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Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claims; reliance on confirmation bias rather than rigorous attempts at refutation; lack of openness to evaluation by other experts; absence of systematic practices when developing hypotheses; and continued adherence long after the pseudoscientific hypotheses have been experimentally discredited. It is not the same as junk science. The demarcation between science and pseudoscience has scientific, philosophical, and political implications. Philosophers debate the nature of science and the general criteria for drawing the line between scientific theories and pseudoscientific beliefs, but there is widespread agreement "that creationism, astrology, homeopathy, Kirlian photography, dowsing, ufology, ancient astronaut theory, Holocaust denialism, Velikovskian catastrophism, and climate change denialism are pseudosciences." There are implications for health care, the use of expert testimony, and weighing environmental policies. Recent empirical research has shown that individuals who indulge in pseudoscientific beliefs generally show lower evidential criteria, meaning they often require significantly less evidence before coming to conclusions. This can be coined as a 'jump-to-conclusions' bias that can increase the spread of pseudoscientific beliefs. Addressing pseudoscience is part of science education and developing scientific literacy. Pseudoscience can have dangerous effects. For example, pseudoscientific anti-vaccine activism and promotion of homeopathic remedies as alternative disease treatments can result in people forgoing important medical treatments with demonstrable health benefits, leading to ill-health and deaths. Furthermore, people who refuse legitimate medical treatments for contagious diseases may put others at risk. Pseudoscientific theories about racial and ethnic classifications have led to racism and genocide. The term pseudoscience is often considered pejorative, particularly by its purveyors, because it suggests something is being presented as science inaccurately or even deceptively. Therefore, practitioners and advocates of pseudoscience frequently dispute the characterization. == Etymology == The word pseudoscience is derived from the Greek root pseudo meaning "false" and the English word science, from the Latin word scientia, meaning "knowledge". Although the term has been in use since at least the late 18th century (e.g., in 1796 by James Pettit Andrews in reference to alchemy), the concept of pseudoscience as distinct from real or proper science seems to have become more widespread during the mid-19th century. Among the earliest uses of "pseudo-science" was in an 1844 article in the Northern Journal of Medicine, issue 387: That opposite kind of innovation which pronounces what has been recognized as a branch of science, to have been a pseudo-science, composed merely of so-called facts, connected together by misapprehensions under the disguise of principles. An earlier use of the term was in 1843 by the French physiologist François Magendie, that refers to phrenology as "a pseudo-science of the present day". During the 20th century, the word was used pejoratively to describe explanations of phenomena which were claimed to be scientific, but which were not in fact supported by reliable experimental evidence. Dismissing the separate issue of intentional fraud – such as the Fox sisters' "rappings" in the 1850s – the pejorative label pseudoscience distinguishes the scientific 'us', at one extreme, from the pseudo-scientific 'them', at the other, and asserts that 'our' beliefs, practices, theories, etc., by contrast with that of 'the others', are scientific. There are four criteria: (a) the 'pseudoscientific' group asserts that its beliefs, practices, theories, etc., are 'scientific'; (b) the 'pseudoscientific' group claims that its allegedly established facts are justified true beliefs; (c) the 'pseudoscientific' group asserts that its 'established facts' have been justified by genuine, rigorous, scientific method; and (d) this assertion is false or deceptive: "it is not simply that subsequent evidence overturns established conclusions, but rather that the conclusions were never warranted in the first place" From time to time, however, the usage of the word occurred in a more formal, technical manner in response to a perceived threat to individual and institutional security in a social and cultural setting. == Relationship to science == Pseudoscience is differentiated from science because – although it usually claims to be science – pseudoscience does not adhere to scientific standards, such as the scientific method, falsifiability of claims, and Mertonian norms. === Scientific method === A number of basic principles are accepted by scientists as standards for determining whether a body of knowledge, method, or practice is scientific. Experimental results should be reproducible and verified by other researchers. These principles are intended to ensure experiments can be reproduced measurably given the same conditions, allowing further investigation to determine whether a hypothesis or theory related to given phenomena is valid and reliable. Standards require the scientific method to be applied throughout, and bias to be controlled for or eliminated through randomization, fair sampling procedures, blinding of studies, and other methods. All gathered data, including the experimental or environmental conditions, are expected to be documented for scrutiny and made available for peer review, allowing further experiments or studies to be conducted to confirm or falsify results. Statistical quantification of significance, confidence, and error are also important tools for the scientific method. === Falsifiability === During the mid-20th century, the philosopher Karl Popper emphasized the criterion of falsifiability to distinguish science from non-science. Statements, hypotheses, or theories have falsifiability or refutability if there is the inherent possibility that they can be proven false, that is, if it is possible to conceive of an observation or an argument that negates them. Popper used astrology and psychoanalysis as examples of pseudoscience and Einstein's theory of relativity as an example of science. He subdivided non-science into philosophical, mathematical, mythological, religious and metaphysical formulations on one hand, and pseudoscientific formulations on the other. Another example which shows the distinct need for a claim to be falsifiable was stated in Carl Sagan's publication The Demon-Haunted World when he discusses an invisible dragon that he has in his garage. The point is made that there is no physical test to refute the claim of the presence of this dragon. Whatever test one thinks can be devised, there is a reason why it does not apply to the invisible dragon, so one can never prove that the initial claim is wrong. Sagan concludes; "Now, what's the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all?". He states that "your inability to invalidate my hypothesis is not at all the same thing as proving it true", once again explaining that even if such a claim were true, it would be outside the realm of scientific inquiry. === Mertonian norms === During 1942, Robert K. Merton identified a set of five "norms" which characterize real science. If any of the norms were violated, Merton considered the enterprise to be non-science. His norms were: Originality: The tests and research done must present something new to the scientific community. Detachment: The scientists' reasons for practicing this science must be simply for the expansion of their knowledge. The scientists should not have personal reasons to expect certain results. Universality: No person should be able to more easily obtain the information of a test than another person. Social class, religion, ethnicity, or any other personal factors should not be factors in someone's ability to receive or perform a type of science. Skepticism: Scientific facts must not be based on faith. One should always question every case and argument and constantly check for errors or invalid claims. Public accessibility: Any scientific knowledge one obtains should be made available to everyone. The results of any research should be published and shared with the scientific community. === Refusal to acknowledge problems === In 1978, Paul Thagard proposed that pseudoscience is primarily distinguishable from science when it is less progressive than alternative theories over a long period of time, and its proponents fail to acknowledge or address problems with the theory. In 1983, Mario Bunge suggested the categories of "belief fields" and "research fields" to help distinguish between pseudoscience and science, where the former is primarily personal and subjective and the latter involves a certain systematic method. The 2018 book about scientific skepticism by Steven Novella, et al. The Skeptics' Guide to the Universe lists hostility to criticism as one of the major features of pseudoscience. === Criticism of the term === Larry Laudan has suggested pseudoscience has no scientific meaning and is mostly used to describe human emotions: "If we would stand up and be counted on the side of reason, we ought to drop terms like 'pseudo-science' and 'unscientific' from our vocabulary; they are just hollow phrases which do only emotive work for us". Likewise, Richard McNally states, "The term 'pseudoscience' has become little more than an inflammatory buzzword for quickly dismissing one's opponents in media sound-bites" and "When therapeutic entrepreneurs make claims on behalf of their interventions, we should not waste our time trying to determine whether their interventions qualify as pseudoscientific. Rather, we should ask them: How do you know that your intervention works? What is your evidence?" === Alternative definition === For philosophers Silvio Funtowicz and Jerome R. Ravetz "pseudo-science may be defined as one where the uncertainty of its inputs must be suppressed, lest they render its outputs totally indeterminate". The definition, in the book Uncertainty and Quality in Science for Policy, alludes to the loss of craft skills in handling quantitative information, and to the bad practice of achieving precision in prediction (inference) only at the expenses of ignoring uncertainty in the input which was used to formulate the prediction. This use of the term is common among practitioners of post-normal science. Understood in this way, pseudoscience can be fought using good practices to assess uncertainty in quantitative information, such as NUSAP and – in the case of mathematical modelling – sensitivity auditing. == History == The history of pseudoscience is the study of pseudoscientific theories over time. A pseudoscience is a set of ideas that presents itself as science, while it does not meet the criteria to be properly called such. Distinguishing between proper science and pseudoscience is sometimes difficult. One proposal for demarcation between the two is the falsification criterion, attributed most notably to the philosopher Karl Popper. In the history of science and the history of pseudoscience it can be especially difficult to separate the two, because some sciences developed from pseudosciences. An example of this transformation is the science of chemistry, which traces its origins to the pseudoscientific or pre-scientific study of alchemy. The vast diversity in pseudosciences further complicates the history of science. Some modern pseudosciences, such as astrology and acupuncture, originated before the scientific era. Others developed as part of an ideology, such as Lysenkoism, or as a response to perceived threats to an ideology. Examples of this ideological process are creation science and intelligent design, which were developed in response to the scientific theory of evolution. == Indicators of possible pseudoscience == A topic, practice, or body of knowledge might reasonably be termed pseudoscientific when it is presented as consistent with the norms of scientific research, but it demonstrably fails to meet these norms. === Use of vague, exaggerated or untestable claims === Assertion of scientific claims that are vague rather than precise, and that lack specific measurements. Assertion of a claim with little or no explanatory power. Failure to make use of operational definitions (i.e., publicly accessible definitions of the variables, terms, or objects of interest so that persons other than the definer can measure or test them independently) (See also: Reproducibility). Failure to make reasonable use of the principle of parsimony, i.e., failing to seek an explanation that requires the fewest possible additional assumptions when multiple viable explanations are possible (See: Occam's razor). Lack of boundary conditions: Most well-supported scientific theories possess well-articulated limitations under which the predicted phenomena do and do not apply. Lack of effective controls in experimental design, such as the use of placebos and double-blinding. Lack of understanding of basic and established principles of physics and engineering. === Improper collection of evidence === Assertions that do not allow the logical possibility that they can be shown to be false by observation or physical experiment (See also: Falsifiability). Assertion of claims that a theory predicts something that it has not been shown to predict. Scientific claims that do not confer any predictive power are considered at best "conjectures", or at worst "pseudoscience" (e.g., ignoratio elenchi). Assertion that claims which have not been proven false must therefore be true, and vice versa (See: Argument from ignorance). Over-reliance on testimonial, anecdotal evidence, or personal experience: This evidence may be useful for the context of discovery (i.e., hypothesis generation), but should not be used in the context of justification (e.g., statistical hypothesis testing). Use of myths and religious texts as if they were fact, or basing evidence on readings of such texts. Use of concepts and scenarios from science fiction as if they were fact. This technique appeals to the familiarity that many people already have with science fiction tropes through the popular media. Presentation of data that seems to support claims while suppressing or refusing to consider data that conflict with those claims. This is an example of selection bias or cherry picking, a distortion of evidence or data that arises from the way that the data are collected. It is sometimes referred to as the selection effect. Repeating excessive or untested claims that have been previously published elsewhere, and promoting those claims as if they were facts; an accumulation of such uncritical secondary reports, which do not otherwise contribute their own empirical investigation, is called the Woozle effect. Reversed burden of proof: science places the burden of proof on those making a claim, not on the critic. "Pseudoscientific" arguments may neglect this principle and demand that skeptics demonstrate beyond a reasonable doubt that a claim (e.g., an assertion regarding the efficacy of a novel therapeutic technique) is false. It is essentially impossible to prove a universal negative, so this tactic incorrectly places the burden of proof on the skeptic rather than on the claimant. Appeals to holism as opposed to reductionism to dismiss negative findings: proponents of pseudoscientific claims, especially in organic medicine, alternative medicine, naturopathy and mental health, often resort to the "mantra of holism" . === Lack of openness to testing by other experts === Evasion of peer review before publicizing results (termed "science by press conference"): Some proponents of ideas that contradict accepted scientific theories avoid subjecting their ideas to peer review, sometimes on the grounds that peer review is biased towards established paradigms, and sometimes on the grounds that assertions cannot be evaluated adequately using standard scientific methods. By remaining insulated from the peer review process, these proponents forgo the opportunity of corrective feedback from informed colleagues. Some agencies, institutions, and publications that fund scientific research require authors to share data so others can evaluate a paper independently. Failure to provide adequate information for other researchers to reproduce the claims contributes to a lack of openness. Appealing to the need for secrecy or proprietary knowledge when an independent review of data or methodology is requested. Substantive debate on the evidence by knowledgeable proponents of all viewpoints is not encouraged. === Absence of progress === Failure to progress towards additional evidence of its claims. Terence Hines has identified astrology as a subject that has changed very little in the past two millennia. Lack of self-correction: scientific research programmes make mistakes, but they tend to reduce these errors over time. By contrast, ideas may be regarded as pseudoscientific because they have remained unaltered despite contradictory evidence. The work Scientists Confront Velikovsky (1976) Cornell University, also delves into these features in some detail, as does the work of Thomas Kuhn, e.g., The Structure of Scientific Revolutions (1962) which also discusses some of the items on the list of characteristics of pseudoscience. Statistical significance of supporting experimental results does not improve over time and are usually close to the cutoff for statistical significance. Normally, experimental techniques improve or the experiments are repeated, and this gives ever stronger evidence. If statistical significance does not improve, this typically shows the experiments have just been repeated until a success occurs due to chance variations. === Personalization of issues === Tight social groups and authoritarian personality, suppression of dissent and groupthink can enhance the adoption of beliefs that have no rational basis. In attempting to confirm their beliefs, the group tends to identify their critics as enemies. Assertion of a conspiracy on the part of the mainstream scientific community, government, or educational facilities to suppress pseudoscientific information. People who make these accusations often compare themselves to Galileo Galilei and his persecution by the Roman Catholic Church; this comparison is commonly known as the Galileo gambit. Attacking the motives, character, morality, or competence of critics, rather than their arguments (see ad hominem) === Use of misleading language === Creating scientific-sounding terms to persuade non-experts to believe statements that may be false or meaningless: for example, a long-standing hoax refers to water by the rarely used formal name "dihydrogen monoxide" and describes it as the main constituent in most poisonous solutions to show how easily the general public can be misled. Using established terms in idiosyncratic ways, thereby demonstrating unfamiliarity with mainstream work in the discipline. == Prevalence of pseudoscientific beliefs == === Countries === The Ministry of AYUSH in the Government of India is purposed with developing education, research and propagation of indigenous alternative medicine systems in India. The ministry has faced significant criticism for funding systems that lack biological plausibility and are either untested or conclusively proven as ineffective. Quality of research has been poor, and drugs have been launched without any rigorous pharmacological studies and meaningful clinical trials on Ayurveda or other alternative healthcare systems. There is no credible efficacy or scientific basis of any of these forms of treatment. In his book The Demon-Haunted World, Carl Sagan discusses the government of China and the Chinese Communist Party's concern about Western pseudoscience developments and certain ancient Chinese practices in China. He sees pseudoscience occurring in the United States as part of a worldwide trend and suggests its causes, dangers, diagnosis and treatment may be universal. A large percentage of the United States population lacks scientific literacy, not adequately understanding scientific principles and method. In the Journal of College Science Teaching, Art Hobson writes, "Pseudoscientific beliefs are surprisingly widespread in our culture even among public school science teachers and newspaper editors, and are closely related to scientific illiteracy." However, a 10,000-student study in the same journal concluded there was no strong correlation between science knowledge and belief in pseudoscience. During 2006, the U.S. National Science Foundation (NSF) issued an executive summary of a paper on science and engineering which briefly discussed the prevalence of pseudoscience in modern times. It said, "belief in pseudoscience is widespread" and, referencing a Gallup Poll, stated that belief in the 10 commonly believed examples of paranormal phenomena listed in the poll were "pseudoscientific beliefs". The items were "extrasensory perception (ESP), that houses can be haunted, ghosts, telepathy, clairvoyance, astrology, that people can mentally communicate with the dead, witches, reincarnation, and channelling". Such beliefs in pseudoscience represent a lack of knowledge of how science works. The scientific community may attempt to communicate information about science out of concern for the public's susceptibility to unproven claims. The NSF stated that pseudoscientific beliefs in the U.S. became more widespread during the 1990s, peaked about 2001, and then decreased slightly since with pseudoscientific beliefs remaining common. According to the NSF report, there is a lack of knowledge of pseudoscientific issues in society and pseudoscientific practices are commonly followed. Surveys indicate about a third of adult Americans consider astrology to be scientific. In Russia, in the late 20th and early 21st century, significant budgetary funds were spent on programs for the experimental study of "torsion fields", the extraction of energy from granite, the study of "cold nuclear fusion", and astrological and extrasensory "research" by the Ministry of Defense, the Ministry of Emergency Situations, the Ministry of Internal Affairs, and the State Duma (see Military Unit 10003). In 2006, Deputy Chairman of the Security Council of the Russian Federation Nikolai Spassky published an article in Rossiyskaya Gazeta, where among the priority areas for the development of the Russian