinal vowels\'. Sounds such as these are claimed to be less common in the world\'s languages. Other vowel sounds are also recognised on the vowel chart of the International Phonetic Alphabet.
Jones argued that to be able to use the cardinal vowel system effectively one must undergo training with an expert phonetician, working both on the recognition and the production of the vowels.
Cardinal vowels are not vowels of any particular language, but a measuring system. However, some languages contain vowel or vowels that are close to the cardinal vowel(s). An example of such language is Ngwe, which is spoken in Cameroon. It has been cited as a language with a vowel system that has eight vowels which are rather similar to the eight primary cardinal vowels (Ladefoged 1971:67).
Number IPA Description
-------- ----- -----------------------------------
1 Close front unrounded vowel
2 Close-mid front unrounded vowel
3 Open-mid front unrounded vowel
4 Open front unrounded vowel
5 Open back unrounded vowel
6 Open-mid back rounded vowel
7 Close-mid back rounded vowel
8 Close back rounded vowel
9 Close front rounded vowel
10 Close-mid front rounded vowel
11 Open-mid front rounded vowel
12 Open front rounded vowel
13 Open back rounded vowel
14 Open-mid back unrounded vowel
15 Close-mid back unrounded vowel
16 Close back unrounded vowel
17 Close central unrounded vowel
18 Close central rounded vowel
19 Close-mid central unrounded vowel
20 Close-mid central rounded vowel
21 Open-mid central unrounded vowel
22 Open-mid central rounded vowel
Cardinal vowels 19--22 were added by David Abercrombie. In IPA Numbers, cardinal vowels 1--18 have the same numbers but added to 300.
## Limits on the accuracy of the system {#limits_on_the_accuracy_of_the_system}
The usual explanation of the cardinal vowel system implies that the competent user can reliably distinguish between sixteen Primary and Secondary vowels plus a small number of central vowels. The provision of diacritics by the International Phonetic Association further implies that intermediate values may also be reliably recognized, so that a phonetician might be able to produce and recognize not only a close-mid front unrounded vowel `{{IPA|[e]}}`{=mediawiki} and an open-mid front unrounded vowel `{{IPA|[ɛ]}}`{=mediawiki} but also a mid front unrounded vowel `{{IPA|[e̞]}}`{=mediawiki}, a centralized mid front unrounded vowel `{{IPA|[ë]}}`{=mediawiki}, and so on. This suggests a range of vowels nearer to forty or fifty than to twenty in number. Empirical evidence for this ability in trained phoneticians is hard to come by.
Ladefoged, in a series of pioneering experiments published in the 1950s and 60s, studied how trained phoneticians coped with the vowels of a dialect of Scottish Gaelic. He asked eighteen phoneticians to listen to a recording of ten words spoken by a native speaker of Gaelic and to place the vowels on a cardinal vowel quadrilateral. He then studied the degree of agreement or disagreement among the phoneticians. Ladefoged himself drew attention to the fact that the phoneticians who were trained in the British tradition established by Daniel Jones were closer to each other in their judgments than those who had not had this training. However, the most striking result is the great divergence of judgments among *all* the listeners regarding vowels that were distant from Cardinal values.
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Cross-country skiing
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**Cross-country skiing** is a form of skiing whereby skiers traverse snow-covered terrain without use of ski lifts or other assistance. Cross-country skiing is widely practiced as a sport and recreational activity; however, some still use it as a means of travel. Variants of cross-country skiing are adapted to a range of terrain which spans unimproved, sometimes mountainous terrain to groomed courses that are specifically designed for the sport.
Modern cross-country skiing is similar to the original form of skiing, from which all skiing disciplines evolved, including alpine skiing, ski jumping and Telemark skiing. Skiers propel themselves either by striding forward (classic style) or side-to-side in a skating motion (skate skiing), aided by arms pushing on ski poles against the snow. It is practised in regions with snow-covered landscapes, including Europe, Canada, Russia, the United States, Australia and New Zealand.
Competitive cross-country skiing is one of the Nordic skiing sports. Cross-country skiing and rifle marksmanship are the two components of biathlon. Ski orienteering is a form of cross-country skiing, which includes map navigation along snow trails and tracks.
## History
The word ski comes from the Old Norse word *skíð* which means stick of wood. Skiing started as a technique for traveling cross-country over snow on skis, starting almost five millennia ago with beginnings in Scandinavia. It may have been practised as early as 600 BCE in Daxing\'anling, in what is now China. Early historical evidence includes Procopius\'s (around CE 550) description of Sami people as *skrithiphinoi* translated as \"ski running samis\". Birkely argues that the Sami people have practiced skiing for more than 6000 years, evidenced by the very old Sami word *čuoigat* for skiing. Egil Skallagrimsson\'s 950 CE saga describes King Haakon the Good\'s practice of sending his tax collectors out on skis. The Gulating law (1274) stated that \"No moose shall be disturbed by skiers on private land.\" Cross-country skiing evolved from a utilitarian means of transportation to being a worldwide recreational activity and sport, which branched out into other forms of skiing starting in the mid-1800s.
Early skiers used one long pole or spear in addition to the skis. The first depiction of a skier with two ski poles dates to 1741. Traditional skis, used for snow travel in Norway and elsewhere into the 1800s, often comprised one short ski with a natural fur traction surface, the *andor*, and one long for gliding, the *langski*---one being up to 100 cm longer than the other---allowing skiers to propel themselves with a scooter motion. This combination has a long history among the Sami people. Skis up to 280 cm have been produced in Finland, and the longest recorded ski in Norway is 373 cm.
### Transportation
Ski warfare, the use of ski-equipped troops in war, is first recorded by the Danish historian Saxo Grammaticus in the 13th century. These troops were reportedly able to cover distances comparable to that of light cavalry. The garrison in Trondheim used skis at least from 1675, and the Danish-Norwegian army included specialized skiing battalions from 1747---details of military ski exercises from 1767 are on record. Skis were used in military exercises in 1747. In 1799 French traveller Jacques de la Tocnaye recorded his visit to Norway in his travel diary: Norwegian immigrants used skis (\"Norwegian snowshoes\") in the US midwest from around 1836. Norwegian immigrant \"Snowshoe Thompson\" transported mail by skiing across the Sierra Nevada between California and Nevada from 1856. In 1888 Norwegian explorer Fridtjof Nansen and his team crossed the Greenland icecap on skis. Norwegian workers on the Buenos Aires - Valparaiso railway line introduced skiing in South America around 1890. In 1910 Roald Amundsen used skis on his South Pole Expedition. In 1902 the Norwegian consul in Kobe imported ski equipment and introduced skiing to the Japanese, motivated by the death of Japanese soldiers during a snow storm. Starting in 1919, Vladimir Lenin helped popularize the activity in the Soviet Union.
### Sport
`{{main article|Cross-country skiing (sport)}}`{=mediawiki} Norwegian skiing regiments organized military skiing contests in the 18th century, divided in four classes: shooting at a target while skiing at \"top speed\", downhill racing among trees, downhill racing on large slopes without falling, and \"long racing\" on \"flat ground\". An early record of a public ski competition occurred in Tromsø, 1843. In Norwegian, *langrenn* refers to \"competitive skiing where the goal is to complete a specific distance in groomed tracks in the shortest possible time\". In Norway, *ski touring competitions* (*turrenn*) are long-distance cross-country competitions open to the public, competition is usually within age intervals.
A new technique, skate skiing, was experimented with early in the 20th Century, but was not widely adopted until the 1980s. Johan Grøttumsbråten used the skating technique at the 1931 World Championship in Oberhof, one of the earliest recorded use of skating in competitive cross-country skiing. This technique was later used in ski orienteering in the 1960s on roads and other firm surfaces. It became widespread during the 1980s after the success of Bill Koch (United States) in 1982 Cross-country Skiing Championships drew more attention to the skating style. Norwegian skier Ove Aunli started using the technique in 1984, when he found it to be much faster than classic style. Finnish skier, Pauli Siitonen, developed a one-sided variant of the style in the 1970s, leaving one ski in the track while skating to the side with the other one during endurance events; this became known as the \"marathon skate\".
### Terminology
The word *ski* comes from the Old Norse word *skíð* which means \"cleft wood\", \"stick of wood\" or \"ski\". Norwegian language does not use a verb-form equivalent in idiomatic speech, unlike English \"to ski\". In modern Norwegian, a variety of terms refer to cross-country skiing, including:
- (literally \"walk on skis\")---a general term for self-propelled skiing
- (literally \"hiking on skis\")---refers to ski touring as recreation
- (literally \"long race\")---refers to cross-country ski racing
In contrast, alpine skiing is referred to as *stå på ski* (literally \"stand on skis\").
Fridtjof Nansen, describes the crossing of Greenland as *På ski over Grønland*, literally \"On skis across Greenland\", while the English edition of the report was titled, *The first crossing of Greenland*. Nansen referred to the activity of traversing snow on skis as *skilöbning* (he used the term also in the English translation), which may be translated as *ski running*. Nansen used *skilöbning*, regarding all forms of skiing, but noted that ski jumping is purely a competitive sport and not for amateurs. He further noted that in some competitions the skier \"is also required to show his skill in turning his ski to one side or the other within given marks\" at full speed on a steep hill. Nansen regarded these forms (i.e., jumping and slalom) as \"special arts\", and believed that the most important branch of skiing was travel \"in an ordinary way across the country\". In Germany, Nansen\'s Greenland report was published as *Auf Schneeschuhen durch Grönland* (literally \"On snowshoes through Greenland\"). The German term, *Schneeschuh*, was supplanted by the borrowed Norwegian word, *Ski*, in the late 19th century. The Norwegian encyclopedia of sports also uses the term, *skiløping*, (literally \"ski running\") for all forms of skiing. Around 1900 the word *Skilaufen* was used in German in the same sense as *skiløping*.
## Recreation
Recreational cross-country skiing includes ski touring and groomed-trail skiing, typically at resorts or in parklands. It is an accessible form of recreation for persons with vision and mobility impairments. A related form of recreation is dog skijoring---a winter sport where a cross-country skier is assisted by one or more dogs.
### Ski touring {#ski_touring}
Ski touring takes place off-piste and outside of ski resorts. Tours may extend over multiple days. Typically, skis, bindings, and boots allow for free movement of the heel to enable a walking pace, as with Nordic disciplines and unlike Alpine skiing. Ski touring\'s subgenre ski mountaineering involves independently navigating and route finding through potential avalanche terrain and often requires familiarity with meteorology along with skiing skills. Ski touring can be faster and easier than summer hiking in some terrain, allowing for traverses and ascents that would be harder in the summer. Skis can also be used to access backcountry alpine climbing routes when snow is off the technical route, but still covers the hiking trail. In some countries, organizations maintain a network of huts for use by cross-country skiers in wintertime. For example, the Norwegian Trekking Association maintains over 400 huts stretching across thousands of kilometres of trails which hikers can use in the summer and skiers in the winter.
### Groomed-trail skiing {#groomed_trail_skiing}
Groomed trail skiing occurs at facilities such as Nordmarka (Oslo), Royal Gorge Cross Country Ski Resort and Gatineau Park in Quebec, where trails are laid out and groomed for both classic and skate-skiing. Such grooming and track setting (for classic technique) requires specialized equipment and techniques that adapt to the condition of the snow. Trail preparation employs snow machines which tow snow-compaction, texturing and track-setting devices. Groomers must adapt such equipment to the condition of the snow---crystal structure, temperature, degree of compaction, moisture content, etc. Depending on the initial condition of the snow, grooming may achieve an increase in density for new-fallen snow or a decrease in density for icy or compacted snow. Cross-country ski facilities may incorporate a course design that meets homologation standards for such organizations as the International Olympic Committee, the International Ski Federation, or national standards. Standards address course distances, degree of difficulty with maximums in elevation difference and steepness---both up and downhill, plus other factors. Some facilities have night-time lighting on select trails---called *lysløype* (light trails) in Norwegian and *elljusspår* (electric-light trails) in Swedish. The first *lysløype* opened in 1946 in Nordmarka and at Byåsen (Trondheim).
## Competition
Cross-country ski competition encompasses a variety of formats for races over courses of varying lengths according to rules sanctioned by the International Ski and Snowboard Federation (FIS) and by national organizations, such as the U.S. Ski and Snowboard Association and Cross Country Ski Canada. It also encompasses cross-country ski marathon events, sanctioned by the Worldloppet Ski Federation, cross-country ski orienteering events, sanctioned by the International Orienteering Federation, and Paralympic cross-country skiing, sanctioned by the International Paralympic Committee.
### FIS-sanctioned competition {#fis_sanctioned_competition}
The FIS Nordic World Ski Championships have been held in various numbers and types of events since 1925 for men and since 1954 for women. From 1924 to 1939, the World Championships were held every year, including the Winter Olympic Games. After World War II, the World Championships were held every four years from 1950 to 1982. Since 1985, the World Championships have been held in odd-numbered years. Notable cross-country ski competitions include the Winter Olympics, the FIS Nordic World Ski Championships, and the FIS World Cup events (including the Holmenkollen).
### Other sanctioned competition {#other_sanctioned_competition}
Cross-country ski marathons---races with distances greater than 40 kilometers---have two cup series, the Ski Classics, which started in 2011, and the Worldloppet. Skiers race in classic or free-style (skating) events, depending on the rules of the race. Notable ski marathons, include the *Vasaloppet* in Sweden, *Birkebeineren* in Norway, the Tartu Maraton in Estonia, the Engadin Skimarathon in Switzerland, the American Birkebeiner, the Tour of Anchorage in Anchorage, Alaska, and the Boreal Loppet, held in Forestville, Quebec, Canada.
Biathlon combines cross-country skiing and rifle shooting. Depending on the shooting performance, extra distance or time is added to the contestant\'s total running distance/time. For each shooting round, the biathlete must hit five targets; the skier receives a penalty for each missed target, which varies according to the competition rules.
Ski orienteering is a form of cross-country skiing competition that requires navigation in a landscape, making optimal route choices at racing speeds. Standard orienteering maps are used, but with special green overprinting of trails and tracks to indicate their navigability in snow; other symbols indicate whether any roads are snow-covered or clear. Standard skate-skiing equipment is used, along with a map holder attached to the chest. It is one of the four orienteering disciplines recognized by the International Orienteering Federation. Upper body strength is especially important because of frequent double poling along narrow snow trails.
Paralympic cross-country ski competition is an adaptation of cross-country skiing for athletes with disabilities. Paralympic cross-country skiing includes standing events, sitting events (for wheelchair users), and events for visually impaired athletes under the rules of the International Paralympic Committee. These are divided into several categories for people who are missing limbs, have amputations, are blind, or have any other physical disability, to continue their sport.
