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in the shells, which sell for more than US$1,400 per metric tonne. Ormers ("Haliotis tuberculata") are considered a delicacy in the British Channel Islands as well as in adjacent areas of France, and are pursued with great alacrity by the locals. This, and a recent lethal bacterial disease, has led to a dramatic depletion in numbers since the latter half of the 19th century, and "ormering" is now strictly regulated in order to preserve stocks. The gathering of ormers is now restricted to a number of 'ormering tides', from January 1 to April 30, which occur on the full or
Abalone
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5602
new moon and two days following. No ormers may be taken from the beach that are under in shell length. Gatherers are not allowed to wear wetsuits or even put their heads underwater. Any breach of these laws is a criminal offense and can lead to fine of up to £5,000 or six months in prison. The demand for ormers is such that they led to the world's first underwater arrest, when Mr. Kempthorne-Leigh of Guernsey was arrested by a police officer in full diving gear when illegally diving for ormers. The highly iridescent inner nacre layer of the shell
Abalone
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5603
of abalone has traditionally been used as a decorative item, in jewelry, buttons, and as inlay in furniture and in musical instruments such as on fret boards and binding of guitars, etc. Abalone pearl jewelry is very popular in New Zealand and Australia, in no minor part due to the marketing and farming efforts of pearl companies. Unlike the Oriental Natural, the Akoya pearl, and the South Sea and Tahitian cultured pearls, abalone pearls are not primarily judged by their roundness. The inner shell of the abalone is an iridescent swirl of intense colours, ranging from deep cobalt blue and
Abalone
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5604
peacock green to purples, creams and pinks. Therefore, each pearl, natural or cultured, will have its own unique collage of colours. The shells of abalone are occasionally used in New Age smudging ceremonies to catch falling ash. They have also been used as incense burners. Abalone has been an important staple in native cultures around the world, specifically in Africa and on the North American West coast. The meat was used as food, and the shell was used as currency for many tribes. Abalones have been identified as one of the many classes of organism threatened with extinction due to
Abalone
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5605
overfishing and the acidification of oceans from anthropogenic carbon dioxide, as reduced pH erodes their shells. It is predicted that abalones will become extinct in the wild within 200 years at current rates of carbon dioxide production. Currently the white, pink, and green abalone are on the federal endangered species list, and possible restoration sites have been proposed for the San Clemente Island and Santa Barbara Island areas. The possibility of farming abalone to be reintroduced into the wild has also been proposed, with these abalone having special tags to help track the population. The number of species that are
Abalone
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5606
recognized within the genus "Haliotis" has fluctuated over time, and depends on the source that is consulted. The number of recognized species range from 30 to 130. This list finds a compromise using the "WoRMS database", plus some species that have been added, for a total of 57. The majority of abalone have not been rated for conservation status. Those that have been reviewed tend to show that the abalone in general is an animal that is declining in numbers, and will need protection throughout the globe. Abalone Abalone ( or ; via Spanish "", from Rumsen "aulón") is a
Abalone
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5607
Abbess In Christianity, an abbess (Latin "abbatissa", feminine form of "abbas," abbot) is the female superior of a community of nuns, which is often an abbey. In the Catholic Church (both the Latin Church and Eastern Catholic), Eastern Orthodox, Coptic and Anglican abbeys, the mode of election, position, rights, and authority of an abbess correspond generally with those of an abbot. She must be at least 40 years old and have been a nun for 10 years. The age requirement in the Catholic Church has evolved over time, ranging from 30 to 60. The requirement of 10 years as a
Abbess
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5608
nun is only 8 in Catholicism. In the rare case of there not being a nun with the qualifications, the requirements may be lowered to 30 years of age and 5 of those in an "upright manner", as determined by the superior. A woman who is of illegitimate birth, is not a virgin, has undergone non-salutory public penance, is a widow, or is blind or deaf, is typically disqualified for the position, saving by permission of the Holy See. The office is elective, the choice being by the secret votes of the nuns belonging to the community. Like an abbot,
Abbess
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5609
after being confirmed in her office by the Holy See, an abbess is solemnly admitted to her office by a formal blessing, conferred by the bishop in whose territory the monastery is located, or by an abbot or another bishop with appropriate permission. Unlike the abbot, the abbess receives only the ring, the crosier, and a copy of the rule of the order. She does not receive a mitre as part of the ceremony. The abbess also traditionally adds a pectoral cross to the outside of her habit as a symbol of office, though she continues to wear a modified
Abbess
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5610
form of her religious habit or dress, as she is unordained—females cannot be ordained—and so does not vest or use choir dress in the liturgy. An abbess serves for life, except in Italy and some adjacent islands. Abbesses are, like abbots, major superiors according to canon law, the equivalents of abbots or bishops (the ordained male members of the church hierarchy who have, by right of their own office, executive jurisdiction over a building, diocesan territory, or a communal or non-communal group of persons—juridical entities under church law). They receive the vows of the nuns of the abbey; they may
Abbess
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5611
admit candidates to their order's novitiate; they may send them to study; and they may send them to do pastoral or missionary, or to work or assist—to the extent allowed by canon and civil law—in the administration and ministry of a parish or diocese (these activities could be inside or outside the community's territory). They have full authority in its administration. However, there are significant limitations. They may not administer the sacraments, whose celebration is reserved to bishops, priests, deacons (clerics), namely, those in Holy Orders. They may make provision for an ordained cleric to help train and to admit
Abbess
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5612
some of their members, if needed, as altar servers, extraordinary ministers of Holy Communion, or lectors—all ministries which are now open to the unordained. They may not serve as a witness to a marriage except by special rescript. They may not administer Penance (Reconciliation), Anointing of the Sick (Extreme Unction), or function as an ordained celebrant or concelebrant of the Mass (by virtue of their office and their training and institution, they may act, if the need arises, as altar servers, lectors, ushers, porters, or extraordinary ministers of Holy Communion, and if need be, the Host). They may preside over
Abbess
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5613
the Liturgy of the Hours which they are obliged to say with their community, speak on Scripture to their community, and give certain types of blessings not reserved to the clergy. On the other hand, they may not ordinarily preach a sermon or homily, nor read the Gospel during Mass. As they do not receive episcopal ordination in the Catholic, Orthodox and Oriental Churches, they do not possess the ability to ordain others, nor do they exercise the authority they do possess under canon law over any territories outside of their monastery and its territory (though non-cloistered, non-contemplative female religious