energy sector, the task of extracting energy from a vacuum was in the first place. The Clean Water project was adopted as a United Russia party project; in the version submitted to the government, the program budget for 2010–2017 exceeded $14 billion. === Racism === There have been many connections between pseudoscientific writers and researchers and their anti-semitic, racist and neo-Nazi backgrounds. They often use pseudoscience to reinforce their beliefs. One of the most predominant pseudoscientific writers is Frank Collin, a self-proclaimed Nazi who goes by Frank Joseph in his writings. The majority of his works include the topics of Atlantis, extraterrestrial encounters, and Lemuria as well as other ancient civilizations, often with white supremacist undertones. For example, he posited that European peoples migrated to North America before Columbus, and that all Native American civilizations were initiated by descendants of white people. The Alt-Right using pseudoscience to base their ideologies on is not a new issue. The entire foundation of anti-semitism is based on pseudoscience, or scientific racism. In an article from Newsweek by Sander Gilman, Gilman describes the pseudoscience community's anti-semitic views. "Jews as they appear in this world of pseudoscience are an invented group of ill, stupid or stupidly smart people who use science to their own nefarious ends. Other groups, too, are painted similarly in 'race science', as it used to call itself: African-Americans, the Irish, the Chinese and, well, any and all groups that you want to prove inferior to yourself". Neo-Nazis and white supremacist often try to support their claims with studies that "prove" that their claims are more than just harmful stereotypes. For example Bret Stephens published a column in The New York Times where he claimed that Ashkenazi Jews had the highest IQ among any ethnic group. However, the scientific methodology and conclusions reached by the article Stephens cited has been called into question repeatedly since its publication. It has been found that at least one of that study's authors has been identified by the Southern Poverty Law Center as a white nationalist. The journal Nature has published a number of editorials in the last few years warning researchers about extremists looking to abuse their work, particularly population geneticists and those working with ancient DNA. One article in Nature, titled "Racism in Science: The Taint That Lingers" notes that early-twentieth-century eugenic pseudoscience has been used to influence public policy, such as the Immigration Act of 1924 in the United States, which sought to prevent immigration from Asia and parts of Europe. == Explanations == In a 1981 report Singer and Benassi wrote that pseudoscientific beliefs have their origin from at least four sources: Common cognitive errors from personal experience Erroneous sensationalistic mass media coverage Sociocultural factors Poor or erroneous science education A 1990 study by Eve and Dunn supported the findings of Singer and Benassi and found pseudoscientific belief being promoted by high school life science and biology teachers. === Psychology === The psychology of pseudoscience attempts to explore and analyze pseudoscientific thinking by means of thorough clarification on making the distinction of what is considered scientific vs. pseudoscientific. The human proclivity for seeking confirmation rather than refutation (confirmation bias), the tendency to hold comforting beliefs, and the tendency to overgeneralize have been proposed as reasons for pseudoscientific thinking. According to Beyerstein, humans are prone to associations based on resemblances only, and often prone to misattribution in cause-effect thinking. Michael Shermer's theory of belief-dependent realism is driven by the idea that the brain is essentially a "belief engine" which scans data perceived by the senses and looks for patterns and meaning. There is also the tendency for the brain to create cognitive biases, as a result of inferences and assumptions made without logic and based on instinct – usually resulting in patterns in cognition. These tendencies of patternicity and agenticity are also driven "by a meta-bias called the bias blind spot, or the tendency to recognize the power of cognitive biases in other people but to be blind to their influence on our own beliefs". Lindeman states that social motives (i.e., "to comprehend self and the world, to have a sense of control over outcomes, to belong, to find the world benevolent and to maintain one's self-esteem") are often "more easily" fulfilled by pseudoscience than by scientific information. Furthermore, pseudoscientific explanations are generally not analyzed rationally, but instead experientially. Operating within a different set of rules compared to rational thinking, experiential thinking regards an explanation as valid if the explanation is "personally functional, satisfying and sufficient", offering a description of the world that may be more personal than can be provided by science and reducing the amount of potential work involved in understanding complex events and outcomes. Anyone searching for psychological help that is based in science should seek a licensed therapist whose techniques are not based in pseudoscience. Hupp and Santa Maria provide a complete explanation of what that person should look for. === Education and scientific literacy === There is a trend to believe in pseudoscience more than scientific evidence. Some people believe the prevalence of pseudoscientific beliefs is due to widespread scientific illiteracy. Individuals lacking scientific literacy are more susceptible to wishful thinking, since they are likely to turn to immediate gratification powered by System 1, our default operating system which requires little to no effort. This system encourages one to accept the conclusions they believe, and reject the ones they do not. Further analysis of complex pseudoscientific phenomena require System 2, which follows rules, compares objects along multiple dimensions and weighs options. These two systems have several other differences which are further discussed in the dual-process theory. The scientific and secular systems of morality and meaning are generally unsatisfying to most people. Humans are, by nature, a forward-minded species pursuing greater avenues of happiness and satisfaction, but we are all too frequently willing to grasp at unrealistic promises of a better life. Psychology has much to discuss about pseudoscience thinking, as it is the illusory perceptions of causality and effectiveness of numerous individuals that needs to be illuminated. Research suggests that illusionary thinking happens in most people when exposed to certain circumstances such as reading a book, an advertisement or the testimony of others are the basis of pseudoscience beliefs. It is assumed that illusions are not unusual, and given the right conditions, illusions are able to occur systematically even in normal emotional situations. One of the things pseudoscience believers quibble most about is that academic science usually treats them as fools. Minimizing these illusions in the real world is not simple. To this aim, designing evidence-based educational programs can be effective to help people identify and reduce their own illusions. == Boundaries with science == === Classification === Philosophers classify types of knowledge. In English, the word science is used to indicate specifically the natural sciences and related fields, which are called the social sciences. Different philosophers of science may disagree on the exact limits – for example, is mathematics a formal science that is closer to the empirical ones, or is pure mathematics closer to the philosophical study of logic and therefore not a science? – but all agree that all of the ideas that are not scientific are non-scientific. The large category of non-science includes all matters outside the natural and social sciences, such as the study of history, metaphysics, religion, art, and the humanities. Dividing the category again, unscientific claims are a subset of the large category of non-scientific claims. This category specifically includes all matters that are directly opposed to good science. Un-science includes both "bad science" (such as an error made in a good-faith attempt at learning something about the natural world) and pseudoscience. Thus pseudoscience is a subset of un-science, and un-science, in turn, is subset of non-science. Science is also distinguishable from revelation, theology, or spirituality in that it offers insight into the physical world obtained by empirical research and testing. The most notable disputes concern the evolution of living organisms, the idea of common descent, the geologic history of the Earth, the formation of the Solar System, and the origin of the universe. Systems of belief that derive from divine or inspired knowledge are not considered pseudoscience if they do not claim either to be scientific or to overturn well-established science. Moreover, some specific religious claims, such as the power of intercessory prayer to heal the sick, although they may be based on untestable beliefs, can be tested by the scientific method. Some statements and common beliefs of popular science may not meet the criteria of science. "Pop" science may blur the divide between science and pseudoscience among the general public, and may also involve science fiction. Indeed, pop science is disseminated to, and can also easily emanate from, persons not accountable to scientific methodology and expert peer review. If claims of a given field can be tested experimentally and standards are upheld, it is not pseudoscience, regardless of how odd, astonishing, or counterintuitive those claims are. If claims made are inconsistent with existing experimental results or established theory, but the method is sound, caution should be used, since science consists of testing hypotheses which may turn out to be false. In such a case, the work may be better described as ideas that are "not yet generally accepted". Protoscience is a term sometimes used to describe a hypothesis that has not yet been tested adequately by the scientific method, but which is otherwise consistent with existing science or which, where inconsistent, offers reasonable account of the inconsistency. It may also describe the transition from a body of practical knowledge into a scientific field. === Philosophy === Karl Popper stated it is insufficient to distinguish science from pseudoscience, or from metaphysics (such as the philosophical question of what existence means), by the criterion of rigorous adherence to the empirical method, which is essentially inductive, based on observation or experimentation. He proposed a method to distinguish between genuine empirical, nonempirical or even pseudoempirical methods. The latter case was exemplified by astrology, which appeals to observation and experimentation. While it had empirical evidence based on observation, on horoscopes and biographies, it crucially failed to use acceptable scientific standards. Popper proposed falsifiability as an important criterion in distinguishing science from pseudoscience. To demonstrate this point, Popper gave two cases of human behavior and typical explanations from Sigmund Freud and Alfred Adler's theories: "that of a man who pushes a child into the water with the intention of drowning it; and that of a man who sacrifices his life in an attempt to save the child." From Freud's perspective, the first man would have suffered from psychological repression, probably originating from an Oedipus complex, whereas the second man had attained sublimation. From Adler's perspective, the first and second man suffered from feelings of inferiority and had to prove himself, which drove him to commit the crime or, in the second case, drove him to rescue the child. Popper was not able to find any counterexamples of human behavior in which the behavior could not be explained in the terms of Adler's or Freud's theory. Popper argued it was that the observation always fitted or confirmed the theory which, rather than being its strength, was actually its weakness. In contrast, Popper gave the example of Einstein's gravitational theory, which predicted "light must be attracted by heavy bodies (such as the Sun), precisely as material bodies were attracted." Following from this, stars closer to the Sun would appear to have moved a small distance away from the Sun, and away from each other. This prediction was particularly striking to Popper because it involved considerable risk. The brightness of the Sun prevented this effect from being observed under normal circumstances, so photographs had to be taken during an eclipse and compared to photographs taken at night. Popper states, "If observation shows that the predicted effect is definitely absent, then the theory is simply refuted." Popper summed up his criterion for the scientific status of a theory as depending on its falsifiability, refutability, or testability. Paul R. Thagard used astrology as a case study to distinguish science from pseudoscience and proposed principles and criteria to delineate them. First, astrology has not progressed in that it has not been updated nor added any explanatory power since Ptolemy. Second, it has ignored outstanding problems such as the precession of equinoxes in astronomy. Third, alternative theories of personality and behavior have grown progressively to encompass explanations of phenomena which astrology statically attributes to heavenly forces. Fourth, astrologers have remained uninterested in furthering the theory to deal with outstanding problems or in critically evaluating the theory in relation to other theories. Thagard intended this criterion to be extended to areas other than astrology. He believed it would delineate as pseudoscientific such practices as witchcraft and pyramidology, while leaving physics, chemistry, astronomy, geoscience, biology, and archaeology in the realm of science. In the philosophy and history of science, Imre Lakatos stresses the social and political importance of the demarcation problem, the normative methodological problem of distinguishing between science and pseudoscience. His distinctive historical analysis of scientific methodology based on research programmes suggests: "scientists regard the successful theoretical prediction of stunning novel facts – such as the return of Halley's comet or the gravitational bending of light rays – as what demarcates good scientific theories from pseudo-scientific and degenerate theories, and in spite of all scientific theories being forever confronted by 'an ocean of counterexamples'". Lakatos offers a "novel fallibilist analysis of the development of Newton's celestial dynamics, [his] favourite historical example of his methodology" and argues in light of this historical turn, that his account answers for certain inadequacies in those of Karl Popper and Thomas Kuhn. "Nonetheless, Lakatos did recognize the force of Kuhn's historical criticism of Popper – all important theories have been surrounded by an 'ocean of anomalies', which on a falsificationist view would require the rejection of the theory outright...Lakatos sought to reconcile the rationalism of Popperian falsificationism with what seemed to be its own refutation by history". Many philosophers have tried to solve the problem of demarcation in the following terms: a statement constitutes knowledge if sufficiently many people believe it sufficiently strongly. But the history of thought shows us that many people were totally committed to absurd beliefs. If the strengths of beliefs were a hallmark of knowledge, we should have to rank some tales about demons, angels, devils, and of heaven and hell as knowledge. Scientists, on the other hand, are very sceptical even of their best theories. Newton's is the most powerful theory science has yet produced, but Newton himself never believed that bodies attract each other at a distance. So no degree of commitment to beliefs makes them knowledge. Indeed, the hallmark of scientific behaviour is a certain scepticism even towards one's most cherished theories. Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime. Thus a statement may be pseudoscientific even if it is eminently 'plausible' and everybody believes in it, and it may be scientifically valuable even if it is unbelievable and nobody believes in it. A theory may even be of supreme scientific value even if no one understands it, let alone believes in it. The boundary between science and pseudoscience is disputed and difficult to determine analytically, even after more than a century of study by philosophers of science and scientists, and despite some basic agreements on the fundamentals of the scientific method. The concept of pseudoscience rests on an understanding that the scientific method has been misrepresented or misapplied with respect to a given theory, but many philosophers of science maintain that different kinds of methods are held as appropriate across different fields and different eras of human history. According to Lakatos, the typical descriptive unit of great scientific achievements is not an isolated hypothesis but "a powerful problem-solving machinery, which, with the help of sophisticated mathematical techniques, digests anomalies and even turns them into positive evidence". To Popper, pseudoscience uses induction to generate theories, and only performs experiments to seek to verify them. To Popper, falsifiability is what determines the scientific status of a theory. Taking a historical approach, Kuhn observed that scientists did not follow Popper's rule, and might ignore falsifying data, unless overwhelming. To Kuhn, puzzle-solving within a paradigm is science. Lakatos attempted to resolve this debate, by suggesting history shows that science occurs in research programmes, competing according to how progressive they are. The leading idea of a programme could evolve, driven by its heuristic to make predictions that can be supported by evidence. Feyerabend claimed that Lakatos was selective in his examples, and the whole history of science shows there is no universal rule of scientific method, and imposing one on the scientific community impedes progress. Laudan maintained that the demarcation between science and non-science was a pseudo-problem, preferring to focus on the more general distinction between reliable and unreliable knowledge. [Feyerabend] regards Lakatos's view as being closet anarchism disguised as methodological rationalism. Feyerabend's claim was not that standard methodological rules should never be obeyed, but rather that sometimes progress is made by abandoning them. In the absence of a generally accepted rule, there is a need for alternative methods of persuasion. According to Feyerabend, Galileo employed stylistic and rhetorical techniques to convince his reader, while he also wrote in Italian rather than Latin and directed his arguments to those already temperamentally inclined to accept them. == Politics, health, and education == === Political implications === The demarcation problem between science and pseudoscience brings up debate in the realms of science, philosophy and politics. Imre Lakatos, for instance, points out that the Communist Party of the Soviet Union at one point declared that Mendelian genetics was pseudoscientific and had its advocates, including well-established scientists such as Nikolai Vavilov, sent to a Gulag and that the "liberal Establishment of the West" denies freedom of speech to topics it regards as pseudoscience, particularly where they run up against social mores. Something becomes pseudoscientific when science cannot be separated from ideology, scientists misrepresent scientific findings to promote or draw attention for publicity, when politicians, journalists and a nation's intellectual elite distort the facts of science for short-term political gain, or when powerful individuals of the public conflate causation and cofactors by clever wordplay. These ideas reduce the authority, value, integrity and independence of science in society. === Health and education implications === Distinguishing science from pseudoscience has practical implications in the case of health care, expert testimony, environmental policies, and science education. Treatments with a patina of scientific authority which have not actually been subjected to actual scientific testing may be ineffective, expensive and dangerous to patients and confuse health providers, insurers, government decision makers and the public as to what treatments are appropriate. Claims advanced by pseudoscience may result in government officials and educators making bad decisions in selecting curricula. The extent to which students acquire a range of social and cognitive thinking skills related to the proper usage of science and technology determines whether they are scientifically literate. Education in the sciences encounters new dimensions with the changing landscape of science and technology, a fast-changing culture and a knowledge-driven era. A reinvention of the school science curriculum is one that shapes students to contend with its changing influence on human welfare. Scientific literacy, which allows a person to distinguish science from pseudosciences such as astrology, is among the attributes that enable students to adapt to the changing world. Its characteristics are embedded in a curriculum where students are engaged in resolving problems, conducting investigations, or developing projects. Alan J. Friedman mentions why most scientists avoid educating about pseudoscience, including that paying undue attention to pseudoscience could dignify it. On the other hand, Robert L. Park emphasizes how pseudoscience can be a threat to society and considers that scientists have a responsibility to teach how to distinguish science from pseudoscience. Pseudosciences such as homeopathy, even if generally benign, are used by charlatans. This poses a serious issue because it enables incompetent practitioners to administer health care. True-believing zealots may pose a more serious threat than typical con men because of their delusion to homeopathy's ideology. Irrational health care is not harmless and it is careless to create patient confidence in pseudomedicine. On 8 December 2016, journalist Michael V. LeVine pointed out the dangers posed by the Natural News website: "Snake-oil salesmen have pushed false cures since the dawn of medicine, and now websites like Natural News flood social media with dangerous anti-pharmaceutical, anti-vaccination and anti-GMO pseudoscience that puts millions at risk of contracting preventable illnesses." The anti-vaccine movement has persuaded large numbers of parents not to vaccinate their children, citing pseudoscientific research that links childhood vaccines with the onset of autism. These include the study by Andrew Wakefield, which claimed that a combination of gastrointestinal disease and developmental regression, which are often seen in children with ASD, occurred within two weeks of receiving vaccines. The study was eventually retracted by its publisher, and Wakefield was stripped of his license to practice medicine. Alkaline water is water that has a pH of higher than 7, purported to host numerous health benefits, with no empirical backing. A practitioner known as Robert O. Young who promoted alkaline water and an "Alkaline diet" was sent to jail for 3 years in 2017 for practicing medicine without a license. == See also == == Notes == == References == == Bibliography == === Works cited === === Further reading ===