## Techniques
thumb\|Video of skiers demonstrating a variety of techniques. Cross-country skiing has two basic propulsion techniques, which apply to different surfaces: classic (undisturbed snow and tracked snow) and skate skiing (firm, smooth snow surfaces). The classic technique relies on a wax or texture on the ski bottom under the foot for traction on the snow to allow the skier to slide the other ski forward in virgin or tracked snow. With the skate skiing technique a skier slides on alternating skis on a firm snow surface at an angle from each other in a manner similar to ice skating. Both techniques employ poles with baskets that allow the arms to participate in the propulsion. Specialized equipment is adapted to each technique and each type of terrain. A variety of turns are used, when descending.
Poles contribute to forward propulsion, either simultaneously (usual for the skate technique) or in alternating sequence (common for the classical technique as the \"diagonal stride\"). Double poling is also used with the classical technique when higher speed can be achieved on flats and slight downhills than is available in the diagonal stride, which is favored to achieve higher power going uphill.
### Classic
The classic style is often used on prepared trails (pistes) that have pairs of parallel grooves (tracks) cut into the snow. It is also the most usual technique where no tracks have been prepared. With this technique, each ski is pushed forward from the other stationary ski in a striding and gliding motion, alternating foot to foot. With the \"diagonal stride\" variant the poles are planted alternately on the opposite side of the forward-striding foot; with the \"kick-double-pole\" variant the poles are planted simultaneously with every other stride. At times, especially with gentle descents, double poling is the sole means of propulsion. On uphill terrain, techniques include the \"side step\" for steep slopes, moving the skis perpendicular to the fall line, the \"herringbone\" for moderate slopes, where the skier takes alternating steps with the skis splayed outwards, and, for gentle slopes, the skier uses the diagonal technique with shorter strides and greater arm force on the poles.
### Skate skiing {#skate_skiing}
With skate skiing, the skier provides propulsion on a smooth, firm snow surface by pushing alternating skis away from one another at an angle, in a manner similar to ice skating. Skate-skiing usually involves a coordinated use of poles and the upper body to add impetus. Three common techniques are \"V1\", \"V2\" and \"V2 alternate\". In \"V1\" the skier pushes with a double pole plant each time the ski is extended on a temporarily \"dominant\" side, this technique is optimal for climbing. In \"V2 alternate\" the skier performs the double pole plant before the \"dominant\" ski is extended, this technique allows for maintaining a higher speed and is often used on slightly downhill terrain. In \"V2\" the skier performs the double pole plant each time the ski is extended on either side, on flat ground and in slight inclines this technique is often the fastest and most efficient of the 3. Skiers climb hills with these techniques by widening the angle of the \"V\" and by making more frequent, shorter strides and more forceful use of poles. A variant of the technique is the \"marathon skate\" or \"Siitonen step\", where the skier leaves one ski in the track while skating outwards to the side with the other ski.
### Turns
Turns, used while descending or for braking, include the snowplough (or \"wedge turn\"), the stem christie (or \"wedge christie\"), parallel turn, and the Telemark turn. The step turn is used for maintaining speed during descents or out of track on flats.
## Equipment
Equipment comprises skis, poles, boots and bindings; these vary according to:
- Technique, classic vs skate
- Terrain, which may vary from groomed trails to wilderness
- Performance level, from recreational use to competition at the elite level
### Skis
Skis used in cross-country are lighter and narrower than those used in alpine skiing. Ski bottoms are designed to provide a gliding surface and, for classic skis, a traction zone under foot. The base of the gliding surface is a plastic material that is designed both to minimize friction and, in many cases, to accept waxes. Glide wax may be used on the tails and tips of classic skis and across the length of skate skis.
#### Types
Each type of ski is sized and designed differently. Length affects maneuverability; camber affects pressure on the snow beneath the feet of the skier; side-cut affects the ease of turning; width affects forward friction; overall area on the snow affects bearing capacity; and tip geometry affects the ability to penetrate new snow or to stay in a track. Each of the following ski types has a different combination of these attributes:
- **Classic skis**: Designed for skiing in tracks. For adult skiers (between 155 cm/50 kg and 185 cm/75 kg), recommended lengths are between 180 and 210 centimetres (approximately 115% of the skier\'s height). Traction comes from a \"grip zone\" underfoot that when bearing the skier\'s weight engages either a textured gripping surface or a grip wax. Accordingly, these skis are classified as \"waxable\" or \"waxless\". Recreational waxless skis generally require little attention and are adapted for casual use. Waxable skis, if prepared correctly, provide better grip and glide.
: When the skier\'s weight is distributed on both skis, the ski\'s camber diminishes the pressure of the grip zone on the snow and promotes bearing on the remaining area of the ski---the \"glide zone\". A test for stiffness of camber is made with a piece of paper under the skier\'s foot, standing on skis on a flat, hard surface---the paper should be pinned throughout the grip zone of the ski on which all the skier\'s weight is placed, but slide freely when the skier\'s weight is bearing equally on both skis.
- **Skate skis**: Designed for skiing on groomed surfaces. The usual recommended length is skier length +5-15cm. The entire bottom of each skate ski is a glide zone---prepared for maximum glide. Traction comes from the skier pushing away from the edge of the previous ski onto the next ski.
- **Back country skis**: Designed for ski touring on natural snow conditions. Recommended lengths are between 150 and 195 centimeters for adult skiers, depending on height and weight of the user. Back country skis are typically heavier and wider than classic and skate skis; they often have metal edges for better grip on hard snow; and their greater sidecut helps to carve turns.
: The geometry of a back country ski depends on its purpose---skis suited for forested areas where loose powder can predominate may be shorter and wider than those selected for open, exposed areas where compacted snow may prevail. Sidecut on Telemark skis promotes turning in forest and rugged terrain. Width and short length aid turning in loose and deep snow. Longer, narrower and more rigid skis with sharp edges are suited for snow that has been compacted by wind or freeze-thaw. Touring ski design may represent a general-purpose compromise among these different ski conditions, plus being acceptable for use in groomed tracks. Traction may come from a textured or waxed grip zone, as with classic skis, or from ski skins, which are applied to the ski bottom for long, steep ascents and have hairs or mechanical texture that prevents sliding backwards.
#### Gliding surface {#gliding_surface}
Glide waxes enhance the speed of the gliding surface. The wax is either melted on the base using an iron or applied in a liquid form. The excess wax is first scraped off and then finished by brushing. Most glide waxes are based on paraffin that is combined with additive materials. The paraffin hardness and additives are varied based on snow type, humidity and temperature. Since the 2021-2022 race season, fluorinated products are banned in FIS sanctioned competitions. Before the ban, most race waxes combined fluorinated hydrocarbon waxes with fluorocarbon overlays. Fluorocarbons decrease surface tension and surface area of the water between the ski and the snow, increasing speed and glide of the ski under specific conditions. Either combined with the wax or applied after in a spray, powder, or block form, fluorocarbons significantly improve the glide of the ski.
#### Traction surface {#traction_surface}
Skis designed for classic technique, both in track and in virgin snow, rely on a traction zone, called the \"grip zone\" or \"kick zone\", underfoot. This comes either from a) *texture*, such as \"fish scales\" or mohair skins, designed to slide forward but not backwards, that is built into the grip zone of waxless skis, or from applied devices, e.g. climbing skins, or b) from *grip waxes*. Grip waxes are classified according to their hardness: harder waxes are for colder and newer snow. An incorrect choice of grip wax for the snow conditions encountered may cause ski slippage (wax too hard for the conditions) or snow sticking to the grip zone (wax too soft for the conditions). Grip waxes generate grip by interacting with snow crystals, which vary with temperature, age and compaction. Hard grip waxes do not work well for snow which has metamorphosed to having coarse grains, whether icy or wet. In these conditions, skiers opt for a stickier substance, called *klister*.
### Boots and bindings {#boots_and_bindings}
Ski boots are attached to the ski only at the toe, leaving the heel free. Depending on application, boots may be lightweight (performance skiing) or heavier and more supportive (back-country skiing).
Bindings connect the boot to the ski. There are three primary groups of binding systems used in cross-country skiing (in descending order of importance):
- **Standardized system**: Boots and bindings have an integrated connection, typically a bar across the front end of the sole of the boot, and platform on which the boot rests. Two families of standards prevail: NNN (New Nordic Norm) and SNS (Salomon Nordic System) Profil. Both systems have variants for skiing on groomed surfaces and in back country. These systems are the most common type of binding.
- **Three-pin**: The boot-gripping system comprises three pins that correspond to three holes in the sole of the boot\'s toe, used primarily for back-country skiing.
- **Cable**: A cable secures the free-moving heel and keeps the toe of the boot pushed into a boot-gripping section, used primarily for back-country and telemark skiing.
### Poles
Ski poles are used for balance and propulsion. Modern cross-country ski poles are made from aluminium, fibreglass-reinforced plastic, or carbon fibre, depending on weight, cost and performance parameters. Formerly they were made of wood or bamboo. They feature a foot (called a basket) near the end of the shaft that provides a pushing platform, as it makes contact with the snow. Baskets vary in size, according to the expected softness/firmness of the snow. Racing poles feature smaller, lighter baskets than recreational poles. Poles designed for skating are longer than those designed for classic skiing. Traditional skiing in the 1800s used a single pole for both cross-country and downhill. The single pole was longer and stronger than the poles that are used in pairs. In competitive cross-country poles in pairs were introduced around 1900.
## Gallery
Image:Skigudinne.jpg\|An early depiction of a skier---a Sami woman or goddess hunting on skis by Olaus Magnus (1553). <File:Birkebeinerne> ski01.jpg\|Loyal retainers transporting Prince Haakon IV of Norway to safety on skis during the winter of 1206---1869 depiction by Knud Bergslien. <File:138>. Kronprins Olav - no-nb digifoto 20150710 00006 bldsa pk kgl0061.jpg\|Olav V of Norway as crown-prince in 1939 Image:olympic skier in ice storm.jpg\|A skate-skier in Gatineau Park, Quebec, a North American groomed-trail ski venue. <File:AchenseeWinter01.JPG%7CA> recreational cross-country trail, groomed for classic skiing only, in Tyrol. <File:Blind> skier and guide.jpg\|A blind cross-country skier with guide at a regional Ski for Light event. <File:Skijor> worlds.jpg\|Dog skijoring---dogs provide added propulsion to the cross-country skier.
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Cy Young Award
|
The **Cy Young Award** is given annually to the best pitchers in Major League Baseball (MLB), one each for the American League (AL) and National League (NL). The award was introduced in 1956 by Baseball Commissioner Ford C. Frick in honor of Hall of Fame pitcher Cy Young, who died in 1955. The award was originally given to the single best pitcher in the major leagues, but in 1967, after the retirement of Frick, the award was given to one pitcher in each league.
Each league\'s award is voted on by members of the Baseball Writers\' Association of America (BBWAA). Local BBWAA chapter chairmen in each MLB city recommend two writers to vote for each award. Final approval comes from the BBWAA national secretary-treasurer. Writers vote for either the American League or National League awards, depending on the league in which their local team plays. A total of 30 writers vote for each league\'s awards. Writers cast their votes prior to the start of postseason play.
As of the 2010 season, each voter places a vote for first, second, third, fourth, and fifth place among the pitchers of each league. The formula used to calculate the final scores is a weighted sum of the votes.`{{ref label|Formula|A|A}}`{=mediawiki} The pitcher with the highest score in each league wins the award. If two pitchers receive the same number of votes, the award is shared. From 1970 to 2009, writers voted for three pitchers, with the formula of five points for a first-place vote, three for a second-place vote and one for a third-place vote. Before 1970, writers only voted for the best pitcher and used a formula of one point per vote.
## History
The Cy Young Award was introduced in 1956 by Commissioner of Baseball Ford C. Frick in honor of Hall of Fame pitcher Cy Young, who died in 1955. Originally given to the single best pitcher in the major leagues, the award changed its format over time. From 1956 to 1966, the award was given to one pitcher in Major League Baseball. After Frick retired in 1967, William Eckert became the new Commissioner of Baseball. Due to fan requests, Eckert announced that the Cy Young Award would be given out both in the American League and the National League. From 1956 to 1958, a pitcher was not allowed to win the award on more than one occasion; this rule was eliminated in 1959. After a tie in the 1969 voting for the Cy Young Award, the process was changed, in which each writer was to vote for three pitchers: the first-place vote received five points, the second-place vote received three points, and the third-place vote received one point.
The first recipient of the Cy Young Award was Don Newcombe of the Dodgers. The Dodgers are the franchise with the most Cy Young Awards. In 1957, Warren Spahn became the first left-handed pitcher to win the award. In 1963, Sandy Koufax became the first pitcher to win the award in a unanimous vote; two years later he became the first multiple winner. In 1978, Gaylord Perry (age 40) became the oldest pitcher to receive the award, a record that stood until broken in 2004 by Roger Clemens (age 42). The youngest recipient was Dwight Gooden (age 20 in 1985). In 2012, R. A. Dickey became the first knuckleball pitcher to win the award.
In 1974, Mike Marshall became the first relief pitcher to win the award. In 1992, Dennis Eckersley was the first modern closer (first player to be used almost exclusively in ninth-inning situations) to win the award. Since then only one other relief pitcher has won the award, Éric Gagné in 2003 (also a closer). Nine relief pitchers have won the Cy Young Award across both leagues.
Steve Carlton in 1982 became the first pitcher to win more than three Cy Young Awards, while Greg Maddux in 1994 became the first to win at least three in a row (and received a fourth straight the following year), a feat later repeated by Randy Johnson.
## Winners
------- ------------------------------------------------------------------------------------------------------------
Year Each year is linked to an article about that Major League Baseball season.
