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# Constantine II of Scotland
## Æthelstan
By 926 Sihtric had evidently acknowledged Æthelstan as overlord, adopting Christianity and marrying a sister of Æthelstan at Tamworth. Within the year he appears to have forsaken his new faith and repudiated his wife, but before Æthelstan could respond, Sihtric died suddenly in 927. His kinsman, perhaps brother, Gofraid, who had remained as his deputy in Dublin, came from Ireland to take power in York but failed. Æthelstan moved quickly, seizing much of Northumbria. In less than a decade, the kingdom of the English had become by far the greatest power in Britain and Ireland, perhaps stretching as far north as the Firth of Forth.
John of Worcester\'s chronicle suggests that Æthelstan faced opposition from Constantine, Owain, and the Welsh kings. William of Malmesbury writes that Gofraid, together with Sihtric\'s young son Olaf Cuaran fled north and received refuge from Constantine, which led to war with Æthelstan. A meeting at Eamont Bridge on 12 July 927 was sealed by an agreement that Constantine, Owain, Hywel Dda, and Ealdred would \"renounce all idolatry\": that is, they would not ally with the Viking kings. William states that Æthelstan stood godfather to a son of Constantine, probably Indulf (Ildulb mac Constantín), during the conference.
Æthelstan followed up his advances in the north by securing the recognition of the Welsh kings. For the next seven years, the record of events in the north is blank. Æthelstan\'s court was attended by the Welsh kings, but not by Constantine or Owain. This absence of record means that Æthelstan\'s reasons for marching north against Constantine in 934 are unclear.
Æthelstan\'s invasion is reported in brief by the *Anglo-Saxon Chronicle*, and later chroniclers such as John of Worcester, William of Malmesbury, Henry of Huntingdon and Symeon of Durham add detail to that bald account. Æthelstan\'s army began gathering at Winchester by 28 May 934 and travelled north to Nottingham by 7 June. He was accompanied by many leaders, including the Welsh kings Hywel Dda, Idwal Foel and Morgan ab Owain. From Mercia, the army continued to Chester-le-Street, before resuming the march accompanied by a fleet of ships. Owain was defeated and Symeon states that the army went as far north as Dunnottar and Fortriu, while the fleet is said to have raided Caithness, by which a much larger area, including Sutherland, is probably intended. It is unlikely that Constantine\'s personal authority extended so far north, so the attacks were probably directed at his allies, comprising simple looting expeditions.
The *Annals of Clonmacnoise* state that \"the Scottish men compelled \[Æthelstan\] to return without any great victory\", while Henry of Huntingdon claims that the English faced no opposition. A negotiated settlement might have ended matters: according to John of Worcester, a son of Constantine was given as a hostage to Æthelstan and Constantine himself accompanied the English king on his return south. He witnessed a charter with Æthelstan at Buckingham on 13 September 934 in which he is described as *subregulus*, *i.e.*, a king acknowledging Æthelstan\'s overlordship, the only place there is any record of such a description. However, there is no record of Constantine having ever submitted to Æthelstan\'s overlordship or that he considered himself such. The following year, Constantine was again in England at Æthelstan\'s court, this time at Cirencester where he appears as a witness, as the first of several kings, followed by Owain and Hywel Dda, who subscribed to the diploma. At Christmas of 935, Owain was once more at Æthelstan\'s court along with the Welsh kings, but Constantine was not. His return to England less than two years later would be in very different circumstances.
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# Constantine II of Scotland
## Brunanburh and after {#brunanburh_and_after}
Following his departure from Æthelstan\'s court after 935, there is no further report of Constantine until 937. In that year, together with Owain and Olaf Guthfrithson of Dublin, Constantine invaded England. The resulting battle of Brunanburh --- *Dún Brunde* --- is reported in the *Annals of Ulster* as follows: `{{blockquote|a great battle, lamentable and terrible was cruelly fought... in which fell uncounted thousands of the Northmen. ... And on the other side, a multitude of Saxons fell; but Æthelstan, the king of the Saxons, obtained a great victory.<ref>Anderson, ''Early Sources'', pp. 428–429; ''Annals of Ulster'', s.a. 937.</ref>}}`{=mediawiki} The battle was remembered in England a generation later as \"the Great Battle\". When reporting the battle, the *Anglo-Saxon Chronicle* abandons its usual terse style in favour of a heroic poem vaunting the great victory. In this, the \"hoary\" Constantine, by now around 60 years of age, is said to have lost a son in the battle, a claim which the *Chronicle of the Kings of Alba* confirms. The *Annals of Clonmacnoise* give his name as Cellach. For all its fame, the site of the battle is uncertain and several sites have been advanced, with Bromborough on the Wirral the most favoured location.
Brunanburh, for all that it had been a famous and bloody battle, settled nothing. On 27 October 939 Æthelstan, the \"pillar of the dignity of the western world\" in the words of the *Annals of Ulster*, died at Malmesbury. He was succeeded by his brother Edmund, then aged 18. Æthelstan\'s realm, seemingly made safe by the victory of Brunanburh, collapsed in little more than a year from his death when Amlaíb returned from Ireland and seized Northumbria and the Mercian Danelaw. Edmund spent the remainder of Constantín\'s reign rebuilding his kingdom.
For Constantine\'s last years as king, there is only the meagre record of the *Chronicle of the Kings of Alba*. The death of Æthelstan is reported, as are two others. The first of these, in 938, is that of Dubacan, mormaer of Angus or son of the mormaer. Unlike the report of 918, on this occasion, the title mormaer is attached to a geographical area, but it is unknown whether the Angus of 938 was in any way similar to the later mormaerdom or earldom. The second death entered with that of Æthelstan, is that of Eochaid mac Ailpín, who might, from his name, have been a kinsman of Constantín.
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# Constantine II of Scotland
## Abdication and posterity {#abdication_and_posterity}
By the early 940s, Constantine was an old man in his late sixties or seventies. The kingdom of Alba was too new to be said to have a customary rule of succession, but Pictish and Irish precedents favoured an adult successor descended from Kenneth MacAlpin. Constantine\'s surviving son Indulf, probably baptised in 927, would have been too young to be a serious candidate for the kingship in the early 940s, and the obvious heir was Constantine\'s nephew, Malcolm I. As Malcolm was born no later than 901, by the 940s he was no longer a young man and may have been impatient. Willingly or not --- the 11th century *The Prophecy of Berchán*, a verse history in the form of a supposed prophecy, states that it was not a voluntary decision --- Constantine abdicated in 943 and entered a monastery, leaving the kingdom to Malcolm.
Although his retirement might have been involuntary, the *Life* of Cathróe of Metz and *The Prophecy of Berchán* portray Constantine as a devout king. The monastery to which Constantine retired, and where he is said to have been abbot, was probably that of St Andrews. This had been refounded in his reign and given to the reforming Céli Dé (Culdee) movement. The Céli Dé were subsequently to be entrusted with many monasteries throughout the kingdom of Alba until replaced in the 12th century by new orders imported from France.
Seven years later the *Chronicle of the Kings of Alba* says: `{{blockquote|[Malcolm I] plundered the English as far as the [[river Tees]], and he seized a multitude of people and many herds of cattle: and the Scots called this the raid of Albidosorum, that is, Nainndisi. But others say that Constantine made this raid, asking of the king, Malcolm I, that the kingship should be given to him for a week's time so that he could visit the English. In fact, it was Malcolm I who made the raid, but Constantine incited him, as I have said.<ref>Anderson, ''Early Sources'', pp. 452–453.</ref>}}`{=mediawiki} Woolf suggests that the association of Constantine with the raid is a late addition, one derived from a now-lost saga or poem.
Constantine\'s death in 952 is recorded by the Irish annals, who enter it among ecclesiastics. His son Indulf would become king on Malcolm\'s death. The last of Constantine\'s certain descendants to be king in Alba was a great-grandson, Constantine III (Constantín mac Cuiléin). Another son had died at Brunanburh and according to John of Worcester, Amlaíb mac Gofraid was married to a daughter of Constantine. It is possible that Constantine had other children, but like the name of his wife, or wives, this has not been recorded.
The form of kingdom which appeared in Constantine\'s reign continued in much the same way until the Davidian Revolution in the 12th century. As with his ecclesiastical reforms, his political legacy was the creation of a new form of Scottish kingship that lasted for two centuries after his death.
## Family
The name of Constantine\'s wife is not known, however, they are known to have had at least 3 children:
- Ildulb mac Causantín (Indulf or Indulph)(died 962), king of Alba 954--962;
- Cellach, died in 937 in the Battle of Brunanburh;
- A daughter, name not recorded, married Amlaíb mac Gofraid
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# Common Language Infrastructure
The **Common Language Infrastructure** (**CLI**) is an open specification and technical standard originally developed by Microsoft and standardized by ISO/IEC (**ISO/IEC 23271**) and Ecma International (**ECMA 335**) that describes executable code and a runtime environment that allows multiple high-level languages to be used on different computer platforms without being rewritten for specific architectures. This implies it is platform agnostic. The .NET Framework, .NET and Mono are implementations of the CLI. The metadata format is also used to specify the API definitions exposed by the Windows Runtime.
## Overview
Among other things, the CLI specification describes the following five aspects:
The Common Type System (CTS)
: A set of data types and operations that are shared by all CTS-compliant programming languages.
The Metadata
: Information about program structure is language-agnostic, so that it can be referenced between languages and tools, making it easy to work with code written in a language the developer is not using.
The Common Language Specification (CLS)
: The CLS, a subset of the CTS, are rules to which components developed with/for the supported languages must adhere.
: They apply to consumers (developers who are programmatically accessing a component that is CLS-compliant), frameworks (developers who are using a language compiler to create CLS-compliant libraries), and extenders (developers who are creating a tool such as a language compiler or a code parser that creates CLS-compliant components).
The Virtual Execution System (VES)
: The VES loads and executes CLI-compatible programs, using the metadata to combine separately generated pieces of code at runtime.
: All compatible languages compile to Common Intermediate Language (CIL), which is an intermediate language that is abstracted from the platform hardware. When the code is executed, the platform-specific VES will compile the CIL to the machine language according to the specific hardware and operating system.
: In the CLI standard initially developed by Microsoft, the VES is implemented by the Common Language Runtime (CLR).
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The Standard Libraries
: A set of libraries providing many common functions, such as file reading and writing. Their core is the Base Class Library (BCL).
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# Common Language Infrastructure
## Standardization and licensing {#standardization_and_licensing}
In August 2000, Microsoft, Hewlett-Packard, Intel, and others worked to standardize CLI. By December 2001, it was ratified by the Ecma, with ISO/IEC standardization following in April 2003.
Microsoft and its partners hold patents for CLI. Ecma and ISO/IEC require that all patents essential to implementation be made available under \"reasonable and non-discriminatory (RAND) terms.\" It is common for RAND licensing to require some royalty payment, which could be a cause for concern with Mono. `{{as of|2013|January}}`{=mediawiki}, neither Microsoft nor its partners have identified any patents essential to CLI implementations subject to RAND terms.
, Microsoft added C# and CLI to the list of specifications that the Microsoft Community Promise applies to, so anyone can safely implement specified editions of the standards without fearing a patent lawsuit from Microsoft. To implement the CLI standard requires conformance to one of the supported and defined profiles of the standard, the minimum of which is the kernel profile. The kernel profile is actually a very small set of types to support in comparison to the well known core library of default .NET installations. However, the conformance clause of the CLI allows for extending the supported profile by adding new methods and types to classes, as well as deriving from new namespaces. But it does not allow for adding new members to interfaces. This means that the features of the CLI can be used and extended, as long as the conforming profile implementation does not change the behavior of a program intended to run on that profile, while allowing for unspecified behavior from programs written specifically for that implementation.
In 2012, Ecma and ISO/IEC published the new edition of the CLI standard.
## Implementations
- .NET Framework is Microsoft\'s original commercial implementation of the CLI. It only supports Windows. It was superseded by .NET in November 2020.
- .NET, previously known as .NET Core, is the free and open-source multi-platform successor to .NET Framework, released under the MIT License
- .NET Compact Framework is Microsoft\'s commercial implementation of the CLI for portable devices and Xbox 360.
- .NET Micro Framework is an open source implementation of the CLI for resource-constrained devices.
- Mono is an alternative open source implementation of CLI and accompanying technologies, mainly used for mobile and game development.
- DotGNU is a decommissioned part of the GNU Project started in January 2001 that aimed to provide a free and open source software alternative to Microsoft\'s .NET Framework
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# Chinese classics
The **Chinese classics** or **canonical texts** are the works of Chinese literature authored prior to the establishment of the imperial Qin dynasty in 221 BC. Prominent examples include the Four Books and Five Classics in the Neo-Confucian tradition, themselves an abridgment of the Thirteen Classics. The Chinese classics used a form of written Chinese consciously imitated by later authors, now known as Classical Chinese. A common Chinese word for \"classic\" (`{{zhi|first=t|t=經|s=经|p=jīng}}`{=mediawiki}) literally means \'warp thread\', in reference to the techniques by which works of this period were bound into volumes.
Texts may include *shi* (*史*, \'histories\') *zi* (*子* \'master texts\'), philosophical treatises usually associated with an individual and later systematized into schools of thought but also including works on agriculture, medicine, mathematics, astronomy, divination, art criticism, and other miscellaneous writings) and *ji* (*集}}* \'literary works\') as well as the cultivation of *jing*, \'essence\' in Chinese medicine.
In the Ming and Qing dynasties, the Four Books and Five Classics were the subjects of mandatory study by those Confucian scholars who wished to take the imperial examination and needed to pass them in order to become scholar-officials. Any political discussion was full of references to this background, and one could not become part of the literati---or even a military officer in some periods---without having memorized them. Generally, children first memorized the Chinese characters of the *Three Character Classic* and *Hundred Family Surnames* and they then went on to memorize the other classics. The literate elite therefore shared a common culture and set of values.
## Qin dynasty {#qin_dynasty}
### Loss of texts {#loss_of_texts}
According to Sima Qian\'s *Records of the Grand Historian*, after Qin Shi Huang, the first emperor of China, unified China in 221 BC, his chancellor Li Si suggested suppressing intellectual discourse to unify thought and political opinion. This was alleged to have destroyed philosophical treatises of the Hundred Schools of Thought, with the goal of strengthening the official Qin governing philosophy of Legalism. According to the *Shiji*, three categories of books were viewed by Li Si to be most dangerous politically. These were poetry, history (especially historical records of other states than Qin), and philosophy. The ancient collection of poetry and historical records contained many stories concerning the ancient virtuous rulers. Li Si believed that if the people were to read these works they were likely to invoke the past and become dissatisfied with the present. The reason for opposing various schools of philosophy was that they advocated political ideas often incompatible with the totalitarian regime.
Modern historians doubt the details of the story, which first appeared more than a century later. Regarding the alleged Qin objective of strengthening Legalism, the traditional account is anachronistic in that Legalism was not yet a defined category of thought during the Qin period, and the \"schools of thought\" model is no longer considered to be an accurate portrayal of the intellectual history of pre-imperial China. Michael Nylan observes that despite its mythic significance, the \"burning of books and burying of scholars\" legend does not bear close scrutiny. Nylan suggests that the reason Han dynasty scholars charged the Qin with destroying the Confucian Five Classics was partly to \"slander\" the state they defeated and partly because Han scholars misunderstood the nature of the texts, for it was only after the founding of the Han that Sima Qian labeled the Five Classics as Confucian. Nylan also points out that the Qin court appointed classical scholars who were specialists on the *Classic of Poetry* and the *Book of Documents*, which meant that these texts would have been exempted, and that the *Book of Rites* and the *Zuo Zhuan* did not contain the glorification of defeated feudal states which the First Emperor gave as his reason for destroying them. Nylan further suggests that the story might be based on the fact that the Qin palace was razed in 207 BC and many books were undoubtedly lost at that time. Martin Kern adds that Qin and early Han writings frequently cite the Classics, especially the *Documents* and the *Classic of Poetry*, which would not have been possible if they had been burned, as reported.
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# Chinese classics
## Western Han dynasty {#western_han_dynasty}
### Five Classics {#five_classics}
The **Five Classics** (`{{zhi|t=五經|p=Wǔjīng}}`{=mediawiki}) are five pre-Qin texts that became part of the state-sponsored curriculum during the Western Han dynasty, which adopted Confucianism as its official ideology. It was during this period that the texts first began to be considered together as a set collection, and to be called collectively the \"Five Classics\". Several of the texts were already prominent by the Warring States period, but the literature culture at the time did not lend itself to clear boundaries between works, so a high degree of variance between individual witnesses of the same title was common, as well as considerable intertextuality and cognate chapters between different titles. Mencius, the leading Confucian scholar of the time, regarded the *Spring and Autumn Annals* as being equally important as the semi-legendary chronicles of earlier periods.
*Classic of Poetry*
: A collection of 305 poems divided into 160 folk songs, 105 festal songs sung at court ceremonies, and 40 hymns and eulogies sung at sacrifices to heroes and ancestral spirits of the royal house.
*Book of Documents*
: A collection of documents and speeches alleged to have been written by rulers and officials of the early Zhou period and before. It is possibly the oldest Chinese narrative, and may date from the 6th century BC. It includes examples of early Chinese prose.
*Book of Rites*
: Describes ancient rites, social forms and court ceremonies. The version studied today is a re-worked version compiled by scholars in the third century BC rather than the original text, which is said to have been edited by Confucius himself.
*I Ching*
: The book contains a divination system comparable to Western geomancy or the West African Ifá system. In Western cultures and modern East Asia, it is still widely used for this purpose.
*Spring and Autumn Annals*
: A historical record of the State of Lu, Confucius\'s native state, 722--481 BC.
Up to the Western Han, authors would typically list the Classics in the order Poems-Documents-Rituals-Changes-Spring and Autumn. However, from the Eastern Han the default order instead became Changes-Documents-Poems-Rituals-Spring and Autumn.
### Han imperial library {#han_imperial_library}
In 26 BCE, at the command of the emperor, Liu Xiang (77--6 BC) compiled the first catalogue of the imperial library, the *Abstracts* (`{{zhi|first=t|t=別錄|s=别录|p=Bielu}}`{=mediawiki}), and is the first known editor of the *Classic of Mountains and Seas*, which was finished by his son. Liu also edited collections of stories and biographies, the *Biographies of Exemplary Women*. He has long erroneously been credited with compiling the *Biographies of the Immortals*, a collection of Taoist hagiographies and hymns.`{{better source needed|date=April 2024}}`{=mediawiki} Liu Xiang was also a poet, being credited with the \"Nine Laments\" that appears in the *Chu Ci*.
The works edited and compiled by Liu Xiang include:
This work was continued by his son, Liu Xin, who finally completed the task after his father\'s death. The transmitted corpus of these classical texts all derives from the versions edited down by Liu Xiang and Liu Xin. Michael Nylan has characterised the scope of the Liu pair\'s editing as having been so vast that it affects our understanding of China\'s pre-imperial period to the same degree as the Qin unification does.
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# Chinese classics
## Song dynasty {#song_dynasty}
### Four Books {#four_books}
The **Four Books** (`{{zhi|t=四書|p=Sìshū}}`{=mediawiki}) are texts illustrating the core value and belief systems in Confucianism. They were selected by Zhu Xi (1130--1200) during the Song dynasty to serve as general introduction to Confucian thought, and they were, in the Ming and Qing dynasties, made the core of the official curriculum for the civil service examinations. They are:
*Great Learning*
: Originally one chapter in the *Book of Rites*. It consists of a short main text attributed to Confucius and nine commentary chapters by Zengzi, one of the disciples of Confucius. Its importance is illustrated by Zengzi\'s foreword that this is the gateway of learning. It is significant because it expresses many themes of Chinese philosophy and political thinking, and has therefore been extremely influential both in classical and modern Chinese thought. Government, self-cultivation and investigation of things are linked.
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*Doctrine of the Mean*
: Another chapter in *Book of Rites*, attributed to Confucius\'s grandson Zisi. The purpose of this small, 33-chapter book is to demonstrate the usefulness of a golden way to gain perfect virtue. It focuses on the Tao that is prescribed by a heavenly mandate not only to the ruler but to everyone. To follow these heavenly instructions by learning and teaching will automatically result in a Confucian virtue of *de*. Because Heaven has laid down what is the way to perfect virtue, it is not that difficult to follow the steps of the holy rulers of old if one only knows what is the right way.
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*Analects*
: Thought to be a compilation of speeches by Confucius and his disciples, as well as the discussions they held. Since Confucius\'s time, the *Analects* has heavily influenced the philosophy and moral values of China and later other East Asian countries as well. The imperial examinations, started in the Sui dynasty and eventually abolished with the founding of the Republic of China, emphasized Confucian studies and expected candidates to quote and apply the words of Confucius in their essays.
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*Mencius*
: A collection of conversations of the scholar Mencius with kings of his time. In contrast to the sayings of Confucius, which are short and self-contained, the *Mencius* consists of long dialogues with extensive prose.
## Ming dynasty {#ming_dynasty}
### Thirteen Classics {#thirteen_classics}
The official curriculum of the imperial examination system from the Song dynasty onward are the Thirteen Classics. In total, these works total to more than 600,000 characters that must be memorized in order to pass the examination. Moreover, these works are accompanied by extensive commentary and annotation, containing approximately 300 million characters by some estimates.
- *I Ching*
- *Book of Documents*
- *Classic of Poetry*
- The Three Ritual Classics (`{{zhi|c=三禮|p=Sānlǐ}}`{=mediawiki})
- *Rites of Zhou*
- *Ceremonies and Rites*
- *Book of Rites*
- \"Great Learning\" chapter (`{{zhi|c=大學|p=Dà xué}}`{=mediawiki})
- \"Doctrine of the Mean\" chapter (`{{zhi|c=中庸|p=Zhōng yōng}}`{=mediawiki})
- The Three Commentaries on the *Spring and Autumn Annals*
- *Zuo Zhuan*
- *The Commentary of Gongyang*
- *The Commentary of Guliang*
- *Analects*
- *Classic of Filial Piety*
- *Erya*
- *Mencius*
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# Chinese classics
## List of classics {#list_of_classics}
### Before 221 BC {#before_221_bc}
It is often difficult or impossible to precisely date pre-Qin works beyond their being \"pre-Qin\", a period of 1000 years. Information in ancient China was often by oral tradition and passed down from generations before so was rarely written down, so the older the composition of the texts may not be in a chronological order as that which was arranged and presented by their attributed \"authors\".