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https://en.wikipedia.org/wiki/Pseudoscience
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Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, origin, evolution, and distribution of life. Central to biology are five fundamental themes: the cell as the basic unit of life, genes and heredity as the basis of inheritance, evolution as the driver of biological diversity, energy transformation for sustaining life processes, and the maintenance of internal stability (homeostasis). Biology examines life across multiple levels of organization, from molecules and cells to organisms, populations, and ecosystems. Subdisciplines include molecular biology, physiology, ecology, evolutionary biology, developmental biology, and systematics, among others. Each of these fields applies a range of methods to investigate biological phenomena, including observation, experimentation, and mathematical modeling. Modern biology is grounded in the theory of evolution by natural selection, first articulated by Charles Darwin, and in the molecular understanding of genes encoded in DNA. The discovery of the structure of DNA and advances in molecular genetics have transformed many areas of biology, leading to applications in medicine, agriculture, biotechnology, and environmental science. Life on Earth is believed to have originated over 3.7 billion years ago. Today, it includes a vast diversity of organisms—from single-celled archaea and bacteria to complex multicellular plants, fungi, and animals. Biologists classify organisms based on shared characteristics and evolutionary relationships, using taxonomic and phylogenetic frameworks. These organisms interact with each other and with their environments in ecosystems, where they play roles in energy flow and nutrient cycling. As a constantly evolving field, biology incorporates new discoveries and technologies that enhance the understanding of life and its processes, while contributing to solutions for challenges such as disease, climate change, and biodiversity loss. == History == The earliest of roots of science, which included medicine, can be traced to ancient Egypt and Mesopotamia in around 3000 to 1200 BCE. Their contributions shaped ancient Greek natural philosophy. Ancient Greek philosophers such as Aristotle (384–322 BCE) contributed extensively to the development of biological knowledge. He explored biological causation and the diversity of life. His successor, Theophrastus, began the scientific study of plants. Scholars of the medieval Islamic world who wrote on biology included al-Jahiz (781–869), Al-Dīnawarī (828–896), who wrote on botany, and Rhazes (865–925) who wrote on anatomy and physiology. Medicine was especially well studied by Islamic scholars working in Greek philosopher traditions, while natural history drew heavily on Aristotelian thought. Biology began to quickly develop with Anton van Leeuwenhoek's dramatic improvement of the microscope. It was then that scholars discovered spermatozoa, bacteria, infusoria and the diversity of microscopic life. Investigations by Jan Swammerdam led to new interest in entomology and helped to develop techniques of microscopic dissection and staining. Advances in microscopy had a profound impact on biological thinking. In the early 19th century, biologists pointed to the central importance of the cell. In 1838, Schleiden and Schwann began promoting the now universal ideas that (1) the basic unit of organisms is the cell and (2) that individual cells have all the characteristics of life, although they opposed the idea that (3) all cells come from the division of other cells, continuing to support spontaneous generation. However, Robert Remak and Rudolf Virchow were able to reify the third tenet, and by the 1860s most biologists accepted all three tenets which consolidated into cell theory. Meanwhile, taxonomy and classification became the focus of natural historians. Carl Linnaeus published a basic taxonomy for the natural world in 1735, and in the 1750s introduced scientific names for all his species. Georges-Louis Leclerc, Comte de Buffon, treated species as artificial categories and living forms as malleable—even suggesting the possibility of common descent. Serious evolutionary thinking originated with the works of Jean-Baptiste Lamarck, who presented a coherent theory of evolution. The British naturalist Charles Darwin, combining the biogeographical approach of Humboldt, the uniformitarian geology of Lyell, Malthus's writings on population growth, and his own morphological expertise and extensive natural observations, forged a more successful evolutionary theory based on natural selection; similar reasoning and evidence led Alfred Russel Wallace to independently reach the same conclusions. The basis for modern genetics began with the work of Gregor Mendel in 1865. This outlined the principles of biological inheritance. However, the significance of his work was not realized until the early 20th century when evolution became a unified theory as the modern synthesis reconciled Darwinian evolution with classical genetics. In the 1940s and early 1950s, a series of experiments by Alfred Hershey and Martha Chase pointed to DNA as the component of chromosomes that held the trait-carrying units that had become known as genes. A focus on new kinds of model organisms such as viruses and bacteria, along with the discovery of the double-helical structure of DNA by James Watson and Francis Crick in 1953, marked the transition to the era of molecular genetics. From the 1950s onwards, biology has been vastly extended in the molecular domain. The genetic code was cracked by Har Gobind Khorana, Robert W. Holley and Marshall Warren Nirenberg after DNA was understood to contain codons. The Human Genome Project was launched in 1990 to map the human genome. == Chemical basis == === Atoms and molecules === All organisms are made up of chemical elements; oxygen, carbon, hydrogen, and nitrogen account for most (96%) of the mass of all organisms, with calcium, phosphorus, sulfur, sodium, chlorine, and magnesium constituting essentially all the remainder. Different elements can combine to form compounds such as water, which is fundamental to life. Biochemistry is the study of chemical processes within and relating to living organisms. Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including molecular synthesis, modification, mechanisms, and interactions. === Water === Life arose from the Earth's first ocean, which formed some 3.8 billion years ago. Since then, water continues to be the most abundant molecule in every organism. Water is important to life because it is an effective solvent, capable of dissolving solutes such as sodium and chloride ions or other small molecules to form an aqueous solution. Once dissolved in water, these solutes are more likely to come in contact with one another and therefore take part in chemical reactions that sustain life. In terms of its molecular structure, water is a small polar molecule with a bent shape formed by the polar covalent bonds of two hydrogen (H) atoms to one oxygen (O) atom (H2O). Because the O–H bonds are polar, the oxygen atom has a slight negative charge and the two hydrogen atoms have a slight positive charge. This polar property of water allows it to attract other water molecules via hydrogen bonds, which makes water cohesive. Surface tension results from the cohesive force due to the attraction between molecules at the surface of the liquid. Water is also adhesive as it is able to adhere to the surface of any polar or charged non-water molecules. Water is denser as a liquid than it is as a solid (or ice). This unique property of water allows ice to float above liquid water such as ponds, lakes, and oceans, thereby insulating the liquid below from the cold air above. Water has the capacity to absorb energy, giving it a higher specific heat capacity than other solvents such as ethanol. Thus, a large amount of energy is needed to break the hydrogen bonds between water molecules to convert liquid water into water vapor. As a molecule, water is not completely stable as each water molecule continuously dissociates into hydrogen and hydroxyl ions before reforming into a water molecule again. In pure water, the number of hydrogen ions balances (or equals) the number of hydroxyl ions, resulting in a pH that is neutral. === Organic compounds === Organic compounds are molecules that contain carbon bonded to another element such as hydrogen. With the exception of water, nearly all the molecules that make up each organism contain carbon. Carbon can form covalent bonds with up to four other atoms, enabling it to form diverse, large, and complex molecules. For example, a single carbon atom can form four single covalent bonds such as in methane, two double covalent bonds such as in carbon dioxide (CO2), or a triple covalent bond such as in carbon monoxide (CO). Moreover, carbon can form very long chains of interconnecting carbon–carbon bonds such as octane or ring-like structures such as glucose. The simplest form of an organic molecule is the hydrocarbon, which is a large family of organic compounds that are composed of hydrogen atoms bonded to a chain of carbon atoms. A hydrocarbon backbone can be substituted by other elements such as oxygen (O), hydrogen (H), phosphorus (P), and sulfur (S), which can change the chemical behavior of that compound. Groups of atoms that contain these elements (O-, H-, P-, and S-) and are bonded to a central carbon atom or skeleton are called functional groups. There are six prominent functional groups that can be found in organisms: amino group, carboxyl group, carbonyl group, hydroxyl group, phosphate group, and sulfhydryl group. In 1953, the Miller–Urey experiment showed that organic compounds could be synthesized abiotically within a closed system mimicking the conditions of early Earth, thus suggesting that complex organic molecules could have arisen spontaneously in early Earth (see abiogenesis). === Macromolecules === Macromolecules are large molecules made up of smaller subunits or monomers. Monomers include sugars, amino acids, and nucleotides. Carbohydrates include monomers and polymers of sugars. Lipids are the only class of macromolecules that are not made up of polymers. They include steroids, phospholipids, and fats, largely nonpolar and hydrophobic (water-repelling) substances. Proteins are the most diverse of the macromolecules. They include enzymes, transport proteins, large signaling molecules, antibodies, and structural proteins. The basic unit (or monomer) of a protein is an amino acid. Twenty amino acids are used in proteins. Nucleic acids are polymers of nucleotides. Their function is to store, transmit, and express hereditary information. == Cells == Cell theory states that cells are the fundamental units of life, that all living things are composed of one or more cells, and that all cells arise from preexisting cells through cell division. Most cells are very small, with diameters ranging from 1 to 100 micrometers and are therefore only visible under a light or electron microscope. There are generally two types of cells: eukaryotic cells, which contain a nucleus, and prokaryotic cells, which do not. Prokaryotes are single-celled organisms such as bacteria, whereas eukaryotes can be single-celled or multicellular. In multicellular organisms, every cell in the organism's body is derived ultimately from a single cell in a fertilized egg. === Cell structure === Every cell is enclosed within a cell membrane that separates its cytoplasm from the extracellular space. A cell membrane consists of a lipid bilayer, including cholesterols that sit between phospholipids to maintain their fluidity at various temperatures. Cell membranes are semipermeable, allowing small molecules such as oxygen, carbon dioxide, and water to pass through while restricting the movement of larger molecules and charged particles such as ions. Cell membranes also contain membrane proteins, including integral membrane proteins that go across the membrane serving as membrane transporters, and peripheral proteins that loosely attach to the outer side of the cell membrane, acting as enzymes shaping the cell. Cell membranes are involved in various cellular processes such as cell adhesion, storing electrical energy, and cell signalling and serve as the attachment surface for several extracellular structures such as a cell wall, glycocalyx, and cytoskeleton. Within the cytoplasm of a cell, there are many biomolecules such as proteins and nucleic acids. In addition to biomolecules, eukaryotic cells have specialized structures called organelles that have their own lipid bilayers or are spatially units. These organelles include the cell nucleus, which contains most of the cell's DNA, or mitochondria, which generate adenosine triphosphate (ATP) to power cellular processes. Other organelles such as endoplasmic reticulum and Golgi apparatus play a role in the synthesis and packaging of proteins, respectively. Biomolecules such as proteins can be engulfed by lysosomes, another specialized organelle. Plant cells have additional organelles that distinguish them from animal cells such as a cell wall that provides support for the plant cell, chloroplasts that harvest sunlight energy to produce sugar, and vacuoles that provide storage and structural support as well as being involved in reproduction and breakdown of plant seeds. Eukaryotic cells also have cytoskeleton that is made up of microtubules, intermediate filaments, and microfilaments, all of which provide support for the cell and are involved in the movement of the cell and its organelles. In terms of their structural composition, the microtubules are made up of tubulin (e.g., α-tubulin and β-tubulin) whereas intermediate filaments are made up of fibrous proteins. Microfilaments are made up of actin molecules that interact with other strands of proteins. === Metabolism === All cells require energy to sustain cellular processes. Metabolism is the set of chemical reactions in an organism. The three main purposes of metabolism are: the conversion of food to energy to run cellular processes; the conversion of food/fuel to monomer building blocks; and the elimination of metabolic wastes. These enzyme-catalyzed reactions allow organisms to grow and reproduce, maintain their structures, and respond to their environments. Metabolic reactions may be categorized as catabolic—the breaking down of compounds (for example, the breaking down of glucose to pyruvate by cellular respiration); or anabolic—the building up (synthesis) of compounds (such as proteins, carbohydrates, lipids, and nucleic acids). Usually, catabolism releases energy, and anabolism consumes energy. The chemical reactions of metabolism are organized into metabolic pathways, in which one chemical is transformed through a series of steps into another chemical, each step being facilitated by a specific enzyme. Enzymes are crucial to metabolism because they allow organisms to drive desirable reactions that require energy that will not occur by themselves, by coupling them to spontaneous reactions that release energy. Enzymes act as catalysts—they allow a reaction to proceed more rapidly without being consumed by it—by reducing the amount of activation energy needed to convert reactants into products. Enzymes also allow the regulation of the rate of a metabolic reaction, for example in response to changes in the cell's environment or to signals from other cells. === Cellular respiration === Cellular respiration is a set of metabolic reactions and processes that take place in cells to convert chemical energy from nutrients into adenosine triphosphate (ATP), and then release waste products. The reactions involved in respiration are catabolic reactions, which break large molecules into smaller ones, releasing energy. Respiration is one of the key ways a cell releases chemical energy to fuel cellular activity. The overall reaction occurs in a series of biochemical steps, some of which are redox reactions. Although cellular respiration is technically a combustion reaction, it clearly does not resemble one when it occurs in a cell because of the slow, controlled release of energy from the series of reactions. Sugar in the form of glucose is the main nutrient used by animal and plant cells in respiration. Cellular respiration involving oxygen is called aerobic respiration, which has four stages: glycolysis, citric acid cycle (or Krebs cycle), electron transport chain, and oxidative phosphorylation. Glycolysis is a metabolic process that occurs in the cytoplasm whereby glucose is converted into two pyruvates, with two net molecules of ATP being produced at the same time. Each pyruvate is then oxidized into acetyl-CoA by the pyruvate dehydrogenase complex, which also generates NADH and carbon dioxide. Acetyl-CoA enters the citric acid cycle, which takes places inside the mitochondrial matrix. At the end of the cycle, the total yield from 1 glucose (or 2 pyruvates) is 6 NADH, 2 FADH2, and 2 ATP molecules. Finally, the next stage is oxidative phosphorylation, which in eukaryotes, occurs in the mitochondrial cristae. Oxidative phosphorylation comprises the electron transport chain, which is a series of four protein complexes that transfer electrons from one complex to another, thereby releasing energy from NADH and FADH2 that is coupled to the pumping of protons (hydrogen ions) across the inner mitochondrial membrane (chemiosmosis), which generates a proton motive force. Energy from the proton motive force drives the enzyme ATP synthase to synthesize more ATPs by phosphorylating ADPs. The transfer of electrons terminates with molecular oxygen being the final electron acceptor. If oxygen were not present, pyruvate would not be metabolized by cellular respiration but undergoes a process of fermentation. The pyruvate is not transported into the mitochondrion but remains in the cytoplasm, where it is converted to waste products that may be removed from the cell. This serves the purpose of oxidizing the electron carriers so that they can perform glycolysis again and removing the excess pyruvate. Fermentation oxidizes NADH to NAD+ so it can be re-used in glycolysis. In the absence of oxygen, fermentation prevents the buildup of NADH in the cytoplasm and provides NAD+ for glycolysis. This waste product varies depending on the organism. In skeletal muscles, the waste product is lactic acid. This type of fermentation is called lactic acid fermentation. In strenuous exercise, when energy demands exceed energy supply, the respiratory chain cannot process all of the hydrogen atoms joined by NADH. During anaerobic glycolysis, NAD+ regenerates when pairs of hydrogen combine with pyruvate to form lactate. Lactate formation is catalyzed by lactate dehydrogenase in a reversible reaction. Lactate can also be used as an indirect precursor for liver glycogen. During recovery, when oxygen becomes available, NAD+ attaches to hydrogen from lactate to form ATP. In yeast, the waste products are ethanol and carbon dioxide. This type of fermentation is known as alcoholic or ethanol fermentation. The ATP generated in this process is made by substrate-level phosphorylation, which does not require oxygen. === Photosynthesis === Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that can later be released to fuel the organism's metabolic activities via cellular respiration. This chemical energy is stored in carbohydrate molecules, such as sugars, which are synthesized from carbon dioxide and water. In most cases, oxygen is released as a waste product. Most plants, algae, and cyanobacteria perform photosynthesis, which is largely responsible for producing and maintaining the oxygen content of the Earth's atmosphere, and supplies most of the energy necessary for life on Earth. Photosynthesis has four stages: Light absorption, electron transport, ATP synthesis, and carbon fixation. Light absorption is the initial step of photosynthesis whereby light energy is absorbed by chlorophyll pigments attached to proteins in the thylakoid membranes. The absorbed light energy is used to remove electrons from a donor (water) to a primary electron acceptor, a quinone designated as Q. In the second stage, electrons move from the quinone primary electron acceptor through a series of electron carriers until they reach a final electron acceptor, which is usually the oxidized form of NADP+, which is reduced to NADPH, a process that takes place in a protein complex called photosystem I (PSI). The transport of electrons is coupled to the movement of protons (or hydrogen) from the stroma to the thylakoid membrane, which forms a pH gradient across the membrane as hydrogen becomes more concentrated in the lumen than in the stroma. This is analogous to the proton-motive force generated across the inner mitochondrial membrane in aerobic respiration. During the third stage of photosynthesis, the movement of protons down their concentration gradients from the thylakoid lumen to the stroma through the ATP synthase is coupled to the synthesis of ATP by that same ATP synthase. The NADPH and ATPs generated by the light-dependent reactions in the second and third stages, respectively, provide the energy and electrons to drive the synthesis of glucose by fixing atmospheric carbon dioxide into existing