ERA Earned run average
\(#\) Number of wins by pitchers who have won the award multiple times
\* Also named Most Valuable Player (11 occurrences `{{As of|2025|lc=y}}`{=mediawiki})
\*\* Also named Rookie of the Year (1 occurrence `{{As of|2025|lc=y}}`{=mediawiki}, by Fernando Valenzuela)
Member of the National Baseball Hall of Fame and Museum (22 individuals `{{As of|2025|lc=y}}`{=mediawiki})
------- ------------------------------------------------------------------------------------------------------------
: Key
### Major Leagues combined (1956--1966) {#major_leagues_combined_19561966}
Year Pitcher Team Record`{{ref label|Decisions|B|a}}`{=mediawiki} Saves`{{ref label|Decisions|C|a}}`{=mediawiki} ERA K\'s
------ ----------------------------------------------------- -------------------------- ------------------------------------------------- ------------------------------------------------ ------ ------
\* Brooklyn Dodgers (NL) 27--7 0 3.06 139
Milwaukee Braves (NL) 21--11 3 2.69 111
New York Yankees (AL) 21--7 1 2.97 168
Chicago White Sox (AL) 22--10 0 3.17 179
Pittsburgh Pirates (NL) 20--9 0 3.08 120
New York Yankees (AL) 25--4 0 3.21 209
Los Angeles Dodgers (NL) 25--9 1 2.84 232
\*`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} Los Angeles Dodgers (NL) 25--5 0 1.88 306
Los Angeles Angels (AL) 20--9 4 1.65 207
\(2\) Los Angeles Dodgers (NL) 26--8 2 2.04 382
\(3\) Los Angeles Dodgers (NL) 27--9 0 1.73 317
### American League (1967--present) {#american_league_1967present}
Year Pitcher Team data-sort-type=\"number\"\|Record`{{ref label|Decisions|B|a}}`{=mediawiki} Saves`{{ref label|Decisions|C|a}}`{=mediawiki} ERA K\'s
------ ----------------------------------------------------- ------------------------------- ---------------------------------------------------------------------------- ------------------------------------------------ ------ ----------------------
Boston Red Sox 22--9 0 3.16 246
\* Detroit Tigers 31--6 0 1.96 280
Baltimore Orioles 23--11 0 2.38 182
\(2\) Detroit Tigers 24--9 0 2.80 181
Minnesota Twins 24--12 0 3.04 168
\* Oakland Athletics 24--8 0 1.82 301
Cleveland Indians 24--16 1 1.92 234
Baltimore Orioles 22--9 1 2.40 168
Oakland Athletics 25--12 0 2.49 143
\(2\) Baltimore Orioles 23--11 1 2.09 193
\(3\) Baltimore Orioles 22--13 0 2.51 159
New York Yankees 13--5 26 2.17 68
New York Yankees 25--3 0 1.74 248
Baltimore Orioles 23--9 0 3.08 190
Baltimore Orioles 25--7 0 3.23 149
\*`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} Milwaukee Brewers 6--3 28 1.04 61
Milwaukee Brewers 18--6 0 3.34 105
Chicago White Sox 24--10 0 3.66 148
\* Detroit Tigers 9--3 32 1.92 112
Kansas City Royals 20--6 0 2.87 158
\* Boston Red Sox 24--4 0 2.48 238
\(2\) Boston Red Sox 20--9 0 2.97 256
Minnesota Twins 24--7 0 2.64 193
\(2\) Kansas City Royals 23--6 0 2.16 193
Oakland Athletics 27--6 0 2.95 127
\(3\) Boston Red Sox 18--10 0 2.62 241
\*`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} Oakland Athletics 7--1 51 1.91 93
Chicago White Sox 22--10 0 3.37 158
Kansas City Royals 16--5 0 2.94 132
Seattle Mariners 18--2 0 2.48 294
Toronto Blue Jays 20--10 0 3.22 177
\(4\) Toronto Blue Jays 21--7 0 2.05 292
\(5\) Toronto Blue Jays 20--6 0 2.65 271
\(2\) Boston Red Sox 23--4 0 2.07 313
\(3\) Boston Red Sox 18--6 0 1.74 284
\(6\) New York Yankees 20--3 0 3.51 213
Oakland Athletics 23--5 0 2.75 182
Toronto Blue Jays 22--7 0 3.25 204
Minnesota Twins 20--6 0 2.61 265
Los Angeles Angels of Anaheim 21--8 0 3.48 157
\(2\) Minnesota Twins 19--6 0 2.77 265
Cleveland Indians 19--7 0 3.21 209
Cleveland Indians 22--3 0 2.54 170
Kansas City Royals 16--8 0 2.16 242
Seattle Mariners 13--12 0 2.27 232
\* Detroit Tigers 24--5 0 2.40 250
Tampa Bay Rays 20--5 0 2.56 205
Detroit Tigers 21--3 0 2.90 240
Cleveland Indians 18--9 0 2.44 269 \|-Rick Porcello
Boston Red Sox 22--4 0 3.15 189
\(2\) Cleveland Indians 18--4 0 2.25 265
Tampa Bay Rays 21--5 0 1.89 221
\(2\) Houston Astros 21--6 0 2.58 300
Cleveland Indians 8--1 0 1.63 122
Toronto Blue Jays 13--7 0 2.84 248
\(3\) Houston Astros 18--4 0 1.75 185
New York Yankees 15--4 0 2.63 222
Detroit Tigers 18--4 0 2.39 228
### National League (1967--present) {#national_league_1967present}
Year Pitcher Team data-sort-type=\"number\"\|Record`{{ref label|Decisions|B|a}}`{=mediawiki} Saves`{{ref label|Decisions|C|a}}`{=mediawiki} ERA K\'s
------ ----------------------------------------------------- ----------------------- ---------------------------------------------------------------------------- ------------------------------------------------ ------ ------
San Francisco Giants 22--10 0 2.85 150
\*`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} St. Louis Cardinals 22--9 0 1.12 268
New York Mets 25--7 0 2.21 208
\(2\) St. Louis Cardinals 23--7 0 3.12 274
Chicago Cubs 24--13 0 2.77 263
Philadelphia Phillies 27--10 0 1.98 310
\(2\) New York Mets 19--10 0 2.08 251
Los Angeles Dodgers 15--12 21 2.42 143
\(3\) New York Mets 22--9 0 2.38 243
San Diego Padres 22--14 0 2.74 93
\(2\) Philadelphia Phillies 23--10 0 2.64 198
\(2\) San Diego Padres 21--6 0 2.73 154
Chicago Cubs 6--6 37 2.22 110
\(3\) Philadelphia Phillies 24--9 0 2.34 286
\*\* Los Angeles Dodgers 13--7 0 2.48 180
\(4\) Philadelphia Phillies 23--11 0 3.11 286
Philadelphia Phillies 19--6 0 2.37 139
Chicago Cubs 16--1 0 2.69 155
New York Mets 24--4 0 1.53 268
Houston Astros 18--10 0 2.22 306
Philadelphia Phillies 5--3 40 2.83 74
Los Angeles Dodgers 23--8 1 2.26 178
San Diego Padres 4--3 44 1.85 92
Pittsburgh Pirates 22--6 0 2.76 131
Atlanta Braves 20--11 0 2.55 192
Chicago Cubs 20--11 0 2.18 199
\(2\) Atlanta Braves 20--10 0 2.36 197
\(3\) Atlanta Braves 16--6 0 1.56 156
\(4\) Atlanta Braves 19--2 0 1.63 181
Atlanta Braves 24--8 0 2.94 276
Montreal Expos 17--8 0 1.90 305
\(2\) Atlanta Braves 20--6 0 2.47 157
\(2\) Arizona Diamondbacks 17--9 0 2.49 364
\(3\) Arizona Diamondbacks 19--7 0 2.64 347
\(4\) Arizona Diamondbacks 21--6 0 2.49 372
\(5\) Arizona Diamondbacks 24--5 0 2.32 334
Los Angeles Dodgers 2--3 55 1.20 137
\(7\) Houston Astros 18--4 0 2.98 218
St. Louis Cardinals 21--5 0 2.83 213
Arizona Diamondbacks 16--8 0 3.10 178
San Diego Padres 19--6 0 2.54 240
San Francisco Giants 18--5 0 2.62 265
\(2\) San Francisco Giants 15--7 0 2.48 261
\(2\) Philadelphia Phillies 21--10 0 2.44 219
Los Angeles Dodgers 21--5 0 2.28 248
New York Mets 20--6 0 2.73 230
\(2\) Los Angeles Dodgers 16--9 0 1.83 232
\* (3) Los Angeles Dodgers 21--3 0 1.77 239
Chicago Cubs 22--6 0 1.77 236
\(2\) Washington Nationals 20--7 0 2.96 284
\(3\) Washington Nationals 16--6 0 2.51 268
New York Mets 10--9 0 1.70 269
\(2\) New York Mets 11--8 0 2.43 255
Cincinnati Reds 5--4 0 1.73 100
Milwaukee Brewers 11--5 0 2.43 234
Miami Marlins 14--9 0 2.28 207
Blake Snell (2) San Diego Padres 14--9 0 2.25 234
Chris Sale Atlanta Braves 18--3 0 2.38 225
### Multiple winners {#multiple_winners}
Twenty-two (22) pitchers have won the award multiple times. Roger Clemens has won the most awards won, seven. His first and last wins were 18 years apart. Greg Maddux (1992--1995) and Randy Johnson (1999--2002) share the record for the most consecutive awards won with four. Clemens, Johnson, Pedro Martínez, Gaylord Perry, Roy Halladay, Max Scherzer, and Blake Snell are the only pitchers to win the award in both the American League and National League. Sandy Koufax is the only pitcher to win multiple awards during the period when only one award was presented for all of MLB. Roger Clemens was the youngest pitcher to win a second Cy Young Award, while Tim Lincecum is the youngest pitcher to do so in the National League, and Clayton Kershaw is the youngest left-hander to do so. Kershaw is the youngest pitcher to win a third Cy Young Award. Clemens is also the only pitcher to win the award with four different teams; nobody else has done so with more than two different teams. Justin Verlander has the most seasons separating his first (2011) and second (2019) Cy Young Awards.
Pitcher \# of Awards Years
--------------------------------------------------- -------------- ------------------------------------------
7 1986, 1987, 1991, 1997, 1998, 2001, 2004
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 5 1995, 1999, 2000, 2001, 2002
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 4 1972, 1977, 1980, 1982
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1992, 1993, 1994, 1995
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 3 1963, 1965, 1966
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1969, 1973, 1975
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1973, 1975, 1976
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1997, 1999, 2000
2011, 2013, 2014
2013, 2016, 2017
2011, 2019, 2022
2 1968, 1969
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1968, 1970
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1972, 1978
1985, 1989
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 1991, 1998
2004, 2006
2008, 2009
`{{sup|{{dagger|alt=Hall of Fame}}}}`{=mediawiki} 2003, 2010
2014, 2017
2018, 2019
2018, 2023
### Wins by teams {#wins_by_teams}
Only two teams have never had a pitcher win the Cy Young Award. The Brooklyn/Los Angeles Dodgers have won more than any other team with 12.
scope=\"col\| Team scope=\"col\| \# of Awards scope=\"col\| Years
------------------------------------- ---------------------------- ------------------------------------------------------------------------
Brooklyn/Los Angeles Dodgers 12 1956, 1962, 1963, 1965, 1966, 1974, 1981, 1988, 2003, 2011, 2013, 2014
Milwaukee/Atlanta Braves 8 1957, 1991, 1993--1996, 1998, 2024
Philadelphia Phillies 7 1972, 1977, 1980, 1982, 1983, 1987, 2010
Boston Red Sox 1967, 1986, 1987, 1991, 1999, 2000, 2016
New York Mets 1969, 1973, 1975, 1985, 2012, 2018, 2019
Baltimore Orioles 6 1969, 1973, 1975, 1976, 1979, 1980
Cleveland Indians 1972, 2007, 2008, 2014, 2017, 2020
Detroit Tigers 1968, 1969, 1984, 2011, 2013, 2024
New York Yankees 1958, 1961, 1977, 1978, 2001, 2023
Arizona Diamondbacks 5 1999--2002, 2006
Oakland Athletics 1971, 1974, 1990, 1992, 2002
Chicago Cubs 1971, 1979, 1984, 1992, 2015
Toronto Blue Jays 1996--1998, 2003, 2021
Houston Astros 1986, 2004, 2015, 2019, 2022
San Diego Padres 1976, 1978, 1989, 2007, 2023
Kansas City Royals 4 1985, 1989, 1994, 2009
Minnesota Twins 1970, 1988, 2004, 2006
Chicago White Sox 3 1959, 1983, 1993
San Francisco Giants 1967, 2008, 2009
St. Louis Cardinals 1968, 1970, 2005
Montreal Expos/Washington Nationals 1997, 2016, 2017
Milwaukee Brewers 1981, 1982, 2021
Los Angeles Angels 2 1964, 2005
Pittsburgh Pirates 1960, 1990
Seattle Mariners 1995, 2010
Tampa Bay Rays 2012, 2018
Cincinnati Reds 1 2020
Miami Marlins 2022
Colorado Rockies 0 none
Texas Rangers none
### Unanimous winners {#unanimous_winners}
There have been 21 players who unanimously won the Cy Young Award, for a total of 28 wins.
Six of these unanimous wins were accompanied by a win of the Most Valuable Player award (marked with \* below; \*\* denotes that the player\'s unanimous win was accompanied by a unanimous win of the MVP Award).
In the National League, 12 players have unanimously won the Cy Young Award, for a total of 15 wins.
- Sandy Koufax (1963\*, 1965, 1966)
- Greg Maddux (1994, 1995)
- Bob Gibson (1968\*)
- Steve Carlton (1972)
- Rick Sutcliffe (1984)
- Dwight Gooden (1985)
- Orel Hershiser (1988)
- Randy Johnson (2002)
- Jake Peavy (2007)
- Roy Halladay (2010)
- Clayton Kershaw (2014\*)
- Sandy Alcántara (2022)
In the American League, nine players have unanimously won the Cy Young Award, for a total of 13 wins.
- Denny McLain (1968\*\*)
- Ron Guidry (1978)
- Roger Clemens (1986\*, 1998)
- Pedro Martínez (1999, 2000)
- Johan Santana (2004, 2006)
- Justin Verlander (2011\*, 2022)
- Shane Bieber (2020)
- Gerrit Cole (2023)
- Tarik Skubal (2024)
| 2025-06-20T00:00:00 |
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Constantius II
|
Constantine II\|Julius Constantius\|Constantius III}} `{{Use dmy dates|date=September 2021}}`{=mediawiki}
**Constantius II** (*Flavius Julius Constantius*; *Kōnstántios*; 7 August 317 -- 3 November 361) was Roman emperor from 337 to 361. His reign saw constant warfare on the borders against the Sasanian Empire and Germanic peoples, while internally the Roman Empire went through repeated civil wars, court intrigues, and usurpations. His religious policies inflamed domestic conflicts that would continue after his death.
Constantius was a son of Constantine the Great, who elevated him to the imperial rank of *Caesar* on 8 November 324 and after whose death Constantius became *Augustus* together with his brothers, Constantine II and Constans on 9 September 337. He promptly oversaw the massacre of his father-in-law, an uncle, and several cousins, consolidating his hold on power. The brothers divided the empire among themselves, with Constantius receiving Greece, Thrace, the Asian provinces, and Egypt in the east. For the following decade a costly and inconclusive war against Persia took most of Constantius\'s time and attention. In the meantime, his brothers Constantine and Constans warred over the western provinces of the empire, leaving the former dead in 340 and the latter as sole ruler of the west. The two remaining brothers maintained an uneasy peace with each other until, in 350, Constans was overthrown and assassinated by the usurper Magnentius.
Unwilling to accept Magnentius as co-ruler, Constantius waged a civil war against the usurper, defeating him at the battles of Mursa Major in 351 and Mons Seleucus in 353. Magnentius died by suicide after the latter battle, leaving Constantius as sole ruler of the empire. In 351, Constantius elevated his cousin Constantius Gallus to the subordinate rank of *Caesar* to rule in the east, but had him executed three years later after receiving scathing reports of his violent and corrupt nature. Shortly thereafter, in 355, Constantius promoted his last surviving cousin, Gallus\'s younger half-brother Julian, to the rank of *Caesar*.