The below list is therefore organized in the order which is found in the *Siku Quanshu* (*Complete Library of the Four Treasuries*), the encyclopedic collation of the works found in the imperial library of the Qing dynasty under the Qianlong Emperor. The *Siku Quanshu* classifies all works into 4 top-level branches: the Confucian Classics and their secondary literature; history; philosophy; and poetry. There are sub-categories within each branch, but due to the small number of pre-Qin works in the Classics, History and Poetry branches, the sub-categories are only reproduced for the Philosophy branch.
#### Classics branch {#classics_branch}
Title Description
---------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
*I Ching* A manual of divination based on the eight trigrams attributed to the mythical figure Fuxi---by at least the Eastern Zhou, these eight trigrams had been multiplied to create 64 hexagrams.
*Book of Documents* A collection of documents and speeches allegedly from the Xia, Shang and Western Zhou periods, and even earlier. It contains some of the earliest examples of Chinese prose.
*Classic of Poetry* Made up of 305 poems divided into 160 folk songs, 74 minor festal songs, traditionally sung at court festivities, 31 major festal songs, sung at more solemn court ceremonies, and 40 hymns and eulogies, sung at sacrifices to gods and ancestral spirits of the royal house. This book is traditionally credited as a compilation edited by Confucius. A standard version, named *Maoshi Zhengyi*, was compiled in the mid-7th century under the leadership of Kong Yingda.
The Three Rites
*Rites of Zhou* Conferred the status of a classic in the 12th century, in place of the lost *Classic of Music*.
*Book of Etiquette and Ceremony* Describes ancient rites, social forms and court ceremonies.
*Classic of Rites* Describes social forms, administration, and ceremonial rites.
*Spring and Autumn Annals* Chronologically the earliest of the annals; comprising about 16,000 characters, it records the events of the state of Lu from 722 to 481 BC, with implied condemnation of usurpations, murder, incest, etc.
*Zuo zhuan* A different report of the same events as the *Spring and Autumn Annals* with a few significant differences. It covers a longer period than the *Spring and Autumn Annals* .
*Commentary of Gongyang* Another surviving commentary on the same events (see *Spring and Autumn Annals*).
*Commentary of Guliang* Another surviving commentary on the same events (see *Spring and Autumn Annals*).
*Classic of Filial Piety* A small book giving advice on filial piety; how to behave towards a senior (such as a father, an elder brother, or ruler).
The Four Books
*Mencius* A book of anecdotes and conversations of Mencius.
*Analects* A twenty-chapter work of dialogues attributed to Confucius and his disciples; traditionally believed to have been written by Confucius\'s own circle it is thought to have been set down by later Confucian scholars.
Doctrine of the Mean A chapter from the Book of Rites made into an independent work by Zhu Xi
Great Learning A chapter from the Book of Rites made into an independent work by Zhu Xi
Philology
*Erya* A dictionary explaining the meaning and interpretation of words in the context of the Confucian Canon.
#### History branch {#history_branch}
Title Description
------------------------------------ ------------------------------------------------------------------------------------------------------------
*Bamboo Annals* History of Zhou dynasty excavated from a Wei tomb in the Jin dynasty.
*Yi Zhou Shu* Similar in style to the *Book of Documents*
*Guoyu* A collection of historical records of numerous states recorded the period from the Western Zhou to 453 BC.
*Strategies of the Warring States* Edited by Liu Xiang.
*Yanzi chunqiu* Attributed to the statesman Yan Ying, a contemporary of Confucius
#### Philosophy branch {#philosophy_branch}
The philosophical typology of individual pre-imperial texts has in every case been applied retroactively, rather than consciously within the text itself. The categorization of works of these genera has been highly contentious, especially in modern times. Many modern scholars reject the continued usefulness of this model as a heuristic for understanding the shape of the intellectual landscape of the time.
Title Description
------------------------------------------------------ ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Confucianism (excluding Classics branch)
*Kongzi Jiayu* Collection of stories about Confucius and his disciples. Authenticity disputed.
*Xunzi* Attributed to Xun Kuang, an ancient Chinese collection of philosophical writings that makes the distinction between what is born in man and what must be learned through rigorous education.
Seven Military Classics
*Six Secret Teachings* Attributed to Jiang Ziya
*The Art of War* Attributed to Sunzi.
*Wuzi* Attributed to Wu Qi.
*The Methods of the Sima* Attributed to Sima Rangju.
*Wei Liaozi* Attributed to Wei Liao.
*Three Strategies of Huang Shigong* Attributed to Jiang Ziya.
*Thirty-Six Stratagems* Recently recovered.
Legalism
*Guanzi* Attributed to Guan Zhong.
*Deng Xizi*`{{csni|date=August 2024}}`{=mediawiki} Fragment
*The Book of Lord Shang* Attributed to Shang Yang.
*Han Feizi* Attributed to Han Fei.
*Shenzi* Attributed to Shen Buhai. All but one chapter is lost.
*Canon of Laws* Attributed to Li Kui.
Medicine
*Huangdi Neijing*
*Nan Jing*
Miscellaneous
*Yuzi*`{{csni|date=August 2024}}`{=mediawiki} Fragment
*Mozi* Attributed to Mozi.
*Yinwenzi*`{{csni|date=August 2024}}`{=mediawiki} Fragment
*Shenzi* Attributed to Shen Dao. It originally consisted of ten volumes and forty-two chapters, of which all but seven chapters have been lost.
*Heguanzi*
*Gongsun longzi*
*Guiguzi*
*Lüshi Chunqiu* An encyclopedia of ancient classics edited by Lü Buwei.
*Shizi* Attributed to Shi Jiao
Mythology
*Classic of Mountains and Seas* A compilation of early geography descriptions of animals and myths from various locations around China.
Tale of King Mu, Son of Heaven tells the tale of king mu and his quest for immortality and after receiving it sadness over the death of his lover.
Taoism
*Tao Te Ching* Attributed to Laozi.
*Guan Yinzi*`{{csni |date=August 2024}}`{=mediawiki} Fragment
*Liezi* Attributed to Lie Yukou.
*Zhuangzi* Attributed to Zhuang Zhou.
*Wenzi*
#### Poetry
Title Description
---------- --------------------------------------------------------------------------------------------------------------------------------------------------------------
*Chu Ci* Aside from the Shi Jing (see Classics branch) the only surviving pre-Qin poetry collection. Attributed to the southern state of Chu, and especially Qu Yuan.
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# Chinese classics
## List of classics {#list_of_classics}
### After 206 BC {#after_206_bc}
- The *Twenty-Four Histories*, a collection of authoritative histories of China for various dynasties:
- The *Records of the Grand Historian* by Sima Qian
- The *Book of Han* by Ban Gu.
- The *Book of Later Han* by Fan Ye
- The *Records of Three Kingdoms* by Chen Shou
- The *Book of Jin* by Fang Xuanling
- The *Book of Song* by Shen Yue
- The *Book of Southern Qi* by Xiao Zixian
- The *Book of Liang* by Yao Silian
- The *Book of Chen* by Yao Silian
- The *History of the Southern Dynasties* by Li Yanshou
- The *Book of Wei* by Wei Shou
- The *Book of Zhou* by Linghu Defen
- The *Book of Northern Qi* by Li Baiyao
- The *History of the Northern Dynasties* by Li Yanshou
- The *Book of Sui* by Wei Zheng
- The *Old Book of Tang* by Liu Xu
- The *New Book of Tang* by Ouyang Xiu
- The *Old History of Five Dynasties* by Xue Juzheng
- The *New History of Five Dynasties* by Ouyang Xiu
- The *History of Song* by Toqto\'a
- The *History of Liao* by Toqto\'a
- The *History of Jin* by Toqto\'a
- The *History of Yuan* by Song Lian
- The *History of Ming* by Zhang Tingyu
- The *Draft History of Qing* by Zhao Erxun is usually referred as the 25th classic of history records
- The *New History of Yuan* by Ke Shaomin is sometimes referred as the 26th classic of history records
- The *Chronicles of Huayang*, an old record of ancient history and tales of southwestern China, attributed to Chang Qu.
- The *Biographies of Exemplary Women*, a biographical collection of exemplary women in ancient China, compiled by Liu Xiang.
- The *Spring and Autumn Annals of the Sixteen Kingdoms*, a historical record of the Sixteen Kingdoms, attributed to Cui Hong, is lost.
- The *Shiming*, is a dictionary compiled by Liu Xi by the end of 2nd century.
- *A New Account of the Tales of the World*, a collection of historical anecdotes and character sketches of some 600 literati, musicians, and painters.
- The *Thirty-Six Strategies*, a military strategy book attributed to Tan Daoji.
- *The Literary Mind and the Carving of Dragons*, a review book on ancient Chinese literature and writings by Liu Xie.
- The *Commentary on the Water Classic*, a book on hydrology of rivers in China attributed to the great geographer Li Daoyuan.
- The *Dialogues between Li Jing and Tang Taizong*, a military strategy book attributed to Li Jing
- The *Zizhi Tongjian*, with Sima Guang as its main editor.
- The *Spring and Autumn Annals of Wu and Yue*, a historical record of the states of Wu and Yue during the Spring and Autumn period, attributed to Zhao Ye.
- The *Zhenguan Zhengyao*, a record of governance strategies and leadership of Emperor Taizong of Tang, attributed to Wu Jing.
- The *Jiaoshi Yilin*, a work modeled after the *I Ching*, composed during the Western Han dynasty and attributed to Jiao Yanshou.
- *The Nine Chapters on the Mathematical Art*, a mathematics Chinese book composed by several generations scholars of Han dynasty.
- The *Thousand Character Classic*, attributed to Zhou Xingsi.
- The *Treatise on Astrology of the Kaiyuan Era*, compiled by Gautama Siddha, is a Chinese encyclopedia on astrology and divination.
- The *Shitong*, written by Liu Zhiji, a work on historiography.
- The *Tongdian*, written by Du You, a contemporary text focused on the Tang dynasty.
- The *Tang Huiyao*, compiled by Wang Pu, a text based on the institutional history of the Tang dynasty.
- The *Great Tang Records on the Western Regions*, compiled by Bianji; a recount of Xuanzang\'s journey.
- The *Miscellaneous Morsels from Youyang*, written by Duan Chengshi, records fantastic stories, anecdotes, and exotic customs.
- The *Four Great Books of Song*, a term referring to the four large compilations during the beginning of Song dynasty:
- The *Taiping Yulan,* a *leishu* encyclopedia.
- The *Taiping Guangji*, a collection of folk tales and theology.
- The *Wenyuan Yinghua*, an anthology of poetry, odes, songs and other writings.
- The *Cefu Yuangui*, a *leishu* encyclopedia of political essays, autobiographies, memorials and decrees.
- The *Dream Pool Essays*, a collection of essays on science, technology, military strategies, history, politics, music and arts, written by Shen Kuo.
- The *Tiangong Kaiwu*, an encyclopedia compiled by Song Yingxing.
- The *Compendium of Materia Medica*, a classic book of medicine written by Li Shizhen.
- The *Complete Library of the Four Treasuries*, the largest compilation of literature in Chinese history.
- The *New Songs from the Jade Terrace*, a poetry collection from the Six Dynasties period.
- The *Complete Tang Poems*, compiled during the Qing dynasty, published in 1705.
- The *Xiaolin Guangji*, a collection of jokes compiled during the Qing dynasty
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# Charles Messier
**Charles Messier** (`{{IPA|fr|ʃaʁl me.sje|lang}}`{=mediawiki}; 26 June 1730 -- 12 April 1817) was a French astronomer. He published an astronomical catalogue consisting of 110 nebulae and star clusters, which came to be known as the *Messier objects*, referred to with the letter M and their number between 1 and 110. Messier\'s purpose for the catalogue was to help astronomical observers distinguish between permanent and transient visually diffuse objects in the sky.
## Biography
Messier was born in Badonviller in the Lorraine region of France, in 1730, the tenth of twelve children of Françoise B. Grandblaise and Nicolas Messier, a Court usher. Six of his brothers and sisters died while young, and his father died in 1741. Charles\' interest in astronomy was stimulated by the appearance of the great six-tailed comet in 1744 and by an annular solar eclipse visible from his hometown on 25 July 1748.
In 1751, Messier entered the employ of Joseph Nicolas Delisle, the astronomer of the French Navy, who instructed him to keep careful records of his observations. Messier\'s first documented observation was that of the Mercury transit of 6 May 1753, followed by his observations journals at Cluny Hotel and at the French Navy observatories.
In 1764, Messier was made a fellow of the Royal Society; in 1769, he was elected a foreign member of the Royal Swedish Academy of Sciences; and on 30 June 1770, he was elected to the French Academy of Sciences. He was given the nickname \"Ferret of Comets\" by King Louis XV.
Messier discovered 13 comets:
- C/1760 B1 (Messier)
- C/1763 S1 (Messier)
- C/1764 A1 (Messier)
- C/1766 E1 (Messier)
- C/1769 P1 (Messier)
- D/1770 L1 (Lexell)
- C/1771 G1 (Messier)
- C/1773 T1 (Messier)
- C/1780 U2 (Messier)
- C/1785 A1 (Messier--Méchain)
- C/1788 W1 (Messier)
- C/1793 S2 (Messier)
- C/1798 G1 (Messier)
He also co-discovered comet C/1801 N1 (Pons), a discovery shared with several other observers including Pons, Méchain, and Bouvard.
Near the end of his life, Messier self-published a booklet connecting the great comet of 1769 to the birth of Napoleon, who was in power at the time of publishing. According to Maik Meyer:`{{quotation| As hard as it may seem to accept, the memoir is an ingratiation to Napoleon in order to receive attention and monetary support. It is full of servility and opportunism. Messier did not even refrain from utilizing astrology to reach his goal. Messier comes quickly to the point on the first page of the memoir, by stating that the beginning of the epoch of Napoleon the Great ... coincides with the discovery of one of the greatest comets ever observed.}}`{=mediawiki}
Messier is buried in Père Lachaise Cemetery in the 20th arrondissement of Paris.
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# Charles Messier
## Messier catalogue {#messier_catalogue}
Messier\'s occupation as a comet hunter led him to continually come across fixed diffuse objects in the night sky which could be mistaken for comets. He compiled a list of them, in collaboration with his friend and assistant Pierre Méchain (who may have found at least 20 of the objects), to avoid wasting time sorting them out from the comets for which they were looking. The entries are now known to be 39 galaxies, 4 planetary nebulae, 7 other types of nebulae, 26 open star clusters and 29 globular star clusters.
Messier did his observing with a 100 mm (four-inch) refracting telescope from Hôtel de Cluny (now the Musée national du Moyen Âge), in downtown Paris, France. The list he compiled only contains objects found in the area of the sky Messier could observe, from the north celestial pole to a declination of about −35.7° . They are not organized scientifically by object type, or by location. The first version of Messier\'s catalogue contained 45 objects and was published in 1774 in the journal of the French Academy of Sciences in Paris. In addition to his own discoveries, this version included objects previously observed by other astronomers, with only 17 of the 45 objects being discovered by Messier himself. By 1780 the catalog had increased to 80 objects.
The final version of the catalogue was published in 1781, in the 1784 issue of *Connaissance des Temps*. The final list of Messier objects had grown to 103. On several occasions between 1921 and 1966, astronomers and historians discovered evidence of another seven objects that were observed either by Messier or by Méchain, shortly after the final version was published. These seven objects, M 104 through M 110, are accepted by astronomers as \"official\" Messier objects.
The objects\' Messier designations, from M 1 to M 110, are still used by professional and amateur astronomers today and their relative brightness makes them popular objects in the amateur astronomical community.
## Legacy
thumb\|right\|upright=1.3\|Commemorative plaque in Messier\'s hometown of Badonviller The lunar crater Messier and the asteroid 7359 Messier were named in his honour
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# Crankshaft
thumb\|upright=1.2\|Crankshaft (red), pistons (gray), cylinders (blue) and flywheel (black)
A **crankshaft** is a mechanical component used in a piston engine to convert the reciprocating motion into rotational motion. The crankshaft is a rotating shaft containing one or more crankpins, that are driven by the pistons via the connecting rods.
The crankpins are also called *rod bearing journals*, and they rotate within the \"big end\" of the connecting rods.
Most modern crankshafts are located in the engine block. They are made from steel or cast iron, using either a forging, casting or machining process.
## Design
The crankshaft is located within the engine block and held in place via main bearings which allow the crankshaft to rotate within the block. The up-down motion of each piston is transferred to the crankshaft via connecting rods. A flywheel is often attached to one end of the crankshaft, in order to smoothen the power delivery and reduce vibration.
A crankshaft is subjected to enormous stresses, in some cases more than 19000 lb per cylinder. Crankshafts for single-cylinder engines are usually a simpler design than for engines with multiple cylinders.
### Bearings
The crankshaft is able to rotate in the engine block due to the \'main bearings\'. Since the crankshaft is subject to large horizontal and torsional forces from each cylinder, these main bearings are located at various points along the crankshaft, rather than just one at each end. The number of main bearings is determined based on the overall load factor and the maximum engine speed. Crankshafts in diesel engines often use a main bearing between every cylinder and at both ends of the crankshaft, due to the high forces of combustion present.
Flexing of the crankshaft was a factor in replacing straight-eight engines in the 1950s; the long crankshafts suffered from an unacceptable amount of flex when engine designers began using higher compression ratios and higher engine speeds (RPM).
### Piston stroke {#piston_stroke}
The distance between the axis of the crankpins and the axis of the crankshaft determines the stroke length of the engine.
Most modern car engines are classified as \"over square\" or short-stroke, wherein the stroke is less than the diameter of the cylinder bore. A common way to increase the low-RPM torque of an engine is to increase the stroke, sometimes known as \"stroking\" the engine. Historically, the trade-off for a long-stroke engine was a lower rev limit and increased vibration at high RPM, due to the increased piston velocity.
### Cross-plane and flat-plane configurations {#cross_plane_and_flat_plane_configurations}
When designing an engine, the crankshaft configuration is closely related to the engine\'s firing order.
Most production V8 engines (such as the Ford Modular engine and the General Motors LS engine) use a cross-plane crank whereby the crank throws are spaced 90 degrees apart. However, some high-performance V8 engines (such as the Ferrari 488) instead use a flat-plane crank, whereby the throws are spaced 180° apart, which essentially results in two inline-four engines sharing a common crankcase. Flat-plane engines are usually able to operate at higher RPM, however they have higher second-order vibrations, so they are better suited to racing car engines.
### Engine balance {#engine_balance}
For some engines it is necessary to provide counterweights for the reciprocating mass of the piston, conrods and crankshaft, in order to improve the engine balance. These counterweights are typically cast as part of the crankshaft but, occasionally, are bolt-on pieces.
### Flying arms {#flying_arms}
In some engines, the crankshaft contains direct links between adjacent crankpins, without the usual intermediate main bearing. These links are called *flying arms*.`{{refpage |pages=16, 41}}`{=mediawiki} This arrangement is sometimes used in V6 and V8 engines, in order to maintain an even firing interval while using different V angles, and to reduce the number of main bearings required. The downside of flying arms is that the rigidity of the crankshaft is reduced, which can cause problems at high RPM or high power outputs.
### Counter-rotating crankshafts {#counter_rotating_crankshafts}
In most engines, each connecting rod is attached a single crankshaft, which results in the angle of the connecting rod varying as the piston moves through its stroke. This variation in angle pushes the pistons against the cylinder wall, which causes friction between the piston and cylinder wall. To prevent this, some early engines -- such as the 1900--1904 Lanchester Engine Company flat-twin engines -- connected each piston to two crankshafts that are rotating in opposite directions. This arrangement cancels out the lateral forces and reduces the requirement for counterweights. This design is rarely used, however a similar principle applies to balance shafts, which are occasionally used.
### Eccentricity and dynamic displacement of diesel engines {#eccentricity_and_dynamic_displacement_of_diesel_engines}
Eccentricity and dynamic displacement are critical factors influencing the performance, efficiency, and durability of diesel engines. These phenomena arise due to the flexibility of the crankshaft, secondary piston motion, and varying loads during engine operation. Understanding these effects is essential for reducing mechanical wear, improving fuel efficiency, and optimizing engine design.
## Construction
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# Crankshaft
## Construction
### Forged crankshafts {#forged_crankshafts}
thumb\|upright=0.8\|Forged crankshaft
Crankshafts can be created from a steel bar using roll forging. Today, manufacturers tend to favour the use of forged crankshafts due to their lighter weight, more compact dimensions and better inherent damping. With forged crankshafts, vanadium micro-alloyed steels are mainly used as these steels can be air-cooled after reaching high strengths without additional heat treatment, except for the surface hardening of the bearing surfaces. The low alloy content also makes the material cheaper than high-alloy steels. Carbon steels also require additional heat treatment to reach the desired properties.
### Cast crankshafts {#cast_crankshafts}
Another construction method is to cast the crankshaft from ductile iron. Cast iron crankshafts are today mostly found in cheaper production engines where the loads are lower.
### Machined crankshafts {#machined_crankshafts}
Crankshafts can also be machined from billet, often a bar of high quality vacuum remelted steel. Though the fiber flow (local inhomogeneities of the material\'s chemical composition generated during casting) does not follow the shape of the crankshaft (which is undesirable), this is usually not a problem since higher quality steels, which normally are difficult to forge, can be used. Per unit, these crankshafts tend to be expensive due to the large amount of material that must be removed with lathes and milling machines, the high material cost, and the additional heat treatment required. However, since no expensive tooling is needed, this production method allows small production runs without high up-front costs.