Abbess
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5614
members who are based in a convent or monastery but who participate in external affairs may assist as needed by the diocesan bishop and local secular clergy and laity, in certain pastoral ministries and administrative and non-administrative functions not requiring ordained ministry or status as a male cleric in those churches or programs). There are exigent circumstances, where due to Apostolical privilege, certain Abbesses have been granted rights and responsibilities above the normal, such as the Abbess of the Cistercian Monastery of the Abbey of Santa María la Real de Las Huelgas near Burgos, Spain. Also granted exceptional rights was
Abbess
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5615
the Abbess of the Cistercian order in Conversano Italy. She was granted the ability to appoint her own vicar-general, select and approve the confessors, along with the practice of receiving the public homage of her clergy. This practice continued until some of the duties were modified due to an appeal by the clergy to Rome. Finally in 1750, the public homage was abolished. Historically, in some Celtic monasteries, abbesses presided over joint-houses of monks and nuns, the most famous example being Saint Brigid of Kildare's leadership in the founding of the monastery at Kildare in Ireland. This custom accompanied Celtic
Abbess
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5616
monastic missions to France, Spain, and even to Rome itself. In 1115, Robert, the founder of Fontevraud Abbey near Chinon and Saumur, France, committed the government of the whole order, men as well as women, to a female superior. In Lutheran churches, the title of abbess (German "Äbtissin") has in some cases (e.g. ) survived to designate the heads of abbeys which since the Protestant Reformation have continued as monasteries or convents (German "Stifte"). These positions continued, merely changing from Catholic to Lutheran. The first to make this change was the Abbey of Quedlinburg, whose last Catholic Abbess died in
Abbess
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5617
1514. These are collegiate foundations, which provide a home and an income for unmarried ladies, generally of noble birth, called canonesses (German "Kanonissinen") or more usually "Stiftsdamen" or "Kapitularinnen". The office of abbess is of considerable social dignity, and in the past, was sometimes filled by princesses of the reigning houses. Until the dissolution of Holy Roman Empire and mediatisation of smaller imperial fiefs by Napoleon, the evangelical Abbess of Quedlinburg was also per officio the head of that "reichsunmittelbar" state. The last such ruling abbess was Sofia Albertina, Princess of Sweden. In the Hradčany of Prague is a Catholic
Abbess
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5618
institute whose mistress is titled an Abbess. It was founded in 1755 by the Empress Maria Theresa, and traditionally was responsible for the coronation of the Queen of Bohemia. The Abbess is required to be an Austrian Archduchess. During the Middle Ages abbesses were known to attempt usurpation of the spiritual power forbidden them. Attempts were made to bless, give penance, make the sign of the cross on the foreheads of men, even administer the sacrament. The pope has categorized these forays into the forbidden as "unheard of, most indecorous, and highly preposterous," adding that "these Abbesses had evidently overrated
Abbess
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theor spiritual powers a trifle." The Roman Catholic Church has around 200 abbesses at present. The oldest women's abbey in Germany being St. Marienthal Abbey of Cistercian nuns, near Ostritz, established during the early 13th-century. On September 10, 2018, the priory of Our Lady of Ephesus in Gower, MO was elevated to an Abbey and the prioress, Mother Cecilia Snell, OSB, was consecrated as the first abbess. The Benedictines of Mary Queen of Apostles are a traditional order of Benedictines nuns whose monastery is in the Diocese of Kansas City-St. Joseph. Abbess In Christianity, an abbess (Latin "abbatissa", feminine form
Abbess
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5620
Abdominal surgery The term abdominal surgery broadly covers surgical procedures that involve opening the abdomen. Surgery of each abdominal organ is dealt with separately in connection with the description of that organ (see stomach, kidney, liver, etc.) Diseases affecting the abdominal cavity are dealt with generally under their own names (e.g. appendicitis). The most common abdominal surgeries are described below. Complications of abdominal surgery include, but are not limited to: Sterile technique, aseptic post-operative care, antibiotics, use of the WHO Surgical Safety Checklist, and vigilant post-operative monitoring greatly reduce the risk of these complications. Planned surgery performed under sterile conditions
"Abdominal surgery"
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5621
is much less risky than that performed under emergency or unsterile conditions. The contents of the bowel are unsterile, and thus leakage of bowel contents, as from trauma, substantially increases the risk of infection. Globally, there are few studies comparing perioperative mortality following abdominal surgery across different health systems. One major prospective study of 10,745 adult patients undergoing emergency laparotomy from 357 centres in 58 high-, middle-, and low-income countries found that mortality is three times higher in low- compared with high-HDI countries even when adjusted for prognostic factors. In this study the overall global mortality rate was 1·6 per
"Abdominal surgery"
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5622
cent at 24 hours (high 1·1 per cent, middle 1·9 per cent, low 3·4 per cent; P < 0·001), increasing to 5·4 per cent by 30 days (high 4·5 per cent, middle 6·0 per cent, low 8·6 per cent; P < 0·001). Of the 578 patients who died, 404 (69·9 per cent) did so between 24 h and 30 days following surgery (high 74·2 per cent, middle 68·8 per cent, low 60·5 per cent). Patient safety factors were suggested to play an important role, with use of the WHO Surgical Safety Checklist associated with reduced mortality at 30 days. Taking
"Abdominal surgery"
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5623
a similar approach, a unique global study of 1,409 children undergoing emergency laparotomy from 253 centres in 43 countries showed that adjusted mortality in children following surgery may be as high as 7 times greater in low-HDI and middle-HDI countries compared with high-HDI countries, translating to 40 excess deaths per 1000 procedures performed in these settings. Internationally, the most common operations performed were appendectomy, small bowel resection, pyloromyotomy and correction of intussusception. After adjustment for patient and hospital risk factors, child mortality at 30 days was significantly higher in low-HDI (adjusted OR 7.14 (95% CI 2.52 to 20.23), p<0.001) and
"Abdominal surgery"
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5624
middle-HDI (4.42 (1.44 to 13.56), p=0.009) countries compared with high-HDI countries. Abdominal surgery The term abdominal surgery broadly covers surgical procedures that involve opening the abdomen. Surgery of each abdominal organ is dealt with separately in connection with the description of that organ (see stomach, kidney, liver, etc.) Diseases affecting the abdominal cavity are dealt with generally under their own names (e.g. appendicitis). The most common abdominal surgeries are described below. Complications of abdominal surgery include, but are not limited to: Sterile technique, aseptic post-operative care, antibiotics, use of the WHO Surgical Safety Checklist, and vigilant post-operative monitoring greatly reduce