As emperor, Constantius promoted Arianism, banned pagan sacrifices, and issued laws against Jews. His military campaigns against Germanic tribes were successful: he defeated the Alamanni in 354 and campaigned across the Danube against the Quadi and Sarmatians in 357. The war against the Sasanians, which had been in a lull since 350, erupted with renewed intensity in 359 and Constantius travelled to the east in 360 to restore stability after the loss of several border fortresses. However, Julian claimed the rank of *Augustus* in 360, leading to war between the two after Constantius\'s attempts to persuade Julian to back down failed. No battle was fought, as Constantius became ill and died of fever on 3 November 361 in Mopsuestia, allegedly naming Julian as his rightful successor before his death.
## Early life {#early_life}
Flavius Julius Constantius was born in 317 at Sirmium, Pannonia, now Serbia. He was the third son of Constantine the Great, and second by his second wife Fausta, the daughter of Maximian. Constantius was made *caesar* by his father on 8 November 324. In 336, religious unrest in Armenia and tense relations between Constantine and king Shapur II caused war to break out between Rome and Sassanid Persia. Though he made initial preparations for the war, Constantine fell ill and sent Constantius east to take command of the eastern frontier. Before Constantius arrived, the Persian general Narses, who was possibly the king\'s brother, overran Mesopotamia and captured Amida. Constantius promptly attacked Narses, and after suffering minor setbacks defeated and killed Narses at the Battle of Narasara. Constantius captured Amida and initiated a major refortification of the city, enhancing the city\'s circuit walls and constructing large towers. He also built a new stronghold in the hinterland nearby, naming it *Antinopolis*.
## Augustus in the east {#augustus_in_the_east}
In early 337, Constantius hurried to Constantinople after receiving news that his father was near death. After Constantine died, Constantius buried him with lavish ceremony in the Church of the Holy Apostles. Soon after his father\'s death, the army massacred his relatives descended from the marriage of his paternal grandfather Constantius Chlorus to Flavia Maximiana Theodora, though the details are unclear. Two of Constantius\'s uncles (Julius Constantius and Flavius Dalmatius) and seven of his cousins were killed, including Hannibalianus and Dalmatius, rulers of Pontus and Moesia respectively, leaving Constantius, his two brothers Constantine II and Constans, and three cousins Gallus, Julian and Nepotianus as the only surviving male relatives of Constantine the Great. While the "official version" was that Constantius\'s relatives were merely the victims of a mutinous army, Ammianus Marcellinus, Zosimus, Libanius, Athanasius and Julian all blamed Constantius for the event. Burgess considered the latter version to be "consistent with all the evidence", pointing to multiple factors that he believed lined up with the massacre being a planned attack rather than a spontaneous mutiny - the lack of high-profile punishments as a response, the sparing of all women, the attempted damnatio memoriae on the deceased, and the exile of the survivors Gallus and Julian.
Soon after, Constantius met his brothers in Pannonia at Sirmium to formalize the partition of the empire. Constantius received the eastern provinces, including Constantinople, Thrace, Asia Minor, Syria, Egypt, and Cyrenaica; Constantine received Britannia, Gaul, Hispania, and Mauretania; and Constans, initially under the supervision of Constantine II, received Italy, Africa, Illyricum, Pannonia, Macedonia, and Achaea.
Constantius then hurried east to Antioch to resume the war with Persia. While Constantius was away from the eastern frontier in early 337, King Shapur II assembled a large army, which included war elephants, and launched an attack on Roman territory, laying waste to Mesopotamia and putting the city of Nisibis under siege. Despite initial success, Shapur lifted his siege after his army missed an opportunity to exploit a collapsed wall. When Constantius learned of Shapur\'s withdrawal from Roman territory, he prepared his army for a counter-attack.
Constantius repeatedly defended the eastern border against invasions by the Sassanid Empire under Shapur. These conflicts were mainly limited to Sassanid sieges of the major fortresses of Roman Mesopotamia, including Nisibis (Nusaybin), Singara, and Amida (Diyarbakir). Although Shapur seems to have been victorious in most of these confrontations, the Sassanids were able to achieve little. However, the Romans won a decisive victory at the Battle of Narasara, killing Shapur\'s brother, Narses. Ultimately, Constantius was able to push back the invasion, and Shapur failed to make any significant gains.
Meanwhile, Constantine II desired to retain control of Constans\'s realm, leading the brothers into open conflict. Constantine was killed in 340 near Aquileia during an ambush. As a result, Constans took control of his deceased brother\'s realms and became sole ruler of the Western two-thirds of the empire. This division lasted until January 350, when Constans was assassinated by forces loyal to the usurper Magnentius.
### War against Magnentius {#war_against_magnentius}
Constantius was determined to march west to fight the usurper. However, feeling that the east still required some sort of imperial presence, he elevated his cousin Constantius Gallus to *caesar* of the eastern provinces. As an extra measure to ensure the loyalty of his cousin, he married the elder of his two sisters, Constantina, to him.
Before facing Magnentius, Constantius first came to terms with Vetranio, a loyal general in Illyricum who had recently been acclaimed emperor by his soldiers. Vetranio immediately sent letters to Constantius pledging his loyalty, which Constantius may have accepted simply in order to stop Magnentius from gaining more support. These events may have been spurred by the action of Constantina, who had since traveled east to marry Gallus. Constantius subsequently sent Vetranio the imperial diadem and acknowledged the general\'s new position as *augustus*. However, when Constantius arrived, Vetranio willingly resigned his position and accepted Constantius\'s offer of a comfortable retirement in Bithynia.
In 351, Constantius clashed with Magnentius in Pannonia with a large army. The ensuing Battle of Mursa Major was one of the largest and bloodiest battles ever between two Roman armies. The result was a victory for Constantius, but a costly one. Magnentius survived the battle and, determined to fight on, withdrew into northern Italy. Rather than pursuing his opponent, however, Constantius turned his attention to securing the Danubian border, where he spent the early months of 352 campaigning against the Sarmatians along the middle Danube. After achieving his aims, Constantius advanced on Magnentius in Italy. This action led the cities of Italy to switch their allegiance to him and eject the usurper\'s garrisons. Again, Magnentius withdrew, this time to southern Gaul.
In 353, Constantius and Magnentius met for the final time at the Battle of Mons Seleucus in southern Gaul, and again Constantius emerged the victor. Magnentius, realizing the futility of continuing his position, committed suicide on 10 August 353.
## Solo reign {#solo_reign}
Constantius spent much of the rest of 353 and early 354 on campaign against the Alamanni on the Danube frontier. The campaign was successful and raiding by the Alamanni ceased temporarily. In the meantime, Constantius had been receiving disturbing reports regarding the actions of his cousin Gallus. Possibly as a result of these reports, Constantius concluded a peace with the Alamanni and traveled to Mediolanum (Milan).
In Mediolanum, Constantius first summoned Ursicinus, Gallus\'s *magister equitum*, for reasons that remain unclear. Constantius then summoned Gallus and Constantina. Although Gallus and Constantina complied with the order at first, when Constantina died in Bithynia, Gallus began to hesitate. However, after some convincing by one of Constantius\'s agents, Gallus continued his journey west, passing through Constantinople and Thrace to Poetovio (Ptuj) in Pannonia.
In Poetovio, Gallus was arrested by the soldiers of Constantius under the command of Barbatio. Gallus was then moved to Pola and interrogated. Gallus claimed that it was Constantina who was to blame for all the trouble while he was in charge of the eastern provinces. This angered Constantius so greatly that he immediately ordered Gallus\'s execution. He soon changed his mind, however, and recanted the order. Unfortunately for Gallus, this second order was delayed by Eusebius, one of Constantius\'s eunuchs, and Gallus was executed.
### Religious issues {#religious_issues}
*Main article: Religious policies of Constantius II*
#### Paganism
Laws dating from the 350s prescribed the death penalty for those who performed or attended pagan sacrifices, and for the worshipping of idols. Pagan temples were shut down, and the Altar of Victory was removed from the Senate meeting house. There were also frequent episodes of ordinary Christians destroying, pillaging and desecrating many ancient pagan temples, tombs and monuments. Paganism was still popular among the population at the time. The emperor\'s policies were passively resisted by many governors and magistrates.
In spite of this, Constantius never made any attempt to disband the various Roman priestly colleges or the Vestal Virgins. He never acted against the various pagan schools. At times, he actually made some effort to protect paganism. In fact, he even ordered the election of a priest for Africa. Also, he remained pontifex maximus and was deified by the Roman Senate after his death. His relative moderation toward paganism is reflected by the fact that it was over twenty years after his death, during the reign of Gratian, that any pagan senator protested his treatment of their religion.
#### Christianity
Although often considered an Arian, Constantius ultimately preferred a third, compromise version that lay somewhere in between Arianism and the Nicene Creed, retrospectively called Semi-Arianism. During his reign he attempted to mold the Christian church to follow this compromise position, convening several Christian councils. \"Unfortunately for his memory the theologians whose advice he took were ultimately discredited and the malcontents whom he pressed to conform emerged victorious,\" writes the historian A. H. M. Jones. \"The great councils of 359--60 are therefore not reckoned ecumenical in the tradition of the church, and Constantius II is not remembered as a restorer of unity, but as a heretic who arbitrarily imposed his will on the church.\"
According to the Greek historian Philostorgius (d. 439) in his *Ecclesiastical History*, Constantius sent an Arian bishop known as Theophilus the Indian (also known as \"Theophilus of Yemen\") to Tharan Yuhanim, then the king of the South Arabian Himyarite Kingdom to convert the people to Christianity. According to the report, Theophilus succeeded in establishing three churches, one of them in the capital Zafar.
#### Judaism
Judaism faced some severe restrictions under Constantius, who seems to have followed an anti-Jewish policy in line with that of his father. This included edicts to limit the ownership of slaves by Jewish people and banning marriages between Jews and Christian women. Later edicts sought to discourage conversions from Christianity to Judaism by confiscating the apostate\'s property. However, Constantius\'s actions in this regard may not have been so much to do with Jewish religion as with Jewish business---apparently, privately owned Jewish businesses were often in competition with state-owned businesses. As a result, Constantius may have sought to provide an advantage to state-owned businesses by limiting the skilled workers and slaves available to Jewish businesses.
### Further crises {#further_crises}
On 11 August 355, the *magister militum* Claudius Silvanus revolted in Gaul. Silvanus had surrendered to Constantius after the Battle of Mursa Major. Constantius had made him *magister militum* in 353 with the purpose of blocking the German threats, a feat that Silvanus achieved by bribing the German tribes with the money he had collected. A plot organized by members of Constantius\'s court led the emperor to recall Silvanus. After Silvanus revolted, he received a letter from Constantius recalling him to Milan, but which made no reference to the revolt. Ursicinus, who was meant to replace Silvanus, bribed some troops, and Silvanus was killed.
Constantius realised that too many threats still faced the Empire, however, and he could not possibly handle all of them by himself. So on 6 November 355, he elevated his last remaining male relative, Julian, to the rank of *caesar*. A few days later, Julian was married to Helena, the last surviving sister of Constantius. Constantius soon sent Julian off to Gaul. Constantius spent the next few years overseeing affairs in the western part of the empire primarily from his base at Mediolanum. In April--May 357 he visited Rome for the only time in his life. The same year, he forced Sarmatian and Quadi invaders out of Pannonia and Moesia Inferior, then led a successful counter-attack across the Danube.
In the winter of 357--58, Constantius received ambassadors from Shapur II who demanded that Rome restore the lands surrendered by Narseh. Despite rejecting these terms, Constantius tried to avert war with the Sassanid Empire by sending two embassies to Shapur II. Shapur II nevertheless launched another invasion of Roman Mesopotamia. In 360, when news reached Constantius that Shapur II had destroyed Singara (Sinjar), and taken Kiphas (Hasankeyf), Amida (Diyarbakır), and Ad Tigris (Cizre), he decided to travel east to face the re-emergent threat.
### Usurpation of Julian and crises in the east {#usurpation_of_julian_and_crises_in_the_east}
In the meantime, Julian had won some victories against the Alamanni, who had once again invaded Roman Gaul. However, when Constantius requested reinforcements from Julian\'s army for the eastern campaign, the Gallic legions revolted and proclaimed Julian *augustus*.
On account of the immediate Sassanid threat, Constantius was unable to directly respond to his cousin\'s usurpation, other than by sending missives in which he tried to convince Julian to resign the title of *augustus* and be satisfied with that of *caesar*. By 361, Constantius saw no alternative but to face the usurper with force, and yet the threat of the Sassanids remained. Constantius had already spent part of early 361 unsuccessfully attempting to re-take the fortress of Ad Tigris. After a time he had withdrawn to Antioch to regroup and prepare for a confrontation with Shapur II. The campaigns of the previous year had inflicted heavy losses on the Sassanids, however, and they did not attempt another round of campaigns that year. This temporary respite in hostilities allowed Constantius to turn his full attention to facing Julian.
### Death
Constantius immediately gathered his forces and set off west. However, by the time he reached Mopsuestia in Cilicia, it was clear that he was fatally ill and would not survive to face Julian. The sources claim that realising his death was near, Constantius had himself baptised by Euzoius, the Semi-Arian bishop of Antioch, and then declared that Julian was his rightful successor. Constantius II died of fever on 3 November 361.
Like Constantine the Great, he was buried in the Church of the Holy Apostles, in a porphyry sarcophagus that was described in the 10th century by Constantine VII Porphyrogenitus in the *De Ceremoniis*.
## Marriages and children {#marriages_and_children}
Constantius II was married three times:
First to a daughter of his half-uncle Julius Constantius, whose name is unknown. She was a full-sister of Gallus and a half-sister of Julian. She died c. 352/3.
Second, to Eusebia, a woman of Macedonian origin, originally from the city of Thessalonica, whom Constantius married before his defeat of Magnentius in 353. She died before 361.
Third and lastly, in 361, to Faustina, who gave birth to Constantius\'s only child, a posthumous daughter named Constantia, who later married Emperor Gratian.