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# Crankshaft
## History
### Crankshaft
In 9th century Abbasid Baghdad, automatically operated cranks appear in several of the hydraulic devices described by the Banū Mūsā brothers in the *Book of Ingenious Devices*. These automatically operated cranks appear in several devices, two of which contain an action which approximates to that of a crankshaft, five centuries before the earliest known European description of a crankshaft. However, the automatic crank mechanism described by the Banū Mūsā would not have allowed a full rotation, but only a small modification was required to convert it to a crankshaft.
In the Artuqid Sultanate, Arab engineer Ismail al-Jazari (1136--1206) described a crank and connecting rod system in a rotating machine for two of his water-raising machines, which include both crank and shaft mechanisms.
thumb\|right\|upright=0.8\|15th century paddle-wheel boatThe Italian physician Guido da Vigevano (c. 1280), planning for a new Crusade, made illustrations for a paddle boat and war carriages that were propelled by manually turned compound cranks and gear wheels, identified as an early crankshaft prototype by Lynn Townsend White.
thumb\|right\|upright=0.8\|1661 water pump by Georg Andreas Böckler Crankshafts were described by Leonardo da Vinci (1452--1519) and a Dutch farmer and windmill owner by the name Cornelis Corneliszoon van Uitgeest in 1592. His wind-powered sawmill used a crankshaft to convert a windmill\'s circular motion into a back-and-forward motion powering the saw. Corneliszoon was granted a patent for his crankshaft in 1597.
From the 16th century onwards, evidence of cranks and connecting rods integrated into machine design becomes abundant in the technological treatises of the period: Agostino Ramelli\'s *The Diverse and Artifactitious Machines* of 1588 depicts eighteen examples, a number that rises in the *Theatrum Machinarum Novum* by Georg Andreas Böckler to 45 different machines. Cranks were formerly common on some machines in the early 20th century; for example almost all phonographs before the 1930s were powered by clockwork motors wound with cranks. Reciprocating piston engines use cranks to convert the linear piston motion into rotational motion. Internal combustion engines of early 20th century automobiles were usually started with hand cranks, before electric starters came into general use
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# Central nervous system
The **central nervous system** (**CNS**) is the part of the nervous system consisting primarily of the brain, spinal cord and retina. The CNS is so named because the brain integrates the received information and coordinates and influences the activity of all parts of the bodies of bilaterally symmetric and triploblastic animals---that is, all multicellular animals except sponges and diploblasts. It is a structure composed of nervous tissue positioned along the rostral (nose end) to caudal (tail end) axis of the body and may have an enlarged section at the rostral end which is a brain. Only arthropods, cephalopods and vertebrates have a true brain, though precursor structures exist in onychophorans, gastropods and lancelets.
The rest of this article exclusively discusses the vertebrate central nervous system, which is radically distinct from all other animals.
## Overview
In vertebrates, the brain and spinal cord are both enclosed in the meninges. The meninges provide a barrier to chemicals dissolved in the blood, protecting the brain from most neurotoxins commonly found in food. Within the meninges the brain and spinal cord are bathed in cerebral spinal fluid which replaces the body fluid found outside the cells of all bilateral animals.
In vertebrates, the CNS is contained within the dorsal body cavity, while the brain is housed in the cranial cavity within the skull. The spinal cord is housed in the spinal canal within the vertebrae. Within the CNS, the interneuronal space is filled with a large amount of supporting non-nervous cells called neuroglia or glia from the Greek for \"glue\".
In vertebrates, the CNS also includes the retina and the optic nerve (cranial nerve II), as well as the olfactory nerves and olfactory epithelium. As parts of the CNS, they connect directly to brain neurons without intermediate ganglia. The olfactory epithelium is the only central nervous tissue outside the meninges in direct contact with the environment, which opens up a pathway for therapeutic agents which cannot otherwise cross the meninges barrier.
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# Central nervous system
## Structure
The CNS consists of two major structures: the brain and spinal cord. The brain is encased in the skull, and protected by the cranium. The spinal cord is continuous with the brain and lies caudally to the brain. It is protected by the vertebrae. The spinal cord reaches from the base of the skull, and continues through or starting below the foramen magnum, and terminates roughly level with the first or second lumbar vertebra, occupying the upper sections of the vertebral canal.
### White and gray matter {#white_and_gray_matter}
Microscopically, there are differences between the neurons and tissue of the CNS and the peripheral nervous system (PNS). The CNS is composed of white and gray matter. This can also be seen macroscopically on brain tissue. The white matter consists of axons and oligodendrocytes, while the gray matter consists of neurons and unmyelinated fibers. Both tissues include a number of glial cells (although the white matter contains more), which are often referred to as supporting cells of the CNS. Different forms of glial cells have different functions, some acting almost as scaffolding for neuroblasts to climb during neurogenesis such as bergmann glia, while others such as microglia are a specialized form of macrophage, involved in the immune system of the brain as well as the clearance of various metabolites from the brain tissue. Astrocytes may be involved with both clearance of metabolites as well as transport of fuel and various beneficial substances to neurons from the capillaries of the brain. Upon CNS injury astrocytes will proliferate, causing gliosis, a form of neuronal scar tissue, lacking in functional neurons.
The brain (cerebrum as well as midbrain and hindbrain) consists of a cortex, composed of neuron-bodies constituting gray matter, while internally there is more white matter that form tracts and commissures. Apart from cortical gray matter there is also subcortical gray matter making up a large number of different nuclei.
### Spinal cord {#spinal_cord}
From and to the spinal cord are projections of the peripheral nervous system in the form of spinal nerves (sometimes segmental nerves). The nerves connect the spinal cord to skin, joints, muscles etc. and allow for the transmission of efferent motor as well as afferent sensory signals and stimuli. This allows for voluntary and involuntary motions of muscles, as well as the perception of senses. All in all 31 spinal nerves project from the brain stem, some forming plexa as they branch out, such as the brachial plexa, sacral plexa etc. Each spinal nerve will carry both sensory and motor signals, but the nerves synapse at different regions of the spinal cord, either from the periphery to sensory relay neurons that relay the information to the CNS or from the CNS to motor neurons, which relay the information out.
The spinal cord relays information up to the brain through spinal tracts through the final common pathway to the thalamus and ultimately to the cortex.
<File:1615> Locations Spinal Fiber Tracts.jpg\|Schematic image showing the locations of a few tracts of the spinal cord. <File:1507> Short and Long Reflexes.jpg\|Reflexes may also occur without engaging more than one neuron of the CNS as in the below example of a short reflex.
#### Cranial nerves {#cranial_nerves}
Apart from the spinal cord, there are also peripheral nerves of the PNS that synapse through intermediaries or ganglia directly on the CNS. These 12 nerves exist in the head and neck region and are called cranial nerves. Cranial nerves bring information to the CNS to and from the face, as well as to certain muscles (such as the trapezius muscle, which is innervated by accessory nerves as well as certain cervical spinal nerves).
Two pairs of cranial nerves; the olfactory nerves and the optic nerves are often considered structures of the CNS. This is because they do not synapse first on peripheral ganglia, but directly on CNS neurons. The olfactory epithelium is significant in that it consists of CNS tissue expressed in direct contact to the environment, allowing for administration of certain pharmaceuticals and drugs.
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# Central nervous system
## Structure
### Brain
At the anterior end of the spinal cord lies the brain. The brain makes up the largest portion of the CNS. It is often the main structure referred to when speaking of the nervous system in general. The brain is the major functional unit of the CNS. While the spinal cord has certain processing ability such as that of spinal locomotion and can process reflexes, the brain is the major processing unit of the nervous system.
#### Brainstem
The brainstem consists of the medulla, the pons and the midbrain. The medulla can be referred to as an extension of the spinal cord, which both have similar organization and functional properties. The tracts passing from the spinal cord to the brain pass through here.
Regulatory functions of the medulla nuclei include control of blood pressure and breathing. Other nuclei are involved in balance, taste, hearing, and control of muscles of the face and neck.
The next structure rostral to the medulla is the pons, which lies on the ventral anterior side of the brainstem. Nuclei in the pons include pontine nuclei which work with the cerebellum and transmit information between the cerebellum and the cerebral cortex. In the dorsal posterior pons lie nuclei that are involved in the functions of breathing, sleep, and taste.
The midbrain, or mesencephalon, is situated above and rostral to the pons. It includes nuclei linking distinct parts of the motor system, including the cerebellum, the basal ganglia and both cerebral hemispheres, among others. Additionally, parts of the visual and auditory systems are located in the midbrain, including control of automatic eye movements.
The brainstem at large provides entry and exit to the brain for a number of pathways for motor and autonomic control of the face and neck through cranial nerves, Autonomic control of the organs is mediated by the tenth cranial nerve. A large portion of the brainstem is involved in such autonomic control of the body. Such functions may engage the heart, blood vessels, and pupils, among others.
The brainstem also holds the reticular formation, a group of nuclei involved in both arousal and alertness.
#### Cerebellum
The cerebellum lies behind the pons. The cerebellum is composed of several dividing fissures and lobes. Its function includes the control of posture and the coordination of movements of parts of the body, including the eyes and head, as well as the limbs. Further, it is involved in motion that has been learned and perfected through practice, and it will adapt to new learned movements. Despite its previous classification as a motor structure, the cerebellum also displays connections to areas of the cerebral cortex involved in language and cognition. These connections have been shown by the use of medical imaging techniques, such as functional MRI and Positron emission tomography.
The body of the cerebellum holds more neurons than any other structure of the brain, including that of the larger cerebrum, but is also more extensively understood than other structures of the brain, as it includes fewer types of different neurons. It handles and processes sensory stimuli, motor information, as well as balance information from the vestibular organ.
#### Diencephalon
The two structures of the diencephalon worth noting are the thalamus and the hypothalamus. The thalamus acts as a linkage between incoming pathways from the peripheral nervous system as well as the optical nerve (though it does not receive input from the olfactory nerve) to the cerebral hemispheres. Previously it was considered only a \"relay station\", but it is engaged in the sorting of information that will reach cerebral hemispheres (neocortex).
Apart from its function of sorting information from the periphery, the thalamus also connects the cerebellum and basal ganglia with the cerebrum. In common with the aforementioned reticular system the thalamus is involved in wakefulness and consciousness, such as though the SCN.
The hypothalamus engages in functions of a number of primitive emotions or feelings such as hunger, thirst and maternal bonding. This is regulated partly through control of secretion of hormones from the pituitary gland. Additionally the hypothalamus plays a role in motivation and many other behaviors of the individual.
#### Cerebrum
The cerebrum of cerebral hemispheres make up the largest visual portion of the human brain. Various structures combine to form the cerebral hemispheres, among others: the cortex, basal ganglia, amygdala and hippocampus. The hemispheres together control a large portion of the functions of the human brain such as emotion, memory, perception and motor functions. Apart from this the cerebral hemispheres stand for the cognitive capabilities of the brain.
Connecting each of the hemispheres is the corpus callosum as well as several additional commissures. One of the most important parts of the cerebral hemispheres is the cortex, made up of gray matter covering the surface of the brain. Functionally, the cerebral cortex is involved in planning and carrying out of everyday tasks.
The hippocampus is involved in storage of memories, the amygdala plays a role in perception and communication of emotion, while the basal ganglia play a major role in the coordination of voluntary movement.
### Difference from the peripheral nervous system {#difference_from_the_peripheral_nervous_system}
The PNS consists of neurons, axons, and Schwann cells. Oligodendrocytes and Schwann cells have similar functions in the CNS and PNS, respectively. Both act to add myelin sheaths to the axons, which acts as a form of insulation allowing for better and faster proliferation of electrical signals along the nerves. Axons in the CNS are often very short, barely a few millimeters, and do not need the same degree of isolation as peripheral nerves. Some peripheral nerves can be over 1 meter in length, such as the nerves to the big toe. To ensure signals move at sufficient speed, myelination is needed.
The way in which the Schwann cells and oligodendrocytes myelinate nerves differ. A Schwann cell usually myelinates a single axon, completely surrounding it. Sometimes, they may myelinate many axons, especially when in areas of short axons. Oligodendrocytes usually myelinate several axons. They do this by sending out thin projections of their cell membrane, which envelop and enclose the axon.
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# Central nervous system
## Development
During early development of the vertebrate embryo, a longitudinal groove on the neural plate gradually deepens and the ridges on either side of the groove (the neural folds) become elevated, and ultimately meet, transforming the groove into a closed tube called the neural tube. The formation of the neural tube is called neurulation. At this stage, the walls of the neural tube contain proliferating neural stem cells in a region called the ventricular zone. The neural stem cells, principally radial glial cells, multiply and generate neurons through the process of neurogenesis, forming the rudiment of the CNS.
The neural tube gives rise to both brain and spinal cord. The anterior (or \'rostral\') portion of the neural tube initially differentiates into three brain vesicles (pockets): the prosencephalon at the front, the mesencephalon, and, between the mesencephalon and the spinal cord, the rhombencephalon. (By six weeks in the human embryo) the prosencephalon then divides further into the telencephalon and diencephalon; and the rhombencephalon divides into the metencephalon and myelencephalon. The spinal cord is derived from the posterior or \'caudal\' portion of the neural tube.
As a vertebrate grows, these vesicles differentiate further still. The telencephalon differentiates into, among other things, the striatum, the hippocampus and the neocortex, and its cavity becomes the first and second ventricles (lateral ventricles). Diencephalon elaborations include the subthalamus, hypothalamus, thalamus and epithalamus, and its cavity forms the third ventricle. The tectum, pretectum, cerebral peduncle and other structures develop out of the mesencephalon, and its cavity grows into the mesencephalic duct (cerebral aqueduct). The metencephalon becomes, among other things, the pons and the cerebellum, the myelencephalon forms the medulla oblongata, and their cavities develop into the fourth ventricle.
<File:EmbryonicBrain.svg%7CDiagram> depicting the main subdivisions of the embryonic vertebrate brain, later forming forebrain, midbrain and hindbrain. <File:Development> of the neural tube.png\|Development of the neural tube
----- ------------- ---------------- ----------------- --------------------------------------------------------------------------------------------------
CNS Brain Prosencephalon Telencephalon Rhinencephalon, amygdala, hippocampus, neocortex, basal ganglia, lateral ventricles
Diencephalon Epithalamus, thalamus, hypothalamus, subthalamus, pituitary gland, pineal gland, third ventricle
Brain stem Mesencephalon Tectum, cerebral peduncle, pretectum, mesencephalic duct
Rhombencephalon Metencephalon
Myelencephalon
Spinal cord
----- ------------- ---------------- ----------------- --------------------------------------------------------------------------------------------------
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# Central nervous system
## Development
### Evolution
#### Planaria
Planarians, members of the phylum Platyhelminthes (flatworms), have the simplest, clearly defined delineation of a nervous system into a CNS and a PNS. Their primitive brains, consisting of two fused anterior ganglia, and longitudinal nerve cords form the CNS. Like vertebrates, have a distinct CNS and PNS. The nerves projecting laterally from the CNS form their PNS.
A molecular study found that more than 95% of the 116 genes involved in the nervous system of planarians, which includes genes related to the CNS, also exist in humans.
#### Arthropoda
In arthropods, the ventral nerve cord, the subesophageal ganglia and the supraesophageal ganglia are usually seen as making up the CNS. Arthropoda, unlike vertebrates, have inhibitory motor neurons due to their small size. `{{see also|Lateral horn of insect brain}}`{=mediawiki}
#### Chordata
The CNS of chordates differs from that of other animals in being placed dorsally in the body, above the gut and notochord/spine. The basic pattern of the CNS is highly conserved throughout the different species of vertebrates and during evolution. The major trend that can be observed is towards a progressive telencephalisation: the telencephalon of reptiles is only an appendix to the large olfactory bulb, while in mammals it makes up most of the volume of the CNS. In the human brain, the telencephalon covers most of the diencephalon and the entire mesencephalon. Indeed, the allometric study of brain size among different species shows a striking continuity from rats to whales, and allows us to complete the knowledge about the evolution of the CNS obtained through cranial endocasts.
##### Mammals
Mammals -- which appear in the fossil record after the first fishes, amphibians, and reptiles -- are the only vertebrates to possess the evolutionarily recent, outermost part of the cerebral cortex (main part of the telencephalon excluding olfactory bulb) known as the neocortex. This part of the brain is, in mammals, involved in higher thinking and further processing of all senses in the sensory cortices (processing for smell was previously only done by its bulb while those for non-smell senses were only done by the tectum). The neocortex of monotremes (the duck-billed platypus and several species of spiny anteaters) and of marsupials (such as kangaroos, koalas, opossums, wombats, and Tasmanian devils) lack the convolutions -- gyri and sulci -- found in the neocortex of most placental mammals (eutherians). Within placental mammals, the size and complexity of the neocortex increased over time. The area of the neocortex of mice is only about 1/100 that of monkeys, and that of monkeys is only about 1/10 that of humans. In addition, rats lack convolutions in their neocortex (possibly also because rats are small mammals), whereas cats have a moderate degree of convolutions, and humans have quite extensive convolutions. Extreme convolution of the neocortex is found in dolphins, possibly related to their complex echolocation.
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# Central nervous system
## Clinical significance {#clinical_significance}
### Diseases
There are many CNS diseases and conditions, including infections such as encephalitis and poliomyelitis, early-onset neurological disorders including ADHD and autism, seizure disorders such as epilepsy, headache disorders such as migraine, late-onset neurodegenerative diseases such as Alzheimer\'s disease, Parkinson\'s disease, and essential tremor, autoimmune and inflammatory diseases such as multiple sclerosis and acute disseminated encephalomyelitis, genetic disorders such as Krabbe\'s disease and Huntington\'s disease, as well as amyotrophic lateral sclerosis and adrenoleukodystrophy. Lastly, cancers of the central nervous system can cause severe illness and, when malignant, can have very high mortality rates. Symptoms depend on the size, growth rate, location and malignancy of tumors and can include alterations in motor control, hearing loss, headaches and changes in cognitive ability and autonomic functioning.
Specialty professional organizations recommend that neurological imaging of the brain be done only to answer a specific clinical question and not as routine screening
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# Connection (dance)
In partner dancing, **connection** is physical, non-verbal communication between dancers to facilitate synchronized or coordinated dance movements. Some forms of connection involve \"lead/follow\" in which one dancer (the \"lead\") directs the movements of the other dancer (the \"follower\") by means of non-verbal directions conveyed through a physical connection between the dancers. In other forms, connection involves multiple dancers (more than two) without a distinct leader or follower (e.g. contact improvisation). Connection refers to a host of different techniques in many types of partner dancing, especially (but not exclusively) those that feature significant physical contact between the dancers, including the Argentine Tango, Lindy Hop, Balboa, East Coast Swing, West Coast Swing, Salsa, and other ballroom dances.
Other forms of communication, such as visual cues or spoken cues, sometimes aid in connecting with one\'s partner, but are often used in specific circumstances (e.g., practicing figures, or figures which are purposely danced without physical connection). Connection can be used to transmit power and energy as well as information and signals; some dance forms (and some dancers) primarily emphasize power or signaling, but most are probably a mixture of both. Philosopher of dance Ilya Vidrin argues that connection between partners involves norm-based communication that include "a physical exchange of information on the basis of ethically-bound conditions" (proximity, orientation, and points of contact) which constrain agency and predictability.
## Lead/Follow
Following and leading in a partner dance is accomplished by maintaining a physical connection called the frame that allows the leader to transmit body movement to the follower, and for the follower to suggest ideas to the leader. A frame is a stable structural combination of both bodies maintained through the dancers\' arms and/or legs.
Connection occurs in both open and closed dance positions (also called \"open frame\" and \"closed frame\").
In closed position with body contact, connection is achieved by maintaining the frame. The follower moves to match the leader, maintaining the pressure between the two bodies as well as the position.
When creating frame, tension is the primary means of establishing communication. Changes in tension are made to create rhythmic variations in moves and movements, and are communicated through points of contact. In an open position or a closed position without body contact, the hands and arms alone provide the connection, which may be one of three forms: tension, compression or neutral.
- During *tension* or *leverage connection*, the dancers are pulling away from each other with an equal and opposite force. The arms do not originate this force alone: they are often assisted by tension in trunk musculature, through body weight or by momentum.
- During *compression connection*, the dancers are pushing towards each other.
- In a neutral position, the hands do not impart any force other than the touch of the follower\'s hands in the leader\'s.
In swing dances, tension and compression may be maintained for a significant period of time. In other dances, such as Latin, tension and compression may be used as indications of upcoming movement. However, in both styles, tension and compression do not signal immediate movement: the follow must be careful not to move prior to actual movement by the lead. Until then, the dancers must match pressures without moving their hands. In some styles of Lindy Hop, the tension may become quite high without initiating movement.
The general rule for open connections is that moves of the leader\'s hands back, forth, left or right are originated through moves of the entire body. Accordingly, for the follower, a move of the connected hand is immediately transformed into the corresponding move of the body. Tensing the muscles and locking the arm achieves this effect but is neither comfortable nor correct. Such tension eliminates the subtler communication in the connection, and eliminates free movement up and down, such as is required to initiate many turns.
Instead of just tensing the arms, connection is achieved by engaging the shoulder, upper body and torso muscles. Movement originates in the body\'s core. A leader leads by moving himself and maintaining frame and connection. Different forms of dance and different movements within each dance may call for differences in the connection. In some dances the separation distance between the partners remains pretty constant. In others e.g. Modern Jive moving closer together and further apart are fundamental to the dance, requiring flexion and extension of the arms, alternating compression and tension.