"Abdominal surgery"
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Abensberg Abensberg () is a town in the Lower Bavarian district of Kelheim, in Bavaria, Germany, lying around 30 km southwest of Regensburg, 40 km east of Ingolstadt, 50 northwest of Landshut and 100 km north of Munich. It is situated on the Abens river, a tributary of the Danube. The town lies on the Abens river, a tributary of the Danube, around eight kilometres from the river's source. The area around Abensberg is characterized by the narrow valley of the Danube, where the Weltenburg Abbey stands, the valley of the Altmühl in the north, a left tributary of the
Abensberg
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5626
Danube, and the famous Hallertau hops-planting region in the south. The town is divided into the municipalities of Abensberg, Arnhofen, Holzharlanden, Hörlbach, Offenstetten, Pullach and Sandharland. Since the administrative reforms in Bavaria in the 1970s, the town also encompasses the following "Ortsteile": There had been settlement on this part of the Abens river since long before the High Middle Ages, dating back to Neolithic times. Of particular interest and national importance are the Neolithic flint mines at Arnhofen, where, around 7,000 years ago, Stone Age people made flint, which was fashioned into drills, blades and arrowheads, and was regarded as
Abensberg
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5627
the steel of the Stone Age. Traces of over 20,000 individuals were found on this site. The modern history of Abensberg, which is often incorrectly compared with that of the 3rd century Roman castra (military outpost) of Abusina, begins with Gebhard, who was the first to mention Abensberg as a town, in the middle of the 12th century. The earliest written reference to the town, under the name of "Habensperch", came from this time, in around 1138. Gebhard was from the Babonen clan. In 1256, the castrum of "Abensprech" was first mentioned, and on 12 June 1348, Margrave Ludwig of
Abensberg
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Brandenburg, and his brother, Duke Stephen of Bavaria, raised Abensberg to the status of a city, giving it the right to operate lower courts, enclose itself with a wall and hold markets. The wall was built by Count Ulrich III of Abensberg. Some of the thirty-two round towers and eight turrets are still preserved to this day. In the Middle Ages, the people of Abensberg enjoyed a level of autonomy above their lord. They elected a city council, although only a small number of rich families were eligible for election. In around 1390, the Carmelite Monastery of Our Lady of
Abensberg
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5629
Abensberg was founded by Count John II and his wife, Agnes. Although Abensberg was an autonomous city, it remained dependent on the powerful Dukes of Bavaria. The last Lord of Abensberg, Niclas, Graf von Abensberg, supposedly named after his godfather, Nicholas of Kues, a Catholic cardinal, was murdered in 1485 by Christopher, a Duke of Bavaria-Munich. The year before, Niclas had unchivalrously taken Christopher captive as he bathed before a tournament in Munich. Although Christopher renounced his claim for revenge, he lay in wait for Niclas in Freising. When the latter arrived, he was killed by Seitz von Frauenberg. He
Abensberg
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5630
is buried in the former convent of Abensberg. Abensberg then lost its independence and became a part of the Duchy of Bavaria, and from then on was administered by a ducal official, the so-called caretaker. The castle of Abensberg was destroyed during the Thirty Years' War, although the city had bought a guarantee of protection from the Swedish general, Carl Gustaf Wrangel. During the War of the Spanish Succession emperor Leopold I, who had occupied Bavaria, granted the fief of Abensberg to count Ernst von Abensperg und Traun (1608–1668) from an Austrian noble family named Traun that now received the
Abensberg
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5631
name of the former counts of Abensberg (who were believed to be distant relatives). After the occupation ended, he was however dispossessed. Johannes Aventinus (1477–1534) is the city's most famous son, the founder of the study of history in Bavaria. Aventinus, whose name was real name is Johann or Johannes Turmair ("Aventinus" being the Latin name of his birthplace) wrote the "Annals of Bavaria", a valuable record of the early history of Germany and the first major written work on the subject. He is commemorated in the Walhalla temple, a monument near Regensburg to the distinguished figures of German history.
Abensberg
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5632
Until 1800, Abensberg was a municipality belonging to the Straubing district of the Electorate of Bavaria. Abensberg also contained a magistrates' court. In the Battle of Abensberg on 19–20 April 1809, Napoleon gained a significant victory over the Austrians under Archduke Ludwig of Austria and General Johann von Hiller. The arms of the city are divided into two halves. On the left are the blue and white rhombuses of Bavaria, while the right half is split into two silver and black triangles. Two diagonally-crossed silver swords with golden handles rest on top. The town has had a coat of arms
Abensberg
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5633
since 1338, that of the Counts of Abensberg. With the death of the last Count, Nicholas of Abensberg, in 1485, the estates fell to the Duchy of Bavaria-Munich, meaning that henceforth only the Bavarian coat of arms was ever used. On 31 December 1809, a decree of King Maximilian of Bavaria granted the city a new coat of arms, as a recognition of their (mainly humanitarian and logistic) services in the Battle of Abensberg the same year. The diagonally divided field in silver and black came from the old crest of the Counts of Abensberg, while the white and blue
Abensberg
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5634
diamonds came from that of the House of Wittelsbach, the rulers of Bavaria. The swords recall the Battle of Abensberg. The district of Offenstetten previously possessed its own coat of arms. The area around Abensberg, the so-called sand belt between Siegburg, Neustadt an der Donau, Abensberg and Langquaid, is used for the intensive farming of asparagus, due to the optimal soil condition and climate. 212 hectares of land can produce ninety-four asparagus plants. Abensberg asparagus enjoys a reputation among connoisseurs as a particular delicacy. In addition to asparagus, the production of hops plays a major role locally, the region having
Abensberg
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5635
its own label, and there are still three independent breweries in the area. The town of Abensberg marks the start of the "Deutsche Hopfenstraße" ("German Hops Road"), a nickname given to the Bundesstraße 301, a German federal highway which runs through the heartland of Germany's hops-growing industry, ending in Freising. The Abensberg railway station is located on the Danube Valley Railway from Regensburg to Ingolstadt. The city can be reached via the A-93 Holledau-Regensburg road (exit Abensberg). Three Bundesstraße (German federal highways) cross south of Abensberg: B 16, B 299 and B 301. Abensberg has a Grundschule (primary school) and
Abensberg
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5636
Hauptschule (open admission secondary school), and the Johann-Turmair-Realschule(secondary modern school). There is also a College of Agriculture and Home Economics. Since 2007, the Kelheim Berufsschule has had a campus in Abensberg, and outside the state sector is the St. Francis Vocational Training Centre, run by a Catholic youth organisation. In 2008, a former goods shed by the main railway station of Abensberg was converted into a theatre by local volunteers. The "Theater am Bahnhof" ("Theatre at the Railway Station") is mostly used by the "Theatergruppe Lampenfieber" and was opened on 19 October 2008. Abensberg has a long tradition of museums.