## Family tree {#family_tree}
Emperors are shown with a rounded-corner border with their dates as Augusti, names with a thicker border appear in both sections
**1: Constantine\'s parents and half-siblings** `{{Tree chart/start|align=center}}`{=mediawiki} `{{tree chart| | | | | | |CGOTH|CGOTH={{ubl|[[Claudius Gothicus]]|268–270|''fabricated ancestry''}}|boxstyle_CGOTH=border:2px solid; border-radius:1em}}`{=mediawiki} `{{tree chart| | | | | | | |Q|}}`{=mediawiki} `{{tree chart| | |HELEN|y|CCHLO|y|THEO1|HELEN=[[Helena, mother of Constantine I|Helena]]|boxstyle_HELEN=border:2px solid|CCHLO={{ubl|[[Constantius I]]|305–306}}|boxstyle_CCHLO=border:2px solid; border-radius:1em|THEO1=[[Flavia Maximiana Theodora]]}}`{=mediawiki} `{{tree chart| | | | | |!| | | |)|-|v|-|v|-|-|-|v|-|-|-|-|-|v|-|.| | | | | }}`{=mediawiki} `{{tree chart| | | | |CONST| |FLAVD|!|HANN1| |CONS2|y|LICI1|!|ANAST|~|BASSI|CONST={{ubl|'''Constantine I'''|306–337}}|boxstyle_CONST=border:3px solid; border-radius:1em|FLAVD=[[Flavius Dalmatius]]|HANN1=Hannibalianus|CONS2=[[Flavia Julia Constantia]]|LICI1={{ubl|[[Licinius]]|308–324}}|boxstyle_LICI1=border:2px solid; border-radius:1em|ANAST=Anastasia|BASSI=[[Bassianus (executed by Constantine)|Bassianus]]}}`{=mediawiki} `{{tree chart| |,|-|-|-|-|-|-|-|'| |!| | | | | | | |!| | | |!}}`{=mediawiki} `{{tree chart| |!| | | | |GALL1|y|JULIC|y|BASIL| |LICI2| |EUTR2|y|NEPO1|GALL1=[[Galla (wife of Julius Constantius)|Galla]]|JULIC=[[Julius Constantius]]|BASIL=[[Basilina]]|LICI2=[[Licinius II]]|EUTR2=[[Eutropia (sister of Constantine I)|Eutropia]]|NEPO1=Virius Nepotianus}}`{=mediawiki} `{{tree chart| |!| | | | | | | |!| | | |!| | | | | | | | | | | |!}}`{=mediawiki} `{{tree chart|HANN2|~|CONS6|~|GALLU| |JULIA|~|HELE2| | | | | |NEPO2|HANN2=[[Hannibalianus]]|boxstyle_HANN2=border:3px solid|CONS6=[[Constantina]]|boxstyle_CONS6=border:3px solid|GALLU=[[Constantius Gallus]]|boxstyle_GALLU=border:3px solid|JULIA={{ubl|[[Julian (emperor)|Julian]]|360–363}}|boxstyle_JULIA=border:3px solid; border-radius:1em|HELE2=[[Helena (wife of Julian)|Helena]]|boxstyle_HELE2=border:3px solid|NEPO2=[[Nepotianus]]}}`{=mediawiki} `{{tree chart/end}}`{=mediawiki} `{{break}}`{=mediawiki} **2: Constantine\'s children** `{{Tree chart/start|align=center}}`{=mediawiki} `{{tree chart|MINER|y|CONST|y|FAUS1|MINER=[[Minervina]]|CONST={{ubl|'''Constantine I'''|306–337}}|boxstyle_CONST=border:3px solid; border-radius:1em|FAUS1=[[Fausta]]}}`{=mediawiki} `{{tree chart| | | |!| | | |)|-|v|-|v|-|v|-|-|-|-|-|.|}}`{=mediawiki} `{{tree chart| | |CRISP| |CONS3|!|CONS5|!|HANN2|~|CONS6|~|GALLU|CRISP=[[Crispus]]|CONS3={{ubl|[[Constantine II (emperor)|Constantine II]]|337–340}}|boxstyle_CONS3=border:2px solid; border-radius:1em|CONS5={{ubl|[[Constans]]|337–350}}|boxstyle_CONS5=border:2px solid; border-radius:1em|HANN2=[[Hannibalianus]]|boxstyle_HANN2=border:3px solid|CONS6=[[Constantina]]|boxstyle_CONS6=border:3px solid|GALLU=[[Constantius Gallus]]|boxstyle_GALLU=border:3px solid}}`{=mediawiki} `{{tree chart| | | | | | | | | |!| | | |!}}`{=mediawiki} `{{tree chart| | | | |FAUS2|y|CONS4| |HELE2|~|JULIA|FAUS2=[[Faustina (wife of Constantius II)|Faustina]]|CONS4={{ubl|Constantius II|337–361}}|boxstyle_CONS4=border:2px solid; border-radius:1em|JULIA={{ubl|[[Julian (emperor)|Julian]]|360–363}}|boxstyle_JULIA=border:3px solid; border-radius:1em|HELE2=[[Helena (wife of Julian)|Helena]]|boxstyle_HELE2=border:3px solid}}`{=mediawiki} `{{tree chart| | | | | | | |!}}`{=mediawiki} `{{tree chart| | |GRATI|~|CONS7|GRATI={{ubl|[[Gratian]]|367–383}}|boxstyle_GRATI=border:2px solid; border-radius:1em|CONS7=[[Constantia (wife of Gratian)|Constantia]]}}`{=mediawiki} `{{Tree chart/end}}`{=mediawiki} `{{Chart bottom}}`{=mediawiki}
## Reputation
According to DiMaio and Frakes, "\...Constantius is hard for the modern historian to fully understand both due to his own actions and due to the interests of the authors of primary sources for his reign." A. H. M. Jones writes that he \"appears in the pages of Ammianus as a conscientious emperor but a vain and stupid man, an easy prey to flatterers. He was timid and suspicious, and interested persons could easily play on his fears for their own advantage.\" However, Kent and M. and A. Hirmer suggest that the emperor \"has suffered at the hands of unsympathetic authors, ecclesiastical and civil alike. To orthodox churchmen he was a bigoted supporter of the Arian heresy, to Julian the Apostate and the many who have subsequently taken his part he was a murderer, a tyrant and inept as a ruler\". They go on to add, \"Most contemporaries seem in fact to have held him in high esteem, and he certainly inspired loyalty in a way his brother could not\".
Eutropius wrote of him,
> He was a man of a remarkably tranquil disposition, good-natured, trusting too much to his friends and courtiers, and at last too much in the power of his wives. He conducted himself with great moderation in the commencement of his reign; he enriched his friends, and suffered none, whose active services he had experienced, to go unrewarded. He was however somewhat inclined to severity, whenever any suspicion of an attempt on the government was excited in him; otherwise he was gentle. His fortune is more to be praised in civil than in foreign wars.
| 2025-06-20T00:00:00 |
6,751 |
Cottingley Fairies
|
The **Cottingley Fairies** are the subject of a hoax which purports to provide evidence of the existence of fairies. They appear in a series of five photographs taken by Elsie Wright (1901--1988) and Frances Griffiths (1907--1986), two young cousins who lived in Cottingley, near Bradford in England. In 1917, when the first two photographs were taken, Elsie was 16 years old and Frances was 9. The pictures came to the attention of writer Sir Arthur Conan Doyle, who used them to illustrate an article on fairies he had been commissioned to write for the Christmas 1920 edition of *The Strand Magazine*. Doyle was enthusiastic about the photographs, and interpreted them as clear and visible evidence of supernatural phenomena. Public reaction was mixed; some accepted the images as genuine, others believed that they had been faked.
Interest in the Cottingley Fairies gradually declined after 1921. Both girls married and lived abroad for a time after they grew up, and yet the photographs continued to hold the public imagination. In 1966 a reporter from the *Daily Express* newspaper traced Elsie, who had by then returned to the United Kingdom. Elsie left open the possibility that she believed she had photographed her thoughts, and the media once again became interested in the story.
In the early 1980s Elsie and Frances admitted that the photographs were faked, using cardboard cutouts of fairies copied from a popular children\'s book of the time, but Frances maintained that the fifth and final photograph was genuine. As of 2019 the photographs and the cameras used are in the collections of the National Science and Media Museum in Bradford, England.
## 1917 photographs
In mid-1917 nine-year-old Frances Griffiths and her mother`{{snd}}`{=mediawiki}both newly arrived in England from South Africa`{{snd}}`{=mediawiki}were staying with Frances\'s aunt, Elsie Wright\'s mother, Polly, in the village of Cottingley in West Yorkshire; Elsie was then 16 years old. The two girls often played together beside the beck at the bottom of the garden, much to their mothers\' annoyance, because they frequently came back with wet feet and clothes. Frances and Elsie said they only went to the beck to see the fairies, and to prove it, Elsie borrowed her father\'s camera, a Midg quarter-plate. The girls returned about 30 minutes later, \"triumphant\".
Elsie\'s father, Arthur, was a keen amateur photographer, and had set up his own darkroom. The picture on the photographic plate he developed showed Frances behind a bush in the foreground, on which four fairies appeared to be dancing. Knowing his daughter\'s artistic ability, and that she had spent some time working in a photographer\'s studio, he dismissed the figures as cardboard cutouts. Two months later the girls borrowed his camera again, and this time returned with a photograph of Elsie sitting on the lawn holding out her hand to a 1 ft gnome. Exasperated by what he believed to be \"nothing but a prank\", and convinced that the girls must have tampered with his camera in some way, Arthur Wright refused to lend it to them again. His wife Polly, however, believed the photographs to be authentic.
Towards the end of 1918, Frances sent a letter to Johanna Parvin, a friend in Cape Town, South Africa, where Frances had lived for most of her life, enclosing the photograph of herself with the fairies. On the back she wrote \"It is funny, I never used to see them in Africa. It must be too hot for them there.\"
The photographs became public in mid-1919, after Elsie\'s mother attended a meeting of the Theosophical Society in Bradford. The lecture that evening was on \"fairy life\", and at the end of the meeting Polly Wright showed the two fairy photographs taken by her daughter and niece to the speaker. As a result, the photographs were displayed at the society\'s annual conference in Harrogate, held a few months later. There they came to the attention of a leading member of the society, Edward Gardner. One of the central beliefs of theosophy is that humanity is undergoing a cycle of evolution, towards increasing \"perfection\", and Gardner recognised the potential significance of the photographs for the movement:
## Initial examinations {#initial_examinations}
Gardner sent the prints along with the original glass-plate negatives to Harold Snelling, a photography expert. Snelling\'s opinion was that \"the two negatives are entirely genuine, unfaked photographs \... \[with\] no trace whatsoever of studio work involving card or paper models\". He did not go so far as to say that the photographs showed fairies, stating only that \"these are straight forward photographs of whatever was in front of the camera at the time\". Gardner had the prints \"clarified\" by Snelling, and new negatives produced, \"more conducive to printing\", for use in the illustrated lectures he gave around Britain. Snelling supplied the photographic prints which were available for sale at Gardner\'s lectures.
Author and prominent spiritualist Sir Arthur Conan Doyle learned of the photographs from the editor of the spiritualist publication *Light*. Doyle had been commissioned by *The Strand Magazine* to write an article on fairies for their Christmas issue, and the fairy photographs \"must have seemed like a godsend\" according to broadcaster and historian Magnus Magnusson. Doyle contacted Gardner in June 1920 to determine the background to the photographs, and wrote to Elsie and her father to request permission from the latter to use the prints in his article. Arthur Wright was \"obviously impressed\" that Doyle was involved, and gave his permission for publication, but he refused payment on the grounds that, if genuine, the images should not be \"soiled\" by money.
Gardner and Doyle sought a second expert opinion from the photographic company Kodak. Several of the company\'s technicians examined the enhanced prints, and although they agreed with Snelling that the pictures \"showed no signs of being faked\", they concluded that \"this could not be taken as conclusive evidence \... that they were authentic photographs of fairies\". Kodak declined to issue a certificate of authenticity. Gardner believed that the Kodak technicians might not have examined the photographs entirely objectively, observing that one had commented \"after all, as fairies couldn\'t be true, the photographs must have been faked somehow\". The prints were also examined by another photographic company, Ilford, who reported unequivocally that there was \"some evidence of faking\". Gardner and Doyle, perhaps rather optimistically, interpreted the results of the three expert evaluations as two in favour of the photographs\' authenticity and one against.
Doyle also showed the photographs to the physicist and pioneering psychical researcher Sir Oliver Lodge, who believed the photographs to be fake. He suggested that a troupe of dancers had masqueraded as fairies, and expressed doubt as to their \"distinctly \'Parisienne{{\'\"}} hairstyles.
On 4 October 2018 the first two of the photographs, *Alice and the Fairies* and *Iris and the Gnome,* were to be sold by Dominic Winter Auctioneers, in Gloucestershire. The prints, suspected to have been made in 1920 to sell at theosophical lectures, were expected to bring £700--£1000 each. As it turned out, *Iris with the Gnome* sold for a hammer price of £5,400 (plus 24% buyer\'s premium incl. VAT), while *Alice and the Fairies* sold for a hammer price of £15,000 (plus 24% buyer\'s premium incl. VAT).
## 1920 photographs {#photographs_1}
Doyle was preoccupied with organising an imminent lecture tour of Australia, and in July 1920, sent Gardner to meet the Wright family. By this point, Frances was living with her parents in Scarborough, but Elsie\'s father told Gardner that he had been so certain the photographs were fakes that while the girls were away he searched their bedroom and the area around the beck (stream), looking for scraps of pictures or cutouts, but found nothing \"incriminating\".
Gardner believed the Wright family to be honest and respectable. To place the matter of the photographs\' authenticity beyond doubt, he returned to Cottingley at the end of July with two W. Butcher & Sons Cameo folding plate cameras and 24 secretly marked photographic plates. Frances was invited to stay with the Wright family during the school summer holiday so that she and Elsie could take more pictures of the fairies. Gardner described his briefing in his 1945 *Fairies: A Book of Real Fairies*: `{{blockquote|I went off, to Cottingley again, taking the two cameras and plates from London, and met the family and explained to the two girls the simple working of the cameras, giving one each to keep. The cameras were loaded, and my final advice was that they need go up to the glen only on fine days as they had been accustomed to do before and ''tice'' the fairies, as they called their way of attracting them, and see what they could get. I suggested only the most obvious and easy precautions about lighting and distance, for I knew it was essential they should feel free and unhampered and have no burden of responsibility. If nothing came of it all, I told them, they were not to mind a bit.<ref name=Cooper/>}}`{=mediawiki} Until 19 August the weather was unsuitable for photography. Because Frances and Elsie insisted that the fairies would not show themselves if others were watching, Elsie\'s mother was persuaded to visit her sister\'s for tea, leaving the girls alone. In her absence the girls took several photographs, two of which appeared to show fairies. In the first, *Frances and the Leaping Fairy*, Frances is shown in profile with a winged fairy close by her nose. The second, *Fairy offering Posy of Harebells to Elsie*, shows a fairy either hovering or tiptoeing on a branch, and offering Elsie a flower. Two days later the girls took the last picture, *Fairies and Their Sun-Bath*.