The connection between two partners has a different feel in every dance and with every partner. Good social dancers adapt to the conventions of the dance and the responses of their partners
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# CORAL
**CORAL**, short for **Computer On-line Real-time Applications Language** is a programming language originally developed in 1964 at the Royal Radar Establishment (RRE), Malvern, Worcestershire, in the United Kingdom. The R was originally for \"radar\", not \"real-time\". It was influenced primarily by JOVIAL, and thus ALGOL, but is not a subset of either.
The most widely-known version, **CORAL 66**, was subsequently developed by I. F. Currie and M. Griffiths under the auspices of the *Inter-Establishment Committee for Computer Applications* (IECCA). Its official definition, edited by Woodward, Wetherall, and Gorman, was first published in 1970.
In 1971, CORAL was selected by the Ministry of Defence as the language for future military applications and to support this, a standardization program was introduced to ensure CORAL compilers met the specifications. This process was later adopted by the US Department of Defense while defining Ada.
## Overview
Coral 66 is a general-purpose programming language based on ALGOL 60, with some features from Coral 64, JOVIAL, and Fortran. It includes structured record types (as in Pascal) and supports the packing of data into limited storage (also as in Pascal). Like Edinburgh IMP it allows inline (embedded) assembly language, and also offers good runtime checking and diagnostics. It is designed for real-time computing and embedded system applications, and for use on computers with limited processing power, including those limited to fixed-point arithmetic and those without support for dynamic storage allocation.
The language was an inter-service standard for British military programming, and was also widely adopted for civil purposes in the British control and automation industry. It was used to write software for both the Ferranti and General Electric Company (GEC) computers from 1971 onwards. Implementations also exist for the Interdata 8/32, PDP-11, VAX and Alpha platforms and HPE Integrity Servers; for the Honeywell, and for the Computer Technology Limited (CTL, later ITL) Modular-1; and for SPARC running Solaris, and Intel running Linux.
Queen Elizabeth II sent the first email from a head of state from the Royal Signals and Radar Establishment over the ARPANET on March 26, 1976. The message read \"This message to all ARPANET users announces the availability on ARPANET of the Coral 66 compiler provided by the GEC 4080 computer at the Royal Signals and Radar Establishment, Malvern, England, \... Coral 66 is the standard real-time high level language adopted by the Ministry of Defence.\"
As Coral was aimed at a variety of real-time work, rather than general office data processing, there was no standardised equivalent to a stdio library. IECCA recommended a primitive input/output (I/O) package to accompany any compiler (in a document titled *Input/Output of Character data in Coral 66 Utility Programs*). Most implementers avoided this by producing Coral interfaces to extant Fortran and, later, C libraries.
CORAL\'s most significant contribution to computing may have been enforcing quality control in commercial compilers. To have a CORAL compiler approved by IECCA, and thus allowing a compiler to be marketed as a CORAL 66 compiler, the candidate compiler had to compile and execute a standard suite of 25 test programs and 6 benchmark programs. The process was part of the British Standard (BS) 5905 approval process. This methodology was observed and adapted later by the United States Department of Defense for the certification of Ada compilers.
Source code for a Coral 66 compiler (written in BCPL) has been recovered and the *Official Definition of Coral 66* document by Her Majesty\'s Stationery Office (HMSO) has been scanned; the Ministry of Defence patent office has issued a licence to the Edinburgh Computer History project to allow them to put both the code and the language reference online for non-commercial use.
## Variants
A variant of Coral 66 named PO-CORAL was developed during the late 1970s to early 1980s by the British General Post Office (GPO), together with GEC, STC and Plessey, for use on the System X digital telephone exchange control computers. This was later renamed BT-CORAL when British Telecom was spun off from the Post Office. Unique features of this language were the focus on real-time execution, message processing, limits on statement execution between waiting for input, and a prohibition on recursion to remove the need for a stack
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# Chapter 11, Title 11, United States Code
**Chapter 11 of the United States Bankruptcy Code** (Title 11 of the United States Code) permits reorganization under the bankruptcy laws of the United States. Such reorganization, known as **Chapter 11 bankruptcy**, is available to every business, whether organized as a corporation, partnership or sole proprietorship, and to individuals, although it is most prominently used by corporate entities. In contrast, Chapter 7 governs the process of a liquidation bankruptcy, though liquidation may also occur under Chapter 11; while Chapter 13 provides a reorganization process for the majority of private individuals.
## Chapter 11 overview {#chapter_11_overview}
When a business is unable to service its debt or pay its creditors, the business or its creditors can file with a federal bankruptcy court for protection under either Chapter 7 or Chapter 11.
In Chapter 7, the business ceases operations, a trustee sells all of its assets, and then distributes the proceeds to its creditors. Any residual amount is returned to the owners of the company.
In Chapter 11, in most instances the debtor remains in control of its business operations as a debtor in possession, and is subject to the oversight and jurisdiction of the court.
A Chapter 11 bankruptcy will result in one of three outcomes for the debtor: reorganization, conversion to Chapter 7 bankruptcy, or dismissal. In order for a Chapter 11 debtor to reorganize, the debtor must file (and the court must confirm) a plan of reorganization. In effect, the plan is a compromise between the major stakeholders in the case, including the debtor and its creditors. Most Chapter 11 cases aim to confirm a plan, but that may not always be possible.
If the judge approves the reorganization plan and the creditors all agree, then the plan can be confirmed. Section 1129 of the Bankruptcy Code requires the bankruptcy court reach certain conclusions prior to confirming or approving the plan and making it binding on all parties in the case, most notably that the plan complies with applicable law and was proposed in good faith. The court must also find that the reorganization plan is feasible in that, unless the plan provides otherwise, the plan is not likely to be followed by further reorganization or liquidation.
In a Chapter 11 bankruptcy, the debtor corporation is typically recapitalized so that it emerges from bankruptcy with more equity and less debt, a process through which some of the debtor corporation\'s debts may be discharged. Determinations as to which debts are discharged, and how equity and other entitlements are distributed to various groups of investors, are often based on a valuation of the reorganized business. Bankruptcy valuation is often highly contentious because it is both subjective and important to case outcomes. The methods of valuation used in bankruptcy have changed over time, generally tracking methods used in investment banking, Delaware corporate law, and corporate and academic finance, but with a significant time lag.
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# Chapter 11, Title 11, United States Code
## Features of Chapter 11 reorganization {#features_of_chapter_11_reorganization}
Chapter 11 retains many of the features present in all or most bankruptcy proceedings in the United States. It provides additional tools for debtors as well. Most importantly, `{{usc|11|1108}}`{=mediawiki} empowers the trustee to operate the debtor\'s business. In Chapter 11, unless a separate trustee is appointed for cause, the debtor, as debtor in possession, acts as trustee of the business.
Chapter 11 affords the debtor to possess several mechanisms to restructure its business. A debtor in possession can acquire financing and loans on favorable terms by giving new lenders first priority on the business\'s earnings. The court may also permit the debtor in possession to reject and cancel contracts. Debtors are also protected from other litigation against the business through the imposition of an automatic stay. While the automatic stay is in place, creditors are stayed from any collection attempts or activities against the debtor in possession, and most litigation against the debtor is stayed, or put on hold, until it can be resolved in bankruptcy court, or resumed in its original venue. An example of proceedings that are not necessarily stayed automatically is family law proceedings against a spouse or parent. Further, creditors may file with the court seeking relief from the automatic stay.
If the business is insolvent, its debts exceed its assets, and the business is unable to pay debts as they come due, the bankruptcy restructuring may result in the company\'s owners being left with nothing; instead, the owners\' rights and interests are ended and the company\'s creditors are left with ownership of the newly reorganized company.
All creditors are entitled to be heard by the court. The court is ultimately responsible for determining whether the proposed plan of reorganization complies with bankruptcy laws.
One controversy that has broken out in bankruptcy courts concerns the proper amount of disclosure that the court and other parties are entitled to receive from the members of the creditor\'s committees that play a large role in many proceedings.
### Chapter 11 plan {#chapter_11_plan}
Chapter 11 usually results in the reorganization of the debtor\'s business or personal assets and debts, but can also be used as a mechanism for liquidation. Debtors may \"emerge\" from a Chapter 11 bankruptcy within a few months or within several years, depending on the size and complexity of the bankruptcy. The Bankruptcy Code accomplishes this objective through the use of a bankruptcy plan. The debtor in possession typically has the first opportunity to propose a plan during the period of exclusivity. This period allows the debtor 120 days from the date of filing for Chapter 11 to propose a plan of reorganization before any other party in interest may propose a plan. If the debtor proposes a plan within the 120-day exclusivity period, a 180-day exclusivity period from the date of filing for Chapter 11 is granted in order to allow the debtor to gain confirmation of the proposed plan. With some exceptions, the plan may be proposed by any party in interest. Interested creditors then vote for a plan.
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# Chapter 11, Title 11, United States Code
## Features of Chapter 11 reorganization {#features_of_chapter_11_reorganization}
### Confirmation
If the judge approves the reorganization plan and the creditors agree, the plan can be confirmed. If at least one class of creditors objects and votes against the plan, it may nonetheless be confirmed if the requirements of cramdown are met. In order to be confirmed over the creditors\' objection, the plan must not discriminate against that class of creditors, and the plan must be found fair and equitable to that class. Upon confirmation, the plan becomes binding and identifies the treatment of debts and operations of the business for the duration of the plan. If a plan cannot be confirmed, the court may either convert the case to a liquidation under Chapter 7 or, if, in the best interests of the creditors and the estate, the case may be dismissed, resulting in a return to the status quo before bankruptcy. If the case is dismissed, creditors will look to non-bankruptcy law in order to satisfy their claims.
In order to proceed to the confirmation hearing, the bankruptcy court must approve a disclosure statement. Once the disclosure statement is approved, the plan proponent will solicit votes from the classes of creditors. Solicitation is the process by which creditors vote on the proposed confirmation plan. This process can be complicated if creditors fail or refuse to vote. In this case, the plan proponent might tailor his or her efforts to obtain votes, or the plan itself. The plan may be modified before confirmation, so long as the modified plan meets all the requirements of Chapter 11.
A chapter 11 case typically results in one of three outcomes: a reorganization, a conversion into chapter 7 liquidation, or it is dismissed.
For a Chapter 11 debtor to reorganize, they must file (and the court must confirm) a reorganization plan. Simply put, the plan is a compromise between the major stakeholders in the case, including, but not limited to the debtor and its creditors. Most chapter 11 cases aim to confirm a plan, but that may not always be possible. Section 1121(b) of the Bankruptcy Code provides for an exclusivity period in which only the debtor may file a plan of reorganization. This period lasts 120 days after the date of the order for relief, and if the debtor does file a plan within the first 120 days, the exclusivity period is extended to 180 days after the order for relief for the debtor to seek acceptance of the plan by holders of claims and interests.
If the judge approves the reorganization plan and the creditors all \"agree\", then the plan can be confirmed. §1129 of the Bankruptcy Code requires the bankruptcy court reach certain conclusions prior to \"confirming\" or \"approving\" the plan and making it binding on all parties in the case. Most importantly, the bankruptcy court must find the plan (a) complies with applicable law, and (b) has been proposed in good faith. Furthermore, the court must determine whether the plan is \"feasible,\" In other words, the court must safeguard that confirming the plan will not yield to liquidation down the road.
The plan must ensure that the debtor will be able to pay most administrative and priority claims (priority claims over unsecured claims) on the effective date.
### Automatic stay {#automatic_stay}
Like other forms of bankruptcy, petitions filed under Chapter 11 invoke the automatic stay of § 362. The automatic stay requires all creditors to cease collection attempts, making many post-petition debt collection efforts void or voidable. Under some circumstances, some creditors, or the United States Trustee, can request the court convert the case into a liquidation under Chapter 7 or appoint a trustee to manage the debtor\'s business. The court will grant a motion to convert to Chapter 7 or appoint a trustee if either of these actions is in the best interest of all creditors. Sometimes, a company will liquidate under Chapter 11 (perhaps in a 363 sale), in which the pre-existing management may be able to help get a higher price for divisions or other assets than a Chapter 7 liquidation would be likely to achieve. Section 362(d) of the Bankruptcy Code allows the court to terminate, annul, or modify the continuation of the automatic stay as may be necessary or appropriate to balance the competing interests of the debtor, its estate, creditors, and other parties in interest and grants the bankruptcy court considerable flexibility to tailor relief to the exigencies of the circumstances. Relief from the automatic stay is generally sought by motion and, if opposed, is treated as a contested matter under Bankruptcy Rule 9014. A party seeking relief from the automatic stay must also pay the filing fee required by 28 U.S.C.A. § 1930(b).
### Executory contracts {#executory_contracts}
In the new millennium, airlines have fallen under intense scrutiny for what many see as abusing Chapter 11 bankruptcy as a tool for escaping labor contracts, usually 30--35% of an airline\'s operating cost. Every major US airline has filed for Chapter 11 since 2002. In the space of 2 years (2002--2004) US Airways filed for bankruptcy twice leaving the AFL--CIO, pilot unions and other airline employees claiming the rules of Chapter 11 have helped turn the United States into a corporatocracy. The trustee or debtor-in-possession is given the right, under § 365 of the Bankruptcy Code, subject to court approval, to assume or reject executory contracts and unexpired leases. The trustee or debtor-in-possession must assume or reject an executory contract in its entirety unless some portion of it is severable. The trustee or debtor-in-possession normally assumes a contract or lease if it is needed to operate the reorganized business or if it can be assigned or sold at a profit. The trustee or debtor-in-possession normally rejects a contract or lease to transform damage claims arising from the nonperformance of those obligations into a prepetition claim. In some situations, rejection can limit the damages a contract counterparty can claim against the debtor.
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# Chapter 11, Title 11, United States Code
## Features of Chapter 11 reorganization {#features_of_chapter_11_reorganization}
### Priority
Chapter 11 follows the same priority scheme as other bankruptcy chapters. The priority structure is defined primarily by § 507 of the Bankruptcy Code (`{{usc|11|507}}`{=mediawiki}).
As a general rule, administrative expenses (the actual, necessary expenses of preserving the bankruptcy estate, including expenses such as employee wages and the cost of litigating the Chapter 11 case) are paid first. Secured creditors---creditors who have a security interest, or collateral, in the debtor\'s property---will be paid before unsecured creditors. Unsecured creditors\' claims are prioritized by § 507. For instance, the claims of suppliers of products or employees of a company may be paid before other unsecured creditors are paid. Each priority level must be paid in full before the next lower priority level may receive payment.
### Section 1110 {#section_1110}
Section 1110 (`{{usc|11|1110}}`{=mediawiki}) generally provides a secured party with an interest in an aircraft the ability to take possession of the equipment within 60 days after a bankruptcy filing unless the airline cures all defaults. More specifically, the right of the lender to take possession of the secured equipment is not hampered by the automatic stay provisions of the Bankruptcy Code.
### Subchapter V {#subchapter_v}
In August 2019, the Small Business Reorganization Act of 2019 (\"SBRA\") added Subchapter V to Chapter 11 of the Bankruptcy Code. Subchapter V, which took effect in February 2020, is reserved exclusively for small business debtors to expedite bankruptcy procedures and economically resolve small business bankruptcy cases.
Subchapter V retains many of the advantages of a traditional Chapter 11 case without the unnecessary procedural burdens and costs. It seeks to increase the debtor\'s ability to negotiate a successful reorganization, retain control of the business, increase oversight, and ensure a quick reorganization.
A Subchapter V case contrasts with a traditional Chapter 11 in several key aspects: it is earmarked only for the \"small business debtor\" (as defined by the Bankruptcy Code), so only a debtor can file a plan of reorganization. The SBRA requires the U.S. Trustee to appoint a \"Subchapter V trustee\" to every Subchapter V case to supervise and control estate funds and facilitate the development of a consensual plan. It also eliminates the automatic appointment of an official committee of unsecured creditors and abolishes quarterly fees usually paid to the U.S. Trustee throughout the case. Most notably, Subchapter V allows the small business owner to retain their equity in the business so long as the reorganization plan does not discriminate unfairly and is fair and equitable with respect to each class of claims or interests.
## Considerations
The reorganization and court process may take an inordinate amount of time, limiting the chances of a successful outcome and sufficient debtor-in-possession financing may be unavailable during an economic recession. A preplanned, pre-agreed approach between the debtor and its creditors (sometimes called a pre-packaged bankruptcy) may facilitate the desired result. A company undergoing Chapter 11 reorganization is effectively operating under the \"protection\" of the court until it emerges. An example is the airline industry in the United States; in 2006 over half the industry\'s seating capacity was on airlines that were in Chapter 11. These airlines were able to stop making debt payments, break their previously agreed upon labor union contracts, freeing up cash to expand routes or weather a price war against competitors --- all with the bankruptcy court\'s approval.
Studies on the impact of forestalling the creditors\' rights to enforce their security reach different conclusions.
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# Chapter 11, Title 11, United States Code
## Statistics
### Frequency
Chapter 11 cases dropped by 60% from 1991 to 2003. One 2007 study found this was because businesses were turning to bankruptcy-like proceedings under state law, rather than the federal bankruptcy proceedings, including those under chapter 11. Insolvency proceedings under state law, the study stated, are currently faster, less expensive, and more private, with some states not even requiring court filings. However, a 2005 study claimed the drop may have been due to an increase in the incorrect classification of many bankruptcies as \"consumer cases\" rather than \"business cases\".
Cases involving more than US\$50 million in assets are almost always handled in federal bankruptcy court, and not in bankruptcy-like state proceeding.
### Largest cases {#largest_cases}
The largest bankruptcy in history was of the US investment bank Lehman Brothers Holdings Inc., which listed \$639 billion in assets as of its Chapter 11 filing in 2008. The 16 largest corporate bankruptcies as of December 13, 2011 `{{Plainlist|
*{{color box|white|#|border=silver}} Company did not emerge from Chapter 11 bankruptcy}}`{=mediawiki}
Company Filing date Total Assets pre-filing Assets adjusted to the year 2012 Filing court district
---------------------------------------- ------------- ------------------------- ------------------------------------------------------------------------ -----------------------
Lehman Brothers Holdings Inc. \# \$639,063,000,800 \$`{{Formatprice|{{Inflation|US|639063000000|2008|r=5}}}}`{=mediawiki} NY-S
Washington Mutual \# \$327,913,000,000 \$`{{Formatprice|{{Inflation|US|327913000000|2008|r=5}}}}`{=mediawiki} DE
Worldcom Inc. \$103,914,000,000 \$`{{Formatprice|{{Inflation|US|103914000000|2002|r=5}}}}`{=mediawiki} NY-S
General Motors Corporation \$82,300,000,000 \$`{{Formatprice|{{Inflation|US|82300000000|2009|r=5}}}}`{=mediawiki} NY-S
CIT Group \$71,019,200,000 \$`{{Formatprice|{{Inflation|US|71019200000|2009|r=4}}}}`{=mediawiki} NY-S
Enron Corp. #‡ \$63,392,000,000 \$`{{Formatprice|{{Inflation|US|63392000000|2001|r=4}}}}`{=mediawiki} NY-S
Conseco, Inc. \$61,392,000,000 \$`{{Formatprice|{{Inflation|US|61392000000|2002|r=4}}}}`{=mediawiki} IL-N
MF Global \# \$41,000,000,000 \$`{{Formatprice|{{Inflation|US|41000000000|2011|r=4}}}}`{=mediawiki} NY-S
Chrysler LLC \$39,300,000,000 \$`{{Formatprice|{{Inflation|US|39300000000|2009|r=4}}}}`{=mediawiki} NY-S
Texaco, Inc. \$35,892,000,000 \$`{{Formatprice|{{Inflation|US|35892000000|1987|r=4}}}}`{=mediawiki} NY-S
Financial Corp. of America \$33,864,000,000 \$`{{Formatprice|{{Inflation|US|33864000000|1988|r=4}}}}`{=mediawiki} CA-C
Penn Central Transportation Company \# \$7,000,000,000 \$`{{Formatprice|{{Inflation|US|7000000000|1970|r=4}}}}`{=mediawiki} PA-S
Refco Inc. \# \$33,333,172,000 \$`{{Formatprice|{{Inflation|US|33333172000|2005|r=4}}}}`{=mediawiki} NY-S
Global Crossing Ltd. \$30,185,000,000 \$`{{Formatprice|{{Inflation|US|30185000000|2002|r=4}}}}`{=mediawiki} NY-S
Pacific Gas and Electric Co. \$29,770,000,000 \$`{{Formatprice|{{Inflation|US|29770000000|2001|r=4}}}}`{=mediawiki} CA-N
UAL Corp. \$25,197,000,000 \$`{{Formatprice|{{Inflation|US|25197000000|2002|r=4}}}}`{=mediawiki} IL-N
Delta Air Lines, Inc. \$21,801,000,000 \$`{{Formatprice|{{Inflation|US|21801000000|2005|r=4}}}}`{=mediawiki} NY-S
Delphi Corporation, Inc. \$22,000,000,000 \$`{{Formatprice|{{Inflation|US|21801000000|2005|r=4}}}}`{=mediawiki} NY-S
Enron, Lehman Brothers, MF Global and Refco have all ceased operations while others were acquired by other buyers or emerged as a new company with a similar name.
‡ The Enron assets were taken from the 10-Q filed on November 11, 2001. The company announced that the annual financials were under review at the time of filing for Chapter 11
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# Controversy
\[\[<File:Carl> Schleicher Eine Streitfrage aus dem Talmud.jpg\|thumb\|A scene of rabbis
`in debate in ``Carl Schleicher``'s painting `*`A controversy from the Talmud`*`, 19th century]]`
**Controversy** (`{{IPA-cen|UK|k|ə|n|ˈ|t|r|ɒ|v|ə|r|s|i}}`{=mediawiki}, `{{IPA-cen|US|ˈ|k|ɒ|n|t|r|ə|v|ɜː|r|s|i}}`{=mediawiki}) is a state of prolonged public dispute or debate, usually concerning a matter of conflicting opinion or point of view. The word was coined from the Latin *controversia*, as a composite of *controversus* -- \"turned in an opposite direction\", and also means an exercise in rhetoric practiced in Rome.