Abensberg
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5637
In the nineteenth century, Nicholas Stark und Peter Paul Dollinger began a collection based on local history. This collection and the collection of the "Heimatverein" (local history society) were united in 1963 into the Aventinus Museum, in the cloister of the former Carmelite monastery. On 7 July 2006, the new Town Museum of Abensberg was opened in the former duke's castle in the town. Two blocks west of the Old Town is the Kuchlbauer Brewery and beer garden featuring the Kuchlbauer Tower, a colorful and unconventional observation tower designed by Viennese architect Friedensreich Hundertwasser. The brewery and tower are open
Abensberg
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5638
to the public. Up until the 1950s, Abensberg and the surrounding villages contained a number of graves of victims of a Death March in the Spring of 1945 from the Hersbruck sub-camp of the Dachau concentration camp, who were either murdered by the SS or died of exhaustion. They were originally buried where they died, but were later moved on the orders of the US military government to the cemeteries of their previous homes. At the cemetery in what is now the district of Pullach stood a memorial stone which was mentioned as recently as 1967, but which is no
Abensberg
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5639
longer at the site. The suffering of ten unknown victims of the camp was recorded on the stone. Abensberg Abensberg () is a town in the Lower Bavarian district of Kelheim, in Bavaria, Germany, lying around 30 km southwest of Regensburg, 40 km east of Ingolstadt, 50 northwest of Landshut and 100 km north of Munich. It is situated on the Abens river, a tributary of the Danube. The town lies on the Abens river, a tributary of the Danube, around eight kilometres from the river's source. The area around Abensberg is characterized by the narrow valley of the Danube,
Abensberg
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Arminianism Arminianism is based on theological ideas of the Dutch Reformed theologian Jacobus Arminius (1560–1609) and his historic supporters known as Remonstrants. His teachings held to the five solae of the Reformation, but they were distinct from particular teachings of Martin Luther, Huldrych Zwingli, John Calvin, and other Protestant Reformers. Jacobus Arminius (Jakob Harmenszoon) was a student of Theodore Beza (Calvin's successor) at the Theological University of Geneva. Arminianism is known to some as a soteriological diversification of Protestant Calvinist Christianity; to others, Arminianism is a reclamation of early Church theological consensus. Dutch Arminianism was originally articulated in the Remonstrance
Arminianism
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5641
(1610), a theological statement signed by 45 ministers and submitted to the States General of the Netherlands. The Synod of Dort (1618–19) was called by the States General to consider the Five Articles of Remonstrance. These articles asserted that "These points", note Keith D. Stanglin and Thomas H. McCall, "are consistent with the views of Arminius; indeed, some come verbatim from his "Declaration of Sentiments". Those who signed this remonstrance and others who supported its theology have since been known as Remonstrants." Many Christian denominations have been influenced by Arminian views on the will of man being freed by Grace
Arminianism
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5642
prior to regeneration, notably the Baptists in the 16th century, the Methodists in the 18th century and the Seventh-day Adventist Church in the 19th century. Some falsely assert that Universalists and Unitarians in the 18th and 19th centuries were theologically linked with Arminianism. Denominations such as the Anabaptists (beginning in 1525), Waldensians (pre-Reformation), and other groups prior to the Reformation have also affirmed that each person may choose the contingent response of either resisting God's grace or yielding to it. The original beliefs of Jacobus Arminius himself are commonly defined as Arminianism, but more broadly, the term may embrace the
Arminianism
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5643
teachings of Hugo Grotius, John Wesley, and others as well. Classical Arminianism, to which Arminius is the main contributor, and Wesleyan Arminianism, to which John Wesley is the main contributor, are the two main schools of thought. Wesleyan Arminianism is often identical with Methodism. Some schools of thought, notably semipelagianism—which teaches that the first step of Salvation is by human will—are confused as being Arminian in nature. But classical Arminianism holds that the first step of Salvation is solely the grace of God. Historically, the Council of Orange (529) condemned semi-Pelagian thought (as well as Supralapsarian Calvinism), and is accepted
Arminianism
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5644
by some as a document which can be understood as teaching a doctrine between Augustinian thought and semi-Pelagian thought, relegating Arminianism to the orthodoxy of the early Church fathers. The two systems of Calvinism and Arminianism share both history and many doctrines, and the history of Christian theology. Arminianism is related to Calvinism historically. However, because of their differences over the doctrines of divine predestination and election, many people view these schools of thought as opposed to each other. The distinction is whether God allows His desire to save all to be resisted by an individual's will (in the Arminian
Arminianism
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5645
doctrine) or if God's grace is irresistible and limited to only some (in Calvinism). Put another way, is God's sovereignty shown, in part, through His allowance of free decisions? Some Calvinists assert that the Arminian perspective presents a synergistic system of Salvation and therefore is not only by Grace, while Arminians firmly reject this conclusion. Many consider the theological differences to be crucial differences in doctrine, while others find them to be relatively minor. Jacobus Arminius was a Dutch pastor and theologian in the late 16th and early 17th centuries. He was taught by Theodore Beza, Calvin's hand-picked successor, but
Arminianism
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5646
after examination of the scriptures, he rejected his teacher's theology that it is God who unconditionally elects some for salvation. Instead Arminius proposed that the election of God was "of believers", thereby making it conditional on faith. Arminius's views were challenged by the Dutch Calvinists, especially Franciscus Gomarus, but Arminius died before a national synod could occur. Arminius's followers, not wanting to adopt their leader's name, called themselves the Remonstrants. When Arminius died before he could satisfy Holland's State General's request for a 14-page paper outlining his views, the Remonstrants replied in his stead crafting the Five articles of Remonstrance.
Arminianism
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5647
After some political maneuvering, the Dutch Calvinists were able to convince Prince Maurice of Nassau to deal with the situation. Maurice systematically removed Arminian magistrates from office and called a national synod at Dordrecht. This Synod of Dort was open primarily to Dutch Calvinists (Arminians were excluded) with Calvinist representatives from other countries, and in 1618 published a condemnation of Arminius and his followers as heretics. Part of this publication was the famous Five points of Calvinism in response to the five articles of Remonstrance. Arminians across Holland were removed from office, imprisoned, banished, and sworn to silence. Twelve years
Arminianism
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5648
later Holland officially granted Arminianism protection as a religion, although animosity between Arminians and Calvinists continued. The debate between Calvin's followers and Arminius's followers is distinctive of post-Reformation church history. The emerging Baptist movement in 17th-century England, for example, was a microcosm of the historic debate between Calvinists and Arminians. The first Baptists—called "General Baptists" because of their confession of a "general" or unlimited atonement—were Arminians. The Baptist movement originated with Thomas Helwys, who left his mentor John Smyth (who had moved into shared belief and other distinctives of the Dutch Waterlander Mennonites of Amsterdam) and returned to London to
Arminianism
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5649
start the first English Baptist Church in 1611. Later General Baptists such as John Griffith, Samuel Loveday, and Thomas Grantham defended a Reformed Arminian theology that reflected more the Arminianism of Arminius than that of the later Remonstrants or the English Arminianism of Arminian Puritans like John Goodwin or Anglican Arminians such as Jeremy Taylor and Henry Hammond. The General Baptists encapsulated their Arminian views in numerous confessions, the most influential of which was the Standard Confession of 1660. In the 1640s the Particular Baptists were formed, diverging strongly from Arminian doctrine and embracing the strong Calvinism of the Presbyterians
Arminianism
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5650
and Independents. Their robust Calvinism was publicized in such confessions as the London Baptist Confession of 1644 and the Second London Confession of 1689. The London Confession of 1689 was later used by Calvinistic Baptists in America (called the Philadelphia Baptist Confession), whereas the Standard Confession of 1660 was used by the American heirs of the English General Baptists, who soon came to be known as Free Will Baptists. This same dynamic between Arminianism and Calvinism can be seen in the heated discussions between friends and fellow Anglican ministers John Wesley and George Whitefield. Wesley was a champion of Arminian