The plates were packed in cotton wool and returned to Gardner in London, who sent an \"ecstatic\" telegram to Doyle, by then in Melbourne. Doyle wrote back:
## Publication and reaction {#publication_and_reaction}
Doyle\'s article in the December 1920 issue of *The Strand* contained two higher-resolution prints of the 1917 photographs, and sold out within days of publication. To protect the girls\' anonymity, Frances and Elsie were called Alice and Iris respectively, and the Wright family was referred to as the \"Carpenters\". An enthusiastic and committed spiritualist, Doyle hoped that if the photographs convinced the public of the existence of fairies then they might more readily accept other psychic phenomena. He ended his article with the words: `{{blockquote|The recognition of their existence will jolt the material twentieth-century mind out of its heavy ruts in the mud, and will make it admit that there is a glamour and mystery to life. Having discovered this, the world will not find it so difficult to accept that spiritual message supported by physical facts which have already been put before it.<ref name=Roden/>}}`{=mediawiki} Early press coverage was \"mixed\", generally a combination of \"embarrassment and puzzlement\"; though Japanese scholar Kaori Inuma has noted that there were also open and positive assessments. The historical novelist and poet Maurice Hewlett published a series of articles in the literary journal *John O\' London\'s Weekly*, in which he concluded: \"And knowing children, and knowing that Sir Arthur Conan Doyle has legs, I decide that the Miss Carpenters have pulled one of them.\" The London newspaper *Truth* on 5 January 1921 expressed a similar view; \"For the true explanation of these fairy photographs what is wanted is not a knowledge of occult phenomena but a knowledge of children.\" Some public figures were more sympathetic. Margaret McMillan, the educational and social reformer, wrote: \"How wonderful that to these dear children such a wonderful gift has been vouchsafed.\" The novelist Henry De Vere Stacpoole decided to take the fairy photographs and the girls at face value. In a letter to Gardner he wrote: \"Look at Alice\'s \[Frances\'\] face. Look at Iris\'s \[Elsie\'s\] face. There is an extraordinary thing called Truth which has 10 million faces and forms -- it is God\'s currency and the cleverest coiner or forger can\'t imitate it.\"
Major John Hall-Edwards, a keen photographer and pioneer of medical X-ray treatments in Britain, was a particularly vigorous critic: `{{blockquote|On the evidence I have no hesitation in saying that these photographs could have been "faked". I criticize the attitude of those who declared there is something supernatural in the circumstances attending to the taking of these pictures because, as a medical man, I believe that the inculcation of such absurd ideas into the minds of children will result in later life in manifestations and nervous disorder and mental disturbances.<ref name=Cooper/>}}`{=mediawiki} Doyle used the later photographs in 1921 to illustrate a second article in *The Strand*, in which he described other accounts of fairy sightings. The article formed the foundation for his 1922 book *The Coming of the Fairies*. As before, the photographs were received with mixed credulity. Sceptics noted that the fairies \"looked suspiciously like the traditional fairies of nursery tales\" and that they had \"very fashionable hairstyles\".
## Gardner\'s final visit {#gardners_final_visit}
Gardner made a final visit to Cottingley in August 1921. He again brought cameras and photographic plates for Frances and Elsie, but was accompanied by the occultist Geoffrey Hodson. Although neither of the girls claimed to see any fairies, and there were no more photographs, \"on the contrary, he \[Hodson\] saw them \[fairies\] everywhere\" and wrote voluminous notes on his observations.
By now Elsie and Frances were tired of the whole fairy business. Years later Elsie looked at a photograph of herself and Frances taken with Hodson and said: \"Look at that, fed up with fairies.\" Both Elsie and Frances later admitted that they \"played along\" with Hodson \"out of mischief\", and that they considered him \"a fake\".
## Later investigations {#later_investigations}
Public interest in the Cottingley Fairies gradually subsided after 1921. Elsie and Frances both eventually married, moved away from the area and each lived overseas for varying periods of time. In 1966, a reporter from the *Daily Express* newspaper traced Elsie, who was by then back in England. She admitted in an interview given that year that the fairies might have been \"figments of my imagination\", but left open the possibility she believed that she had somehow managed to photograph her thoughts. The media subsequently became interested in Frances and Elsie\'s photographs once again. BBC television\'s *Nationwide* programme investigated the case in 1971, but Elsie stuck to her story: \"I\'ve told you that they\'re photographs of figments of our imagination, and that\'s what I\'m sticking to\".
Elsie and Frances were interviewed by journalist Austin Mitchell in September 1976, for a programme broadcast on Yorkshire Television. When pressed, both women agreed that \"a rational person doesn\'t see fairies\", but they denied having fabricated the photographs. In 1978 the magician and scientific sceptic James Randi and a team from the Committee for the Scientific Investigation of Claims of the Paranormal examined the photographs, using a \"computer enhancement process\". They concluded that the photographs were fakes, and that strings could be seen supporting the fairies. Geoffrey Crawley, editor of the *British Journal of Photography*, undertook a \"major scientific investigation of the photographs and the events surrounding them\", published between 1982 and 1983, \"the first major postwar analysis of the affair\". He also concluded that the pictures were fakes.
## Confession
In 1983, the cousins admitted in an article published in the magazine *The Unexplained* that the photographs had been faked, although both maintained that they really had seen fairies. Elsie had copied illustrations of three dancing fairies by Claude Shepperson from a book that Frances had brought back with her from South Africa. This was the *Princess Mary\'s Gift Book*, published towards the beginning of the war. Elsie changed few details but added wings. It is possible that a poem attached to the images by Alfred Noyes also inspired Elsie and Frances. They said they had then cut out the cardboard figures and supported them with hatpins, disposing of their props in the beck once the photograph had been taken. But the cousins disagreed about the fifth and final photograph, which Doyle in his *The Coming of the Fairies* described in this way:
Elsie maintained it was a fake, just like all the others, but Frances insisted that it was genuine. In an interview given in the early 1980s Frances said: `{{blockquote|It was a wet Saturday afternoon and we were just mooching about with our cameras and Elsie had nothing prepared. I saw these fairies building up in the grasses and just aimed the camera and took a photograph.<ref name=Cooper/>}}`{=mediawiki} Both Frances and Elsie claimed to have taken the fifth photograph. In a letter published in *The Times* newspaper on 9 April 1983, Geoffrey Crawley explained the discrepancy by suggesting that the photograph was \"an unintended double exposure of fairy cutouts in the grass\", and thus \"both ladies can be quite sincere in believing that they each took it\".
In a 1985 interview on Yorkshire Television\'s *Arthur C. Clarke\'s World of Strange Powers*, Elsie said that she and Frances were too embarrassed to admit the truth after fooling Doyle, the author of Sherlock Holmes: \"Two village kids and a brilliant man like Conan Doyle -- well, we could only keep quiet.\" In the same interview Frances said: \"I never even thought of it as being a fraud -- it was just Elsie and I having a bit of fun and I can\'t understand to this day why they were taken in -- they wanted to be taken in.\"
## Subsequent history {#subsequent_history}
thumb\|right\|upright=0.5\|Elsie Wright and Frances Griffiths, June 1917
Frances died in 1986, and Elsie in 1988. Prints of their photographs of the fairies, along with a few other items including a first edition of Doyle\'s book *The Coming of the Fairies*, were sold at auction in London for £21,620 in 1998. That same year, Geoffrey Crawley sold his Cottingley Fairy material to the National Museum of Film, Photography and Television in Bradford (now the National Science and Media Museum), where it is on display. The collection included prints of the photographs, two of the cameras used by the girls, watercolours of fairies painted by Elsie, and a nine-page letter from Elsie admitting to the hoax. The glass photographic plates were bought for £6,000 by an unnamed buyer at a London auction held in 2001.
Frances\'s daughter, Christine Lynch, appeared in an episode of the television programme *Antiques Roadshow* in Belfast, broadcast on BBC One in January 2009, with the photographs and one of the cameras given to the girls by Doyle. Christine told the expert, Paul Atterbury, that she believed, as her mother had done, that the fairies in the fifth photograph were genuine. Atterbury estimated the value of the items at between £25,000 and £30,000. The first edition of Frances\'s memoirs was published a few months later, under the title *Reflections on the Cottingley Fairies*. The book contains correspondence, sometimes \"bitter\", between Elsie and Frances. In one letter, dated 1983, Frances wrote: `{{blockquote|I hated those photographs from the age of 16 when Mr Gardner presented me with a bunch of flowers and wanted me to sit on the platform [at a Theosophical Society meeting] with him. I realised what I was in for if I did not keep myself hidden.<ref>{{cite news |last=Clayton |first=Emma |title=Cottingley Fairies Back in the Spotlight |date=14 July 2009 |newspaper=Bradford Telegraph & Argus |url=http://www.thetelegraphandargus.co.uk/news/4492364.Book_reveals_story_behind_the_Fairies/ |access-date=3 May 2010 |mode=cs2}}</ref>}}`{=mediawiki}
The 1997 films *FairyTale: A True Story* and *Photographing Fairies* were inspired by the events surrounding the Cottingley Fairies. The photographs were parodied in a 1994 book written by Terry Jones and Brian Froud, *Lady Cottington\'s Pressed Fairy Book*. In A. J. Elwood\'s 2021 novel, *The Cottingley Cuckoo*, a series of letters were written soon after the Cottingley fairy photographs were published claiming further sightings of fairies and proof of their existence.
In 2017 a further two fairy photographs were presented as evidence that the girls\' parents were part of the conspiracy. Dating from 1917 and 1918, both photographs are poorly executed copies of two of the original fairy photographs. One was published in 1918 in *The Sphere* newspaper, which was before the originals had been seen by anyone outside the girls\' immediate family.
In 2019, a print of the first of the five photographs sold for £1,050. A print of the second was also put up for sale but failed to sell as it did not meet its £500 reserve price. The pictures previously belonged to the Reverend George Vale Owen. In December 2019, the third camera used to take the images was acquired by the National Science and Media Museum.
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6,761 |
Unitary patent
|
--
--
: European patent with unitary effect
The **European patent with unitary effect**, also known as the **unitary patent**, is a European patent which benefits from unitary effect in the participating member states of the European Union.`{{refn|States only participate in the unitary patent after they ratify the [[Agreement on a Unified Patent Court|UPC Agreement]] and participate in the enhanced cooperation regarding the unitary patent. All EU member states participated, except Spain and Croatia.|group=notes}}`{=mediawiki} Unitary effect means the patent has a common legal status throughout all the participating states, eliminating scenarios in which a patent may be invalidated by courts in one participating member state yet upheld by courts in another. Unitary effect may be requested by the proprietor within one month of grant of a European patent, replacing validation of the European patent in the individual countries concerned. Infringement and revocation proceedings are conducted before the Unified Patent Court (UPC), which decisions have a uniform effect for the unitary patent in the participating member states as a whole rather than in each country individually. The unitary patent may be only limited, transferred or revoked, or lapse, in respect of all the participating Member States. Licensing is however possible for part of the unitary territory. The unitary patent may coexist with nationally enforceable patents (\"classical\" patents) in the non-participating states. The unitary patent\'s stated aims are to make access to the patent system \"easier, less costly and legally secure within the European Union\" and \"the creation of uniform patent protection throughout the Union\".
European patents are granted in English, French, or German and the unitary effect will not require further translations after a transition period.`{{refn|There is a transition period of maximum 12 years from 1 June 2023 during which one translation must be filed, either into English if the application is in French or German, or into any EU official language if the application was in English.|group=notes}}`{=mediawiki} The maintenance fees of the unitary patents are lower than the sum of the renewal fees for national patents of the corresponding area, being equivalent to the combined maintenance fees of Germany, France, the UK and the Netherlands (although the UK is no longer participating following Brexit).
The negotiations which resulted in the unitary patent can be traced back to various initiatives dating to the 1970s. At different times, the project, or very similar projects, have been referred to as the \"European Union patent\" (the name used in the EU treaties, which serve as the legal basis for EU competency), \"EU patent\", \"Community patent\", \"European Community Patent\", \"EC patent\" and \"COMPAT\".
On 17 December 2012, agreement was reached between the European Council and European Parliament on the two EU regulations`{{refn|Regulation 1257/2012 and Regulation 1260/2012|group=notes}}`{=mediawiki} that made the unitary patent possible through enhanced cooperation at EU level. The legality of the two regulations was challenged by Spain and Italy, but all their claims were rejected by the European Court of Justice. Italy subsequently joined the unitary patent regulation in September 2015, so that all EU member states except Spain and Croatia now participate in the enhanced cooperation for a unitary patent. Unitary effect of newly granted European patents will be available from the date when the related Unified Patent Court Agreement enters into force for those EU countries that have also ratified the UPC,`{{refn|As of June 2022, 16 EU countries have ratified the UPC: Austria, Belgium, Bulgaria, Denmark, Estonia, Finland, France, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Portugal, Slovenia, Sweden |group=notes|name="UPC entry into force"}}`{=mediawiki} and will extend to those participating member states for which the UPC Agreement enters into force at the time of registration of the unitary patent. Previously granted unitary patents will not automatically get their unitary effect extended to the territory of participating states which ratify the UPC agreement at a later date.
The unitary patent system applies since 1 June 2023, the date of entry into force of the UPC Agreement.
## Background
### Legislative history {#legislative_history}
In 2009, three draft documents were published regarding a community patent: a European patent in which the European Community was designated:
1. Council regulation on the community patent,
2. Agreement on the European and Community Patents Court (open to the European Community and all states of the European Patent Convention)
3. Decision to open negotiations regarding this Agreement
Based on those documents, the European Council requested on 6 July 2009 an opinion from the Court of Justice of the European Union, regarding the compatibility of the envisioned Agreement with EU law: \"\'Is the envisaged agreement creating a Unified Patent Litigation System (currently named European and Community Patents Court) compatible with the provisions of the Treaty establishing the European Community?'\"
In December 2010, the use of the enhanced co-operation procedure, under which Articles 326--334 of the Treaty on the Functioning of the European Union provides that a group of member states of the European Union can choose to co-operate on a specific topic, was proposed by twelve Member States to set up a unitary patent applicable in all participating European Union Member States. The use of this procedure had only been used once in the past, for harmonising rules regarding the applicable law in divorce across several EU Member States.
In early 2011, the procedure leading to the enhanced co-operation was reported to be progressing. Twenty-five Member States had written to the European Commission requesting to participate, with Spain and Italy remaining outside, primarily on the basis of ongoing concerns over translation issues. On 15 February, the European Parliament approved the use of the enhanced co-operation procedure for unitary patent protection by a vote of 471 to 160, and on 10 March 2011 the Council gave their authorisation. Two days earlier, on 8 March 2011, the Court of Justice of the European Union had issued its opinion, stating that the draft Agreement creating the European and Community Patent Court would be incompatible with EU law. The same day, the Hungarian Presidency of the Council insisted that this opinion would not affect the enhanced co-operation procedure.
In November 2011, negotiations on the enhanced co-operation system were reportedly advancing rapidly---too fast, in some views. It was announced that implementation required an enabling European Regulation, and a Court agreement between the states that elect to take part. The European Parliament approved the continuation of negotiations in September. A draft of the agreement was issued on 11 November 2011 and was open to all member states of the European Union, but not to other European Patent Convention states. However, serious criticisms of the proposal remained mostly unresolved. A meeting of the Competitiveness Council on 5 December failed to agree on the final text. In particular, there was no agreement on where the Central Division of a Unified Patent Court should be located, \"with London, Munich and Paris the candidate cities.\"
The Polish Presidency acknowledged on 16 December 2011 the failure to reach an agreement \"on the question of the location of the seat of the central division.\" The Danish Presidency therefore inherited the issue. According to the President of the European Commission in January 2012, the only question remaining to be settled was the location of the Central Division of the Court. However, evidence presented to the UK House of Commons European Scrutiny Committee in February suggested that the position was more complicated. At an EU summit at the end of January 2012, participants agreed to press on and finalise the system by June. On 26 April, Herman Van Rompuy, President of the European Council, wrote to members of the council, saying \"This important file has been discussed for many years and we are now very close to a final deal,\.... This deal is needed now, because this is an issue of crucial importance for innovation and growth. I very much hope that the last outstanding issue will be sorted out at the May Competitiveness Council. If not, I will take it up at the June European Council.\" The Competitiveness Council met on 30 May and failed to reach agreement.