organic carbon compounds, such as ribulose bisphosphate (RuBP) in a sequence of light-independent (or dark) reactions called the Calvin cycle. === Cell signaling === Cell signaling (or communication) is the ability of cells to receive, process, and transmit signals with its environment and with itself. Signals can be non-chemical such as light, electrical impulses, and heat, or chemical signals (or ligands) that interact with receptors, which can be found embedded in the cell membrane of another cell or located deep inside a cell. There are generally four types of chemical signals: autocrine, paracrine, juxtacrine, and hormones. In autocrine signaling, the ligand affects the same cell that releases it. Tumor cells, for example, can reproduce uncontrollably because they release signals that initiate their own self-division. In paracrine signaling, the ligand diffuses to nearby cells and affects them. For example, brain cells called neurons release ligands called neurotransmitters that diffuse across a synaptic cleft to bind with a receptor on an adjacent cell such as another neuron or muscle cell. In juxtacrine signaling, there is direct contact between the signaling and responding cells. Finally, hormones are ligands that travel through the circulatory systems of animals or vascular systems of plants to reach their target cells. Once a ligand binds with a receptor, it can influence the behavior of another cell, depending on the type of receptor. For instance, neurotransmitters that bind with an inotropic receptor can alter the excitability of a target cell. Other types of receptors include protein kinase receptors (e.g., receptor for the hormone insulin) and G protein-coupled receptors. Activation of G protein-coupled receptors can initiate second messenger cascades. The process by which a chemical or physical signal is transmitted through a cell as a series of molecular events is called signal transduction. === Cell cycle === The cell cycle is a series of events that take place in a cell that cause it to divide into two daughter cells. These events include the duplication of its DNA and some of its organelles, and the subsequent partitioning of its cytoplasm into two daughter cells in a process called cell division. In eukaryotes (i.e., animal, plant, fungal, and protist cells), there are two distinct types of cell division: mitosis and meiosis. Mitosis is part of the cell cycle, in which replicated chromosomes are separated into two new nuclei. Cell division gives rise to genetically identical cells in which the total number of chromosomes is maintained. In general, mitosis (division of the nucleus) is preceded by the S stage of interphase (during which the DNA is replicated) and is often followed by telophase and cytokinesis; which divides the cytoplasm, organelles and cell membrane of one cell into two new cells containing roughly equal shares of these cellular components. The different stages of mitosis all together define the mitotic phase of an animal cell cycle—the division of the mother cell into two genetically identical daughter cells. The cell cycle is a vital process by which a single-celled fertilized egg develops into a mature organism, as well as the process by which hair, skin, blood cells, and some internal organs are renewed. After cell division, each of the daughter cells begin the interphase of a new cycle. In contrast to mitosis, meiosis results in four haploid daughter cells by undergoing one round of DNA replication followed by two divisions. Homologous chromosomes are separated in the first division (meiosis I), and sister chromatids are separated in the second division (meiosis II). Both of these cell division cycles are used in the process of sexual reproduction at some point in their life cycle. Both are believed to be present in the last eukaryotic common ancestor. Prokaryotes (i.e., archaea and bacteria) can also undergo cell division (or binary fission). Unlike the processes of mitosis and meiosis in eukaryotes, binary fission in prokaryotes takes place without the formation of a spindle apparatus on the cell. Before binary fission, DNA in the bacterium is tightly coiled. After it has uncoiled and duplicated, it is pulled to the separate poles of the bacterium as it increases the size to prepare for splitting. Growth of a new cell wall begins to separate the bacterium (triggered by FtsZ polymerization and "Z-ring" formation). The new cell wall (septum) fully develops, resulting in the complete split of the bacterium. The new daughter cells have tightly coiled DNA rods, ribosomes, and plasmids. === Sexual reproduction and meiosis === Meiosis is a central feature of sexual reproduction in eukaryotes, and the most fundamental function of meiosis appears to be conservation of the integrity of the genome that is passed on to progeny by parents. Two aspects of sexual reproduction, meiotic recombination and outcrossing, are likely maintained respectively by the adaptive advantages of recombinational repair of genomic DNA damage and genetic complementation which masks the expression of deleterious recessive mutations. The beneficial effect of genetic complementation, derived from outcrossing (cross-fertilization) is also referred to as hybrid vigor or heterosis. Charles Darwin in his 1878 book The Effects of Cross and Self-Fertilization in the Vegetable Kingdom at the start of chapter XII noted “The first and most important of the conclusions which may be drawn from the observations given in this volume, is that generally cross-fertilisation is beneficial and self-fertilisation often injurious, at least with the plants on which I experimented.” Genetic variation, often produced as a byproduct of sexual reproduction, may provide long-term advantages to those sexual lineages that engage in outcrossing. == Genetics == === Inheritance === Genetics is the scientific study of inheritance. Mendelian inheritance, specifically, is the process by which genes and traits are passed on from parents to offspring. It has several principles. The first is that genetic characteristics, alleles, are discrete and have alternate forms (e.g., purple vs. white or tall vs. dwarf), each inherited from one of two parents. Based on the law of dominance and uniformity, which states that some alleles are dominant while others are recessive; an organism with at least one dominant allele will display the phenotype of that dominant allele. During gamete formation, the alleles for each gene segregate, so that each gamete carries only one allele for each gene. Heterozygotic individuals produce gametes with an equal frequency of two alleles. Finally, the law of independent assortment, states that genes of different traits can segregate independently during the formation of gametes, i.e., genes are unlinked. An exception to this rule would include traits that are sex-linked. Test crosses can be performed to experimentally determine the underlying genotype of an organism with a dominant phenotype. A Punnett square can be used to predict the results of a test cross. The chromosome theory of inheritance, which states that genes are found on chromosomes, was supported by Thomas Morgans's experiments with fruit flies, which established the sex linkage between eye color and sex in these insects. === Genes and DNA === A gene is a unit of heredity that corresponds to a region of deoxyribonucleic acid (DNA) that carries genetic information that controls form or function of an organism. DNA is composed of two polynucleotide chains that coil around each other to form a double helix. It is found as linear chromosomes in eukaryotes, and circular chromosomes in prokaryotes. The set of chromosomes in a cell is collectively known as its genome. In eukaryotes, DNA is mainly in the cell nucleus. In prokaryotes, the DNA is held within the nucleoid. The genetic information is held within genes, and the complete assemblage in an organism is called its genotype. DNA replication is a semiconservative process whereby each strand serves as a template for a new strand of DNA. Mutations are heritable changes in DNA. They can arise spontaneously as a result of replication errors that were not corrected by proofreading or can be induced by an environmental mutagen such as a chemical (e.g., nitrous acid, benzopyrene) or radiation (e.g., x-ray, gamma ray, ultraviolet radiation, particles emitted by unstable isotopes). Mutations can lead to phenotypic effects such as loss-of-function, gain-of-function, and conditional mutations. Some mutations are beneficial, as they are a source of genetic variation for evolution. Others are harmful if they were to result in a loss of function of genes needed for survival. === Gene expression === Gene expression is the molecular process by which a genotype encoded in DNA gives rise to an observable phenotype in the proteins of an organism's body. This process is summarized by the central dogma of molecular biology, which was formulated by Francis Crick in 1958. According to the Central Dogma, genetic information flows from DNA to RNA to protein. There are two gene expression processes: transcription (DNA to RNA) and translation (RNA to protein). === Gene regulation === The regulation of gene expression by environmental factors and during different stages of development can occur at each step of the process such as transcription, RNA splicing, translation, and post-translational modification of a protein. Gene expression can be influenced by positive or negative regulation, depending on which of the two types of regulatory proteins called transcription factors bind to the DNA sequence close to or at a promoter. A cluster of genes that share the same promoter is called an operon, found mainly in prokaryotes and some lower eukaryotes (e.g., Caenorhabditis elegans). In positive regulation of gene expression, the activator is the transcription factor that stimulates transcription when it binds to the sequence near or at the promoter. Negative regulation occurs when another transcription factor called a repressor binds to a DNA sequence called an operator, which is part of an operon, to prevent transcription. Repressors can be inhibited by compounds called inducers (e.g., allolactose), thereby allowing transcription to occur. Specific genes that can be activated by inducers are called inducible genes, in contrast to constitutive genes that are almost constantly active. In contrast to both, structural genes encode proteins that are not involved in gene regulation. In addition to regulatory events involving the promoter, gene expression can also be regulated by epigenetic changes to chromatin, which is a complex of DNA and protein found in eukaryotic cells. === Genes, development, and evolution === Development is the process by which a multicellular organism (plant or animal) goes through a series of changes, starting from a single cell, and taking on various forms that are characteristic of its life cycle. There are four key processes that underlie development: Determination, differentiation, morphogenesis, and growth. Determination sets the developmental fate of a cell, which becomes more restrictive during development. Differentiation is the process by which specialized cells arise from less specialized cells such as stem cells. Stem cells are undifferentiated or partially differentiated cells that can differentiate into various types of cells and proliferate indefinitely to produce more of the same stem cell. Cellular differentiation dramatically changes a cell's size, shape, membrane potential, metabolic activity, and responsiveness to signals, which are largely due to highly controlled modifications in gene expression and epigenetics. With a few exceptions, cellular differentiation almost never involves a change in the DNA sequence itself. Thus, different cells can have very different physical characteristics despite having the same genome. Morphogenesis, or the development of body form, is the result of spatial differences in gene expression. A small fraction of the genes in an organism's genome called the developmental-genetic toolkit control the development of that organism. These toolkit genes are highly conserved among phyla, meaning that they are ancient and very similar in widely separated groups of animals. Differences in deployment of toolkit genes affect the body plan and the number, identity, and pattern of body parts. Among the most important toolkit genes are the Hox genes. Hox genes determine where repeating parts, such as the many vertebrae of snakes, will grow in a developing embryo or larva. == Evolution == === Evolutionary processes === Evolution is a central organizing concept in biology. It is the change in heritable characteristics of populations over successive generations. In artificial selection, animals were selectively bred for specific traits. Given that traits are inherited, populations contain a varied mix of traits, and reproduction is able to increase any population, Darwin argued that in the natural world, it was nature that played the role of humans in selecting for specific traits. Darwin inferred that individuals who possessed heritable traits better adapted to their environments are more likely to survive and produce more offspring than other individuals. He further inferred that this would lead to the accumulation of favorable traits over successive generations, thereby increasing the match between the organisms and their environment. === Speciation === A species is a group of organisms that mate with one another and speciation is the process by which one lineage splits into two lineages as a result of having evolved independently from each other. For speciation to occur, there has to be reproductive isolation. Reproductive isolation can result from incompatibilities between genes as described by Bateson–Dobzhansky–Muller model. Reproductive isolation also tends to increase with genetic divergence. Speciation can occur when there are physical barriers that divide an ancestral species, a process known as allopatric speciation. === Phylogeny === A phylogeny is an evolutionary history of a specific group of organisms or their genes. It can be represented using a phylogenetic tree, a diagram showing lines of descent among organisms or their genes. Each line drawn on the time axis of a tree represents a lineage of descendants of a particular species or population. When a lineage divides into two, it is represented as a fork or split on the phylogenetic tree. Phylogenetic trees are the basis for comparing and grouping different species. Different species that share a feature inherited from a common ancestor are described as having homologous features (or synapomorphy). Phylogeny provides the basis of biological classification. This classification system is rank-based, with the highest rank being the domain followed by kingdom, phylum, class, order, family, genus, and species. All organisms can be classified as belonging to one of three domains: Archaea (originally Archaebacteria), Bacteria (originally eubacteria), or Eukarya (includes the fungi, plant, and animal kingdoms). === History of life === The history of life on Earth traces how organisms have evolved from the earliest emergence of life to present day. Earth formed about 4.5 billion years ago and all life on Earth, both living and extinct, descended from a last universal common ancestor that lived about 3.5 billion years ago. Geologists have developed a geologic time scale that divides the history of the Earth into major divisions, starting with four eons (Hadean, Archean, Proterozoic, and Phanerozoic), the first three of which are collectively known as the Precambrian, which lasted approximately 4 billion years. Each eon can be divided into eras, with the Phanerozoic eon that began 539 million years ago being subdivided into Paleozoic, Mesozoic, and Cenozoic eras. These three eras together comprise eleven periods (Cambrian, Ordovician, Silurian, Devonian, Carboniferous, Permian, Triassic, Jurassic, Cretaceous, Tertiary, and Quaternary). The similarities among all known present-day species indicate that they have diverged through the process of evolution from their common ancestor. Biologists regard the ubiquity of the genetic code as evidence of universal common descent for all bacteria, archaea, and eukaryotes. Microbial mats of coexisting bacteria and archaea were the dominant form of life in the early Archean eon and many of the major steps in early evolution are thought to have taken place in this environment. The earliest evidence of eukaryotes dates from 1.85 billion years ago, and while they may have been present earlier, their diversification accelerated when they started using oxygen in their metabolism. Later, around 1.7 billion years ago, multicellular organisms began to appear, with differentiated cells performing specialised functions. Algae-like multicellular land plants are dated back to about 1 billion years ago, although evidence suggests that microorganisms formed the earliest terrestrial ecosystems, at least 2.7 billion years ago. Microorganisms are thought to have paved the way for the inception of land plants in the Ordovician period. Land plants were so successful that they are thought to have contributed to the Late Devonian extinction event. Ediacara biota appear during the Ediacaran period, while vertebrates, along with most other modern phyla originated about 525 million years ago during the Cambrian explosion. During the Permian period, synapsids, including the ancestors of mammals, dominated the land, but most of this group became extinct in the Permian–Triassic extinction event 252 million years ago. During the recovery from this catastrophe, archosaurs became the most abundant land vertebrates; one archosaur group, the dinosaurs, dominated the Jurassic and Cretaceous periods. After the Cretaceous–Paleogene extinction event 66 million years ago killed off the non-avian dinosaurs, mammals increased rapidly in size and diversity. Such mass extinctions may have accelerated evolution by providing opportunities for new groups of organisms to diversify. == Diversity == === Bacteria and Archaea === Bacteria are a type of cell that constitute a large domain of prokaryotic microorganisms. Typically a few micrometers in length, bacteria have a number of shapes, ranging from spheres to rods and spirals. Bacteria were among the first life forms to appear on Earth, and are present in most of its habitats. Bacteria inhabit soil, water, acidic hot springs, radioactive waste, and the deep biosphere of the Earth's crust. Bacteria also live in symbiotic and parasitic relationships with plants and animals. Most bacteria have not been characterised, and only about 27 percent of the bacterial phyla have species that can be grown in the laboratory. Archaea constitute the other domain of prokaryotic cells and were initially classified as bacteria, receiving the name archaebacteria (in the Archaebacteria kingdom), a term that has fallen out of use. Archaeal cells have unique properties separating them from the other two domains, Bacteria and Eukaryota. Archaea are further divided into multiple recognized phyla. Archaea and bacteria are generally similar in size and shape, although a few archaea have very different shapes, such as the flat and square cells of Haloquadratum walsbyi. Despite this morphological similarity to bacteria, archaea possess genes and several metabolic pathways that are more closely related to those of eukaryotes, notably for the enzymes involved in transcription and translation. Other aspects of archaeal biochemistry are unique, such as their reliance on ether lipids in their cell membranes, including archaeols. Archaea use more energy sources than eukaryotes: these range from organic compounds, such as sugars, to ammonia, metal ions or even hydrogen gas. Salt-tolerant archaea (the Haloarchaea) use sunlight as an energy source, and other species of archaea fix carbon, but unlike plants and cyanobacteria, no known species of archaea does both. Archaea reproduce asexually by binary fission, fragmentation, or budding; unlike bacteria, no known species of Archaea form endospores. The first observed archaea were extremophiles, living in extreme environments, such as hot springs and salt lakes with no other organisms. Improved molecular detection tools led to the discovery of archaea in almost every habitat, including soil, oceans, and marshlands. Archaea are particularly numerous in the oceans, and the archaea in plankton may be one of the most abundant groups of organisms on the planet. Archaea are a major part of Earth's life. They are part of the microbiota of all organisms. In the human microbiome, they are important in the gut, mouth, and on the skin. Their morphological, metabolic, and geographical diversity permits them to play multiple ecological roles: carbon fixation; nitrogen cycling; organic compound turnover; and maintaining microbial symbiotic and syntrophic communities, for example. === Eukaryotes === Eukaryotes are hypothesized to have split from archaea, which was followed by their endosymbioses with bacteria (or symbiogenesis) that gave rise to mitochondria and chloroplasts, both of which are now part of modern-day eukaryotic cells. The major lineages of eukaryotes diversified in the Precambrian about 1.5 billion years ago and can be classified into eight major clades: alveolates, excavates, stramenopiles, plants, rhizarians, amoebozoans, fungi, and animals. Five of these clades are collectively known as protists, which are mostly microscopic eukaryotic organisms that are not plants, fungi, or animals. While it is likely that protists share a common ancestor (the last eukaryotic common ancestor), protists by themselves do not constitute a separate clade as some protists may be more closely related to plants, fungi, or animals than they are to other protists. Like groupings such as algae, invertebrates, or protozoans, the protist grouping is not a formal taxonomic group but is used for convenience. Most protists are unicellular; these are called microbial eukaryotes. Plants are mainly multicellular organisms, predominantly photosynthetic eukaryotes of the kingdom Plantae, which would exclude fungi and some algae. Plant cells were derived by endosymbiosis of a cyanobacterium into an early eukaryote about one billion years ago, which gave rise to chloroplasts. The first several clades that emerged following primary endosymbiosis were aquatic and most of the aquatic photosynthetic eukaryotic organisms are collectively described as algae, which is a term of convenience as not all algae are closely related. Algae comprise several distinct clades such as glaucophytes, which are microscopic freshwater algae that may have resembled in form to the early unicellular ancestor of Plantae. Unlike glaucophytes, the other algal clades such as red and green algae are multicellular. Green algae comprise three major clades: chlorophytes, coleochaetophytes, and stoneworts. Fungi are eukaryotes that digest foods outside their bodies, secreting digestive enzymes that break down large food molecules before absorbing them through their cell membranes. Many fungi are also saprobes, feeding on dead organic matter, making them important decomposers in ecological systems. Animals are multicellular eukaryotes. With few exceptions, animals consume organic material, breathe oxygen, are able to move, can reproduce sexually, and grow from a hollow sphere of cells, the blastula, during embryonic development. Over 1.5 million living animal species have been described—of which around 1 million are insects—but it has been estimated there are over 7 million animal species in total. They have complex interactions with each other and their environments, forming intricate food webs. === Viruses === Viruses are submicroscopic infectious agents that replicate inside the cells of organisms. Viruses infect all types of life forms, from animals and plants to microorganisms, including bacteria and archaea. More than 6,000 virus species have been described in detail. Viruses are found in almost every ecosystem on Earth and are the most numerous type of biological entity. The origins of viruses in the evolutionary history of life are unclear: some may have evolved from plasmids—pieces of DNA that can move between cells—while others may have evolved from bacteria. In evolution, viruses are an important means of horizontal gene transfer, which increases genetic diversity in a way analogous to sexual reproduction. Because viruses possess some but not all characteristics of life, they have been described as "organisms at the edge of life", and as self-replicators. == Ecology == Ecology is the study of the distribution and abundance of life, the interaction between organisms and their environment. === Ecosystems === The community of living (biotic) organisms in conjunction with the nonliving (abiotic) components (e.g., water, light, radiation, temperature, humidity, atmosphere, acidity, and soil) of their environment is called an ecosystem. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy from the sun enters the system through photosynthesis and is incorporated into plant tissue. By feeding on plants and on one another, animals move matter and energy through the system. They also influence the quantity of plant and microbial biomass present. By breaking down dead organic matter, decomposers release carbon back to the atmosphere and facilitate nutrient cycling by converting nutrients stored in dead biomass back to a form that can be readily used by plants and other microbes. === Populations === A population is the group of organisms of the same species that occupies an area and reproduce from generation to generation. Population size can be estimated by multiplying population density by the area or volume. The carrying capacity of an environment is the maximum population size of a species that can be sustained by that specific environment, given the food, habitat, water, and other resources that are available. The carrying capacity of a population can be affected by changing environmental conditions such as changes in the availability of resources and the cost of maintaining them. In human populations, new technologies such as the Green revolution have helped increase the Earth's carrying capacity for humans over time, which has stymied the attempted predictions of impending population decline, the most famous of which was by Thomas Malthus in the 18th century. === Communities === A community is a group of populations of species occupying the same geographical area at the same time. A biological interaction is the effect that a pair of organisms living together in a community have on each other. They can be either of the same species (intraspecific interactions), or of different species (interspecific interactions). These effects may be short-term, like pollination and predation, or long-term; both often strongly influence the evolution of the species involved. A long-term interaction is called a symbiosis. Symbioses range from mutualism, beneficial to both partners, to competition, harmful to both partners. Every species participates as a consumer, resource, or both in consumer–resource interactions, which form the core of food chains or food webs. There are different trophic levels within any food web, with the lowest level being the primary producers (or autotrophs) such as plants and algae that convert energy and inorganic material into organic compounds, which can then be used by the rest of the community. At the next level are the heterotrophs, which are the species that obtain energy by breaking apart organic compounds from other organisms. Heterotrophs that consume plants are primary consumers (or herbivores) whereas heterotrophs that consume herbivores are secondary consumers (or carnivores). And those that eat secondary consumers are tertiary consumers and so on. Omnivorous heterotrophs are able to consume at multiple levels. Finally, there are decomposers that feed on the waste products or dead bodies of organisms. On average, the total amount of energy incorporated into the biomass of a trophic level per unit of time is about one-tenth of the energy of the trophic level that it consumes. Waste and dead material used by decomposers as well as heat lost from metabolism make up the other ninety percent of energy that is not consumed by the next trophic level. === Biosphere === In the global ecosystem or biosphere, matter exists as different interacting compartments, which can be biotic or abiotic as well as accessible or inaccessible, depending on their forms and locations. For example, matter from terrestrial autotrophs are both biotic and accessible to other organisms whereas the matter in rocks and minerals are abiotic and inaccessible. A biogeochemical cycle is a pathway by which specific elements of matter are turned over or moved through the biotic (biosphere) and the abiotic (lithosphere, atmosphere, and hydrosphere) compartments of Earth. There are biogeochemical cycles for nitrogen, carbon, and water. === Conservation === Conservation biology is the study of the conservation of Earth's biodiversity with the aim of protecting species, their habitats, and ecosystems from excessive rates of extinction and the erosion of biotic interactions. It is concerned with factors that influence the maintenance, loss, and restoration of biodiversity and the science of sustaining evolutionary processes that engender genetic, population, species, and ecosystem diversity. The concern stems from estimates suggesting that up to 50% of all species on the planet will disappear within the next 50 years, which has contributed to poverty, starvation, and will reset the course of evolution on this planet. Biodiversity affects the functioning of ecosystems, which provide a variety of services upon which people depend. Conservation biologists research and educate on the trends of biodiversity loss, species extinctions, and the negative effect these are having on our capabilities to sustain the well-being of human society. Organizations and citizens are responding to the current biodiversity crisis through conservation action plans that direct research, monitoring, and education programs that engage concerns at local through global scales. == See also == == References == == Further reading == == External links == OSU's Phylocode Biology Online – Wiki Dictionary MIT video lecture series on biology OneZoom Tree of Life Journal of the History of Biology (springer.com) Journal links PLOS ONE PLOS Biology A peer-reviewed, open-access journal published by the Public Library of Science Current Biology: General journal publishing original research from all areas of biology Biology Letters: A high-impact Royal Society journal publishing peer-reviewed biology papers of general interest Science: Internationally renowned AAAS science journal – see sections of the life sciences International Journal of Biological Sciences: A biological journal publishing significant peer-reviewed scientific papers Perspectives in Biology and Medicine: An interdisciplinary scholarly journal publishing essays of broad relevance
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Science is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. Science is based in Washington, D.C., United States, with a second office in Cambridge, UK. == Contents == The major focus of the journal is publishing important original scientific research and research reviews, but Science also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, Science and its rival Nature cover the full range of scientific disciplines. According to the Journal Citation Reports, Science's 2023 impact factor was 44.7. Studies of methodological quality and reliability have found that some high-prestige journals including Science "publish significantly substandard structures", and overall "reliability of published research works in several fields may be decreasing with increasing journal rank". Although it is the journal of the AAAS, membership in the AAAS is not required to publish in Science. Papers are accepted from authors around the world. Competition to publish in Science is very intense, as an article published in such a highly cited journal can lead to attention and career advancement for the authors. Fewer than 7% of articles submitted are accepted for publication. == History == Science was founded by New York journalist John Michels in 1880 with financial support from Thomas Edison and later from Alexander Graham Bell. (Edison received favorable editorial treatment in return, without disclosure of the financial relationship, at a time when his reputation was suffering due to delays producing the promised commercially viable light bulb.) However, the journal never gained enough subscribers to succeed and ended publication in March 1882. Alexander Graham Bell and Gardiner Greene Hubbard bought the magazine rights and hired young entomologist Samuel H. Scudder to resurrect the journal one year later. They had some success while covering the meetings of prominent American scientific societies, including the AAAS. However, by 1894, Science was again in financial difficulty and was sold to psychologist James McKeen Cattell for $500 (equivalent to $18,170 in 2024). In an agreement worked out by Cattell and AAAS secretary Leland O. Howard, Science became the journal of the American Association for the Advancement of Science in 1900. During the early part of the 20th century, important articles published in Science included papers on fruit fly genetics by Thomas Hunt Morgan, gravitational lensing by Albert Einstein, and spiral nebulae by Edwin Hubble. After Cattell died in 1944, the ownership of the journal was transferred to the AAAS. After Cattell's death in 1944, the journal lacked a consistent editorial presence until Graham DuShane became editor in 1956. In 1958, under DuShane's leadership, Science absorbed The Scientific Monthly, thus increasing the journal's circulation by over 62% from 38,000 to more than 61,000. Physicist Philip Abelson, a co-discoverer of neptunium, served as editor from 1962 to 1984. Under Abelson the efficiency of the review process was improved and the publication practices were brought up to date. During this time, papers on the Apollo program missions and some of the earliest reports on AIDS were published. Biochemist Daniel E. Koshland Jr. served as editor from 1985 until 1995. From 1995 until 2000, neuroscientist Floyd E. Bloom held that position. Biologist Donald Kennedy became the editor of Science in 2000. Biochemist Bruce Alberts took his place in March 2008. Geophysicist Marcia McNutt became editor-in-chief in June 2013. During her tenure the family of journals expanded to include Science Robotics and Science Immunology, and open access publishing with Science Advances. Jeremy M. Berg became editor-in-chief on July 1, 2016. Former Washington University in St. Louis Provost Holden Thorp was named editor-in-chief on Monday, August 19, 2019. In February 2001, draft results of the human genome were simultaneously published by Nature and Science with Science publishing the Celera Genomics paper and Nature publishing the publicly funded Human Genome Project. In 2007, Science (together with Nature) received the Prince of Asturias Award for Communications and Humanity. In 2015, Rush D. Holt Jr., chief executive officer of the AAAS and executive publisher of Science, stated that the journal was becoming increasingly international: "[I]nternationally co-authored papers are now the norm—they represent almost 60 percent of the papers. In 1992, it was slightly less than 20 percent." == Availability == The latest editions of the journal are available online, through the main journal website, only to subscribers, AAAS members, and for delivery to IP addresses at institutions that subscribe; students, K–12 teachers, and some others can subscribe at a reduced fee. However, research articles published after 1997 are available free (with online registration) one year after they are published i.e. delayed open access. Significant public-health related articles are also available free, sometimes immediately after publication. AAAS members may also access the pre-1997 Science archives at the Science website, where it is called "Science Classic". The journal also participates in initiatives that provide free or low-cost access to readers in developing countries, including HINARI, OARE, AGORA, and Scidev.net. Other features of the Science website include the free "ScienceNow" section with "up to the minute news from science", and "ScienceCareers", which provides free career resources for scientists and engineers. Science Express (Sciencexpress) provides advance electronic publication of selected Science papers. == Affiliations == Science received funding for COVID-19-related coverage from the Pulitzer Center and the Heising-Simons Foundation. == See also == AAAS publications Breakthrough of the Year List of scientific journals == References == === AAAS references === == External links == Official website
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https://en.wikipedia.org/wiki/Science_(journal)
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In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer. == Value and representation == The value of an item with an integral type is the mathematical integer that it corresponds to. Integral types may be unsigned (capable of representing only non-negative integers) or signed (capable of representing negative integers as well). An integer value is typically specified in the source code of a program as a sequence of digits optionally prefixed with + or −. Some programming languages allow other notations, such as hexadecimal (base 16) or octal (base 8). Some programming languages also permit digit group separators. The internal representation of this datum is the way the value is stored in the computer's memory. Unlike mathematical integers, a typical datum in a computer has some minimal and maximum possible value. The most common representation of a positive integer is a string of bits, using the binary numeral system. The order of the memory bytes storing the bits varies; see endianness. The width, precision, or bitness of an integral type is the number of bits in its representation. An integral type with n bits can encode 2n numbers; for example an unsigned type typically represents the non-negative values 0 through 2n − 1. Other encodings of integer values to bit patterns are sometimes used, for example binary-coded decimal or Gray code, or as printed character codes such as ASCII. There are four well-known ways to represent signed numbers in a binary computing system. The most common is two's complement, which allows a signed integral type with n bits to represent numbers from −2(n−1) through 2(n−1) − 1. Two's complement arithmetic is convenient because there is a perfect one-to-one correspondence between representations and values (in particular, no separate +0 and −0), and because addition, subtraction and multiplication do not need to distinguish between signed and unsigned types. Other possibilities include offset binary, sign-magnitude, and ones' complement. Some computer languages define integer sizes in a machine-independent way; others have varying definitions depending on the underlying processor word size. Not all language implementations define variables of all integer sizes, and defined sizes may not even be distinct in a particular implementation. An integer in one programming language may be a different size in a different language, on a different processor, or in an execution context of different bitness; see § Words. Some older computer architectures used decimal representations of integers, stored in binary-coded decimal (BCD) or other format. These values generally require data sizes of 4 bits per decimal digit (sometimes called a nibble), usually with additional bits for a sign. Many modern CPUs provide limited support for decimal integers as an extended datatype, providing instructions for converting such values to and from binary values. Depending on the architecture, decimal integers may have fixed sizes (e.g., 7 decimal digits plus a sign fit into a 32-bit word), or may be variable-length (up to some maximum digit size), typically occupying two digits per byte (octet). == Common integral data types == Different CPUs support different integral data types. Typically, hardware will support both signed and unsigned types, but only a small, fixed set of widths. The table above lists integral type widths that are supported in hardware by common processors. High-level programming languages provide more possibilities. It is common to have a 'double width' integral type that has twice as many bits as the biggest hardware-supported type. Many languages also have bit-field types (a specified number of bits, usually constrained to be less than the maximum hardware-supported width) and range types (that can represent only the integers in a specified range). Some languages, such as Lisp, Smalltalk, REXX, Haskell, Python, and Raku, support arbitrary precision integers (also known as infinite precision integers or bignums). Other languages that do not support this concept as a top-level construct may have libraries available to represent very large numbers using arrays of smaller variables, such as Java's BigInteger class or Perl's "bigint" package. These use as much of the computer's memory as is necessary to store the numbers; however, a computer has only a finite amount of storage, so they, too, can only represent a finite subset of the mathematical integers. These schemes support very large numbers; for example one kilobyte of memory could be used to store numbers up to 2466 decimal digits long. A Boolean type is a type that can represent only two values: 0 and 1, usually identified with false and true respectively. This type can be stored in memory using a single bit, but is often given a full byte for convenience of addressing and speed of access. A four-bit quantity is known as a nibble (when eating, being smaller than a bite) or nybble (being a pun on the form of the word byte). One nibble corresponds to one digit in hexadecimal and holds one digit or a sign code in binary-coded decimal. === Bytes and octets === The term byte initially meant 'the smallest addressable unit of memory'. In the past, 5-, 6-, 7-, 8-, and 9-bit bytes have all been used. There have also been computers that could address individual bits ('bit-addressed machine'), or that could only address 16- or 32-bit quantities ('word-addressed machine'). The term byte was usually not used at all in connection with bit- and word-addressed machines. The term octet always refers to an 8-bit quantity. It is mostly used in the field of computer networking, where computers with different byte widths might have to communicate. In modern usage byte almost invariably means eight bits, since all other sizes have fallen into disuse; thus byte has come to be synonymous with octet. === Words === The term 'word' is used for a small group of bits that are handled simultaneously by processors of a particular architecture. The size of a word is thus CPU-specific. Many different word sizes have been used, including 6-, 8-, 12-, 16-, 18-, 24-, 32-, 36-, 39-, 40-, 48-, 60-, and 64-bit. Since it is architectural, the size of a word is usually set by the first CPU in a family, rather than the characteristics of a later compatible CPU. The meanings of terms derived from word, such as longword, doubleword, quadword, and halfword, also vary with the CPU and OS. Practically all new desktop processors are capable of using 64-bit words, though embedded processors with 8- and 16-bit word size are still common. The 36-bit word length was common in the early days of computers. One important cause of non-portability of software is the incorrect assumption that all computers have the same word size as the computer used by the programmer. For example, if a programmer using the C language incorrectly declares as int a variable that will be used to store values greater than 215−1, the program will fail on computers with 16-bit integers. That variable should have been declared as long, which has at least 32 bits on any computer. Programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information, which may work on (some) 32-bit computers, but fail on 64-bit computers with 64-bit pointers and 32-bit integers. This issue is resolved by C99 in stdint.h in the form of intptr_t. The bitness of a program may refer to the word size (or bitness) of the processor on which it runs, or it may refer to the width of a memory address or pointer, which can differ between execution modes or contexts. For example, 64-bit versions of Microsoft Windows support existing 32-bit binaries, and programs compiled for Linux's x32 ABI run in 64-bit mode yet use 32-bit memory addresses. === Standard integer === The standard integer size is platform-dependent. In C, it is denoted by int and required to be at least 