Arminianism
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5651
teachings, defending his soteriology in a periodical titled "The Arminian" and writing articles such as "Predestination Calmly Considered". He defended Arminianism against charges of semi-Pelagianism, holding strongly to beliefs in original sin and total depravity. At the same time, Wesley attacked the determinism that he claimed characterized unconditional election and maintained a belief in the ability to lose salvation. Wesley also clarified the doctrine of prevenient grace and preached the ability of Christians to attain to perfection (fully mature, not "sinlessness"). While Wesley freely made use of the term "Arminian," he did not self-consciously root his soteriology in the theology
Arminianism
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5652
of Arminius but was highly influenced by 17th-century English Arminianism and thinkers such as John Goodwin, Jeremy Taylor and Henry Hammond of the Anglican "Holy Living" school, and the Remonstrant Hugo Grotius. Advocates of both Arminianism and Calvinism find a home in many Protestant denominations, and sometimes both exist within the same denomination. Faiths leaning at least in part in the Arminian direction include Methodists, Free Will Baptists, Christian Churches and Churches of Christ, General Baptists, the Seventh-day Adventist Church, Church of the Nazarene, The Wesleyan Church, The Salvation Army, Conservative Mennonites, Old Order Mennonites, Amish and Charismatics. Denominations leaning
Arminianism
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5653
in the Calvinist direction are grouped as the Reformed churches and include Particular Baptists, Reformed Baptists, Presbyterians, and Congregationalists. The majority of Southern Baptists, including Billy Graham, accept Arminianism with an exception allowing for a doctrine of perseverance of the saints ("eternal security"). Many see Calvinism as growing in acceptance, and some prominent Reformed Baptists, such as Albert Mohler and Mark Dever, have been pushing for the Southern Baptist Convention to adopt a more Calvinistic orientation (no Baptist church is bound by any resolution adopted by the Southern Baptist Convention). Lutherans espouse a view of salvation and election distinct from
Arminianism
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5654
both the Calvinist and Arminian schools of soteriology. The current scholarly support for Arminianism is wide and varied. One particular thrust is a return to the teachings of Arminius. F. Leroy Forlines, Robert Picirilli, Stephen Ashby and Matthew Pinson (see citations) are four of the more prominent supporters. Forlines has referred to this type of Arminianism as "Classical Arminianism," while Picirilli, Pinson, and Ashby have termed it "Reformation Arminianism" or "Reformed Arminianism." Through Methodism, Wesley's teachings also inspire a large scholarly following, with vocal proponents including J. Kenneth Grider, Stanley Hauerwas, Thomas Oden, Thomas Jay Oord, and William Willimon. Recent
Arminianism
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5655
influence of the New Perspective on Paul movement has also reached Arminianism — primarily through a view of corporate election. The New Perspective scholars propose that the 1st-century Second Temple Judaism understood election primarily as national (Israelites) and racial (Jews), not as individual. Their conclusion is thus that Paul's writings on election should be interpreted in a similar corporate light. Arminian theology usually falls into one of two groups — Classical Arminianism, drawn from the teaching of Jacobus Arminius — and Wesleyan Arminian, drawing primarily from Wesley. Both groups overlap substantially. Classical Arminianism is the theological system that was presented
Arminianism
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5656
by Jacobus Arminius and maintained by some of the Remonstrants; its influence serves as the foundation for all Arminian systems. A list of beliefs is given below: On whether a believer could commit apostasy (i.e., desert Christ by cleaving again to this evil world, losing a good conscience, or by failing to hold on to sound doctrine), Arminius declared that this matter required further study in the Scriptures. Nevertheless, Arminius believed the Scriptures taught that believers are graciously empowered by Christ and the Holy Spirit "to fight against Satan, sin, the world and their own flesh, and to gain the
Arminianism
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5657
victory over these enemies." Furthermore, Christ and the Spirit are ever present to aid and assist believers through various temptations. But this security was not unconditional but conditional—"provided they [believers] stand prepared for the battle, implore his help, and be not wanting to themselves, Christ preserves them from falling." Arminius goes on to say, "I never taught that a true believer can, either totally or finally fall away from the faith, and perish; yet I will not conceal, that there are passages of scripture which seem to me to wear this aspect; and those answers to them which I have
Arminianism
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5658
been permitted to see, are not of such a kind as to approve themselves on all points to my understanding." After the death of Arminius in 1609, the Remonstrants maintained their leader's view on conditional security and his uncertainty regarding the possibility of believers committing apostasy. This is evidenced in the fifth article drafted by its leaders in 1610. However, sometime between 1610, and the official proceeding of the Synod of Dort (1618), the Remonstrants became fully persuaded in their minds that the Scriptures taught that a true believer was capable of falling away from faith and perishing eternally as
Arminianism
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5659
an unbeliever. They formalized their views in "The Opinion of the Remonstrants" (1618). Picirilli remarks: "Ever since that early period, then, when the issue was being examined again, Arminians have taught that those who are truly saved need to be warned against apostasy as a real and possible danger." The core beliefs of Jacobus Arminius and the Remonstrants are summarized as such by theologian Stephen Ashby: John Wesley has historically been the most influential advocate for the teachings of Arminian soteriology. Wesley thoroughly agreed with the vast majority of what Arminius himself taught, maintaining strong doctrines of original sin, total
Arminianism
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5660
depravity, conditional election, prevenient grace, unlimited atonement, and the possibility of apostasy. Wesley departs from Classical Arminianism primarily on three issues: Since the time of Arminius, his name has come to represent a very large variety of beliefs. Some of these beliefs, such as Pelagianism and semi-Pelagianism (see below) are not considered to be within Arminian orthodoxy and are dealt with elsewhere. Some doctrines, however, do adhere to the Arminian foundation and, while minority views, are highlighted below. The doctrine of open theism states that God is omnipresent, omnipotent, and omniscient, but differs on the nature of the future. Open
Arminianism
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5661
theists claim that the future is not completely determined (or "settled") because people have not made their free decisions yet. God therefore knows the future partially in possibilities (human free actions) rather than solely certainties (divinely determined events). As such, open theists resolve the issue of human free will and God's sovereignty by claiming that God is sovereign because he does not ordain each human choice, but rather works in cooperation with his creation to bring about his will. This notion of sovereignty and freedom is foundational to their understanding of love since open theists believe that love is not
Arminianism
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5662
genuine unless it is freely chosen. The power of choice under this definition has the potential for as much harm as it does good, and open theists see free will as the best answer to the problem of evil. Well-known proponents of this theology are Greg Boyd, Clark Pinnock, Thomas Jay Oord, William Hasker, and John E. Sanders. Some Arminians, such as professor and theologian Robert Picirilli, reject the doctrine of open theism as a "deformed Arminianism". Joseph Dongell stated that "open theism actually moves beyond classical Arminianism towards process theology." There are also some Arminians, like Roger Olson, who
Arminianism
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5663
believe Open theism to be an alternative view that a Christian can have. The majority Arminian view accepts classical theism – the belief that God's power, knowledge, and presence have no external limitations, that is, outside of his divine nature. Most Arminians reconcile human free will with God's sovereignty and foreknowledge by holding three points: The majority Arminian view is that election is individual and based on God's foreknowledge of faith, but a second perspective deserves mention. These Arminians reject the concept of individual election entirely, preferring to understand the doctrine in corporate terms. According to this corporate election, God
Arminianism
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5664