A compromise agreement on the seat(s) of the unified court was eventually reached at the June European Council (28--29 June 2012), splitting the central division according to technology between Paris (the main seat), London and Munich. However, on 2 July 2012, the European Parliament decided to postpone the vote following a move by the European Council to modify the arrangements previously approved by MEPs in negotiations with the European Council. The modification was considered controversial and included the deletion of three key articles (6--8) of the legislation, seeking to reduce the competence of the European Union Court of Justice in unitary patent litigation. On 9 July 2012, the Committee on Legal Affairs of the European Parliament debated the patent package following the decisions adopted by the General Council on 28--29 June 2012 in camera in the presence of MEP Bernhard Rapkay. A later press release by Rapkay quoted from a legal opinion submitted by the Legal Service of the European Parliament, which affirmed the concerns of MEPs to approve the decision of a recent EU summit to delete said articles as it \"nullifies central aspects of a substantive patent protection\". A Europe-wide uniform protection of intellectual property would thus not exist with the consequence that the requirements of the corresponding EU treaty would not be met and that the European Court of Justice could therefore invalidate the legislation. By the end of 2012 a new compromise was reached between the European Parliament and the European Council, including a limited role for the European Court of Justice. The Unified Court will apply the Unified Patent Court Agreement, which is considered national patent law from an EU law point of view, but still is equal for each participant. \[However the [draft statutory instrument](http://www.legislation.gov.uk/ukdsi/2016/9780111142899) aimed at implementation of the Unified Court and UPC in the UK provides for different infringement laws for: European patents (unitary or not) litigated through the Unified Court; European patents (UK) litigated before UK courts; and national patents\]. The legislation for the enhanced co-operation mechanism was approved by the European Parliament on 11 December 2012 and the regulations were signed by the European Council and European Parliament officials on 17 December 2012.
On 30 May 2011, Italy and Spain challenged the council\'s authorisation of the use of enhanced co-operation to introduce the trilingual (English, French, German) system for the unitary patent, which they viewed as discriminatory to their languages, with the CJEU on the grounds that it did not comply with the EU treaties. In January 2013, Advocate General Yves Bot delivered his recommendation that the court reject the complaint. Suggestions by the Advocate General are advisory only, but are generally followed by the court. The case was dismissed by the court in April 2013, however Spain launched two new challenges with the EUCJ in March 2013 against the regulations implementing the unitary patent package. The court hearing for both cases was scheduled for 1 July 2014. Advocate-General Yves Bot published his opinion on 18 November 2014, suggesting that both actions be dismissed (`{{ECLI|ECLI:EU:C:2014:2380}}`{=mediawiki} and `{{ECLI|ECLI:EU:C:2014:2381}}`{=mediawiki}). The court handed down its decisions on 5 May 2015 as `{{ECLI|ECLI:EU:C:2015:298}}`{=mediawiki} and `{{ECLI|ECLI:EU:C:2015:299}}`{=mediawiki} fully dismissing the Spanish claims. Following a request by its government, Italy became a participant of the unitary patent regulations in September 2015.
### European patents {#european_patents}
European patents are granted in accordance with the provisions of the European Patent Convention (EPC), via a unified procedure before the European Patent Office (EPO). While upon filing of a European patent application, all 39 Contracting States are automatically designated, a European patent becomes a bundle of \"national\" European patents upon grant. In contrast to the unified character of a European patent application, a granted European patent has, in effect, no unitary character, except for the centralized opposition procedure (which can be initiated within 9 months from grant, by somebody else than the patent proprietor), and the centralized limitation and revocation procedures (which can only be instituted by the patent proprietor). In other words, a European patent in one Contracting State, i.e. a \"national\" European patent,`{{refn|There is no consistent usage of a particular expression to refer to "the European patent in a particular designated Contracting State for which it is granted". The article uses the expression "a "national" European patent"|group=notes}}`{=mediawiki} is effectively independent of the same European patent in each other Contracting State, except for the opposition, limitation and revocation procedures. The enforcement of a European patent is dealt with by national law. The abandonment, revocation or limitation of the European patent in one state does not affect the European patent in other states.
While the EPC already provided the possibility for a group of member states to allow European patents to have a unitary character also after grant, until now, only Liechtenstein and Switzerland have opted to create a unified protection area (see Unitary patent (Switzerland and Liechtenstein)).
By requesting unitary effect within one month of grant, the patent proprietor is now able to obtain uniform protection in the participating members states of the European Union in a single step, considerably simplifying obtaining patent protection in a large part of the EU. The unitary patent system co-exists with national patent systems and European patent without unitary effects. The unitary patent does not cover EPC countries that are not member of the European Union, such as UK or Turkey.
## Legal basis and implementation {#legal_basis_and_implementation}
The implementation of the unitary patent is based on three legal instruments:
- Regulation (EU) No 1257/2012 of the European Parliament and of the Council of 17 December 2012 implementing enhanced cooperation in the area of the creation of unitary patent protection;
- Council Regulation (EU) No 1260/2012 of 17 December 2012 implementing enhanced cooperation in the area of the creation of unitary patent protection with regard to the applicable translation arrangements;
- Agreement on a Unified Patent Court.
Thus the unitary patent is based on EU law as well as the European Patent Convention (EPC). `{{EPC Article|142}}`{=mediawiki} provides the legal basis for establishing a common system of patents for Parties to the EPC. as authorized by `{{EPC Article|143|1}}`{=mediawiki}. These tasks include the collection of renewal fees and registration of unitary effect upon grant, recording licenses and statements that licenses are available to any person. Decisions of the European Patent Office regarding the unitary patent are open to appeal to the Unified Patent Court, rather than to the EPO Boards of Appeal.`{{refn|[[s:Agreement on a Unified Patent Court#Article 32 .E2.80.93 Competence of the Court|Article 32(1)i, Agreement on a Unified Patent Court]], implementing Article 9.3 of Regulation (EU) No 1257/2012.<ref name="32012R1257"/>}}`{=mediawiki}
### Translation requirements for the European patent with unitary effect {#translation_requirements_for_the_european_patent_with_unitary_effect}
For a unitary patent, ultimately no translation will be required (except under certain circumstances in the event of a dispute), which is expected to significantly reduce the cost for protection in the whole area. However, Regulation 1260/2012 provides that, during a transitional period of minimum six years and no more than twelve years, one translation needs to be provided. Namely, a full translation of the European patent specification needs to be provided either into English if the language of the proceedings at the EPO was French or German, or into any other EU official language if the language of the proceedings at the EPO was English. Such translation will have no legal effect and will be \"for information purposes only". In addition, machine translations will be provided, which will be, in the words of the regulation, \"for information purposes only and should not have any legal effect\".
#### Comparison with the current translation requirements for traditional bundle European patents {#comparison_with_the_current_translation_requirements_for_traditional_bundle_european_patents}
In several EPC contracting states, for the national part of a traditional bundle European patent (i.e., for a European patent without unitary effect), a translation has to be filed within a three-month time limit after the publication of grant in the European Patent Bulletin under `{{EPC Article|65}}`{=mediawiki},`{{refn|{{EPC Article|2|2}} provides that "[t]he European patent shall, in each of the Contracting States for which it is granted, have the effect of and be subject to the same conditions as a national patent granted by that State, unless this Convention provides otherwise." The provision of Article 65 EPC may therefore be viewed as an exception to Article 2(2) EPC. See also [[London Agreement (2000)]].|group=notes}}`{=mediawiki} otherwise the patent is considered never to have existed (void ab initio) in that state. For the 22 parties to the London Agreement, this requirement has already been abolished or reduced (e.g. by dispensing with the requirement if the patent is available in English, and/or only requiring translation of the claims).
Translation requirements for the participating states in the enhanced cooperation for a unitary patent are shown below:
+------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Participating member State (**bold: unitary patents apply**) | Translation requirements for a European patent without unitary effect | Translation requirements for a European patent with unitary effect |
+========================================================================================================================+===================================================================================+=======================================================================================================================================================================================+
| **Belgium, France, Germany,** Ireland, **Luxembourg** | None | During a transitional period of minimum 6 years and maximum 12 years: one translation, so that the unitary patent is available in English and at least another EU official language.\ |
| | | After the transitional period: none. |
+------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **Latvia, Lithuania**, **Slovenia** | Claims in the official language of the concerned State | |
+------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **Denmark, Finland,** Hungary, **Netherlands, Sweden** | Description in English, claims in the official language of the concerned State | |
+------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **Austria, Bulgaria,** Cyprus, Czech Republic, **Estonia,** Greece, **Malta**, Poland, **Portugal, Romania**, Slovakia | Translation of the complete patent in an official language of the concerned State | |
+------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
### Unitary patent as an object of property {#unitary_patent_as_an_object_of_property}
Article 7 of Regulation 1257/2012 provides that, as an object of property, a European patent with unitary effect will be treated \"in its entirety and in all participating Member States as a national patent of the participating Member State in which that patent has unitary effect and in which the applicant had her/his residence or principal place of business or, by default, had a place of business on the date of filing the application for the European patent.\" When the applicant had no domicile in a participating Member State, German law will apply. Ullrich has the criticized the system, which is similar to the Community Trademark and the Community Design, as being \"in conflict with both the purpose of the creation of unitary patent protection and with primary EU law.\"
### Agreement on a Unified Patent Court {#agreement_on_a_unified_patent_court}
The Agreement on a Unified Patent Court provides the legal basis for the Unified Patent Court (UPC): a patent court for European patents (with and without unitary effect), with jurisdiction in those countries where the Agreement is in effect. In addition to regulations regarding the court structure, it also contains substantive provisions relating to the right to prevent use of an invention and allowed use by non-patent proprietors (e.g. for private non-commercial use), preliminary and permanent injunctions. Entry into force for the UPC took place after Germany deposited its instrument of ratification of the UPC Agreement, which triggered the countdown until the Agreement\'s entry into force on June 1, 2023.
#### Parties
The UPC Agreement was signed on 19 February 2013 by 24 EU member states, including all states then participating in the enhanced co-operation measures except Bulgaria and Poland. Bulgaria signed the agreement on 5 March 2013 following internal administrative procedures. Italy, which did not originally join the enhanced co-operation measures but subsequently signed up, did sign the UPC agreement. The agreement remains open to accession for all remaining EU member states, with all European Union Member States except Spain and Poland having signed the Agreement. States which do not participate in the unitary patent regulations can still become parties to the UPC agreement, which would allow the new court to handle European patents validated in the country.
On 18 January 2019, Kluwer Patent Blog wrote, \"a recurring theme for some years has been that \'the UPC will start next year\'\". Then, Brexit and German constitutional court complaint were considered as the main obstacles. The German constitutional court first decided in a decision of 13 February 2020 against the German ratification of the Agreement on the ground that the German Parliament did not vote with the required majority (2/3 according to the judgement). After a second vote and further, this time unsuccessful, constitutional complaints, Germany formally ratified the UPC Agreement on 7 August 2021. While the UK ratified the agreement in April 2018, the UK later withdrew from the Agreement following Brexit.
As of the entry into force of the UPC on 1 June 2023, 17 countries had ratified the Agreement. Romania ratified the agreement in May 2024, and will join as the 18th participating member on 1 September 2024.
#### Jurisdiction
The Unified Patent Court has exclusive jurisdiction in infringement and revocation proceedings involving European patents with unitary effect, and during a transition period non-exclusive jurisdiction regarding European patents without unitary effect in the states where the Agreement applies, unless the patent proprietor decides to opt out. It furthermore has jurisdiction to hear cases against decisions of the European Patent Office regarding unitary patents. As a court of several member states of the European Union it may (Court of First Instance) or must (Court of Appeal) ask prejudicial questions to the European Court of Justice when the interpretation of EU law (including the two unitary patent regulations, but excluding the UPC Agreement) is not obvious.
#### Organization
The court has two instances: a court of first instance and a court of appeal. The court of appeal and the registry have their seats in Luxembourg, while the central division of the court of first instance would have its seat in Paris. The central division has a thematic branch in Munich (the London location has yet to be replaced by a new location within the EU). The court of first instance may further have local and regional divisions in all member states that wish to set up such divisions.
### Geographical scope of and request for unitary effect {#geographical_scope_of_and_request_for_unitary_effect}
While the regulations formally apply to all 25 member states participating in the enhanced cooperation for a unitary patent, from the date the UPC agreement has entered into force for the first group of ratifiers,`{{refn|group=notes|name="UPC entry into force"}}`{=mediawiki} unitary patents will only extend to the territory of those participating member states where the UPC Agreement had entered into force when the unitary effect was registered. If the unitary effect territory subsequently expands to additional participating member states for which the UPC Agreement later enters into force, this will be reflected for all subsequently registered unitary patents, but the territorial scope of the unitary effect of existing unitary patents will not be extended to these states.
Unitary effect can be requested up to one month after grant of the European patent directly at the EPO, with retroactive effect from the date of grant. However, according to the *Draft Rules Relating to Unitary Patent Protection*, unitary effect would be registered only if the European patent has been granted with the same set of claims`{{refn|A European patent may be granted by the EPO with claims which are, for one or more States, different from those applicable to the other designated States. This rare situation may arise by virtue of {{EPC Rule|18|2}} or {{EPC Rule|138}}.|group=notes}}`{=mediawiki} for all the 25 participating member states in the regulations,`{{refn|This requires that all 25 states participating in the [[Enhanced cooperation#Unitary patent|enhanced cooperation regulations]] have been designated upon filing of the European patent application. For European patent applications filed after 1 April 2009, all Contracting States party to the [[European Patent Convention|EPC]] at the time of filing of the application are automatically designated,<ref>{{cite web|url=http://www.epo.org/law-practice/legal-texts/html/guidelines/e/a_iii_11_2_2.htm|title=Guidelines for Examination: 11.2.2 Payment of designation fee|publisher=European Patent Office|date= April 2014}}</ref> although designations may be withdrawn before grant.<ref>{{cite web|url=http://www.epo.org/law-practice/legal-texts/html/guidelines/e/a_iii_11_3_8.htm|title=Guidelines for Examiniation: 11.3.8 Withdrawal of designation|publisher=European Patent Office|date=16 September 2013}}</ref> It was not possible to designate Malta before it became a party to the EPC on 1 March 2007.|group=notes}}`{=mediawiki} whether the unitary effect applies to them or not. European patents automatically become a bundle of \"national\" European patents upon grant. Upon the grant of unitary effect, the \"national\" European patents will retroactively be considered to never have existed in the territories where the unitary patent has effect. The unitary effect does not affect \"national\" European patents in states where the unitary patent does not apply. Any \"national\" European patents applying outside the \"unitary effect\" zone will co-exist with the unitary patent.