## Legal
In the theory of law, a controversy differs from a legal case; while legal cases include all suits, criminal as well as civil, a controversy is a purely civil proceeding.
For example, the Case or Controversy Clause of Article Three of the United States Constitution (Section 2, Clause 1) states that \"the judicial Power shall extend \... to Controversies to which the United States shall be a Party\". This clause has been deemed to impose a requirement that United States federal courts are not permitted to cases that do not pose an actual controversy---that is, an actual dispute between adverse parties which is capable of being resolved by the \[court\]. In addition to setting out the scope of the jurisdiction of the federal judiciary, it also prohibits courts from issuing advisory opinions, or from hearing cases that are either unripe, meaning that the controversy has not arisen yet, or moot, meaning that the controversy has already been resolved.
## Benford\'s law {#benfords_law}
Benford\'s law of controversy, as expressed by the astrophysicist and science fiction author Gregory Benford in 1980, states: *Passion is inversely proportional to the amount of real information available.* In other words, it claims that the less factual information is available on a topic, the more controversy can arise around that topic -- and the more facts are available, the less controversy can arise. Thus, for example, controversies in physics would be limited to subject areas where experiments cannot be carried out yet, whereas controversies would be inherent to politics, where communities must frequently decide on courses of action based on insufficient information.
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# Controversy
## Psychological bases {#psychological_bases}
Controversies are frequently thought to be a result of a lack of confidence on the part of the disputants -- as implied by Benford\'s law of controversy, which only talks about lack of information (\"passion is inversely proportional to the amount of real information available\"). For example, in analyses of the political controversy over anthropogenic climate change, which is exceptionally virulent in the United States, it has been proposed that those who are opposed to the scientific consensus do so because they don\'t have enough information about the topic. A study of 1540 US adults found instead that levels of scientific literacy correlated with the strength of opinion on climate change, but not on which side of the debate that they stood.
The puzzling phenomenon of two individuals being able to reach different conclusions after being exposed to the same facts has been frequently explained (particularly by Daniel Kahneman) by reference to a \'bounded rationality\' -- in other words, that most judgments are made using fast acting heuristics that work well in every day situations, but are not amenable to decision-making about complex subjects such as climate change. Anchoring has been particularly identified as relevant in climate change controversies as individuals are found to be more positively inclined to believe in climate change if the outside temperature is higher, if they have been primed to think about heat, and if they are primed with higher temperatures when thinking about the future temperature increases from climate change.
In other controversies -- such as that around the HPV vaccine, the same evidence seemed to license inference to radically different conclusions. Kahan et al. explained this by the cognitive biases of biased assimilation and a credibility heuristic.
Similar effects on reasoning are also seen in non-scientific controversies, for example in the gun control debate in the United States. As with other controversies, it has been suggested that exposure to empirical facts would be sufficient to resolve the debate once and for all. In computer simulations of cultural communities, beliefs were found to polarize within isolated sub-groups, based on the mistaken belief of the community\'s unhindered access to ground truth. Such confidence in the group to find the ground truth is explicable through the success of wisdom of the crowd based inferences. However, if there is no access to the ground truth, as there was not in this model, the method will fail.
Bayesian decision theory allows these failures of rationality to be described as part of a statistically optimized system for decision making. Experiments and computational models in multisensory integration have shown that sensory input from different senses is integrated in a statistically optimal way, in addition, it appears that the kind of inferences used to infer single sources for multiple sensory inputs uses a Bayesian inference about the causal origin of the sensory stimuli. As such, it appears neurobiologically plausible that the brain implements decision-making procedures that are close to optimal for Bayesian inference.
Brocas and Carrillo propose a model to make decisions based on noisy sensory inputs, beliefs about the state of the world are modified by Bayesian updating, and then decisions are made based on beliefs passing a threshold. They show that this model, when optimized for single-step decision making, produces belief anchoring and polarization of opinions -- exactly as described in the global warming controversy context -- in spite of identical evidence presented, the pre-existing beliefs (or evidence presented first) has an overwhelming effect on the beliefs formed. In addition, the preferences of the agent (the particular rewards that they value) also cause the beliefs formed to change -- this explains the biased assimilation (also known as confirmation bias) shown above. This model allows the production of controversy to be seen as a consequence of a decision maker optimized for single-step decision making, rather than a result of limited reasoning in the bounded rationality of Daniel Kahneman
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# CuteFTP
**CuteFTP** is a series of FTP (file transfer protocol) client applications distributed and supported since 1996 by GlobalSCAPE, who later bought the rights to the software. Both a Windows-based or Mac-based interface were made for both home and professional use.
CuteFTP is used to transfer files between computers and File Transfer Protocol (FTP) servers to publish web pages, download digital images, music, multi-media files and software, and transfer files of any size or type between home and office. Since 1999, CuteFTP Pro and CuteFTP Mac Pro have also been available alongside CuteFTP Home with free trial periods.
It was originally developed by Alex Kunadze, a Russian programmer
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# Coleco Telstar series
The **Coleco** **Telstar** brand is a series of dedicated first-generation home video game consoles produced, released and marketed by Coleco from 1976 to 1978. Starting with Coleco Telstar *Pong* clone based video game console on General Instrument\'s AY-3-8500 chip in 1976, there were 14 consoles released in the Coleco Telstar series. About one million units of the first model called Coleco Telstar were sold.
Coleco sold over 1 million units at the price of \$50 in 1976. Coleco was unaffected by a chip shortage that year as their early orders meant it was entirely supplied. The large product lineup and the impending fading out of the *Pong* machines led Coleco to face near-bankruptcy in 1980.
## Model comparison {#model_comparison}
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Console | Model and chip | Release date | Integrated games | Description | Size (height x wide x depth) | Cite | Picture |
+====================================+========================================================+==============+============================================================+============================================================================================================================================================================================================================================================================================================================================================================================================+==============================+======+======================+
| Coleco Telstar | No.6040,\ | 1976 | - hockey | Two fixed paddles. Games are *Pong* variants. | Unknown | | |
| | AY-3-8500 | | - handball | | | | |
| | | | - tennis | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Classic | No.6045,\ | 1976 | - hockey | Two fixed paddles. Deluxe wood case. | Unknown | | |
| | AY-3-8500 | | - handball | | | | |
| | | | - tennis | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Deluxe\ | model number unknown, AY-3-8500 | 1977 | - hockey | Two fixed paddles. Brown stand case with wood panel. Made for Canadian market with French and English text. | Unknown | | No picture available |
| (a.k.a. \"Video World of Sports\") | | | - handballs | | | | |
| | | | - tennis ball | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Ranger | No.6046,\ | 1977 | - hockey | Black and white plastic case, includes Colt 45-style light gun and separate paddle controllers. Four ball games, two target games. Special features of the four ball games include automatic serve and variable paddle and speed control for three experience levels (beginner, intermediate, and professional). Uses six C batteries or an optional AC adapter, light gun requires one nine-volt battery. | 4 lb.\ | \ | |
| | AY-3-8500 | | - handball | | 17.5×6×8 in. | | |
| | | | - tennis | | | | |
| | | | - jai alai | | | | |
| | | | - target | | | | |
| | | | - skeet | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Alpha | No.6030,\ | 1977 | - hockey | Black and white plastic case, fixed paddles. The games feature an automatic serve function and variable settings for three skill levels (beginner, intermediate, and pro). Uses six C batteries or optional 9 volt AC adapter. | 2.5 lb.\ | \ | |
| | AY-3-8500 | | - handball | | 13.5×3.5×7.5 in. | | |
| | | | - tennis | | | | |
| | | | - squash | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Colormatic | No.6130,\ | 1977 | - hockey | Black and white plastic case, detached wired paddles. Color graphics - each game is a different color. The games feature an automatic serve function and variable settings for three skill levels (beginner, intermediate, and professional). Uses six C batteries. | 2.5 lb.\ | | |
| | AY-3-8500\ | | - handball | | 13×6.5×7.5 in. | | |
| | Texas Instruments SN76499N (color) | | - tennis | | | | |
| | | | - jai alai | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Regent | No.6036,\ | 1977 | - hockey | Black and white plastic case, detached wired paddles. The games feature an automatic serve function and variable settings for three skill levels (beginner, intermediate, and professional). Uses six C batteries. | 2.5 lb.\ | | |
| | AY-3-8500 | | - handball | | 13.5×4×8 in. | | |
| | | | - tennis | | | | |
| | | | - jai alai | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Sportsman | model number unknown, AY-3-8500 | 1978 | | Black and white plastic case, detached wired paddles, and light gun. | Unknown | | No picture available |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Combat! | No.6065,\ | 1977 | - *Combat* | Four fixed joysticks (two per player). Games are variations on Kee Games\' *Tank*. Uses six C batteries or an optional AC adapter. | 5.5 lb.\ | \ | |
| | General Instrument AY-3-8700 Tank chip | | - *Night Battle* | | 15×8×10.5 in. | | |
| | | | - *Robot Battle* | | | | |
| | | | - *Camouflage Combat* | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Colortron | No.6135,\ | 1978 | - Tennis | In color, built in sound, fixed paddles. Games are *Pong* variants and feature variable settings for three skill levels (beginner, intermediate, and pro). Uses two nine-volt batteries or an optional AC adapter. | 1 lb.\ | | |
| | AY-3-8510 | | - Hockey | | 2×11.25×4 in. | | |
| | | | - Handball | | | | |
| | | | - Jai-alai | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Marksman | No.6136,\ | 1978 | - Tennis | In color, larger light gun with removable stock, fixed paddles. Four *Pong* variants and two gun games. Uses two nine-volt batteries or an optional AC adapter. | 1 lb.\ | | |
| | AY-3-8512 | | - Hockey | | 2×11.25×5 in. | | |
| | | | - Handball | | | | |
| | | | - Jai-alai | | | | |
| | | | - Skeet | | | | |
| | | | - Target | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Galaxy | model number unknown, AY-3-8600 (games)\ | 1977 | 48 variations of: | Separate joysticks and fixed paddles | Unknown | | No picture available |
| | AY-3-8615 (color encoder) | | | | | | |
| | | | - Tennis | | | | |
| | | | - Hockey | | | | |
| | | | - Handball | | | | |
| | | | - Soccer | | | | |
| | | | - Basketball | | | | |
| | | | - Foosball | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Gemini | model number unknown, MOS Technology MPS 7600-004 | 1977 | - Four pinball games | In color, light gun, two flipper buttons on left and right sides of case, pinball launch button and field adjustment sliders on top, light gun. | Unknown | | No picture available |
| | | | - Two light-gun games | | | | |
+------------------------------------+--------------------------------------------------------+--------------+------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------+------+----------------------+
| Coleco Telstar Arcade | model number 6175, MOS Technology MPS-7600 (each cart) | 1977 | - Pack-in game (Tennis, road racing, quick draw) | Cartridge-based, triangular case includes light gun, steering wheel with gear shift, and paddles, one on each side. | 4 lb.\ | \ | |
| | | | | | 7.5×18×16 in
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# Conventional warfare
`{{history of war}}`{=mediawiki} **Conventional warfare** is a form of warfare conducted by using conventional weapons and battlefield tactics between two or more states in open confrontation. The forces on each side are well-defined and fight by using weapons that target primarily the opponent\'s military. It is normally fought by using conventional weapons, not chemical, biological, radiological, or nuclear weapons.
The general purpose of conventional warfare is to weaken or destroy the opponent\'s military, which negates its ability to engage in conventional warfare. In forcing capitulation, however, one or both sides may eventually resort to unconventional warfare tactics.
## History
### Formation of state {#formation_of_state}
The state was first advocated by Plato but found more acceptance in the consolidation of power under the Roman Catholic Church. European monarchs then gained power as the Catholic Church was stripped of temporal power and was replaced by the divine right of kings. In 1648, the powers of Europe signed the Treaty of Westphalia, which ended the religious violence for purely political governance and outlook, signifying the birth of the modern state.
Within the statist paradigm, only the state and its appointed representatives may bear arms and enter into war. In fact, war then became understood only as a conflict between sovereign states. Monarchs strengthened that idea and gave it the force of law. Any noble had been allowed to start a war, but European monarchs had to consolidate military power in response to the Napoleonic Wars.
### Clausewitzian paradigm {#clausewitzian_paradigm}
Prussia was one of the countries that tried to amass military power. Carl von Clausewitz, one of Prussia\'s officers, wrote *On War*, a work rooted solely in the world of the state. All other forms of intrastate conflict, such as rebellion, are not accounted for because in theoretical terms, he could not account for warfare before the state. However, near the end of his life, he grew increasingly aware of the importance of non-state military actors, as is revealed in his conceptions of \"the people in arms\", which he noted arose from the same social and political sources as traditional interstate warfare.
Practices such as raiding or blood feuds were then labeled criminal activities and stripped of legitimacy. That war paradigm reflected the view of most of the modernized world in the early 21st century, as is verified by examination of the conventional armies of the time: large, high-maintenance, and technologically advanced armies designed to compete against similarly designed forces.
Clausewitz also forwarded the issue of *casus belli*. Wars had been fought for social, religious, or even cultural reasons, and Clausewitz taught that war is merely \"a continuation of politics by other means.\" It is a rational calculation in which states fight for their interests (whether they are economic, security-related, or otherwise) once normal discourse has broken down.
### Prevalence
Most modern wars have been conducted using conventional means. Confirmed use of biological warfare by a nation state has not occurred since 1945, and chemical warfare has been used only a few times (the latest known confrontation in which it was utilized being the Syrian Civil War). Nuclear warfare has only occurred once: the American bombing of the Japanese cities of Hiroshima and Nagasaki in August 1945.
### Since World War II {#since_world_war_ii}
The state and Clausewitzian principles peaked in the World Wars, during the 20th century, but they also laid the groundwork for their dilapidation from nuclear proliferation. During the Cold War, the superpowers sought to avoid open conflict between their respective forces, as both sides recognized that such a clash could very easily escalate and quickly involve nuclear weapons. Instead, the superpowers fought each other through their involvement in proxy wars, military buildups, and diplomatic standoffs. Thus, no two nuclear powers have yet fought a conventional war directly except for two brief skirmishes between China and Soviet Union in the 1969 Sino-Soviet conflict and between India and Pakistan in the 1999 Kargil War.
However, conventional wars have been fought since 1945 between countries without nuclear weapons, such as the Iran--Iraq War and Eritrean--Ethiopian War, or between a nuclear state and a weaker non-nuclear state, like the Gulf War and Russo-Ukrainian War
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# Complementary DNA
In genetics, **complementary DNA** (**cDNA**) is DNA that was reverse transcribed (via reverse transcriptase) from an RNA (e.g., messenger RNA or microRNA). cDNA exists in both single-stranded and double-stranded forms and in both natural and engineered forms.
In engineered forms, it often is a copy (replicate) of the naturally occurring DNA from any particular organism\'s natural genome; the organism\'s own mRNA was naturally transcribed from its DNA, and the cDNA is reverse transcribed from the mRNA, yielding a duplicate of the original DNA. Engineered cDNA is often used to express a specific protein in a cell that does not normally express that protein (i.e., heterologous expression), or to sequence or quantify mRNA molecules using DNA based methods (qPCR, RNA-seq). cDNA that codes for a specific protein can be transferred to a recipient cell for expression as part of recombinant DNA, often bacterial or yeast expression systems. cDNA is also generated to analyze transcriptomic profiles in bulk tissue, single cells, or single nuclei in assays such as microarrays, qPCR, and RNA-seq.
In natural forms, cDNA is produced by retroviruses (such as HIV-1, HIV-2, simian immunodeficiency virus, etc.) and then integrated into the host\'s genome, where it creates a provirus.
The term *cDNA* is also used, typically in a bioinformatics context, to refer to an mRNA transcript\'s sequence, expressed as DNA bases (deoxy-GCAT) rather than RNA bases (GCAU).
Patentability of cDNA was a subject of a 2013 US Supreme Court decision in Association for Molecular Pathology v. Myriad Genetics, Inc. As a compromise, the Court declared, that exons-only cDNA is patent-eligible, whereas isolated sequences of naturally occurring DNA comprising introns are not.
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# Complementary DNA
## Synthesis
RNA serves as a template for cDNA synthesis. In cellular life, cDNA is generated by viruses and retrotransposons for integration of RNA into target genomic DNA. In molecular biology, RNA is purified from source material after genomic DNA, proteins and other cellular components are removed. cDNA is then synthesized through *in vitro* reverse transcription.
### RNA purification {#rna_purification}
RNA is transcribed from genomic DNA in host cells and is extracted by first lysing cells then purifying RNA utilizing widely used methods such as phenol-chloroform, silica column, and bead-based RNA extraction methods. Extraction methods vary depending on the source material. For example, extracting RNA from plant tissue requires additional reagents, such as polyvinylpyrrolidone (PVP), to remove phenolic compounds, carbohydrates, and other compounds that will otherwise render RNA unusable. To remove DNA and proteins, enzymes such as DNase and Proteinase K are used for degradation. Importantly, RNA integrity is maintained by inactivating RNases with chaotropic agents such as guanidinium isothiocyanate, sodium dodecyl sulphate (SDS), phenol or chloroform. Total RNA is then separated from other cellular components and precipitated with alcohol. Various commercial kits exist for simple and rapid RNA extractions for specific applications. Additional bead-based methods can be used to isolate specific sub-types of RNA (e.g. mRNA and microRNA) based on size or unique RNA regions.
### Reverse transcription {#reverse_transcription}
#### First-strand synthesis {#first_strand_synthesis}
Using a reverse transcriptase enzyme and purified RNA templates, one strand of cDNA is produced (first-strand cDNA synthesis). The M-MLV reverse transcriptase from the Moloney murine leukemia virus is commonly used due to its reduced RNase H activity suited for transcription of longer RNAs. The AMV reverse transcriptase from the avian myeloblastosis virus may also be used for RNA templates with strong secondary structures (i.e. high melting temperature). cDNA is commonly generated from mRNA for gene expression analyses such as RT-qPCR and RNA-seq. mRNA is selectively reverse transcribed using oligo-dT primers that are the reverse complement of the poly-adenylated tail on the 3\' end of all mRNA. The oligo-dT primer anneals to the poly-adenylated tail of the mRNA to serve as a binding site for the reverse transcriptase to begin reverse transcription. An optimized mixture of oligo-dT and random hexamer primers increases the chance of obtaining full-length cDNA while reducing 5\' or 3\' bias. Ribosomal RNA may also be depleted to enrich both mRNA and non-poly-adenylated transcripts such as some non-coding RNA.
#### Second-strand synthesis {#second_strand_synthesis}
The result of first-strand syntheses, RNA-DNA hybrids, can be processed through multiple second-strand synthesis methods or processed directly in downstream assays. An early method known as hairpin-primed synthesis relied on hairpin formation on the 3\' end of the first-strand cDNA to prime second-strand synthesis. However, priming is random and hairpin hydrolysis leads to loss of information. The Gubler and Hoffman Procedure uses E. Coli RNase H to nick mRNA that is replaced with E. Coli DNA Polymerase I and sealed with E. Coli DNA Ligase. An optimization of this procedure relies on low RNase H activity of M-MLV to nick mRNA with remaining RNA later removed by adding RNase H after DNA Polymerase translation of the second-strand cDNA. This prevents lost sequence information at the 5\' end of the mRNA.
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# Complementary DNA
## Applications
Complementary DNA is often used in gene cloning or as gene probes or in the creation of a cDNA library. When scientists transfer a gene from one cell into another cell in order to express the new genetic material as a protein in the recipient cell, the cDNA will be added to the recipient (rather than the entire gene), because the DNA for an entire gene may include DNA that does not code for the protein or that interrupts the coding sequence of the protein (e.g., introns). Partial sequences of cDNAs are often obtained as expressed sequence tags.
With amplification of DNA sequences via polymerase chain reaction (PCR) now commonplace, one will typically conduct reverse transcription as an initial step, followed by PCR to obtain an exact sequence of cDNA for intra-cellular expression. This is achieved by designing sequence-specific DNA primers that hybridize to the 5\' and 3\' ends of a cDNA region coding for a protein. Once amplified, the sequence can be cut at each end with nucleases and inserted into one of many small circular DNA sequences known as expression vectors. Such vectors allow for self-replication, inside the cells, and potentially integration in the host DNA. They typically also contain a strong promoter to drive transcription of the target cDNA into mRNA, which is then translated into protein.
cDNA is also used to study gene expression via methods such as RNA-seq or RT-qPCR. For sequencing, RNA must be fragmented due to sequencing platform size limitations. Additionally, second-strand synthesized cDNA must be ligated with adapters that allow cDNA fragments to be PCR amplified and bind to sequencing flow cells. Gene-specific analysis methods commonly use microarrays and RT-qPCR to quantify cDNA levels via fluorometric and other methods.
On 13 June 2013, the United States Supreme Court ruled in the case of *Association for Molecular Pathology v. Myriad Genetics* that while naturally occurring genes cannot be patented, cDNA is patent-eligible because it does not occur naturally.
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# Complementary DNA
## Viruses and retrotransposons {#viruses_and_retrotransposons}
Some viruses also use cDNA to turn their viral RNA into mRNA (viral RNA → cDNA → mRNA). The mRNA is used to make viral proteins to take over the host cell.
An example of this first step from viral RNA to cDNA can be seen in the HIV cycle of infection. Here, the host cell membrane becomes attached to the virus\' lipid envelope which allows the viral capsid with two copies of viral genome RNA to enter the host. The cDNA copy is then made through reverse transcription of the viral RNA, a process facilitated by the chaperone CypA and a viral capsid associated reverse transcriptase.
cDNA is also generated by retrotransposons in eukaryotic genomes. Retrotransposons are mobile genetic elements that move themselves within, and sometimes between, genomes via RNA intermediates. This mechanism is shared with viruses with the exclusion of the generation of infectious particles
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# Cellular digital packet data
**Cellular Digital Packet Data** (**CDPD**) is an obsolete wide-area mobile data service which used unused bandwidth normally used by Advanced Mobile Phone System (AMPS) mobile phones between 800 and 900 MHz to transfer data. Speeds up to 19.2 kbit/s were possible, though real world speeds seldom reached higher than 9.6 kbit/s. The service was discontinued in conjunction with the retirement of the parent AMPS service; it has been functionally replaced by faster services such as 1xRTT, Evolution-Data Optimized, and UMTS/High Speed Packet Access (HSPA).