never chose individuals to elect to salvation, but rather He chose to elect the believing church to salvation. Dutch Reformed theologian Herman Ridderbos says "[The certainty of salvation] does not rest on the fact that the church belongs to a certain "number", but that it belongs to Christ, from before the foundation of the world. Fixity does not lie in a hidden decree, therefore, but in corporate unity of the Church with Christ, whom it has come to know in the gospel and has learned to embrace in faith." Corporate election draws support from a similar concept of corporate election
Arminianism
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5665
found in the Old Testament and Jewish law. Indeed most biblical scholarship is in agreement that Judeo-Greco-Roman thought in the 1st century was opposite of the Western world's "individual first" mantra – it was very collectivist or communitarian in nature. Identity stemmed from membership in a group more than individuality. According to Romans 9–11, supporters claim, Jewish election as the chosen people ceased with their national rejection of Jesus as Messiah. As a result of the new covenant, God's chosen people are now the corporate body of Christ, the church (sometimes called "spiritual Israel" – see also Covenant theology). The
Arminianism
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5666
pastor and theologian Brian Abasciano claims "What Paul says about Jews, Gentiles, and Christians, whether of their place in God’s plan, or their election, or their salvation, or how they should think or behave, he says from a corporate perspective which views the group as primary and those he speaks about as embedded in the group. These individuals act as members of the group to which they belong, and what happens to them happens by virtue of their membership in the group." These scholars also maintain that Jesus was the only human ever elected and that individuals must be "in
Arminianism
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5667
Christ" (Eph 1:3–4) through faith to be part of the elect. This was, in fact, Swiss Reformed theologian, Karl Barth's, understanding of the doctrine of election. Joseph Dongell, professor at Asbury Theological Seminary, states "the most conspicuous feature of Ephesians 1:3–2:10 is the phrase 'in Christ', which occurs twelve times in Ephesians 1:3–14 alone...this means that Jesus Christ himself is the chosen one, the predestined one. Whenever one is incorporated into him by grace through faith, one comes to share in Jesus' special status as chosen of God." Markus Barth illustrates the inter-connectedness: "Election in Christ must be understood as
Arminianism
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the election of God's people. Only as members of that community do individuals share in the benefits of God's gracious choice." Understanding Arminianism is aided by understanding the theological alternatives: Pelagianism, Semi-Pelagianism, Lutheranism, and Calvinism. Arminianism, like any major belief system, is frequently misunderstood both by critics and would-be supporters. Arminian beliefs compared to other Protestants. Many Calvinist critics of Arminianism, both historically and currently, claim that Arminianism condones, accepts, or even explicitly supports Pelagianism or Semi-Pelagianism. Arminius referred to Pelagianism as "the grand falsehood" and stated that he "must confess that I detest, from my heart, the consequences [of
Arminianism
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5669
that theology]." David Pawson, a British pastor, decries this association as "libelous" when attributed to Arminius' or Wesley's doctrine. Indeed, most Arminians reject all accusations of Pelagianism; nonetheless, primarily due to Calvinist opponents, the two terms remain intertwined in popular usage. Ever since Arminius and his followers revolted against Calvinism in the early 17th century, Protestant soteriology has been largely divided between Calvinism and Arminianism. The extreme of Calvinism is hyper-Calvinism, which insists that signs of election must be sought before evangelization of the unregenerate takes place and that the eternally damned have no obligation to repent and believe, and
Arminianism
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5670
on the extreme of Arminianism is Pelagianism, which rejects the doctrine of original sin on grounds of moral accountability; but the overwhelming majority of Protestant, evangelical pastors and theologians hold to one of these two systems or somewhere in between. Arminianism Arminianism is based on theological ideas of the Dutch Reformed theologian Jacobus Arminius (1560–1609) and his historic supporters known as Remonstrants. His teachings held to the five solae of the Reformation, but they were distinct from particular teachings of Martin Luther, Huldrych Zwingli, John Calvin, and other Protestant Reformers. Jacobus Arminius (Jakob Harmenszoon) was a student of Theodore Beza
Arminianism
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5671
The Alan Parsons Project The Alan Parsons Project were an English rock band active between 1975 and 1990, whose core membership consisted of Alan Parsons and Eric Woolfson. They were accompanied by a varying number of session musicians and some relatively consistent band members such as guitarist Ian Bairnson, arranger Andrew Powell, bassist and vocalist David Paton, drummer Stuart Elliott, and vocalists Lenny Zakatek and Chris Rainbow. Parsons was an audio engineer and producer by profession, but also a musician and a composer. A songwriter by profession, Woolfson was also a composer, a pianist, and a singer. Almost all the
"The Alan Parsons Project"
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5672
songs on the Project's albums are credited to "Woolfson/Parsons". Alan Parsons met Eric Woolfson in the canteen of Abbey Road Studios in the summer of 1974. Parsons had already acted as Assistant Engineer on the Beatles' albums "Abbey Road" (1969) and "Let It Be" (1970), had recently engineered Pink Floyd's "The Dark Side of the Moon" (1973), and had produced several acts for EMI Records. Woolfson, a songwriter and composer, was working as a session pianist; he had also composed material for a concept album idea based on the work of Edgar Allan Poe. When Parsons asked Woolfson to become
"The Alan Parsons Project"
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5673
his manager, he accepted and subsequently managed Parsons's career as a producer and engineer through a string of successes, including Pilot, Steve Harley, Cockney Rebel, John Miles, Al Stewart, Ambrosia, and the Hollies. Parsons commented at the time that he felt frustrated in having to accommodate the views of some of the musicians, which he felt interfered with his production. Woolfson came up with the idea of making an album based on developments in the film industry, where the focal point of the films' promotion shifted from film stars to directors such as Alfred Hitchcock and Stanley Kubrick. If the
"The Alan Parsons Project"
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5674
film industry was becoming a director's medium, Woolfson felt the music business might well become a producer's medium. Recalling his earlier Edgar Allan Poe material, Woolfson saw a way to combine his and Parsons's respective talents. Parsons would produce and engineer songs written and composed by the two, and the first Alan Parsons Project was begun. The Project's first album, "Tales of Mystery and Imagination" (1976), which was released by 20th Century Fox Records and included major contributions by all members of Pilot and Ambrosia, was a success, reaching the Top 40 in the US "Billboard" 200 chart. The song
"The Alan Parsons Project"
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5675
"The Raven" featured lead vocals by the actor Leonard Whiting, and, according to the 2007 remastered album liner notes, was the first rock song to use a digital vocoder, with Alan Parsons speaking lyrics through it. Arista Records then signed the Alan Parsons Project participants for further albums. Through the late 1970s and early 1980s, the Project's popularity continued to grow. (However, the Project was always more popular in North America, Ibero-America, and Continental Europe than in Parsons's home country, never achieving a UK Top 40 single or Top 20 album). The singles "I Wouldn't Want to Be Like You",
"The Alan Parsons Project"
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5676
"Games People Play", "Damned If I Do", "Time" (the first single to feature Woolfson's lead vocal) and "Eye in the Sky" had a notable impact on the "Billboard" Hot 100. "Don't Answer Me" became the Project's last successful single in the United States; it reached the top 15 on the American charts in 1984. After those successes, however, the Project began to fade from view. There were fewer hit singles, and declining album sales. 1987's "Gaudi" would be the Project's final release, though it had planned to record an album called "Freudiana" (1990) next. Even though the studio version of
"The Alan Parsons Project"
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5677
"Freudiana" was produced by Parsons (and featured the regular Project backing musicians, making it an 'unofficial' Project album), it was primarily Woolfson's idea to turn it into a musical. This eventually led to a rift between the two artists. While Parsons pursued his own solo career and took many members of the Project on the road for the first time in a successful worldwide tour, Woolfson went on to produce musical plays influenced by the Project's music. "Freudiana", "Gaudi", and "Gambler" were three musicals that included some Project songs like "Eye in the Sky", "Time", "Inside Looking Out", and "Limelight".