#### Special territories of participating member states {#special_territories_of_participating_member_states}
As the unitary patent is introduced by an EU regulation, it is expected to not only be valid in the mainland territory of the participating member states that are party to the UPC, but also in those of their special territories that are part of the European Union. As of April 2014, this includes the following fourteen territories:
- Cyprus: UN Buffer Zone
- Finland: Åland
- France: French Guiana, Guadeloupe, Martinique, Mayotte, Réunion, Saint Martin
- Germany: Büsingen am Hochrhein, Helgoland
- Greece: Mount Athos
- Portugal: Azores, Madeira
In addition to the territories above, the European Patent Convention has been extended by two member states participating in the enhanced cooperation for a unitary patent to cover some of their dependent territories outside the European Union: In following of those territories, the unitary patent is de facto extended through application of national (French, or Dutch) law:
- France: French Southern and Antarctic Lands, Saint Barthélemy, Saint-Pierre and Miquelon and Wallis and Futuna
- Netherlands: Caribbean Netherlands, Curaçao, Sint Maarten
However, the unitary patent does not apply in the French territories French Polynesia and New Caledonia as implementing legislation would need to be passed by those jurisdictions (rather than the French national legislation required in the other territories) and this has not been done.
## Costs
+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| ImageSize = width:auto height:180 barincrement:40 PlotArea = left:50 bottom:15 top:10 right:18 AlignBars = justify DateFormat = yyyy Period = from:0 till:5000 TimeAxis = orientation:vertical ScaleMajor = unit:year increment:1000 start:0 PlotData= |
| |
| ` color:skyblue width:40`\ |
| ` bar:2 from:start till:35 text:€ 35`\ |
| ` bar:3 from:start till:105 text:€ 105`\ |
| ` bar:4 from:start till:145 text:€ 145`\ |
| ` bar:5 from:start till:315 text:€ 315 `\ |
| ` bar:6 from:start till:475 text:€ 475`\ |
| ` bar:7 from:start till:630 text:€ 630`\ |
| ` bar:8 from:start till:815 text:€ 815`\ |
| ` bar:9 from:start till:990 text:€ 990`\ |
| ` bar:10 from:start till:1175 text:€ 1175`\ |
| ` bar:11 from:start till:1460 text:€ 1460`\ |
| ` bar:12 from:start till:1775 text:€ 1775`\ |
| ` bar:13 from:start till:2105 text:€ 2105`\ |
| ` bar:14 from:start till:2455 text:€ 2455`\ |
| ` bar:15 from:start till:2830 text:€ 2830 `\ |
| ` bar:16 from:start till:3240 text:€ 3240`\ |
| ` bar:17 from:start till:3640 text:€ 3640`\ |
| ` bar:18 from:start till:4055 text:€ 4055`\ |
| ` bar:19 from:start till:4455 text:€ 4455`\ |
| ` bar:20 from:start till:4855 text:€ 4855` |
+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
: Yearly renewal fee for the unitary patent
The renewal fees are planned to be based on the cumulative renewal fees due in the four countries where European patents were most often validated in 2015 (Germany, France, the UK and the Netherlands). This is despite the UK leaving the unitary patent system following Brexit. The renewal fees of the unitary patent would thus be ranging from 35 Euro in the second year to 4855 in the 20th year. The renewal fees will be collected by the EPO, with the EPO keeping 50% of the fees and the other 50% being redistributed to the participating member states.
Translation requirements as well as the requirement to pay yearly patent maintenance fees in individual countries presently renders the European patent system costly to obtain protection in the whole of the European Union.
In an impact assessment from 2011, the European Commission estimated that the costs of obtaining a patent in all 27 EU countries would drop from over 32 000 euro (mainly due to translation costs) to 6 500 euro (for the combination of an EU, Spanish and Italian patent) due to introduction of the Unitary patent. Per capita costs of an EU patent were estimated at just 6 euro/million in the original 25 participating countries (and 12 euro/million in the 27 EU countries for protection with a Unitary, Italian and Spanish patent).
How the EU Commission has presented the expected cost savings has however been sharply criticized as exaggerated and based on unrealistic assumptions. The EU Commission has notably considered the costs for validating a European patent in 27 countries while in reality only about 1% of all granted European patents are currently validated in all 27 EU states. Based on more realistic assumptions, the cost savings are expected to be much lower than actually claimed by the commission. For example, the EPO calculated that for an average EP patent validated and maintained in 4 countries, the overall savings to be between 3% and 8%.
## Statistics
During the first year of the unitary patent, that is, from 1 June 2023, to 31 May 2024, more than 27500 European patents with unitary effect have been registered. This corresponds to almost a quarter of all European patents granted during that period.
## Earlier attempts {#earlier_attempts}
### 1970s and 1980s: proposed Community Patent Convention {#s_and_1980s_proposed_community_patent_convention}
Work on a Community patent started in the 1970s, but the resulting Community Patent Convention (CPC) was a failure.
The \"Luxembourg Conference on the Community Patent\" took place in 1975 and the **Convention for the European Patent for the common market**, or (Luxembourg) Community Patent Convention (CPC), was signed at Luxembourg on 15 December 1975, by the 9 member states of the European Economic Community at that time. However, the CPC never entered into force. It was not ratified by enough countries.
Fourteen years later, the **Agreement relating to Community patents** was made at Luxembourg on 15 December 1989. It attempted to revive the CPC project, but also failed. This Agreement consisted of an amended version of the original Community Patent Convention. Twelve states signed the Agreement: Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, and United Kingdom. All of those states would need to have ratified the Agreement to cause it to enter into force, but only seven did so: Denmark, France, Germany, Greece, Luxembourg, the Netherlands, and United Kingdom.
Nevertheless, a majority of member states of the EEC at that time introduced some harmonisation into their national patent laws in anticipation of the entry in force of the CPC. A more substantive harmonisation took place at around the same time to take account of the European Patent Convention and the Strasbourg Convention.
### 2000 to 2004: EU Regulation proposal {#to_2004_eu_regulation_proposal}
In 2000, renewed efforts from the European Union resulted in a Community Patent Regulation proposal, sometimes abbreviated as **CPR**. It provides that the patent, once it has been granted by the European Patent Office (EPO) in one of its procedural languages (English, German or French) and published in that language, with a translation of the claims into the two other procedural languages, will be valid without any further translation. This proposal is aimed to achieve a considerable reduction in translation costs.
Nevertheless, additional translations could become necessary in legal proceedings against a suspected infringer. In such a situation, a suspected infringer who has been unable to consult the text of the patent in the official language of the Member State in which he is domiciled, is presumed, until proven otherwise, not to have knowingly infringed the patent. To protect a suspected infringer who, in such a situation, has not acted in a deliberate manner, it is provided that the proprietor of the patent will not be able to obtain damages in respect of the period prior to the translation of the patent being notified to the infringer.
The proposed Community Patent Regulation should also establish a court holding exclusive jurisdiction to invalidate issued patents; thus, a Community Patent\'s validity will be the same in all EU member states. This court will be attached to the present European Court of Justice and Court of First Instance through use of provisions in the Treaty of Nice.
Discussion regarding the Community patent had made clear progress in 2003 when a political agreement was reached on 3 March 2003. However, one year later in March 2004 under the Irish presidency, the Competitiveness Council failed to agree on the details of the Regulation. In particular the time delays for translating the claims and the authentic text of the claims in case of an infringement remained problematic issues throughout discussions and in the end proved insoluble.
In view of the difficulties in reaching an agreement on the community patent, other legal agreements have been proposed outside the European Union legal framework to reduce the cost of translation (of patents when granted) and litigation, namely the London Agreement, which entered into force on 1 May 2008---and which has reduced the number of countries requiring translation of European patents granted nowadays under the European Patent Convention, and the corresponding costs to obtain a European patent---and the European Patent Litigation Agreement (EPLA), a proposal that has now lapsed.
#### Reactions to the failure {#reactions_to_the_failure}
After the council in March 2004, EU Commissioner Frits Bolkestein said that \"The failure to agree on the Community Patent I am afraid undermines the credibility of the whole enterprise to make Europe the most competitive economy in the world by 2010.\" Adding:
Jonathan Todd, Commission\'s Internal Market spokesman, declared: `{{blockquote|Normally, after the common political approach, the text of the regulation is agreed very quickly. Instead, some Member States appear to have changed their positions. (...) It is extremely unfortunate that European industry's competitiveness, innovation and R&D are being sacrificed for the sake of preserving narrow vested interests.<ref>{{cite web| url = http://cordis.europa.eu/itt/itt-en/04-3/policy03.htm| title = cordis.europa.eu, ''Patently unclear'', 26 May 2004}}</ref>}}`{=mediawiki}
European Commission President Romano Prodi, asked to evaluate his five-year term, cited as his weak point the failure of many EU governments to implement the \"Lisbon Agenda\", agreed in 2001. In particular, he cited the failure to agree on a Europewide patent, or even the languages to be used for such a patent, \"because member states did not accept a change in the rules; they were not coherent\".
### Since 2005: stalemate and new debate {#since_2005_stalemate_and_new_debate}
Thus, in 2005, the Community patent looked unlikely to be implemented in the near future. However, on 16 January 2006 the European Commission \"launched a public consultation on how future action in patent policy to create an EU-wide system of protection can best take account of stakeholders\' needs.\" The Community patent was one of the issues the consultation focused on. More than 2500 replies were received. According to the European Commission, the consultation showed that there is widespread support for the Community patent but not at any cost, and \"in particular not on the basis of the Common Political Approach reached by EU Ministers in 2003\".
In February 2007, EU Commissioner Charlie McCreevy was quoted as saying: `{{blockquote|The proposal for an EU-wide patent is stuck in the mud. It is clear to me from discussions with member states that there is no consensus at present on how to improve the situation.<ref>Chris Jones, [https://web.archive.org/web/20070204044554/http://www.eupolitix.com/EN/News/200702/7be97fa5-3cb6-403f-aadf-103ad99a9950.htm ''McCreevy backs plans for single EU-US market''], TheParliament.com, 1 February 2007. Consulted on 2 February 2007.</ref> }}`{=mediawiki}
The European Commission released a white paper in April 2007 seeking to \"improve the patent system in Europe and revitalise the debate on this issue.\" On 18 April 2007, at the European Patent Forum in Munich, Germany, Günter Verheugen, vice-president of the European Commission, said that his proposal to support the European economy was \"to have the London Agreement ratified by all member states, and to have a European patent judiciary set up, in order to achieve rapid implementation of the Community patent, which is indispensable\". He further said that he believed this could be done within five years.
In October 2007, the Portuguese presidency of the Council of the European Union proposed an EU patent jurisdiction, \"borrowing heavily from the rejected draft European Patent Litigation Agreement (EPLA)\". In November 2007, EU ministers were reported to have made some progress towards a community patent legal system, with \"some specific results\" expected in 2008.
In 2008, the idea of using machine translations to translate patents was proposed to solve the language issue, which is partially responsible for blocking progress on the community patent. Meanwhile, European Commissioner for Enterprise and Industry Günter Verheugen declared at the European Patent Forum in May 2008 that there was an \"urgent need\" for a community patent.
### Agreement in December 2009, and language issue {#agreement_in_december_2009_and_language_issue}
In December 2009, it was reported that the Swedish EU presidency had achieved a breakthrough in negotiations concerning the community patent. The breakthrough was reported to involve setting up a single patent court for the EU, however ministers conceded much work remained to be done before the community patent would become a reality.
According to the agreed plan, the EU would accede to the European Patent Convention as a contracting state, and patents granted by the European Patent Office will, when validated for the EU, have unitary effect in the territory of the European Union. On 10 November 2010, it was announced that no agreement had been reached and that, \"in spite of the progress made, \[the Competitiveness Council of the European Union had\] fallen short of unanimity by a small margin,\" with commentators reporting that the Spanish representative, citing the aim to avoid any discrimination, had \"re-iterated at length the stubborn rejection of the Madrid Government of taking the \'Munich\' three languages regime (English, German, French) of the European Patent Convention (EPC) as a basis for a future EU Patent.\"
| 2025-06-20T00:00:00 |
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Cistron
|
A **cistron** is a region of DNA that is conceptually equivalent to some definitions of a gene, such that the terms are synonymous from certain viewpoints, especially with regard to the molecular gene as contrasted with the Mendelian gene. The question of which scope of a subset of DNA (that is, how large a segment of DNA) constitutes a unit of selection is the question that governs whether cistrons are the same thing as genes . The word *cistron* is used to emphasize that molecular genes exhibit a specific behavior in a complementation test (cis-trans test); distinct positions (or loci) within a genome are **cistronic**.
## History
The words *cistron* and *gene* were coined before the advancing state of biology made it clear to many people that the concepts they refer to, at least in some senses of the word *gene*, are either equivalent or nearly so. The same historical naming practices are responsible for many of the synonyms in the life sciences.
The term *cistron* was coined by Seymour Benzer in an article entitled *The elementary units of heredity*. The cistron was defined by an operational test applicable to most organisms that is sometimes referred to as a cis-trans test, but more often as a complementation test.
Richard Dawkins in his influential book *The Selfish Gene* argues *against* the cistron being the unit of selection and against it being the best definition of a gene. (He also argues against group selection.) He does not argue against the existence of cistrons, or their being elementary, but rather against the idea that natural selection selects them; he argues that it used to, back in earlier eras of life\'s development, but not anymore. He defines a gene as a larger unit, which others may now call gene clusters, as the unit of selection. He also defines replicators, more general than cistrons and genes, in this gene-centered view of evolution.
## Definition
Defining a Cistron as a segment of DNA coding for a polypeptide, the structural gene in a transcription unit could be said as monocistronic (mostly in eukaryotes) or polycistronic (mostly in bacteria and prokaryotes). For example, suppose a mutation at a chromosome position $x$ is responsible for a change in recessive trait in a diploid organism (where chromosomes come in pairs). We say that the mutation is recessive because the organism will exhibit the wild type phenotype (ordinary trait) unless both chromosomes of a pair have the mutation (homozygous mutation). Similarly, suppose a mutation at another position, $y$, is responsible for the same recessive trait. The positions $x$ and $y$ are said to be within the same cistron when an organism that has the mutation at $x$ on one chromosome and has the mutation at position $y$ on the paired chromosome exhibits the recessive trait even though the organism is not homozygous for either mutation. When instead the wild type trait is expressed, the positions are said to belong to distinct cistrons / genes. Or simply put, mutations on the same cistrons will not complement; as opposed to mutations on different cistrons may complement (see Benzer\'s T4 bacteriophage experiments T4 rII system).
For example, an operon is a stretch of DNA that is transcribed to create a contiguous segment of RNA, but contains more than one cistron / gene. The operon is said to be polycistronic, whereas ordinary genes are said to be monocistronic.
| 2025-06-20T00:00:00 |
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