Developed in the early 1990s, CDPD was large on the horizon as a future technology. However, it had difficulty competing against existing slower but less expensive Mobitex and DataTAC systems, and never quite gained widespread acceptance before newer, faster standards such as General Packet Radio Service (GPRS) became dominant.
CDPD had very limited consumer products. AT&T Wireless first sold the technology in the United States under the PocketNet brand. It was one of the first products of wireless web service. Digital Ocean, Inc. an original equipment manufacturer licensee of the Apple Newton, sold the Seahorse product, which integrated the Newton handheld computer, an AMPS/CDPD handset/modem along with a web browser in 1996, winning the CTIA\'s hardware product of the year award as a smartphone, arguably the world\'s first. A company named OmniSky provided service for Palm V devices. OmniSky then filed for bankruptcy in 2001 then was picked up by EarthLink Wireless. The technician that developed the tech support for all of the wireless technology was a man by the name of Myron Feasel he was brought from company to company ending up at Palm. Sierra Wireless sold PCMCIA devices and Airlink sold a serial modem. Both of these were used by police and fire departments for dispatch. Wireless later sold CDPD under the Wireless Internet brand (not to be confused with Wireless Internet Express, their brand for GPRS/EDGE data). PocketNet was generally considered a failure with competition from 2G services such as Sprint\'s Wireless Web. AT&T Wireless sold four PocketNet Phone models to the public: the Samsung Duette and the Mitsubishi MobileAccess-120 were AMPS/CDPD PocketNet phones introduced in October 1997; and two IS-136/CDPD Digital PocketNet phones, the Mitsubishi T-250 and the Ericsson R289LX.
Despite its limited success as a consumer offering, CDPD was adopted in a number of enterprise and government networks. It was particularly popular as a first-generation wireless data solution for telemetry devices (machine to machine communications) and for public safety mobile data terminals.
In 2004, major carriers in the United States announced plans to shut down CDPD service. In July 2005, the AT&T Wireless and Cingular Wireless CDPD networks were shut down.
## CDPD Network and system {#cdpd_network_and_system}
Primary elements of a CDPD network are: 1. **End systems**: physical & logical end systems that exchange information 2. **Intermediate systems**: CDPD infrastructure elements that store, forward & route the information
There are 2 kinds of End systems 1. **Mobile end system**: subscriber unit to access CDPD network over a wireless interface 2. **Fixed end system**: common host/server that is connected to the CDPD backbone and providing access to specific application and data
There are 2 kinds of Intermediate systems 1. **Generic intermediate system**: simple router with no knowledge of mobility issues 2. **mobile data intermediate system**: specialized intermediate system that routes data based on its knowledge of the current location of Mobile end system. It is a set of hardware and software functions that provide switching, accounting, registration, authentication, encryption, and so on.
The design of CDPD was based on several design objectives that are often repeated in designing overlay networks or new networks. A lot of emphasis was laid on open architectures and reusing as much of the existing RF infrastructure as possible. The design goal of CDPD included location independence and independence fro`{{Clarify|date=June 2016}}`{=mediawiki}, service provider, so that coverage could be maximized; application transparency and multiprotocol support, interoperability between products from multiple vendors
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# Creature of statute
A **creature of statute** (also known as **creature of the state**) is a legal entity, such as a corporation, created by statute. Creatures of statute may include municipalities and other artificial legal entities or relationships. Thus, when a statute in some fashion requires the formation of a corporate body---often for governmental purposes---such bodies when formed are known as \"creatures of statute.\" The same concept is also expressed with the phrase \"creature of the state.\"
The term \"creature of statute\" is most common to the United States. In the United Kingdom, these bodies are simply called statutory corporations (or statutory bodies) and generally have some governmental function. The United Kingdom Atomic Energy Authority is an example. In a wider sense, most companies in the UK are created under statute since the Companies Act 1985 specifies how a company may be created by a member of the public, but these companies are not called \'statutory corporations\'. Often, in American legal and business documents that speak of governing bodies (*e.g.*, a board that governs small businesses in China) these bodies are described as \"creatures of statute\" to inform readers of their origins and format although the national governments that created them may not term them as creatures of statute. Australia also uses the term \"creature of statute\" to describe some governmental bodies.
The importance of a corporate body, regardless of its exact function, when such a body is a creature of statute is that its active functions can only be within the scope detailed by the statute which created that corporation. Thereby, the creature of statute is the tangible manifestation of the functions or work described by a given statute. The jurisdiction of a body that is a creature of statute is also therefore limited to the functional scope written into the laws that created that body. Unlike most (private) corporate bodies, creatures of statute cannot expand their business interests into other diverse areas
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# General Conference on Weights and Measures
The **General Conference on Weights and Measures** (abbreviated **CGPM** from the *Conférence générale des poids et mesures*) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre Convention through which member states act together on matters related to measurement science and measurement standards. The CGPM is made up of delegates of the governments of the member states and observers from the Associates of the CGPM. It elects the **International Committee for Weights and Measures** (abbreviated **CIPM** from the *Comité international des poids et mesures*) as the supervisory board of the BIPM to direct and supervise it.
Initially the work of the BIPM concerned the kilogram and the metre, but in 1921 the scope of the Metre Convention was extended to accommodate all physical measurements and hence all aspects of the metric system. `{{anchor|11}}`{=mediawiki}In 1960 the 11th CGPM approved the title International System of Units, usually known as \"SI\".
The General Conference receives the report of the CIPM on work accomplished; it discusses and examines the arrangements required to ensure the propagation and improvement of the International System of Units (SI); it endorses the results of new fundamental metrological determinations and various scientific resolutions of international scope; and it decides all major issues concerning the organization and development of the BIPM, including its financial endowment.
The CGPM meets in Paris, usually once every four years. `{{anchor|25}}`{=mediawiki}The 25th meeting of the CGPM took place from 18 to 20 November 2014, `{{anchor|26}}`{=mediawiki}the 26th meeting of the CGPM took place in Versailles from 13 to 16 November 2018, `{{anchor|27}}`{=mediawiki}and the 27th meeting of the CGPM took place from 15 to 18 November 2022.
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# General Conference on Weights and Measures
## Establishment
On 20 May 1875 an international treaty known as the *Convention du Mètre* (Metre Convention) was signed by 17 states. This treaty established an international organisation, the Bureau international des poids et mesures (BIPM), which has two governing organs:
- Conférence générale des poids et mesures (CGPM), a plenary meeting of official delegates of member states which is the supreme authority for all actions;
- Comité international des poids et mesures (CIPM), consisting of elected scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the organisation.
The organization has a permanent laboratory and secretariat function (sometimes referred to as the Headquarters), the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.
The CGPM acts on behalf of the governments of its members. In so doing, it elects members to the CIPM, receives reports from the CIPM which it passes on to the governments and national laboratories on member states, examines and where appropriate approves proposals from the CIPM in respect of changes to the International System of Units (SI), approves the budget for the BIPM (over €13 million in 2018) and it decides all major issues concerning the organization and development of the BIPM.
The structure is analogous to that of a stock corporation. The BIPM is the organisation, the CGPM is the general meeting of the shareholders, the CIPM is the board of directors appointed by the CGPM, and the staff at the site in Saint-Cloud perform the day-to-day work.
### Membership criteria {#membership_criteria}
The CGPM recognises two classes of membership -- full membership for those states that wish to participate in the activities of the BIPM and associate membership for those countries or economies that only wish to participate in the CIPM MRA program. Associate members have observer status at the CGPM. Since all formal liaison between the convention organisations and national governments is handled by the member state\'s ambassador to France, it is implicit that member states must have diplomatic relations with France, though during both world wars, nations that were at war with France retained their membership of the CGPM. CGPM meetings are chaired by the Président de l\'Académie des Sciences de Paris.
Of the twenty countries that attended the Conference of the Metre in 1875, representatives of seventeen signed the convention on 20 May 1875. In April 1884, H. J. Chaney, Warden of Standards in London unofficially contacted the BIPM inquiring whether the BIPM would calibrate some metre standards that had been manufactured in the United Kingdom. Broch, director of the BIPM replied that he was not authorised to perform any such calibrations for non-member states. On 17 September 1884, the British Government signed the convention on behalf of the United Kingdom. This number grew to 21 in 1900, 32 in 1950, and 49 in 2001. `{{As of|2022|11|18|since=}}`{=mediawiki}, there are 64 Member States and 37 Associate States and Economies of the General Conference (with year of partnership in parentheses):
#### Member states {#member_states}
Argentina (1877)\
Australia (1947)\
Austria (1875)\
Belarus (2020)\
Belgium (1875)\
Brazil (1921)\
Bulgaria (1911)\
Canada (1907)\
Chile (1908)\
China (1977)\
Colombia (2012)\
Costa Rica (2022)\
Croatia (2008)\
Czech Republic (1922)\
Denmark (1875)\
Ecuador (2019)\
Egypt (1962)\
Estonia (2021)\
Finland (1913)\
France (1875)\
Germany (1875)\
Greece (2001)\
Hungary (1925)\
India (1880)\
Indonesia (1960)\
Iran (1975)\
Iraq (2013)\
Ireland (1925)\
Israel (1985)\
Italy (1875)\
Japan (1885)\
Kazakhstan (2008)\
Kenya (2010)\
Lithuania (2015)\
Malaysia (2001)\
Mexico (1890)\
Montenegro (2018)\
Morocco (2019)\
Netherlands (1929)\
New Zealand (1991)\
Norway (1875)\
Pakistan (1973)\
Poland (1925)\
Portugal (1876)\
Romania (1884)\
Russia (1875)\
Saudi Arabia (2011)\
Serbia (2001)\
Singapore (1994)\
Slovakia (1922)\
Slovenia (2016)\
South Africa (1964)\
South Korea (1959)\
Spain (1875)\
Sweden (1875)\
Switzerland (1875)\
Thailand (1912)\
Tunisia (2012)\
Turkey (1875)\
Ukraine (2018)\
United Arab Emirates (2015)\
United Kingdom (1884)\
United States (1878)\
Uruguay (1908)\
`{{div col end}}`{=mediawiki}
##### Former members {#former_members}
Cameroon (1970--2012)\
Dominican Republic (1954--2015)\
North Korea (1982--2012)\
Peru (1875--1956)\
Venezuela (1879--1907, 1960--2018) `{{div col end}}`{=mediawiki}
##### Notes
#### Associates
At the 21st meeting of the CGPM in October 1999, the category of \"associate\" was created for states not yet BIPM members and for economic unions.
Albania (2007)\
Azerbaijan (2015)\
Bangladesh (2010)\
Bolivia (2008)\
Bosnia and Herzegovina (2011)\
Botswana (2012)\
Cambodia (2021)\
Caribbean Community (2005)\
Chinese Taipei (2002)\
Cuba (2000)\
Ethiopia (2018)\
Georgia (2008)\
Ghana (2009)\
Hong Kong (2000)\
Jamaica (2003)\
Kuwait (2018)\
Latvia (2001)\
Luxembourg (2014)\
Malta (2001)\
Mauritius (2010)\
Moldova (2007)\
Mongolia (2013)\
Namibia (2012)\
North Macedonia (2006)\
Oman (2012)\
Panama (2003)\
Paraguay (2009)\
Peru (2009)\
Philippines (2002)\
Qatar (2016)\
Sri Lanka (2007)\
Syria (2012)\
Tanzania (2018)\
Uzbekistan (2018)\
Vietnam (2003)\
Zambia (2010)\
Zimbabwe (2010--2020, 2022)\
`{{div col end}}`{=mediawiki}
##### Former Associates {#former_associates}
Seychelles (2010--2021)\
Sudan (2014--2021)\
`{{div col end}}`{=mediawiki}
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# General Conference on Weights and Measures
## CGPM meetings {#cgpm_meetings}
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1st (1889) The international prototype of the kilogram (IPK), a cylinder made of platinum--iridium, and the international prototype of the metre, an X-cross-section bar also made from platinum--iridium, were selected from batches manufactured by the British firm Johnson Matthey. Working copies of both artifacts were also selected by lot and other copies distributed to member nations, again by lot. The prototypes and working copies were deposited at the International Bureau of Weights and Measures (Bureau international des poids et mesures), Saint-Cloud, France. \|- `{{anchor|2}}`{=mediawiki} 2nd (1895) No resolutions were passed by the 2nd CGPM. \|- `{{anchor|3}}`{=mediawiki} 3rd (1901) The litre was redefined as volume of 1 kg of water. Clarified that kilograms are units of mass, \"standard weight\" defined, standard acceleration of gravity defined endorsing use of grams force and making them well-defined. \|- `{{anchor|4}}`{=mediawiki} 4th (1907) The carat was defined as 200 mg. \|- `{{anchor|5}}`{=mediawiki} 5th (1913) The International Temperature Scale was proposed. The General Conference recommended that the International Committee authorize the Bureau to organise, between establishments possessing a calibration base, the circulation, in groups, of well-defined invar threads, with a view to enabling agreement to be reached on the method of determining these bases, as well as the method of using the threads. \|- `{{anchor|6}}`{=mediawiki} 6th (1921) The Metre Convention revised. \|- `{{anchor|7}}`{=mediawiki} 7th (1927) The Consultative Committee for Electricity (CCE) created. \|- `{{anchor|8}}`{=mediawiki} 8th (1933) The need for absolute electrical unit identified. \|- `{{anchor|9}}`{=mediawiki} 9th (1948) The ampere, bar, coulomb, farad, henry, joule, newton, ohm, volt, watt, weber were defined. The degree Celsius was selected from three names in use as the name of the unit of temperature. The symbol l (lowercase L) was adopted as symbol for litre. Both the comma and dot on a line are accepted as decimal marker symbols. Symbols for the stere and second changed. The universal return to the Long Scale numbering system was proposed but not adopted. \|- `{{anchor|10}}`{=mediawiki} 10th (1954) The kelvin, standard atmosphere defined. Work on the *International System of Units* (metre, kilogram, second, ampere, kelvin, candela) began.
11th (1960) The metre was redefined in terms of wavelengths of light. The units hertz, lumen, lux, tesla were adopted. The new MKSA-based metric system given the official symbol **SI** for ***Système International d\'Unités*** and launched as the \"modernized metric system\". The prefixes *pico-*, *nano-*, *micro-*, *mega-*, *giga-* and *tera-* were confirmed. \|- `{{anchor|12}}`{=mediawiki} 12th (1964) The original definition of litre = 1 dm^3^ restored. The prefixes *atto-* and *femto-* were adopted. \|- `{{anchor|13}}`{=mediawiki} 13th (1967) The second was redefined as duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at a temperature of 0 K. The *Degree Kelvin* renamed *kelvin* and the candela redefined. \|- `{{anchor|14}}`{=mediawiki} 14th (1971) A new SI base unit, the mole defined. The names pascal and siemens as units of pressure and electrical conductance were approved. \|- `{{anchor|15}}`{=mediawiki} 15th (1975) The prefixes *peta-* and *exa-* were adopted. The units gray and becquerel were adopted as radiological units within SI. \|- `{{anchor|16}}`{=mediawiki} 16th (1979) The candela and sievert were defined. Both l and L provisionally allowed as symbols for litre. \|- `{{anchor|17}}`{=mediawiki} 17th (1983) The metre was redefined in terms of the speed of light, i.e. The metre is the length of the path travelled by light in vacuum during a time interval of **1/299,792,458** of a second. \|- `{{anchor|18}}`{=mediawiki} 18th (1987) Conventional values were adopted for Josephson constant, *K~J~*, and von Klitzing constant, *R~K~*, preparing the way for alternative definitions of the ampere and kilogram. \|- `{{anchor|19}}`{=mediawiki} 19th (1991) New prefixes *yocto-*, *zepto-*, *zetta-* and *yotta-* were adopted. \|- `{{anchor|20}}`{=mediawiki} 20th (1995) The SI supplementary units (radian and steradian) become *derived units*. \|- `{{anchor|21}}`{=mediawiki}
25th (2014) Redefining the kilogram in relation to the Planck constant was discussed but not decided on. Progress towards realising the redefinition has been noted. However, it was concluded that the data did not yet appear to be sufficiently robust. Continued effort on improving the data has been encouraged, such that a resolution that would replace the current definition with the revised definition can be adopted at the 26th meeting.
26th (2018) The kilogram, ampere, kelvin, and mole were redefined at this meeting, in terms new permanently fixed values of the Planck constant, elementary charge, Boltzmann constant and Avogadro constant, respectively.
27th (2022) New prefixes *quecto-*, *ronto-*, *ronna-*, and *quetta-* were adopted. Planning was begun to eliminate the leap second and stabilize DUT1 by 2035.
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# General Conference on Weights and Measures
## International Committee for Weights and Measures {#international_committee_for_weights_and_measures}
The International Committee for Weights and Measures consists of eighteen persons, each of a different nationality. elected by the General Conference on Weights and Measures (CGPM) whose principal task is to promote worldwide uniformity in units of measurement by taking direct action or by submitting proposals to the CGPM.
The CIPM meets every year (since 2011 in two sessions per year) at the Pavillon de Breteuil where, among other matters, it discusses reports presented to it by its Consultative Committees. Reports of the meetings of the CGPM, the CIPM, and all the Consultative Committees, are published by the BIPM.
### Mission
The secretariat is based in Saint-Cloud, Hauts-de-Seine, France.
In 1999, the CIPM has established the CIPM *Arrangement de reconnaissance mutuelle* (Mutual Recognition Arrangement, MRA), which serves as the framework for the mutual acceptance of national measurement standards and for recognition of the validity of calibration and measurement certificates issued by national metrology institutes.
A recent focus area of the CIPM has been the revision of the SI.
### Consultative committees {#consultative_committees}
The CIPM has set up a number of consultative committees (CC) to assist it in its work. These committees are under the authority of the CIPM. The president of each committee, who is expected to take the chair at CC meetings, is usually a member of the CIPM. Apart from the CCU, membership of a CC is open to National Metrology Institutes (NMIs) of Member States that are recognized internationally as most expert in the field. NMIs from Member States that are active in the field, but lack the expertise to become Members, are able to attend CC meetings as observers.
These committees are:
- CCAUV: Consultative Committee for Acoustics, Ultrasound and Vibration
- CCEM: Consultative Committee for Electricity and Magnetism
- CCL: Consultative Committee for Length
- CCM: Consultative Committee for Mass and Related Quantities
- CCPR: Consultative Committee for Photometry and Radiometry
- CCQM: Consultative Committee for Amount of Substance -- Metrology in Chemistry and Biology
- CCRI: Consultative Committee for Ionizing Radiation
- CCT: Consultative Committee for Thermometry
- CCTF: Consultative Committee for Time and Frequency
- CCU: Consultative Committee for Units
The CCU\'s role is to advise on matters related to the development of the SI and the preparation of the SI brochure. It has liaison with other international bodies such as International Organization for Standardization (ISO), International Astronomical Union (IAU), International Union of Pure and Applied Chemistry (IUPAC), International Union of Pure and Applied Physics (IUPAP) and International Commission on Illumination (CIE).
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# General Conference on Weights and Measures
## International Committee for Weights and Measures {#international_committee_for_weights_and_measures}
### Major reports {#major_reports}
Official reports of the CIPM include:
- Reports of CIPM meetings (*Procès-Verbaux*) (CIPM Minutes)
- Annual Report to Governments on the financial and administrative situation of the BIPM
- Notification of the contributive parts of the Contracting States
- Convocation to meetings of the CGPM
- Report of the President of the CIPM to the CGPM
From time to time the CIPM has been charged by the CGPM to undertake major investigations related to activities affecting the CGPM or the BIPM. Reports produced include:
#### The Blevin Report {#the_blevin_report}
The **Blevin Report**, published in 1998, examined the state of worldwide metrology. The report originated from a resolution passed at the 20th CGPM (October 1995) which committed the CIPM to `{{Blockquote| study and report on the long-term national and international needs relating to metrology, the appropriate international collaborations and the unique role of the BIPM to meet these needs, and the financial and other commitments that will be required from the Member States in the coming decades.}}`{=mediawiki} The report identified, amongst other things, a need for closer cooperation between the BIPM and other organisations such as International Organization of Legal Metrology (OIML) and International Laboratory Accreditation Cooperation (ILAC) with clearly defined boundaries and interfaces between the organisations. Another major finding was the need for cooperation between accreditation laboratories and the need to involve developing countries in the world of metrology.
#### The Kaarls Report {#the_kaarls_report}
The Kaarls Report published in 2003 examined the role of the BIPM in the evolving needs for metrology in trade, industry and society.