"The Alan Parsons Project"
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5678
The live music from "Gambler" was only distributed at the performance site in Mönchengladbach, Germany. In 1979, Parsons, Woolfson, and their record label Arista, had been stalled in contract renegotiations when the two submitted an all-instrumental album tentatively titled 'The Sicilian Defence', named after an aggressive opening move in chess, arguably to get out of their recording contract. Arista's refusal to release the album had two known effects: the negotiations led to a renewed contract, and the album was not released at that time. In interviews he gave before his death in 2009, Woolfson said he planned to release one
"The Alan Parsons Project"
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5679
track from the "Sicilian" album, which in 2008 appeared as a bonus track on a CD re-issue of the "Eve" album. Sometime later, after he had relocated the original tapes, Parsons had completely changed his mind about the album and announced that it would finally be released on an upcoming Project box set called "The Complete Albums Collection" in 2014 for the first time as a bonus disc. Parsons released titles under his name; these were "Try Anything Once" (1993), "On Air" (1996), "The Time Machine" (1999), and "A Valid Path" (2004). Meanwhile, Woolfson made concept albums titled "Freudiana" (1990),
"The Alan Parsons Project"
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5680
about Sigmund Freud's work on psychology, and "" (2003); this continued from the Alan Parsons Project's first album about Edgar Allan Poe's literature. "Tales of Mystery and Imagination" (1976) was first remixed in 1987 for release on CD, and included narration by Orson Welles which had been recorded in 1975, but arrived too late to be included on the original album. On the 2007 deluxe edition release, it is revealed that parts of this tape were used for the 1976 Griffith Park Planetarium launch of the original album, the 1987 remix, and various radio spots, all of which were included
"The Alan Parsons Project"
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5681
as bonus material. "Sirius", eventually became the best-known, or, at least, the most frequently heard, of all Parsons songs. It was used as entrance music by various American sports teams, most notably by the Chicago Bulls during their 1990s NBA dynasty. It was also used as the entrance theme for Ricky Steamboat in pro wrestling of the mid-1980s. In addition, "Sirius" has been played in a variety of TV shows and movies including the episode "Vanishing Act" of "" and the 2009 film "Cloudy with a Chance of Meatballs". Lead vocal duties were shared by guest vocalists chosen by their
"The Alan Parsons Project"
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5682
style to complement each song. In later years, Woolfson sang lead on many of the group's hits, including "Time", "Eye in the Sky", and "Don't Answer Me". The record company pressured Parsons to use him more. However, Parsons preferred to use more technically polished and proficient singers, which Woolfson admitted he was not. In addition to Woolfson, vocalists Chris Rainbow, Lenny Zakatek, John Miles, David Paton, and Colin Blunstone made regular appearances. Other singers, such as Arthur Brown, Steve Harley, Gary Brooker, Dave Terry a.k.a. Elmer Gantry, Vitamin Z's Geoff Barradale, and Marmalade's Dean Ford, have recorded only once or
"The Alan Parsons Project"
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5683
twice with the Project. Parsons himself only sang lead on one song ("The Raven") through a vocoder and backing on a few others, including "To One in Paradise". Both of those songs appeared on "Tales of Mystery and Imagination" (1976). A small number of musicians worked with the Alan Parsons Project regularly. These core musicians contributed to the recognisable style of a Project song in spite of the varied singer line-up. Together with Parsons and Woolfson, the Project originally consisted of the group Pilot, with Ian Bairnson (guitar), David Paton (bass) and Stuart Tosh (drums). Pilot's keyboardist Billy Lyall also
"The Alan Parsons Project"
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5684
contributed. From "Pyramid" (1978) onwards, Tosh was replaced by Stuart Elliott of Cockney Rebel. Bairnson played on all albums, and Paton stayed almost until the end. Andrew Powell appeared as arranger of orchestra (and often choirs) on all albums except "Vulture Culture" (1985), when he was composing the score of Richard Donner's film "Ladyhawke" (1985). This score was partly in the Project style, recorded by most of the Project regulars, and produced and engineered by Parsons. Powell also composed some material for the first two Project albums. From "Vulture Culture" onwards, Richard Cottle played as a regular member on synthesizers
"The Alan Parsons Project"
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5685
and saxophone. Except for one occasion, the Project never played live during its original incarnation. This was because Woolfson and Parsons saw themselves mainly in the roles of writing and production, and also because of the technical difficulties of reproducing on stage the complex instrumentation used in the studio. In the 1990s things changed with the technology of digital samplers. The one occasion where the band was introduced as 'The Alan Parsons Project' in a live performance was at Night of the Proms in October 1990 (at the time of the group's break-up), featuring all Project regulars except Woolfson, who
"The Alan Parsons Project"
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5686
was present but behind the scenes, while Parsons stayed at the mixer except during the last song, where he played acoustic guitar. Since 1993, a new version of the band has toured, with Parsons performing live acoustic guitar, keyboards and vocals, with various line-ups. This latest incarnation was called Alan Parsons, later renamed the Alan Parsons Live Project to be distinct from 'The Alan Parsons Project', due to founder Parsons' break-up with Woolfson. The band currently features lead singer P.J. Olsson, guitarist Jeffrey Kollman, drummer Danny Thompson, keyboardist Tom Brooks, bass guitarist Guy Erez, vocalist and saxophonist Todd Cooper, and
"The Alan Parsons Project"
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5687
guitarist and vocalist Dan Tracey. In 2013, Alan Parsons Live Project played Colombia with a full choir and orchestra (the Medellin Philharmonic) as 'Alan Parsons Symphonic Project'. A 2-CD live set and a DVD version of this concert were released in May 2016. "The Simpsons" episode "Homerpalooza" features Homer explaining 1970s rock music to Lisa, Bart and Milhouse: "Grand Funk Railroad paved the way for Jefferson Airplane, which cleared the way for Jefferson Starship. The stage was now set for the Alan Parsons Project, which I believe was some sort of hovercraft." In the 1999 comedy film "", the weapon
"The Alan Parsons Project"
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5688
that Dr. Evil has installed on the moon is referred to as 'The Alan Parsons Project', to which his son Scott Evil makes fun of him for using the name and informing him of the band. The Alan Parsons Project The Alan Parsons Project were an English rock band active between 1975 and 1990, whose core membership consisted of Alan Parsons and Eric Woolfson. They were accompanied by a varying number of session musicians and some relatively consistent band members such as guitarist Ian Bairnson, arranger Andrew Powell, bassist and vocalist David Paton, drummer Stuart Elliott, and vocalists Lenny Zakatek
"The Alan Parsons Project"