16 bits. Windows and Unix systems have 32-bit ints on both 32-bit and 64-bit architectures. === Short integer === A short integer can represent a whole number that may take less storage, while having a smaller range, compared with a standard integer on the same machine. In C, it is denoted by short. It is required to be at least 16 bits, and is often smaller than a standard integer, but this is not required. A conforming program can assume that it can safely store values between −(215−1) and 215−1, but it may not assume that the range is not larger. In Java, a short is always a 16-bit integer. In the Windows API, the datatype SHORT is defined as a 16-bit signed integer on all machines. === Long integer === A long integer can represent a whole integer whose range is greater than or equal to that of a standard integer on the same machine. In C, it is denoted by long. It is required to be at least 32 bits, and may or may not be larger than a standard integer. A conforming program can assume that it can safely store values between −(231−1) and 231−1, but it may not assume that the range is not larger. === Long long === In the C99 version of the C programming language and the C++11 version of C++, a long long type is supported that has double the minimum capacity of the standard long. This type is not supported by compilers that require C code to be compliant with the previous C++ standard, C++03, because the long long type did not exist in C++03. For an ANSI/ISO compliant compiler, the minimum requirements for the specified ranges, that is, −(263−1) to 263−1 for signed and 0 to 264−1 for unsigned, must be fulfilled; however, extending this range is permitted. This can be an issue when exchanging code and data between platforms, or doing direct hardware access. Thus, there are several sets of headers providing platform independent exact width types. The C standard library provides stdint.h; this was introduced in C99 and C++11. == Syntax == Integer literals can be written as regular Arabic numerals, consisting of a sequence of digits and with negation indicated by a minus sign before the value. However, most programming languages disallow use of commas or spaces for digit grouping. Examples of integer literals are: 42 10000 -233000 There are several alternate methods for writing integer literals in many programming languages: Many programming languages, especially those influenced by C, prefix an integer literal with 0X or 0x to represent a hexadecimal value, e.g. 0xDEADBEEF. Other languages may use a different notation, e.g. some assembly languages append an H or h to the end of a hexadecimal value. Perl, Ruby, Java, Julia, D, Go, C#, Rust, Python (starting from version 3.6), and PHP (from version 7.4.0 onwards) allow embedded underscores for clarity, e.g. 10_000_000, and fixed-form Fortran ignores embedded spaces in integer literals. C (starting from C23) and C++ use single quotes for this purpose. In C and C++, a leading zero indicates an octal value, e.g. 0755. This was primarily intended to be used with Unix modes; however, it has been criticized because normal integers may also lead with zero. As such, Python, Ruby, Haskell, and OCaml prefix octal values with 0O or 0o, following the layout used by hexadecimal values. Several languages, including Java, C#, Scala, Python, Ruby, OCaml, C (starting from C23) and C++ can represent binary values by prefixing a number with 0B or 0b. == Extreme values == In many programming languages, there exist predefined constants representing the least and the greatest values representable with a given integer type. Names for these include SmallBASIC: MAXINT Java: java.lang.Integer.MAX_VALUE, java.lang.Integer.MIN_VALUE Corresponding fields exist for the other integer classes in Java. C: INT_MAX, etc. GLib: G_MININT, G_MAXINT, G_MAXUINT, ... Haskell: minBound, maxBound Pascal: MaxInt Python 2: sys.maxint Turing: maxint == See also == Arbitrary-precision arithmetic Binary-coded decimal (BCD) C data types Integer overflow Signed number representations == Notes == == References ==
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https://en.wikipedia.org/wiki/Integer_(computer_science)
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"Unified Science" can refer to any of three related strands in contemporary thought. Belief in the unity of science was a central tenet of logical positivism. Different logical positivists construed this doctrine in several different ways, e.g. as a reductionist thesis, that the objects investigated by the special sciences reduce to the objects of a common, putatively more basic domain of science, usually thought to be physics; as the thesis that all of the theories and results of the various sciences can or ought to be expressed in a common language or "universal slang"; or as the thesis that all the special sciences share a common method. The writings of Edward Haskell and a few associates, seeking to rework science into a single discipline employing a common artificial language. This work culminated in the 1972 publication of Full Circle: The Moral Force of Unified Science. The vast part of the work of Haskell and his contemporaries remains unpublished, however. Timothy Wilken and Anthony Judge have recently revived and extended the insights of Haskell and his coworkers. Unified Science has been a consistent thread since the 1940s in Howard T. Odum's systems ecology and the associated Emergy Synthesis, modeling the "ecosystem": the geochemical, biochemical, and thermodynamic processes of the lithosphere and biosphere. Modeling such earthly processes in this manner requires a science uniting geology, physics, biology, and chemistry (H.T.Odum 1995). With this in mind, Odum developed a common language of science based on electronic schematics, with applications to ecology economic systems in mind (H.T.Odum 1994). == See also == Consilience — the unification of knowledge, e.g. science and the humanities Tree of knowledge system == References == Odum, H.T. 1994. Ecological and General Systems: An Introduction to Systems Ecology. Colorado University Press, Colorado. Odum, H.T. 1995. 'Energy Systems and the Unification of Science', in Hall, C.S. (ed.) Maximum Power: The Ideas and Applications of H.T. Odum. Colorado University Press, Colorado: 365-372. == External links == Future Positive Timothy Wilken's website, including a lot of material and diagrams on Edward Haskell's Unified Science Cardioid Attractor Fundamental to Sustainability - 8 transactional games forming the heart of sustainable relationship Anthony Judge's further development of these ideas
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https://en.wikipedia.org/wiki/Unified_Science
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Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature or—in modern mathematics—purely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a proof consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then, the interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics. == Areas of mathematics == Before the Renaissance, mathematics was divided into two main areas: arithmetic, regarding the manipulation of numbers, and geometry, regarding the study of shapes. Some types of pseudoscience, such as numerology and astrology, were not then clearly distinguished from mathematics. During the Renaissance, two more areas appeared. Mathematical notation led to algebra which, roughly speaking, consists of the study and the manipulation of formulas. Calculus, consisting of the two subfields differential calculus and integral calculus, is the study of continuous functions, which model the typically nonlinear relationships between varying quantities, as represented by variables. This division into four main areas—arithmetic, geometry, algebra, and calculus—endured until the end of the 19th century. Areas such as celestial mechanics and solid mechanics were then studied by mathematicians, but now are considered as belonging to physics. The subject of combinatorics has been studied for much of recorded history, yet did not become a separate branch of mathematics until the seventeenth century. At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. Some of these areas correspond to the older division, as is true regarding number theory (the modern name for higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra and calculus do not appear as first-level areas but are respectively split into several first-level areas. Other first-level areas emerged during the 20th century or had not previously been considered as mathematics, such as mathematical logic and foundations. === Number theory === Number theory began with the manipulation of numbers, that is, natural numbers ( N ) , {\displaystyle (\mathbb {N} ),} and later expanded to integers ( Z ) {\displaystyle (\mathbb {Z} )} and rational numbers ( Q ) . {\displaystyle (\mathbb {Q} ).} Number theory was once called arithmetic, but nowadays this term is mostly used for numerical calculations. Number theory dates back to ancient Babylon and probably China. Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler. The field came to full fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss. Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem. This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles, who used tools including scheme theory from algebraic geometry, category theory, and homological algebra. Another example is Goldbach's conjecture, which asserts that every even integer greater than 2 is the sum of two prime numbers. Stated in 1742 by Christian Goldbach, it remains unproven despite considerable effort. Number theory includes several subareas, including analytic number theory, algebraic number theory, geometry of numbers (method oriented), diophantine equations, and transcendence theory (problem oriented). === Geometry === Geometry is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines, angles and circles, which were developed mainly for the needs of surveying and architecture, but has since blossomed out into many other subfields. A fundamental innovation was the ancient Greeks' introduction of the concept of proofs, which require that every assertion must be proved. For example, it is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results (theorems) and a few basic statements. The basic statements are not subject to proof because they are self-evident (postulates), or are part of the definition of the subject of study (axioms). This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane (plane geometry) and the three-dimensional Euclidean space. Euclidean geometry was developed without change of methods or scope until the 17th century, when René Descartes introduced what is now called Cartesian coordinates. This constituted a major change of paradigm: Instead of defining real numbers as lengths of line segments (see number line), it allowed the representation of points using their coordinates, which are numbers. Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. Analytic geometry allows the study of curves unrelated to circles and lines. Such curves can be defined as the graph of functions, the study of which led to differential geometry. They can also be defined as implicit equations, often polynomial equations (which spawned algebraic geometry). Analytic geometry also makes it possible to consider Euclidean spaces of higher than three dimensions. In the 19th century, mathematicians discovered non-Euclidean geometries, which do not follow the parallel postulate. By questioning that postulate's truth, this discovery has been viewed as joining Russell's paradox in revealing the foundational crisis of mathematics. This aspect of the crisis was solved by systematizing the axiomatic method, and adopting that the truth of the chosen axioms is not a mathematical problem. In turn, the axiomatic method allows for the study of various geometries obtained either by changing the axioms or by considering properties that do not change under specific transformations of the space. Today's subareas of geometry include: Projective geometry, introduced in the 16th century by Girard Desargues, extends Euclidean geometry by adding points at infinity at which parallel lines intersect. This simplifies many aspects of classical geometry by unifying the treatments for intersecting and parallel lines. Affine geometry, the study of properties relative to parallelism and independent from the concept of length. Differential geometry, the study of curves, surfaces, and their generalizations, which are defined using differentiable functions. Manifold theory, the study of shapes that are not necessarily embedded in a larger space. Riemannian geometry, the study of distance properties in curved spaces. Algebraic geometry, the study of curves, surfaces, and their generalizations, which are defined using polynomials. Topology, the study of properties that are kept under continuous deformations. Algebraic topology, the use in topology of algebraic methods, mainly homological algebra. Discrete geometry, the study of finite configurations in geometry. Convex geometry, the study of convex sets, which takes its importance from its applications in optimization. Complex geometry, the geometry obtained by replacing real numbers with complex numbers. === Algebra === Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra. Diophantus solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. Al-Khwarizmi introduced systematic methods for transforming equations, such as moving a term from one side of an equation into the other side. The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. Variables allow mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas. Until the 19th century, algebra consisted mainly of the study of linear equations (presently linear algebra), and polynomial equations in a single unknown, which were called algebraic equations (a term still in use, although it may be ambiguous). During the 19th century, mathematicians began to use variables to represent things other than numbers (such as matrices, modular integers, and geometric transformations), on which generalizations of arithmetic operations are often valid. The concept of algebraic structure addresses this, consisting of a set whose elements are unspecified, of operations acting on the elements of the set, and rules that these operations must follow. The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether, and popularized by Van der Waerden's book Moderne Algebra. Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: group theory field theory vector spaces, whose study is essentially the same as linear algebra ring theory commutative algebra, which is the study of commutative rings, includes the study of polynomials, and is a foundational part of algebraic geometry homological algebra Lie algebra and Lie group theory Boolean algebra, which is widely used for the study of the logical structure of computers The study of types of algebraic structures as mathematical objects is the purpose of universal algebra and category theory. The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces; this particular area of application is called algebraic topology. === Calculus and analysis === Calculus, formerly called infinitesimal calculus, was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz. It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by Euler with the introduction of the concept of a function and many other results. Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis" is commonly used for advanced parts. Analysis is further subdivided into real analysis, where variables represent real numbers, and complex analysis, where variables represent complex numbers. Analysis includes many subareas shared by other areas of mathematics which include: Multivariable calculus Functional analysis, where variables represent varying functions Integration, measure theory and potential theory, all strongly related with probability theory on a continuum Ordinary differential equations Partial differential equations Numerical analysis, mainly devoted to the computation on computers of solutions of ordinary and partial differential equations that arise in many applications === Discrete mathematics === Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms—especially their implementation and computational complexity—play a major role in discrete mathematics. The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems. Discrete mathematics includes: Combinatorics, the art of enumerating mathematical objects that satisfy some given constraints. Originally, these objects were elements or subsets of a given set; this has been extended to various objects, which establishes a strong link between combinatorics and other parts of discrete mathematics. For example, discrete geometry includes counting configurations of geometric shapes. Graph theory and hypergraphs Coding theory, including error correcting codes and a part of cryptography Matroid theory Discrete geometry Discrete probability distributions Game theory (although continuous games are also studied, most common games, such as chess and poker are discrete) Discrete optimization, including combinatorial optimization, integer programming, constraint programming === Mathematical logic and set theory === The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians. Before Cantor's study of infinite sets, mathematicians were reluctant to consider actually infinite collections, and considered infinity to be the result of endless enumeration. Cantor's work offended many mathematicians not only by considering actually infinite sets but by showing that this implies different sizes of infinity, per Cantor's diagonal argument. This led to the controversy over Cantor's set theory. In the same period, various areas of mathematics concluded the former intuitive definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour. This became the foundational crisis of mathematics. It was eventually solved in mainstream mathematics by systematizing the axiomatic method inside a formalized set theory. Roughly speaking, each mathematical object is defined by the set of all similar objects and the properties that these objects must have. For example, in Peano arithmetic, the natural numbers are defined by "zero is a number", "each number has a unique successor", "each number but zero has a unique predecessor", and some rules of reasoning. This mathematical abstraction from reality is embodied in the modern philosophy of formalism, as founded by David Hilbert around 1910. The "nature" of the objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs. The approach allows considering "logics" (that is, sets of allowed deducing rules), theorems, proofs, etc. as mathematical objects, and to prove theorems about them. For example, Gödel's incompleteness theorems assert, roughly speaking that, in every consistent formal system that contains the natural numbers, there are theorems that are true (that is provable in a stronger system), but not provable inside the system. This approach to the foundations of mathematics was challenged during the first half of the 20th century by mathematicians led by Brouwer, who promoted intuitionistic logic, which explicitly lacks the law of excluded middle. These problems and debates led to a wide expansion of mathematical logic, with subareas such as model theory (modeling some logical theories inside other theories), proof theory, type theory, computability theory and computational complexity theory. Although these aspects of mathematical logic were introduced before the rise of computers, their use in compiler design, formal verification, program analysis, proof assistants and other aspects of computer science, contributed in turn to the expansion of these logical theories. === Statistics and other decision sciences === The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory. Statisticians generate data with random sampling or randomized experiments. Statistical theory studies decision problems such as minimizing the risk (expected loss) of a statistical action, such as using a procedure in, for example, parameter estimation, hypothesis testing, and selecting the best. In these traditional areas of mathematical statistics, a statistical-decision problem is formulated by minimizing an objective function, like expected loss or cost, under specific constraints. For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence. Because of its use of optimization, the mathematical theory of statistics overlaps with other decision sciences, such as operations research, control theory, and mathematical economics. === Computational mathematics === Computational mathematics is the study of mathematical problems that are typically too large for human, numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis broadly includes the study of approximation and discretization with special focus on rounding errors. Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic-matrix-and-graph theory. Other areas of computational mathematics include computer algebra and symbolic computation. == History == === Etymology === The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning 'something learned, knowledge, mathematics', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning 'mathematical science'. It entered the English language during the Late Middle English period through French and Latin. Similarly, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely the first to constrain the use of the word to just the study of arithmetic and geometry. By the time of Aristotle (384–322 BC) this meaning was fully established. In Latin and English, until around 1700, the term mathematics more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This change has resulted in several mistranslations: For example, Saint Augustine's warning that Christians should beware of mathematici, meaning "astrologers", is sometimes mistranslated as a condemnation of mathematicians. The apparent plural form in English goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, inherited from Greek. In English, the noun mathematics takes a singular verb. It is often shortened to maths or, in North America, math. === Ancient === In addition to recognizing how to count physical objects, prehistoric peoples may have also known how to count abstract quantities, like time—days, seasons, or years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication, and division) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as the Pythagoreans appeared to have considered it a subject in its own right. Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements, is widely considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is often held to be Archimedes (c. 287 – c. 212 BC) of Syracuse. He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC), trigonometry (Hipparchus of Nicaea, 2nd century BC), and the beginnings of algebra (Diophantus, 3rd century AD). The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition and approximation of sine and cosine, and an early form of infinite series. === Medieval and later === During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other achievements of the Islamic period include advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarizmi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. The Greek and Arabic mathematical texts were in turn translated to Latin during the Middle Ages and made available in Europe. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe, with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical calculations, especially for astronomy and marine navigation, the introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them with the discovery and the proof of numerous theorems. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory, number theory, and statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show in part that any consistent axiomatic system—if powerful enough to describe arithmetic—will contain true propositions that cannot be proved. Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made to this very day. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews (MR) database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs." == Symbolic notation and terminology == Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations, unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and formulas. More precisely, numbers and other mathematical objects are represented by symbols called variables, which are generally Latin or Greek letters, and often include subscripts. Operation and relations are generally represented by specific symbols or glyphs, such as + (plus), × (multiplication), ∫ {\textstyle \int } (integral), = (equal), and < (less than). All these symbols are generally grouped according to specific rules to form expressions and formulas. Normally, expressions and formulas do not appear alone, but are included in sentences of the current language, where expressions play the role of noun phrases and formulas play the role of clauses. Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication. An axiom or postulate is a mathematical statement that is taken to be true without need of proof. If a mathematical statement has yet to be proven (or disproven), it is termed a conjecture. Through a series of rigorous arguments employing deductive reasoning, a statement that is proven to be true becomes a theorem. A specialized theorem that is mainly used to prove another theorem is called a lemma. A proven instance that forms part of a more general finding is termed a corollary. Numerous technical terms used in mathematics are neologisms, such as polynomial and homeomorphism. Other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. For example, in mathematics, "or" means "one, the other or both", while, in common language, it is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called "exclusive or"). Finally, many mathematical terms are common words that are used with a completely different meaning. This may lead to sentences that are correct and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module is flat" and "a field is always a ring". == Relationship with sciences == Mathematics is used in most sciences for modeling phenomena, which then allows predictions to be made from experimental laws. The independence of mathematical truth from any experimentation implies that the accuracy of such predictions depends only on the adequacy of the model. Inaccurate predictions, rather than being caused by invalid mathematical concepts, imply the need to change the mathematical model used. For example, the perihelion precession of Mercury could only be explained after the emergence of Einstein's general relativity, which replaced Newton's law of gravitation as a better mathematical model. There is still a philosophical debate whether mathematics is a science. However, in practice, mathematicians are typically grouped with scientists, and mathematics shares much in common with the physical sciences. Like them, it is falsifiable, which means in mathematics that, if a result or a theory is wrong, this can be proved by providing a counterexample. Similarly as in science, theories and results (theorems) are often obtained from experimentation. In mathematics, the experimentation may consist of computation on selected examples or of the study of figures or other representations of mathematical objects (often mind representations without physical support). For example, when asked how he came about his theorems, Gauss once replied "durch planmässiges Tattonieren" (through systematic experimentation). However, some authors emphasize that mathematics differs from the modern notion of science by not relying on empirical evidence. === Pure and applied mathematics === Until the 19th century, the development of mathematics in the West was mainly motivated by the needs of technology and science, and there was no clear distinction between pure and applied mathematics. For example, the natural numbers and arithmetic were introduced for the need of counting, and geometry was motivated by surveying, architecture and astronomy. Later, Isaac Newton introduced infinitesimal calculus for explaining the movement of the planets with his law of gravitation. Moreover, most mathematicians were also scientists, and many scientists were also mathematicians. However, a notable exception occurred with the tradition of pure mathematics in Ancient Greece. The problem of integer factorization, for example, which goes back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem, now widely used for the security of computer networks. In the 19th century, mathematicians such as Karl Weierstrass and Richard Dedekind increasingly focused their research on internal problems, that is, pure mathematics. This led to split mathematics into pure mathematics and applied mathematics, the latter being often considered as having a lower value among mathematical purists. However, the lines between the two are frequently blurred. The aftermath of World War II led to a surge in the development of applied mathematics in the US and elsewhere. Many of the theories developed for applications were found interesting from the point of view of pure mathematics, and many results of pure mathematics were shown to have applications outside mathematics; in turn, the study of these applications may give new insights on the "pure theory". An example of the first case is the theory of distributions, introduced by Laurent Schwartz for validating computations done in quantum mechanics, which became immediately an important tool of (pure) mathematical analysis. An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. For getting an algorithm that can be implemented and can solve systems of polynomial equations and inequalities, George Collins introduced the cylindrical algebraic decomposition that became a fundamental tool in real algebraic geometry. In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". However, these terms are still used in names of some university departments, such as at the Faculty of Mathematics at the University of Cambridge. === Unreasonable effectiveness === The unreasonable effectiveness of mathematics is a phenomenon that was named and first made explicit by physicist Eugene Wigner. It is the fact that many mathematical theories (even the "purest") have applications outside their initial object. These applications may be completely outside their initial area of mathematics, and may concern physical phenomena that were completely unknown when the mathematical theory was introduced. Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. A second historical example is the theory of ellipses. They were studied by the ancient Greek mathematicians as conic sections (that is, intersections of cones with planes). It was almost 2,000 years later that Johannes Kepler discovered that the trajectories of the planets are ellipses. In the 19th century, the internal development of geometry (pure mathematics) led to definition and study of non-Euclidean geometries, spaces of dimension higher than three and manifolds. At this time, these concepts seemed totally disconnected from the physical reality, but at the beginning of the 20th century, Albert Einstein developed the theory of relativity that uses fundamentally these concepts. In particular, spacetime of special relativity is a non-Euclidean space of dimension four, and spacetime of general relativity is a (curved) manifold of dimension four. A striking aspect of the interaction between mathematics and physics is when mathematics drives research in physics. This is illustrated by the discoveries of the positron and the baryon Ω − . {\displaystyle \Omega ^{-}.} In both cases, the equations of the theories had unexplained solutions, which led to conjecture of the existence of an unknown particle, and the search for these particles. In both cases, these particles were discovered a few years later by specific experiments. === Specific sciences === ==== Physics ==== Mathematics and physics have influenced each other over their modern history. Modern physics uses mathematics abundantly, and is also considered to be the motivation of major mathematical developments. ==== Computing ==== Computing is closely related to mathematics in several ways. Theoretical computer science is considered to be mathematical in nature. Communication technologies apply branches of mathematics that may be very old (e.g., arithmetic), especially with respect to transmission security, in cryptography and coding theory. Discrete mathematics is useful in many areas of computer science, such as complexity theory, information theory, and graph theory. In 1998, the Kepler conjecture on sphere packing seemed to also be partially proven by computer. ==== Biology and chemistry ==== Biology uses probability extensively in fields such as ecology or neurobiology. Most discussion of probability centers on the concept of evolutionary fitness. Ecology heavily uses modeling to simulate population dynamics, study ecosystems such as the predator-prey model, measure pollution diffusion, or to assess climate change. The dynamics of a population can be modeled by coupled differential equations, such as the Lotka–Volterra equations. Statistical hypothesis testing, is run on data from clinical trials to determine whether a new treatment works. Since the start of the 20th century, chemistry has used computing to model molecules in three dimensions. ==== Earth sciences ==== Structural geology and climatology use probabilistic models to predict the risk of natural catastrophes. Similarly, meteorology, oceanography, and planetology also use mathematics due to their heavy use of models. ==== Social sciences ==== Areas of mathematics used in the social sciences include probability/statistics and differential equations. These are used in linguistics, economics, sociology, and psychology. Often the fundamental postulate of mathematical economics is that of the rational individual actor – Homo economicus (lit. 'economic man'). In this model, the individual seeks to maximize their self-interest, and always makes optimal choices using perfect information. This atomistic view of economics allows it to relatively easily mathematize its thinking, because individual calculations are transposed into mathematical calculations. Such mathematical modeling allows one to probe economic mechanisms. Some reject or criticise the concept of Homo economicus. Economists note that real people have limited information, make poor choices and care about fairness, altruism, not just personal gain. Without mathematical modeling, it is hard to go beyond statistical observations or untestable speculation. Mathematical modeling allows economists to create structured frameworks to test hypotheses and analyze complex interactions. Models provide clarity and precision, enabling the translation of theoretical concepts into quantifiable predictions that can be tested against real-world data. At the start of the 20th century, there was a development to express historical movements in formulas. In 1922, Nikolai Kondratiev discerned the ~50-year-long Kondratiev cycle, which explains phases of economic growth or crisis. Towards the end of the 19th century, mathematicians extended their analysis into geopolitics. Peter Turchin developed cliodynamics since the 1990s. Mathematization of the social sciences is not without risk. In the controversial book Fashionable Nonsense (1997), Sokal and Bricmont denounced the unfounded or abusive use of scientific terminology, particularly from mathematics or physics, in the social sciences. The study of complex systems (evolution of unemployment, business capital, demographic evolution of a population, etc.) uses mathematical knowledge. However, the choice of counting criteria, particularly for unemployment, or of models, can be subject to controversy. == Philosophy == === Reality === The connection between mathematics and material reality has led to philosophical debates since at least the time of Pythagoras. The ancient philosopher Plato argued that abstractions that reflect material reality have themselves a reality that exists outside space and time. As a result, the philosophical view that mathematical objects somehow exist on their own in abstraction is often referred to as Platonism. Independently of their possible philosophical opinions, modern mathematicians may be generally considered as Platonists, since they think of and talk of their objects of study as real objects. Armand Borel summarized this view of mathematics reality as follows, and provided quotations of G. H. Hardy, Charles Hermite, Henri Poincaré and Albert Einstein that support his views. Something becomes objective (as opposed to "subjective") as soon as we are convinced that it exists in the minds of others in the same form as it does in ours and that we can think about it and discuss it together. Because the language of mathematics is so precise, it is ideally suited to defining concepts for which such a consensus exists. In my opinion, that is sufficient to provide us with a feeling of an objective existence, of a reality of mathematics ... Nevertheless, Platonism and the concurrent views on abstraction do not explain the unreasonable effectiveness of mathematics (as Platonism assumes mathematics exists independently, but does not explain why it matches reality). === Proposed definitions === There is no general consensus about the definition of mathematics or its epistemological status—that is, its place inside knowledge. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science. Some just say, "mathematics is what mathematicians do". A common approach is to define mathematics by its object of study. Aristotle defined mathematics as "the science of quantity" and this definition prevailed until the 18th century. However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart. In the 19th century, when mathematicians began to address topics—such as infinite sets—which have no clear-cut relation to physical reality, a variety of new definitions were given. With the large number of new areas of mathematics that have appeared since the beginning of the 20th century, defining mathematics by its object of study has become increasingly difficult. For example, in lieu of a definition, Saunders Mac Lane in Mathematics, form and function summarizes the basics of several areas of mathematics, emphasizing their inter-connectedness, and observes: the development of Mathematics provides a tightly connected network of formal rules, concepts, and systems. Nodes of this network are closely bound to procedures useful in human activities and to questions arising in science. The transition from activities to the formal Mathematical systems is guided by a variety of general insights and ideas. Another approach for defining mathematics is to use its methods. For example, an area of study is often qualified as mathematics as soon as one can prove theorems—assertions whose validity relies on a proof, that is, a purely-logical deduction. === Rigor === Mathematical reasoning requires rigor. This means that the definitions must be absolutely unambiguous and the proofs must be reducible to a succession of applications of inference rules, without any use of empirical evidence and intuition. Rigorous reasoning is not specific to mathematics, but, in mathematics, the standard of rigor is much higher than elsewhere. Despite mathematics' concision, rigorous proofs can require hundreds of pages to express, such as the 255-page Feit–Thompson theorem. The emergence of computer-assisted proofs has allowed proof lengths to further expand. The result of this trend is a philosophy of the quasi-empiricist proof that can not be considered infallible, but has a probability attached to it. The concept of rigor in mathematics dates back to ancient Greece, where their society encouraged logical, deductive reasoning. However, this rigorous approach would tend to discourage exploration of new approaches, such as irrational numbers and concepts of infinity. The method of demonstrating rigorous proof was enhanced in the sixteenth century through the use of symbolic notation. In the 18th century, social transition led to mathematicians earning their keep through teaching, which led to more careful thinking about the underlying concepts of mathematics. This produced more rigorous approaches, while transitioning from geometric methods to algebraic and then arithmetic proofs. At the end of the 19th century, it appeared that the definitions of the basic concepts of mathematics were not accurate enough for avoiding paradoxes (non-Euclidean geometries and Weierstrass function) and contradictions (Russell's paradox). This was solved by the inclusion of axioms with the apodictic inference rules of mathematical theories; the re-introduction of axiomatic method pioneered by the ancient Greeks. It results that "rigor" is no more a relevant concept in mathematics, as a proof is either correct or erroneous, and a "rigorous proof" is simply a pleonasm. Where a special concept of rigor comes into play is in the socialized aspects of a proof, wherein it may be demonstrably refuted by other mathematicians. After a proof has been accepted for many years or even decades, it can then be considered as reliable. Nevertheless, the concept of "rigor" may remain useful for teaching to beginners what is a mathematical proof. == Training and practice == === Education === Mathematics has a remarkable ability to cross cultural boundaries and time periods. As a human activity, the practice of mathematics has a social side, which includes education, careers, recognition, popularization, and so on. In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines. Prominent careers for professional mathematicians include mathematics teacher or professor, statistician, actuary, financial analyst, economist, accountant, commodity trader, or computer consultant. Archaeological evidence shows that instruction in mathematics occurred as early as the second millennium BCE in ancient Babylonia. Comparable evidence has been unearthed for scribal mathematics training in the ancient Near East and then for the Greco-Roman world starting around 300 BCE. The oldest known mathematics textbook is the Rhind papyrus, dated from c. 1650 BCE in Egypt. Due to a scarcity of books, mathematical teachings in ancient India were communicated using memorized oral tradition since the Vedic period (c. 1500 – c. 500 BCE). In Imperial China during the Tang dynasty (618–907 CE), a mathematics curriculum was adopted for the civil service exam to join the state bureaucracy. Following the Dark Ages, mathematics education in Europe was provided by religious schools as part of the Quadrivium. Formal instruction in pedagogy began with Jesuit schools in the 16th and 17th century. Most mathematical curricula remained at a basic and practical level until the nineteenth century, when it began to flourish in France and Germany. The oldest journal addressing instruction in mathematics was L'Enseignement Mathématique, which began publication in 1899. The Western advancements in science and technology led to the establishment of centralized education systems in many nation-states, with mathematics as a core component—initially for its military applications. While the content of courses varies, in the present day nearly all countries teach mathematics to students for significant amounts of time. During school, mathematical capabilities and positive expectations have a strong association with career interest in the field. Extrinsic factors such as feedback motivation by teachers, parents, and peer groups can influence the level of interest in mathematics. Some students studying mathematics may develop an apprehension or fear about their performance in the subject. This is known as mathematical anxiety, and is considered the most prominent of the disorders impacting academic performance. Mathematical anxiety can develop due to various factors such as parental and teacher attitudes, social stereotypes, and personal traits. Help to counteract the anxiety can come from changes in instructional approaches, by interactions with parents and teachers, and by tailored treatments for the individual. === Psychology (aesthetic, creativity and intuition) === The validity of a mathematical theorem relies only on the rigor of its proof, which could theoretically be done automatically by a computer program. This does not mean that there is no place for creativity in a mathematical work. On the contrary, many important mathematical results (theorems) are solutions of problems that other mathematicians failed to solve, and the invention of a way for solving them may be a fundamental way of the solving process. An extreme example is Apery's theorem: Roger Apery provided only the ideas for a proof, and the formal proof was given only several months later by three other mathematicians. Creativity and rigor are not the only psychological aspects of the activity of mathematicians. Some mathematicians can see their activity as a game, more specifically as solving puzzles. This aspect of mathematical activity is emphasized in recreational mathematics. Mathematicians can find an aesthetic value to mathematics. Like beauty, it is hard to define, it is commonly related to elegance, which involves qualities like simplicity, symmetry, completeness, and generality. G. H. Hardy in A Mathematician's Apology expressed the belief that the aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He also identified other criteria such as significance, unexpectedness, and inevitability, which contribute to mathematical aesthetics. Paul Erdős expressed this sentiment more ironically by speaking of "The Book", a supposed divine collection of the most beautiful proofs. The 1998 book Proofs from THE BOOK, inspired by Erdős, is a collection of particularly succinct and revelatory mathematical arguments. Some examples of particularly elegant results included are Euclid's proof that there are infinitely many prime numbers and the fast Fourier transform for harmonic analysis. Some feel that to consider mathematics a science is to downplay its artistry and history in the seven traditional liberal arts. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematical results are created (as in art) or discovered (as in science). The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions. == Cultural impact == === Artistic expression === Notes that sound well together to a Western ear are sounds whose fundamental frequencies of vibration are in simple ratios. For example, an octave doubles the frequency and a perfect fifth multiplies it by 3 2 {\displaystyle {\frac {3}{2}}} . Humans, as well as some other animals, find symmetric patterns to be more beautiful. Mathematically, the symmetries of an object form a group known as the symmetry group. For example, the group underlying mirror symmetry is the cyclic group of two elements, Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } . A Rorschach test is a figure invariant by this symmetry, as are butterfly and animal bodies more generally (at least on the surface). Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea. Fractals possess self-similarity. === Popularization === Popular mathematics is the act of presenting mathematics without technical terms. Presenting mathematics may be hard since the general public suffers from mathematical anxiety and mathematical objects are highly abstract. However, popular mathematics writing can overcome this by using applications or cultural links. Despite this, mathematics is rarely the topic of popularization in printed or televised media. === Awards and prize problems === The most prestigious award in mathematics is the Fields Medal, established in 1936 and awarded every four years (except around World War II) to up to four individuals. It is considered the mathematical equivalent of the Nobel Prize. Other prestigious mathematics awards include: The Abel Prize, instituted in 2002 and first awarded in 2003 The Chern Medal for lifetime achievement, introduced in 2009 and first awarded in 2010 The AMS Leroy P. Steele Prize, awarded since 1970 The Wolf Prize in Mathematics, also for lifetime achievement, instituted in 1978 A famous list of 23 open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list has achieved great celebrity among mathematicians, and at least thirteen of the problems (depending how some are interpreted) have been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Only one of them, the Riemann hypothesis, duplicates one of Hilbert's problems. A solution to any of these problems carries a 1 million dollar reward. To date, only one of these problems, the Poincaré conjecture, has been solved by the Russian mathematician Grigori Perelman. == See also == == Notes == == References == === Citations === === Other sources === == Further reading ==
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https://en.wikipedia.org/wiki/Mathematics
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In computer science, thrashing occurs in a system with virtual memory when a computer's real storage resources are overcommitted, leading to a constant state of paging and page faults, slowing most application-level processing. This causes the performance of the computer to degrade or even collapse. The situation can continue indefinitely until the user closes some running applications or the active processes free up additional virtual memory resources. After initialization, most programs operate on a small number of code and data pages compared to the total memory the program requires. The pages most frequently accessed at any point are called the working set, which may change over time. When the working set is not significantly greater than the system's total number of real storage page frames, virtual memory systems work most efficiently, and an insignificant amount of computing is spent resolving page faults. As the total of the working sets grows, resolving page faults remains manageable until the growth reaches a critical point at which the number of faults increases dramatically and the time spent resolving them overwhelms the time spent on the computing the program was written to do. This condition is referred to as thrashing. Thrashing may occur on a program that randomly accesses huge data structures, as its large working set causes continual page faults that drastically slow down the system. Satisfying page faults may require freeing pages that will soon have to be re-read from disk. The term is also used for various similar phenomena, particularly movement between other levels of the memory hierarchy, wherein a process progresses slowly because significant time is being spent acquiring resources. "Thrashing" is also used in contexts other than virtual memory systems –for example, to describe cache issues in computing, or silly window syndrome in networking. == Overview == Virtual memory works by treating a portion of secondary storage such as a computer hard disk as an additional layer of the cache hierarchy. Virtual memory allows processes to use more memory than is physically present in main memory. Operating systems supporting virtual memory assign processes a virtual address space and each process refers to addresses in its execution context by a so-called virtual address. To access data such as code or variables at that address, the process must translate the address to a physical address in a process known as virtual address translation. In effect, physical main memory becomes a cache for virtual memory, which is in general stored on disk in memory pages. Programs are allocated a certain number of pages as needed by the operating system. Active memory pages exist in both RAM and on disk. Inactive pages are removed from the cache and written to disk when the main memory becomes full. If processes are utilizing all main memory and need additional memory pages, a cascade of severe cache misses known as page faults will occur, often leading to a noticeable lag in the operating system responsiveness. This process together with the futile, repetitive page swapping that occurs is known as "thrashing". This frequently leads to high, runaway CPU utilization that can grind the system to a halt. In modern computers, thrashing may occur in the paging system (if there is not sufficient physical memory or the disk access time is overly long), or in the I/O communications subsystem (especially in conflicts over internal bus access), etc. Depending on the configuration and algorithms involved, the throughput and latency of a system may degrade by multiple orders of magnitude. Thrashing is when the CPU performs 'productive' work less and 'swapping' work more. The overall memory access time may increase since the higher level memory is only as fast as the next lower level in the memory hierarchy. The CPU is busy swapping pages so much that it cannot respond to users' programs and interrupts as much as required. Thrashing occurs when there are too many pages in memory, and each page refers to another page. Real memory reduces its capacity to contain all the pages, so it uses 'virtual memory'. When each page in execution demands that page that is not currently in real memory (RAM) it places some pages on virtual memory and adjusts the required page on RAM. If the CPU is too busy doing this task, thrashing occurs. === Causes === In virtual memory systems, thrashing may be caused by programs or workloads that present insufficient locality of reference: if the working set of a program or a workload cannot be effectively held within physical memory, then constant data swapping, i.e., thrashing, may occur. The term was first used during the tape operating system days to describe the sound the tapes made when data was being rapidly written to and read. A worst case might occur on VAX processors. A single MOVL crossing a page boundary could have a source operand using a displacement deferred addressing mode, where the longword containing the operand address crosses a page boundary, and a destination operand using a displacement deferred addressing mode, where the longword containing the operand address crosses a page boundary, and the source and destination could both cross page boundaries. This single instruction references ten pages; if not all are in RAM, each will cause a page fault. The total number of pages thus involved in this particular instruction is ten, and all ten pages must be simultaneously present in memory. If any one of the ten pages cannot be swapped in (for example to make room for any of the other pages), the instruction will fault, and every attempt to restart it will fail until all ten pages can be swapped in. A system thrashing is often a result of a sudden spike in page demand from a small number of running programs. Swap-token is a lightweight and dynamic thrashing protection mechanism. The basic idea is to set a token in the system, which is randomly given to a process that has page faults when thrashing happens. The process that has the token is given a privilege to allocate more physical memory pages to build its working set, which is expected to quickly finish its execution and release the memory pages to other processes. A timestamp is used to hand over the tokens one by one. The first version of swap-token is implemented in Linux. The second version is called preempt swap-token. In this updated swap-token implementation, a priority counter is set for each process to track the number of swap-out pages. The token is always given to the process with a high priority, which has a high number of swap-out pages. The length of the time stamp is not a constant but is determined by the priority: the higher the number of swap-out pages of a process, the longer the time stamp for it will be. == Other uses == Thrashing is best known in the context of memory and storage, but analogous phenomena occur for other resources, including: Cache thrashing Where main memory is accessed in a pattern that leads to multiple main memory locations competing for the same cache lines, resulting in excessive cache misses. This is most likely to be problematic for caches with associativity. TLB thrashing Where the translation lookaside buffer (TLB) acting as a cache for the memory management unit (MMU) which translates virtual addresses to physical addresses is too small for the working set of pages. TLB thrashing can occur even if instruction cache or data cache thrashing is not occurring because these are cached in different sizes. Instructions and data are cached in small blocks (cache lines), not entire pages, but address lookup is done at the page level. Thus even if the code and data working sets fit into the cache, if the working sets are fragmented across many pages, the virtual address working set may not fit into TLB, causing TLB thrashing. Heap thrashing Frequent garbage collection, due to failure to allocate memory for an object, due to insufficient free memory or insufficient contiguous free memory due to memory fragmentation is referred to as heap thrashing. Process thrashing A similar phenomenon occurs for processes: when the process working set cannot be coscheduled, i.e. such that not all interacting processes are scheduled to run at the same time, they experience "process thrashing" due to being repeatedly scheduled and unscheduled, progressing only slowly. == See also == Page replacement algorithm – Algorithm for virtual memory implementation Congestion collapse – Reduced quality of service due to high network trafficPages displaying short descriptions of redirect targets Resource contention – In computing, a conflict over access to a shared resource Out of memory – State of computer operation where no additional memory can be allocated Software aging – Tendency of software to fail due to external changes or prolonged operation == References ==
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https://en.wikipedia.org/wiki/Thrashing_(computer_science)
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Speculative fiction is an umbrella genre of fiction that encompasses all the subgenres that depart from realism, or strictly imitating everyday reality, instead presenting fantastical, supernatural, futuristic, or other imaginative realms. This catch-all genre includes, but is not limited to: fantasy, science fiction, science fantasy, superhero, paranormal, supernatural, horror, alternate history, magical realism, slipstream, weird fiction, utopia and dystopia, apocalyptic and post-apocalyptic fiction. In other words, the genre speculates on individuals, events, or places beyond the ordinary real world. The term speculative fiction has been used for works of literature, film, television, drama, video games, radio, and hybrid media. == Speculative versus realistic fiction == The umbrella genre of speculative fiction is characterized by a lesser degree of adherence to plausible depictions of individuals, events, or places, while the umbrella genre of realistic fiction (partly crossing over with literary realism) is characterized by a greater degree of adherence to such depictions. For instance, speculative fiction may depict an entirely imaginary universe or one in which the laws of nature do not strictly apply (often the subgenre of fantasy). Alternatively, the genre depicts actual historical moments, except that they have concluded in an entirely imaginary way or been followed by major imaginary events (i.e., the subgenre of alternative history). As another alternative, the genre depicts impossible technology or technology that defies current scientific understanding or capabilities (i.e., the subgenre of science fiction). By contrast, realistic fiction involves a story whose basic setting is real and whose events could plausibly occur in the real world. One realistic fiction subgenre is historical fiction, which is centred around actual major events and time periods of the past. The attempt to make stories seem faithful to reality or to more objectively describe details—and also the 19th-century artistic movement that vigorously promoted this approach—is called "literary realism"; this includes both fiction and non-fiction works. === Distinguishing science fiction from other speculative fiction === "Speculative fiction" is sometimes abbreviated as spec-fic, spec fic, specfic, S-F, SF, or sf. The last three abbreviations, however, are ambiguous since they have long been used to refer to science fiction (which lies within this general area of literature). The genre is sometimes known as the fantastic or fantastika; the latter term is attributed to science fiction scholar John Clute, who coined it in 2007 after the term for the genre in some Slavic languages. The term speculative fiction has been used by some critics and writers who oppose a perceived limitation of science fiction: the requirement for a story to adhere to scientific principles. These people argue that speculative fiction better defines an expanded, open, imaginative type of fiction than does genre fiction, and the categories of fantasy, mystery, horror and science fiction. Harlan Ellison used the term to avoid being classified as a science fiction writer. Ellison, a fervent proponent of writers embracing more literary and modernist directions, broke out of genre conventions to push the boundaries of speculative fiction. The term suppositional fiction is sometimes used as a subcategory designating fiction in which characters and stories are constrained by an internally consistent world, but not necessarily one defined by any particular genre. == History == Speculative fiction as a category ranges from ancient works to paradigm-changing and neotraditional works of the 21st century. Characteristics of speculative fiction have been recognized in older works whose authors' intentions are now known, or in the social contexts of the stories they tell. An example is the ancient Greek dramatist, Euripides (c. 480 – c. 406 BCE), whose play Medea seems to have offended Athenian audiences; in this play, he speculated that the titular sorceress Medea killed her own children, as opposed to their being killed by other Corinthians after her departure. In historiography, what is now called speculative fiction has previously been termed historical invention, historical fiction, and similar names. These terms have been extensively applied in literary criticism to the works of William Shakespeare. For example, in A Midsummer Night's Dream, he places several characters from different locations and times into the Fairyland of the fictional Merovingian Germanic sovereign Oberon; these characters include the Athenian Duke Theseus, the Amazonian Queen Hippolyta, the English fairy Puck, and the Roman god Cupid. In mythography, the concept of speculative fiction has been termed mythopoesis or mythopoeia. This process involves the creative design and development of lore and mythology for works of fiction. The term's definition comes from use by J. R. R. Tolkien; his series of novels, The Lord of the Rings, shows an application of the process. Themes common in mythopoeia, such as the supernatural, alternate history, and sexuality, continue to be explored in works produced in modern speculative fiction. Speculative fiction in the general sense of hypothetical history, explanation, or ahistorical storytelling has been attributed to authors in ostensibly non-fiction modes since Herodotus of Halicarnassus (fl. 5th century BCE) with his Histories; it was already both created and edited out by early encyclopedic writers such Sima Qian (c. 145 or 135 BCE–86 BCE), author of Shiji. These examples highlight a caveat—many works that are now viewed as speculative fiction long predated the labelling of the genre. In the broadest sense, the genre's concept does two things: it captures both conscious and unconscious aspects of human psychology in making sense of the world, and it responds to the world by creating imaginative, inventive, and artistic expressions. Such expressions can contribute to practical societal progress through interpersonal influences; social and cultural movements; scientific research and advances; and the philosophy of science. In English-language usage in arts and literature since the mid 20th century, the term speculative fiction has often been attributed to Robert A. Heinlein, who first used it in an editorial in The Saturday Evening Post (on 8 February 1947). In the article, Heinlein used Speculative Fiction as a synonym for science fiction; in a later article, he stated explicitly that his use of the term excluded fantasy. Although Heinlein may have invented the term independently, earlier citations exist. An article in Lippincott's Monthly Magazine in 1889 used the term in reference to Edward Bellamy's novel Looking Backward: 2000–1887 and other works; and an article in the May 1900 issue of The Bookman mentioned that John Uri Lloyd's novel Etidorhpa, or, The End of the Earth had "created a great deal of discussion among people interested in speculative fiction". A variant of this term is speculative literature. The use of the term speculative fiction to express dissatisfaction with traditional or establishment science fiction was popularized in the 1960s and early 1970s by Judith Merril, as well as other writers and editors connected with the New Wave movement. However, this use of the term became less popular toward the mid-1970s. During the 2000s, the term speculative fiction came into wider use as a convenient way to describe a set of genres. However, some writers (such as Margaret Atwood) still distinguish "speculative fiction" as a specifically "no Martians" type of science fiction, "about things that really could happen." The term speculative fiction is also used to describe genres combined into a single narrative or fictional world, such as "science fiction, horror, fantasy...[and]...mystery". In documenting this broad genre, the Internet Speculative Fiction Database includes a list of different subtypes. According to publisher statistics, men outnumber women about two to one among English-language speculative fiction writers who seek professional publication. However, the percentages vary considerably by genre, with women outnumbering men in the areas of urban fantasy, paranormal romance and young adult fiction. Academic journals that publish essays on speculative fiction include Extrapolation and Foundation. == Genres == Speculative fiction may include elements from one or more of the following genres: == See also == Biblical speculative fiction Comic genres Genre fiction List of genres Megatext Speculative art Speculative fiction by writers of color Speculative poetry Weird fiction == References == == External links == Internet Speculative Fiction Database The SF Page at Project Gutenberg of Australia
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https://en.wikipedia.org/wiki/Speculative_fiction
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"Computational science, also known as scientific computing, technical computing or scientific comput(...TRUNCATED) |
https://en.wikipedia.org/wiki/Computational_science
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"Botany, also called plant science, is the branch of natural science and biology studying plants, es(...TRUNCATED) |
https://en.wikipedia.org/wiki/Botany
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