#### SI Brochure {#si_brochure}
The CIPM has responsibility for commissioning the SI brochure, which is the formal definition of the International system of units. The brochure is produced by the CCU in conjunction with a number of other international organisations. Initially the brochure was only in French -- the official language of the metre convention, but recent versions have been published simultaneously in both English and French, with the French text being the official text. The 6th edition was published in 1991, the 7th edition was published in 1998, and the 8th, in 2006. The most recent edition is the 9th edition, originally published as version 1 in 2019 to include the 2019 revision of the SI (a.k.a. \"new SI\"); it was updated to version 2 in December 2022 to include the new SI prefixes ronna-, quetta-, ronto- and quecto- introduced in November 2022
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# Carl Barks
*Duckman*}} `{{original research|date=July 2022}}`{=mediawiki} `{{Infobox comics creator
| image = Carl barks.jpg
| caption = Barks in 1982
| alt =
| birth_date = {{birth date|1901|3|27|mf=y}}<ref>[https://familysearch.org/pal:/MM9.1.1/JG4V-6ZF "United States Social Security Death Index", index, FamilySearch] (accessed 20 February 2013), Carl Barks, 25 August 2000; citing U.S. Social Security Administration, Death Master File, database (Alexandria, Virginia: National Technical Information Service, ongoing).</ref>
| birth_place = Near [[Merrill, Oregon]], U.S.
| death_date = {{death date and age|2000|8|25|1901|3|27|mf=y}}
| death_place = [[Grants Pass, Oregon]], U.S.
| art = y
| write = y
| pencil = y
| ink = y
| notable works = [[Scrooge McDuck]], [[Huey, Dewey, and Louie]], [[Daisy Duck]], [[Gyro Gearloose]], [[Gladstone Gander]], [[The Junior Woodchucks]], [[Beagle Boys]], [[Flintheart Glomgold]], [[Magica De Spell]], [[List of Donald Duck universe characters#Neighbor Jones|Neighbor J. Jones]], [[Glittering Goldie]], [[Cornelius Coot]], [[John D. Rockerduck]]<br/><br/>Oil paintings of his duck characters
| spouse = {{Plainlist|
* {{marriage|Pearl Turner|1923|1929|end=div}}
* {{marriage|Clara Balken|1932|1951|end=div}}
* {{marriage|Garé Williams|1954|1993|end=d}}}}
| children = 2
| signature = Carl barks signature.svg
}}`{=mediawiki}
**Carl Barks** (March 27, 1901 -- August 25, 2000) was an American cartoonist, author, and painter. He is best known for his work in Disney comic books, as the writer and artist of the first Donald Duck stories and as the creator of Scrooge McDuck. He worked anonymously until late in his career; fans dubbed him \"The Duck Man\" and \"The Good Duck Artist\". In 1987, Barks was one of the three inaugural inductees of the Will Eisner Comic Book Hall of Fame.
Barks worked for the Disney Studio and Western Publishing where he created Duckburg and many of its inhabitants, such as Scrooge McDuck (1947), Gladstone Gander (1948), the Beagle Boys (1951), The Junior Woodchucks (1951), Gyro Gearloose (1952), Cornelius Coot (1952), Flintheart Glomgold (1956), John D. Rockerduck (1961) and Magica De Spell (1961).
He has been named by animation historian Leonard Maltin as \"the most popular and widely read artist-writer in the world\". Will Eisner called him \"the Hans Christian Andersen of comic books.\" Beginning especially in the 1980s, Barks\' artistic contributions would be a primary source for animated adaptations such as *DuckTales* and its 2017 remake.
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# Carl Barks
## Biography
Barks was born near Merrill, Oregon, to William Barks and his wife, Arminta Johnson. He had an older brother named Clyde. His paternal grandparents were David Barks and his wife Ruth Shrum. Barks\' maternal grandparents were Carl Johnson and his wife, Suzanna Massey, but little else is known about his ancestors. Barks was the descendant of Jacob Barks, who came to Missouri from North Carolina c. 1800. They lived in Marble Hill in Bollinger County. Jacob Barks\' son Isaac was the father of the David Barks noted above.
### Childhood
According to Barks\'s description of his childhood, he was a rather lonely child. His parents owned 1 mi2 of land that served as their farm. The nearest neighbor lived 1/2 mi away, but he was more an acquaintance to Barks\'s parents than a friend. The closest school was about 2 mi away and Barks had to walk that distance every day. The rural area had few children, though, and Barks later remembered that his school had only about eight or ten students including him. He had high praise for the quality of the education he received in that small school. \"Schools were good in those days,\" he used to say. The lessons lasted from nine o\'clock in the morning to four o\'clock in the afternoon and then he had to return to the farm. There he remembered not having anybody to talk to, as his parents were busy, and he had little in common with his brother.
In 1908, William Barks (in an attempt to increase the family income) moved with his family to Midland, Oregon, some miles north of Merrill, to be closer to the new railway lines. He established a new stock-breeding farm and sold his produce to the local slaughterhouses.
Nine-year-old Clyde and seven-year-old Carl worked long hours there. But Carl later remembered that the crowd which gathered at Midland\'s market place made a strong impression on him. This was expected, as he was not used to crowds up until then. According to Barks, his attention was mostly drawn to the cowboys that frequented the market with their revolvers, strange nicknames for each other and sense of humor.
By 1911, they had been successful enough to move to Santa Rosa, California. There they started cultivating vegetables and set up some orchards. Unfortunately, the profits were not as high as William expected and they started having financial difficulties. William\'s anxiety over them was probably what caused his first nervous breakdown.
As soon as William recovered, he made the decision to move back to Merrill. The year was 1913, and Barks was already 12 years old; but, due to the constant moving, he had not yet managed to complete grade school. He resumed his education at this point and finally managed to graduate in 1916.
1916 served as a turning point in Barks\'s life for various reasons. First, Arminta, his mother, died in this year. Second, his hearing problems, which had already appeared earlier, had at the time become severe enough for him to have difficulties listening to his teachers talking. His hearing would continue to get worse later, but at that point he had not yet acquired a hearing aid. Later in life, he couldn\'t do without one. Third, the closest high school to their farm was 5 mi away and even if he did enroll in it, his bad hearing was likely to contribute to his learning problems. He had to decide to stop his school education, much to his disappointment.
### From job to job {#from_job_to_job}
Barks started taking various jobs but had little success in such occupations as a farmer, woodcutter, turner, mule driver, cowboy and printer. From his jobs he learned, he later averred, how eccentric, stubborn and unpredictable men, animals and machines can be. At the same time he interacted with colleagues, fellow breadwinners who had satirical disposition towards even their worst troubles. Barks later declared that he was sure that if not for a little humor in their troubled lives, they would certainly go insane. It was an attitude towards life that Barks would adopt. Later he would say it was natural for him to satirize the secret yearnings and desires, the pompous style and the disappointments of his characters. According to Barks, this period of his life would later influence his best known fictional characters: Walt Disney\'s Donald Duck and his own Scrooge McDuck.
Donald\'s drifting from job to job was reportedly inspired by Barks\'s own experiences. So was his usual lack of success. And even in those that he was successful this would be temporary, just until a mistake or chance event caused another failure, another disappointment for the frustrated duck. Barks also reported that this was another thing he was familiar with.
Scrooge\'s main difference to Donald, according to Barks, was that he too had faced the same difficulties in his past but through intelligence, determination and hard work, he was able to overcome them. Or, as Scrooge himself would say to Huey, Dewey, and Louie: by being \"tougher than the toughies and smarter than the smarties.\" In Barks\'s stories Scrooge would work to solve his many problems, even though the stories would often point out that his constant efforts seemed futile at the end.
Through both characters Barks would often exhibit his rather sarcastic sense of humor. It seems that this difficult period for the artist helped shape many of his later views in life that were expressed through his characters.
### Professional artist {#professional_artist}
At the same time Barks had started thinking about turning a hobby that he always enjoyed into a profession: that of drawing. Since his early childhood he spent his free time by drawing on any material he could find. He had attempted to improve his style by copying the drawings of his favorite comic strip artists from the newspapers where he could find them. As he later said, he wanted to create his own facial expressions, figures and comical situations in his drawings but wanted to study the master comic artists\' use of the pen and their use of color and shading.
Among his early favorites were Winsor McCay (mostly known for *Little Nemo*) and Frederick Burr Opper (mostly known for *Happy Hooligan*) but he would later study any style that managed to draw his attention.
At age 16, he was mostly self-taught but at this point he decided to take some lessons through correspondence. He only followed the first four lessons and then had to stop because his working left him with little free time. But as he later said, the lessons proved very useful in improving his style.
By December 1918, he left his father\'s home to attempt to find a job in San Francisco, California. He worked for a while in a small publishing house while attempting to sell his drawings to newspapers and other printed material with little success.
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# Carl Barks
## Biography
### First and second marriages {#first_and_second_marriages}
While he continued drifting through various jobs, he met Pearl Turner (1904--1987). In 1921 they married and had two daughters:
- Peggy Barks (1923--1963)
- Dorothy Barks (1924--2014)
In 1923 he returned to his paternal farm in Merrill in an attempt to return to the life of a farmer, but that ended soon. He continued searching for a job while attempting to sell his drawings. He soon managed to sell some of them to *Judge* magazine and then started having success submitting to the Minneapolis-based *Calgary Eye-Opener*, a racy men\'s cartoon magazine of the era. He was eventually hired as editor and scripted and drew most of the contents while continuing to sell occasional work to other magazines. His salary of \$90 per month was considered respectable enough for the time. A facsimile of one of the racy magazines he did cartoons for in this period, *Coo Coo* #1, was published by Hamilton Comics in 1997.
Meanwhile, he had his first divorce. He and Pearl were separated in 1929 and divorced in 1930. After he moved to Minneapolis, Minnesota, where *Calgary-Eye-Opener* had its offices, he met Clara Balken, who in 1938 became his second wife.
### Disney
In November 1935, when he learned that Walt Disney was seeking more artists for his studio, Barks decided to apply. He was approved for a try-out which entailed a move to Los Angeles, California. He was one of two in his class of trainees who was hired. His starting salary was 20 dollars a week. He started at Disney Studios in 1935, more than a year after the debut of Donald Duck on June 9, 1934, in the short animated film *The Wise Little Hen*.
Barks initially worked as an inbetweener. This involved being teamed and supervised by one of the head animators who did the key poses of character action (often known as extremes) for which the inbetweeners did the drawings between the extremes to create the illusion of movement. While an inbetweener, Barks submitted gag ideas for cartoon story lines being developed and showed such a knack for creating comical situations that by 1937 he was transferred to the story department. His first story sale was the climax of *Modern Inventions*, for a sequence where a robot barber chair gives Donald Duck a haircut on his bottom.
In 1937, when Donald Duck became the star of his own series of cartoons instead of co-starring with Mickey Mouse and Goofy as previously, a new unit of storymen and animators was created devoted solely to this series. Though he originally just contributed gag ideas to some duck cartoons, by 1937 Barks was (principally with partner Jack Hannah) originating story ideas that were storyboarded and (if approved by Walt) put into production. He collaborated on such cartoons as *Donald\'s Nephews* (1938), *Donald\'s Cousin Gus* (1939), *Mr. Duck Steps Out* (1940), *Timber* (1941), *The Vanishing Private* (1942) and *The Plastics Inventor* (1944).
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# Carl Barks
## Biography
### The Good Duck Artist {#the_good_duck_artist}
Unhappy at the emerging wartime working conditions at Disney, and bothered by ongoing sinus problems caused by the studio\'s air conditioning, Barks quit in 1942. Shortly before quitting, he moonlighted as a comic book artist, contributing half the artwork for a one-shot comic book (the other half of the art being done by story partner Jack Hannah) titled *Donald Duck Finds Pirate Gold*. This 64-page story was adapted by Donald Duck comic strip writer Bob Karp from an unproduced feature, and published in October 1942 in Dell Comics *Four Color Comics* #9. It was the first Donald Duck story originally produced for an American comic book and also the first involving Donald and his nephews in a treasure hunting expedition, in this case for the treasure of Henry Morgan. Barks would later use the treasure hunting theme in many of his stories. This actually was not his first work in comics, as earlier the same year Barks along with Hannah and fellow storyman Nick George scripted *Pluto Saves the Ship*, which was among the first original Disney comic book stories published in the United States.
After quitting the Disney Studio, Barks relocated to the Hemet/San Jacinto area in the semi-desert Inland Empire region east of Los Angeles where he hoped to start a chicken farm.
When asked which of his stories was a favorite in several interviews Barks cited the ten-pager in *Walt Disney\'s Comics and Stories* #146 (Nov. 1952) in which Donald tells the story of the chain of unfortunate events that took place when he owned a chicken farm in a town which subsequently was renamed Omelet. Likely one reason it was a favorite is that it was inspired by Barks\' own experiences in the poultry business.
But to earn a living in the meantime he inquired whether Western Publishing, which had published *Pirate Gold*, had any need for artists for Donald Duck comic book stories. He was immediately assigned to illustrate the script for a ten-page Donald Duck story for the monthly *Walt Disney\'s Comics and Stories*. At the publisher\'s invitation he revised the storyline and the improvements impressed the editor sufficiently to invite Barks to try his hand at contributing both the script and the artwork of his follow-up story. This set the pattern for Barks\' career in that (with rare exceptions) he provided art (pencil, inking, solid blacks and lettering) and scripting for his stories.
*The Victory Garden*, that initial ten-page story published in April, 1943 was the first of about 500 stories featuring the Disney ducks Barks would produce for Western Publishing over the next three decades, well into his purported retirement. These can be mostly divided into three categories:
- One-page gag stories like \"Coffee for Two\" and \"Sorry to be Safe\". These one-pagers were usually printed in black and white (or black and white and red) on the inside front, inside back, and outside back covers. These stories focused on one joke.
- Ten-pagers, comedic Donald Duck stories that were the lead for the monthly flagship title *Walt Disney\'s Comics and Stories*, whose circulation peaked in the mid-1950s at 3 million copies sold a month.
- Humorous adventure stories, usually 24-32 pages in length. In the 1940s these were one-shots in the *Four Color* series (issued 4--6 times a year) that starred Donald and his nephews. Starting in the early 1950s (and through his retirement) Barks\' longer stories were almost exclusively published in Uncle Scrooge\'s own quarterly title.
Barks\' artistic growth during his first decade in comics saw a transformation from rather rudimentary storytelling derived from his years as an animation artist and storyman into a virtuoso creator of complex narratives, notably in his longer adventure tales. According to critic Geoffrey Blum, the process that saw its beginnings in 1942\'s *Pirate Gold* first bore its full fruit in 1950\'s \"Vacation Time\", which he describes as \"a visual primer for reading comics and understanding \... the form\".
He surrounded Donald Duck and nephews Huey, Dewey, and Louie with a cast of eccentric and colorful characters, such as the aforementioned Scrooge McDuck, the wealthiest duck in the world; Gladstone Gander, Donald\'s obscenely lucky cousin; inventor Gyro Gearloose; the persistent Beagle Boys; the sorceress Magica De Spell; Scrooge\'s rivals Flintheart Glomgold and John D. Rockerduck; Daisy\'s nieces April, May and June; Donald\'s neighbor Jones, and The Junior Woodchucks organization.
Barks\'s stories (whether humorous adventures or domestic comedies) often exhibited a wry, dark irony born of hard experience. The ten-pagers showcased Donald as everyman, struggling against the cruel bumps and bruises of everyday life with the nephews often acting as a Greek chorus commenting on the unfolding disasters Donald wrought upon himself. Yet while seemingly defeatist in tone, the humanity of the characters shines through in their persistence despite the obstacles. These stories found popularity not only among young children but adults as well. Despite the fact that Barks had done little traveling, his adventure stories often had the duck clan globe-trotting to the most remote or spectacular of places. This allowed Barks to indulge his penchant for elaborate backgrounds that hinted at his thwarted ambitions of doing realistic stories in the vein of Hal Foster\'s *Prince Valiant*.
### Third marriage {#third_marriage}
As Barks blossomed creatively, his marriage to Clara deteriorated. This is the period referred to in Barks\' famed quip that he could feel his creative juices flowing while the whiskey bottles hurled at him by a tipsy Clara flew by his head. They were divorced in 1951, his second and last divorce. In this period Barks dabbled in fine art, exhibiting paintings at local art shows. It was at one of these in 1952 he became acquainted with fellow exhibitor Margaret Wynnfred Williams (1917 -- March 10, 1993), nicknamed Garé. She was an accomplished landscape artist, some of whose paintings are in the collection of the Leanin\' Tree Museum of Western Art. During her lifetime, and to this day, note cards of her paintings are available from Leanin\' Tree. Her nickname appears as a store name in the story \"Christmas in Duckburg\", featured on page 1 of *Walt Disney\'s Christmas Parade* #9, published in 1958. Soon after they met, she started assisting Barks, handling the solid blacks and lettering, both of which he had found onerous. They married in 1954 and the union lasted until her death.
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# Carl Barks
## Biography
### No longer anonymous {#no_longer_anonymous}
People who worked for Disney (and its comic book licensees) generally did so in relative anonymity; stories would only carry Walt Disney\'s name and (sometimes) a short identification number. Prior to 1960 Barks\' identity remained a mystery to his readers. However, many readers recognized Barks\' work and drawing style and began to call him the Good Duck Artist, a label that stuck even after his true identity was discovered by fans in the late 1950s. Malcolm Willits was the first person to learn Barks\'s name and address, but two brothers named John and Bill Spicer became the first fans to contact Barks after independently discovering the same information. After Barks received a 1960 visit from the Spicer brothers and Ron Leonard, he was no longer anonymous, as word of his identity spread through the emerging network of comic book fandom fanzines and conventions.
### Later life {#later_life}
Carl Barks retired in 1966, but was persuaded by editor Chase Craig to continue to script stories for Western. The last new comic book story drawn by Carl Barks was a Daisy Duck tale (\"The Dainty Daredevil\") published in *Walt Disney Comics Digest* issue 5 (Nov. 1968). When bibliographer Michael Barrier asked Barks why he drew it, Barks\' vague recollection was no one was available and he was asked to do it as a favor by Craig.
He wrote one Uncle Scrooge story, and three Donald Duck stories. From 1970 to 1974, Barks was the main writer for the Junior Woodchucks comic book (issues 6 through 25). The latter included environmental themes that Barks first explored in 1957 \[\"Land of the Pygmy Indians\", *Uncle Scrooge* #18\]. Barks also sold a few sketches to Western that were redrawn as covers. For a time the Barkses lived in Goleta, California, before returning to the Inland Empire by moving to Temecula.
To make a little extra money beyond what his pension and scripting earnings brought in, Barks started doing oil paintings to sell at the local art shows where he and Garé exhibited. Subjects included humorous depictions of life on the farm and portraits of Native American princesses. These skillfully rendered paintings encouraged fan Glenn Bray to ask Barks if he could commission a painting of the ducks (\"A Tall Ship and a Star to Steer Her By\", taken from the cover of *Walt Disney\'s Comics and Stories* #108 by Barks). This prompted Barks to contact George Sherman at Disney\'s Publications Department to request permission to produce and sell oil paintings of scenes from his stories. In July 1971 Barks was granted a royalty-free license by Disney. When word spread that Barks was taking commissions from those interested in purchasing an oil of the ducks, much to his astonishment the response quickly outstripped what he reasonably could produce in the next few years.
When Barks expressed dismay at coping with the backlog of orders he faced, fan/dealers Bruce Hamilton and Russ Cochran suggested Barks instead auction his paintings at conventions and via Cochran\'s catalog *Graphic Gallery*. By September 1974 Barks had discontinued taking commissions.
At Boston\'s NewCon convention, in October 1975, the first Carl Barks oil painting auctioned at a comic book convention (\"She Was Spangled and Flashy\") sold for \$2,500. Subsequent offerings saw an escalation in the prices realized.
In 1976, Barks and Garé went to Boston for the NewCon show, their first comic convention appearance. Among the other attendees was famed *Little Lulu* comic book scripter John Stanley; despite both having worked for Western Publishing this was the first time they met. The highlight of the convention was the auctioning of what was to that time the largest duck oil painting Barks had done, \"July Fourth in Duckburg\", which included depictions of several prominent Barks fans and collectors. It sold for a then record high amount: \$6,400.
Soon thereafter a fan sold unauthorized prints of some of the Scrooge McDuck paintings, leading Disney to withdraw permission for further paintings. To meet demand for new work Barks embarked on a series of paintings of non-Disney ducks and fantasy subjects such as Beowulf and Xerxes. These were eventually collected in the limited-edition book *Animal Quackers*.
As the result of efforts by *Star Wars* producer Gary Kurtz and screenwriter Edward Summer, Disney relented and, in 1981, allowed Barks to produce an oil painting called *Wanderers of Wonderlands* for a limited edition book entitled *Uncle Scrooge McDuck: His Life and Times*. The book collected 11 classic Barks stories of Uncle Scrooge colored by artist Peter Ledger along with a new Scrooge story by Barks done storybook style with watercolor illustrations, \"Go Slowly, Sands of Time\". After being turned down by every major publisher in New York City, Kurtz and Summer published the book through Celestial Arts, which Kurtz acquired partly for this purpose. The book went on to become the model for virtually every important collection of comic book stories.`{{or|date=March 2024}}`{=mediawiki} It was the first book of its kind ever reviewed in *Time* magazine and subsequently in *Newsweek*, and the first book review in *Time* with large color illustrations.
In 1977 and 1982, Barks attended San Diego Comic-Con. As with his appearance in Boston, the response to his presence was overwhelming, with long lines of fans waiting to meet Barks and get his autograph.
In 1981, Bruce Hamilton and Russ Cochran, two long-time Disney comics fans, decided to combine forces to bring greater recognition to the works of Carl Barks. Their first efforts went into establishing Another Rainbow Publishing, the banner under which they produced and issued the award-winning book *The Fine Art of Walt Disney\'s Donald Duck by Carl Barks*, a comprehensive collection of the Disney duck paintings of this artist and storyteller. Not long after, the company began producing fine art lithographs of many of these paintings, in strictly limited editions, all signed by Barks, who eventually produced many original works for the series.
In 1983, Barks relocated one last time to Grants Pass, Oregon, near where he grew up, partly at the urging of friend and *Broom Hilda* artist Russell Myers, who lived in the area. The move also was motivated, Barks stated in another famous quip, by Temecula being too close to Disneyland and thus facilitating a growing torrent of drop-in visits by vacationing fans. In this period Barks made only one public appearance, at a comic book shop near Grants Pass.