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5689
Almost all In mathematics, the term "almost all" means "all but a negligible amount". More precisely, if X is a set, "almost all elements of X" means "all elements of X but those in a negligible subset of X". The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite, countable, or null. In contrast, "almost no" means "a negligible amount"; that is, "almost no elements of X" means "the elements of some negligible subset of X". Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) but finitely many". This
"Almost all"
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5690
use occurs in philosophy as well. Similarly, "almost all" can mean "all (elements of an uncountable set) but countably many". Examples: When speaking about the reals, sometimes "almost all" means "all reals but a null set". Similarly, if S is some set of reals, "almost all numbers in S" can mean "all numbers in S but those in a null set". The real line can be thought of as a one-dimensional Euclidean space. In the more general case of an n-dimensional space (where n is a positive integer), these definitions can be generalised to "all points but those in a
"Almost all"
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5691
null set" or "all points in S but those in a null set" (this time, S is a set of points in the space). Even more generally, "almost all" is sometimes used in the sense of "almost everywhere" in measure theory, or in the closely related sense of "almost surely" in probability theory. Examples: In number theory, "almost all positive integers" can mean "the positive integers in a set whose natural density is 1". That is, if A is a set of positive integers, and if the proportion of positive integers below n that are in A (out of all
"Almost all"
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5692
positive integers below n) tends to 1 as n tends to infinity, then almost all positive integers are in A. More generally, let S be an infinite set of positive integers, such as the set of even positive numbers or of primes. If A is a subset of S, and if the proportion of elements of S below n that are in A (out of all elements of S below n) tends to 1 as n tends to infinity, then it can be said that almost all elements of S are in A. Examples: In graph theory, if A is
"Almost all"
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5693
a set of (finite labelled) graphs, it can be said to contain almost all graphs if the proportion of graphs with n vertices that are in A tends to 1 as n tends to infinity. However, it is sometimes easier to work with probabilities, so the definition is reformulated as follows. The proportion of graphs with n vertices that are in A equals the probability that a random graph with n vertices (chosen with the uniform distribution) is in A, and choosing a graph in this way has the same outcome as generating a graph by flipping a coin for
"Almost all"
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5694
each pair of vertices to decide whether to connect them. Therefore, equivalently to the preceding definition, A contains almost all graphs if the probability that a coin flip-generated graph with n vertices is in A tends to 1 as n tends to infinity. Sometimes the latter definition is modified so that the graph is chosen randomly in some other way, where not all graphs with n vertices have the same probability, and those modified definitions are not always equivalent to the main one. The use of the term "almost all" in graph theory is not standard; the term "asymptotically almost
"Almost all"
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5695
surely" is more commonly used for this concept. Example: In topology and especially dynamical systems theory (including applications in economics), "almost all" of a topological space's points can mean "all of the space's points but those in a meagre set". Some use a more limited definition, where a subset only contains almost all of the space's points if it contains some open dense set. Example: In abstract algebra and mathematical logic, if U is an on a set X, "almost all elements of X" sometimes means "the elements of some "element" of U". For any partition of X into two
"Almost all"
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5696
disjoint sets, one of them necessarily contains almost all elements of X. It is possible to think of the elements of a filter on X as containing almost all elements of X even if it isn't an ultrafilter. Almost all In mathematics, the term "almost all" means "all but a negligible amount". More precisely, if X is a set, "almost all elements of X" means "all elements of X but those in a negligible subset of X". The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite, countable, or null. In contrast, "almost no" means
"Almost all"
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5697
Aromatic hydrocarbon An aromatic hydrocarbon or arene (or sometimes aryl hydrocarbon) is a hydrocarbon with sigma bonds and delocalized pi electrons between carbon atoms forming a circle. In contrast, aliphatic hydrocarbons lack this delocalization. The term "aromatic" was assigned before the physical mechanism determining aromaticity was discovered; the term was coined as such simply because many of the compounds have a sweet or pleasant odour. The configuration of six carbon atoms in aromatic compounds is known as a benzene ring, after the simplest possible such hydrocarbon, benzene. Aromatic hydrocarbons can be "monocyclic" (MAH) or "polycyclic" (PAH). Some non-benzene-based compounds called
"Aromatic hydrocarbon"
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5698
heteroarenes, which follow Hückel's rule (for monocyclic rings: when the number of its π electrons equals 4"n" + 2, where "n" = 0, 1, 2, 3, ...), are also called aromatic compounds. In these compounds, at least one carbon atom is replaced by one of the heteroatoms oxygen, nitrogen, or sulfur. Examples of non-benzene compounds with aromatic properties are furan, a heterocyclic compound with a five-membered ring that includes a single oxygen atom, and pyridine, a heterocyclic compound with a six-membered ring containing one nitrogen atom. Benzene, CH, is the simplest aromatic hydrocarbon, and it was the first one named
"Aromatic hydrocarbon"
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5699
as such. The nature of its bonding was first recognized by August Kekulé in the 19th century. Each carbon atom in the hexagonal cycle has four electrons to share. One goes to the hydrogen atom, and one to each of the two neighbouring carbons. This leaves one electron to share with one of the two neighbouring carbon atoms, thus creating a double bond with one carbon and leaving a single bond with the other, which is why the benzene molecule is drawn with alternating single and double bonds around the hexagon. The structure is alternatively illustrated as a circle around
"Aromatic hydrocarbon"
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5700
the inside of the ring to show six electrons floating around in delocalized molecular orbitals the size of the ring itself. This depiction represents the equivalent nature of the six carbon–carbon bonds all of bond order 1.5; the equivalency is explained by resonance forms. The electrons are visualized as floating above and below the ring with the electromagnetic fields they generate acting to keep the ring flat. General properties of aromatic hydrocarbons: The circle symbol for aromaticity was introduced by Sir Robert Robinson and his student James Armit in 1925 and popularized starting in 1959 by the Morrison & Boyd
"Aromatic hydrocarbon"
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