In 1983, Another Rainbow took up the daunting task of collecting the entire Disney comic book oeuvre of Barks---over 500 stories in all---in the ten-set, thirty-volume *Carl Barks Library*. These oversized hardbound volumes reproduced Barks\' pages in pristine black and white line art, as close as possible to the way he would originally draw them, and included mountains of special features, articles, reminiscences, interviews, storyboards, critiques, and more than a few surprises. This monumental project was finally completed in mid-1990.
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# Carl Barks
## Biography
### Later life {#later_life}
In 1985, a new division was founded, Gladstone Publishing, which took up the then-dormant Disney comic book license. Gladstone introduced a new generation of Disney comic book readers to the storytelling of Barks, Paul Murry, and Floyd Gottfredson, as well as presenting the first works of modern Disney comics artists Don Rosa and William Van Horn. Seven years after Gladstone\'s founding, the *Carl Barks Library* was revived as the *Carl Barks Library in Color*, as full-color, high-quality squarebound comic albums (including the first-ever Carl Barks trading cards).
From 1993 to 1998, Barks\' career was managed by the \"Carl Barks Studio\" (Bill Grandey and Kathy Morby---they had sold Barks original art since 1979). This involved numerous art projects and activities, including a tour of 11 European countries in 1994, Iceland being the first foreign country he ever visited. Barks appeared at the first of many Disneyana conventions in 1993. Silk screen prints of paintings along with high-end art objects (such as original water colors, bronze figurines and ceramic tiles) were produced based on designs by Barks.
During the summer of 1994 and until his death, Barks and his studio personally assigned Peter Reichelt, a museum exhibition producer from Mannheim, Germany, as his agent for Europe. Publisher \"Edition 313\" put out numerous lithographs. In 1997, tensions between Barks and the Studio eventually resulted in a lawsuit that was settled with an agreement that included the disbanding of the Studio. Barks never traveled to make another Disney appearance. He was represented by Ed Bergen, as he completed a final project. Gerry Tank and Jim Mitchell were to assist Barks in his final years.
During his Carl Barks Studio years, Barks created two more stories: the script for the final Uncle Scrooge story \"Horsing Around with History\", which was first published in Denmark in 1994 with Bill Van Horn art. The outlines for Barks\' final Donald Duck story \"Somewhere in Nowhere\", were first published in 1997, in Italy, with art by Pat Block.
Austrian artist Gottfried Helnwein curated and organized the first solo museum-exhibition of Barks. Between 1994 and 1998 the retrospective was shown in ten European museums and seen by more than 400,000 visitors.
At the same time in spring 1994, Reichelt and Ina Brockmann designed a special museum exhibition tour about Barks\' life and work. Also represented for the first time at this exhibition were Disney artists Al Taliaferro and Floyd Gottfredson. Since 1995, more than 500,000 visitors have attended the shows in Europe.
Reichelt also translated Michael Barrier\'s biography of Barks into German and published it in 1994.
### Final days and death {#final_days_and_death}
Barks spent his final years in a new home in Grants Pass, Oregon, which he and Garé, who died in 1993, had built next door to their original home. In July 1999, he was diagnosed with chronic lymphocytic leukemia, a form of cancer arising from the white blood cells in the bone marrow, for which he received oral chemotherapy. However, as the disease progressed, causing him great discomfort, the ailing Barks decided to stop receiving treatment in June 2000. In spite of his terminal condition, Barks remained, according to caregiver Serene Hunicke, \"funny up to the end\".
The year before, Barks had told the university professor Donald Ault:
> I have no apprehension, no fear of death. I do not believe in an afterlife. \... I think of death as total peace. You\'re beyond the clutches of all those who would crush you.
On August 25, 2000, shortly after midnight, Carl Barks died quietly in his sleep at the age of 99. He was interred in Hillcrest Memorial Cemetery in Grants Pass, beside Garé\'s grave.
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# Carl Barks
## Influence
\"(A)n asteroid was named after the Duck Man in 1983 \-\-- 2730 Barks, a carbonaceous C-type asteroid with a diameter of between 10 and 16 kilometers, an ordital period of six years and four months, and a rotation period of just over six hours.\" In a 1983 interview, Barks says that \"Island in the Sky\", a story about the Ducks traveling to the asteroid belt to find a place Uncle Scrooge can store his money, was his favorite story.
Barks\' Donald Duck stories were rated #7 on *The Comics Journal* list of 100 top comics; his Uncle Scrooge stories were rated #20.
Steven Spielberg and George Lucas have acknowledged that the rolling-boulder booby trap in the opening scene of *Raiders of the Lost Ark* was inspired by the 1954 Carl Barks Uncle Scrooge adventure \"The Seven Cities of Cibola\" (*Uncle Scrooge* #7). Lucas and Spielberg have also said that some of Barks\' stories about space travel and the depiction of aliens had an influence on them. Lucas wrote the foreword to the 1982 *Uncle Scrooge McDuck: His Life and Times*. In it he calls Barks\' stories \"cinematic\" and \"a priceless part of our literary heritage\".
The Walt Disney Treasures DVD set *Chronological Donald, Volume 2* includes a salute to Barks.
In Almere, Netherlands, a street was named after him: Carl Barksweg. The same neighborhood also includes a Donald Ducklaan and a Goofystraat.
Japanese animator and cartoonist Osamu Tezuka, who created manga such as *Astro Boy* and *Black Jack*, was a fan of Barks\' work. *New Treasure Island*, one of Tezuka\'s first works, was partly influenced by \"Donald Duck Finds Pirate Gold\".
A 1949 Donald Duck ten-pager features Donald raising a yacht from the ocean floor by filling it with ping pong balls. In December 1965 Karl Krøyer, a Dane, lifted the sunken freight vessel *Al Kuwait* in the Kuwait Harbor by filling the hull with 27 million tiny inflatable balls of polystyrene. Krøyer denies having been inspired by this Barks story. Some sources claim Krøyer was denied a Dutch patent registration (application number NL 6514306) for his invention on the grounds that the Barks story was a prior publication of the invention. Krøyer later successfully raised another ship off Greenland using the same method, and several other sunken vessels worldwide have since been raised by modified versions of this concept. The television show *MythBusters* also tested this method and was able to raise a small boat.
Don Rosa, one of the most popular living Disney artists, and possibly the one who has been most keen on connecting the various stories into a coherent universe and chronology, considers (with few exceptions) all Barks\' duck stories as canon, and all others as apocryphal. Rosa has said that a number of novelists and movie-makers cite Carl Barks as their \'major influence and inspiration\'. Don Rosa created *The Complete Life and Times of Scrooge McDuck* based on Carl Barks references in Scrooge McDuck stories.
When the news of Barks\' passing was hardly covered by the press in America, \"in Europe the sad news was flashed instantly across the airwaves and every newspaper --- they realized the world had lost one of the most beloved, influential and well-known creators in international culture.\"
The video game *Donald Duck: Goin\' Quackers*, released late in 2000, is dedicated to the memory of Carl Barks.
In 2010 Oregon Cartoon Institute produced a video about the influence of Carl Barks and Basil Wolverton on Robert Crumb.
Carl Barks drew an early Andy Panda comic book story published in *New Funnies* #76, 1943. It is one of his few stories to feature humans interacting with talking animal characters (another is *Dangerous Disguise*, *Four Color* #308, 1951. See List of fictional pandas.)
The first image ever to be displayed on an Apple Macintosh was a scan of Carl Barks\' Scrooge McDuck.
The life story of Carl Barks, largely drawing upon his relationship with Disney and the phonetic similarity of his name to Karl Marx, serves as a loose inspiration to one of the subplots in *The Last Song of Manuel Sendero* by Ariel Dorfman.
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# Carl Barks
## Filmography
Films where Barks served as storyman or story director include:
- *Modern Inventions* (May 29, 1937). Barks also drew many of the storyboards for the film.
- *Donald\'s Ostrich* (December 10, 1937).
- *Self Control* (February 11, 1938). Barks served as the story director.
- *Donald\'s Better Self* (March 11, 1938). Barks served as the story director.
- *Donald\'s Nephews* (April 15, 1938).
- *Good Scouts* (July 8, 1938). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Donald\'s Golf Game* (November 4, 1938). Barks served as the story director.
- *Donald\'s Lucky Day* (January 13, 1939). Barks also drew many of the storyboards for the film.
- *The Hockey Champ* (April 28, 1939). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Donald\'s Cousin Gus* (May 19, 1939). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Sea Scouts* (June 30, 1939). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Donald\'s Penguin* (August 11, 1939). Barks served as the story director.
- *The Autograph Hound* (September 1, 1939).
- *Mr. Duck Steps Out* (June 7, 1940). Barks served as the story director.
- *Put-Put Troubles* (June 19, 1940).
- *Bone Trouble* (June 28, 1940).
- *Donald\'s Vacation* (August 9, 1940).
- *Window Cleaners* (September 20, 1940). Barks also drew many of the storyboards for the film.
- *Fire Chief* (December 13, 1940). Barks also drew many of the storyboards for the film.
- *Timber* (January 10, 1941). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Golden Eggs* (March 7, 1941).
- *Early to Bed* (July 11, 1941). Barks also drew many of the storyboards for the film.
- *Truant Officer Donald* (August 1, 1941). Barks also drew many of the storyboards for the film.
- *Old MacDonald Duck* (September 12, 1941). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Chef Donald* (December 5, 1941). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *The Village Smithy* (January 16, 1942).
- *Donald\'s Snow Fight* (April 10, 1942). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Donald Gets Drafted* (May 1, 1942). Barks served as the story director.
- *The Army Mascot* (May 22, 1942).
- *The Vanishing Private* (September 25, 1942). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *Sky Trooper* (November 6, 1942).
- *Bellboy Donald* (December 18, 1942). Barks also drew many of the storyboards for the film.
- *The Spirit of \'43* (January 7, 1943).
- *The Old Army Game* (November 5, 1943). Barks also drew many of the storyboards for the film.
- *Home Defense* (November 26, 1943). Barks also drew many of the storyboards for the film.
- *Trombone Trouble* (February 18, 1944). Barks served as the story director. Barks also drew many of the storyboards for the film.
- *The Plastics Inventor* (September 1, 1944).
## Notable stories {#notable_stories}
- \"Donald Duck Finds Pirate Gold\", *Four Color* #9, October 1942
- \"Donald Duck and the Mummy\'s Ring\", *Four Color* #29, September 1943
- \"Christmas on Bear Mountain\", *Four Color* #178, December 1947, first appearance of Scrooge McDuck.
- \"The Old Castle\'s Secret\", *Four Color* #189 June 1948
- \"Sheriff of Bullet Valley\", *Four Color* #199, October 1948
- \"Lost in the Andes!\", *Four Color* #223, April 1949
- \"Vacation Time\", *Vacation Parade* #1, July 1950
- \"A Financial Fable\", *Walt Disney\'s Comics and Stories* #126, March 1951
- \"Donald Duck in Old California!\", *Four Color* #328, May 1951
- \"A Christmas for Shacktown\", *Four Color* #367, January 1952
- \"Only a Poor Old Man\", *Four Color* #386 (*Uncle Scrooge* #1), March 1952
- \"Flip Decision\", *Walt Disney\'s Comics and Stories* #149, June 1952
- \"The Golden Helmet\", *Four Color* #408, July 1952
- \"Back to the Klondike\", *Four Color* #456 (*Uncle Scrooge* #2), March 1953
- \"Tralla La\", *Uncle Scrooge* #6, June 1954
- \"The Fabulous Philosopher\'s Stone\", *Uncle Scrooge* #10, June 1955
- \"The Golden Fleecing\", *Uncle Scrooge* #12, December 1955
- \"Land Beneath the Ground!\", *Uncle Scrooge* #13, March 1956
- \"The Money Well\", *Uncle Scrooge* #21, March 1958
- \"The Golden River\", *Uncle Scrooge* #22, 1958
- \"Island in the Sky\", *Uncle Scrooge* #29, March 1960
- \"North of the Yukon\", *Uncle Scrooge* #59, September 1965
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# Carl Barks
## Awards
- The Shazam Award for Best Writer (Humor Division) in 1970
- The Academy of Comic Book Arts Hall of Fame Award in 1973
- The Inkpot in 1977 from San Diego Comic-Con
- Inducted into the Eisner Awards Hall of Fame in 1987
- Inducted into the Jack Kirby Hall of Fame in 1987
- Inducted into the William Randolph Hearst Cartoon Hall of Fame.
- The Walt Disney Company bestowed a Duckster award in 1971 and their Disney Legends award in 1991
- The Comics Buyer\'s Guide Fan Award for Favorite Writer in 1996.
- The series *Carl Barks Library* received the Comics Buyer\'s Guide Fan Award for Favorite Reprint Graphic Novel/Album for 1996.
## Art materials {#art_materials}
Barks was an enthusiastic user of Esterbrook pens, and used a Nº 356 model to ink and letter his Donald Duck comic-book pages
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# Centimetre–gram–second system of units
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# Chastity
**Chastity**, also known as **purity**, is a virtue related to temperance. Someone who is *chaste* refrains from sexual activity that is considered immoral or from any sexual activity, according to their state of life. In some contexts, for example when making a vow of chastity, chastity means celibacy.
## Etymology
The words *chaste* and *chastity* stem from the Latin adjective *castus* (\"cut off\", \"separated\", \"pure\"). The words entered the English language around the middle of the 13th century. *Chaste* meant \"virtuous\", \"pure from unlawful sexual intercourse\" or (from the early 14th century on) as a noun, a virgin, while *chastity* meant \"(sexual) purity\".
Thomas Aquinas links *castus* (chastity) to the Latin verb *castigo* (\"chastise, reprimand, correct\"), with a reference to Aristotle\'s *Nicomachean Ethics*: \"Chastity takes its name from the fact that reason \'chastises\' concupiscence, which, like a child, needs curbing, as the Philosopher states\".
## In Abrahamic religions {#in_abrahamic_religions}
For many Jews, Christians, and Muslims, people should restrict their acts of a sexual nature to the context of marriage. For unmarried people, chastity is equivalent to sexual abstinence. Sexual acts outside of or apart from marriage, such as adultery, fornication, masturbation, and prostitution, are considered immoral due to lust. `{{incomplete|chastity in Judaism|date=November 2020}}`{=mediawiki}
### Christianity
`{{Redirect|Vow of chastity|vow of chastity as part of public vows|Religious vows}}`{=mediawiki}
#### Traditions
In many Christian traditions, chastity is synonymous with purity. The Catholic Church teaches that chastity involves, in the words of cardinal bishop Alfonso López Trujillo, \"the successful integration of sexuality within the person and thus the inner unity of man in his bodily and spiritual being\", which according to one\'s marital status requires either having no sexual relationship, or only having sexual relations with one\'s spouse. In Western Christian morality, chastity is placed opposite the deadly sin of lust, and is classified as one of seven virtues. The moderation of sexual desires is also required to be virtuous. Reason, will, and desire can harmoniously work together to do what is good.
As an emblem of inward chastity, some Christians choose to wear a cord, girdle or a cincture of one of the several Confraternities of the Cord or a purity ring. The cord is worn as a symbol of chastity in honour of a chaste saint whom the bearer asks for intercession. The purity ring is worn before holy matrimony by those who marry or for the rest of their lives by those who stay single.
#### Marital chastity {#marital_chastity}
In marriage, the spouses commit to a lifelong relationship that excludes sexual intimacy with other persons. A third form of chastity, often called \"vidual chastity\", is expected by the society for a period after the woman\'s husband dies. For example, Anglican Bishop Jeremy Taylor defined five rules in *Holy Living* (1650), including abstaining from marrying \"so long as she is with child by her former husband\" and \"within the year of mourning\".
#### Celibacy
In the Roman Catholic Church, members of the consecrated life vow or promise celibacy as one of the evangelical counsels. In 306, the Synod of Elvira proscribed clergy from marrying. This was unevenly enforced until the Second Lateran Council in 1139 when it found its way into canon law. Unmarried deacons promise celibacy to their local bishop when ordained.
Eastern Catholic priests are permitted to marry, provided they do so before ordination and outside monastic life.
#### Vows of chastity {#vows_of_chastity}
*Vows of chastity* can be taken either as part of an organised religious life (such as Roman Catholic Beguines and Beghards in the past) or on an individual basis: as a voluntary act of devotion, or as part of an ascetic lifestyle (often devoted to contemplation), or both. Some Protestant religious communities, such as the Bruderhof, take vows of chastity as part of the church membership process.
#### Teaching by denomination {#teaching_by_denomination}
##### Catholicism
Chastity is a central and pivotal concept in Roman Catholic praxis. Roman Catholic teaching regards chastity as essential in maintaining and cultivating the unity of body with spirit and thus the integrity of the human being. It is also fundamental to the practise of the Catholic life because it involves an *apprenticeship in self-mastery*. By attaining mastery over one\'s passions, reason, will, and desire can harmoniously work together to do what is good.
##### Lutheranism
The theology of the body of the Lutheran Churches emphasizes the role of the Holy Spirit, who sanctified the bodies of Christians to be God\'s temple.
Many Lutheran monks and Lutheran nuns practice celibacy, though in some Lutheran religious orders it is not compulsory.
##### The Church of Jesus Christ of Latter-Day Saints {#the_church_of_jesus_christ_of_latter_day_saints}
In the Church of Jesus Christ of Latter-day Saints chastity is very important:
> Physical intimacy between husband and wife is a beautiful and sacred part of God\'s plan for His children. It is an expression of love within marriage and allows husband and wife to participate in the creation of life. God has commanded that this sacred power be expressed only between a man and a woman who are legally married. The law of chastity applies to both men and women. It includes strict abstinence from sexual relations before marriage and complete fidelity and loyalty to one\'s spouse after marriage.
>
> The law of chastity requires that sexual relations be reserved for marriage between a man and a woman.
>
> In addition to reserving sexual intimacy for marriage, we obey the law of chastity by controlling our thoughts, words, and actions. Jesus Christ taught, \"Ye have heard that it was said by them of old time, Thou shalt not commit adultery: but I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart\" (`{{bibleverse|Matthew|5:27–28}}`{=mediawiki}).\"
Teachings of the Church of Jesus Christ of Latter-Day Saints also include that sexual expression within marriage is an important dimension of spousal bonding apart from, but not necessarily avoiding, its procreative result.
### Islam
#### Quran
The most famous personal example of chastity in the Quran is the Virgin Mary (Mariam):
Extramarital sex is forbidden. The Quran says:
In a list of commendable deeds the Quran says:
Because the sex desire is usually attained before a man is financially capable of marriage, the love to God and mindfulness of Him should be sufficient motive for chastity:
#### Sharia (Law) {#sharia_law}
Chastity is mandatory in Islam. Sex outside legitimacy is prohibited, for both men and women, whether married or unmarried. The injunctions and forbiddings in Islam apply equally to men and women. The legal punishment for adultery is equal for men and women.
The prophet\'s prescription to the youth was: `{{Blockquote|text="O young people! Whoever among you can marry, should marry, because it helps him lower his gaze and guard his modesty (i.e. his private parts from committing illegal sexual intercourse etc.), and whoever is not able to marry, should fast, as fasting diminishes his sexual power."|author={{Href|bukhari|5066|b=yl}}}}`{=mediawiki}
Chastity is an attitude and a way of life. In Islam it is both a personal and a social value. A Muslim society should not condone relations entailing or conducive to sexual license. Social patterns and practices calculated to inflame sexual desire are frowned upon by Islam, such incitements to immorality including permissive ideologies, titillating works of art, and the failure to inculcate sound moral principles in the young. At the heart of such a view of human sexuality lies the conviction that the notion of personal freedom should never be misconstrued as the freedom to flout God\'s laws by overstepping the bounds which, in his infinite wisdom, he has set upon the relations of the sexes.
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# Chastity
## In Abrahamic religions {#in_abrahamic_religions}
### Baháʼí Faith {#baháʼí_faith}
Chastity is highly prized in the Baháʼí Faith. Similar to other Abrahamic religions, Baháʼí teachings call for the restriction of sexual activity to that between a wife and husband in Baháʼí marriage, and discourage members from using pornography or engaging in sexually explicit recreational activities. The concept of chastity is extended to include avoidance of alcohol and mind-altering drugs, profanity, and gaudy or immodest attire.
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# Chastity
## In Eastern religions {#in_eastern_religions}
### Hinduism
Hinduism\'s view on premarital sex is rooted in its concept of `{{transliteration|sa|[[Ashrama (stage)|ashrama]]}}`{=mediawiki} or the stages of life. The first of these stages, known as `{{transliteration|sa|[[brahmacharya]]}}`{=mediawiki}, roughly translates as chastity. Celibacy and chastity are considered the appropriate behavior for both male and female students during this stage, which precedes the stage of the married householder (`{{transliteration|sa|[[grihastha]]}}`{=mediawiki}). `{{transliteration|sa|[[Sanyasa|Sanyasis]]}}`{=mediawiki} and Hindu monks or `{{transliteration|sa|[[sadhu]]s}}`{=mediawiki} are also celibate as part of their ascetic discipline.
### Sikhism
In Sikhism, premarital or extramarital sex is strictly forbidden. However, it is encouraged to marry and live as a family unit to provide and nurture children for the perpetual benefit of creation (as opposed to `{{transliteration|sa|[[sannyasa]]}}`{=mediawiki} or living as a monk, which was, and remains, a common spiritual practice in India). A Sikh is encouraged not to live as a recluse, beggar, monk, nun, celibate, or in any similar vein.
### Jainism
The Jain ethical code contains the vow of `{{transliteration|sa|[[brahmacarya]]}}`{=mediawiki} (meaning \"pure conduct\"), which prescribes the expectations for Jains concerning sexual activity. `{{transliteration|sa|Brahmacarya}}`{=mediawiki} is one of the five major and minor vows of Jainism, prescribing slightly different expectations for ascetics and laypeople, respectively.
Complete celibacy is expected only of Jain ascetics (who are also referred to as monks and nuns). For laypeople, chastity is expected, with extramarital sex and adultery being prohibited.
### Buddhism
The teachings of Buddhism include the Noble Eightfold Path, comprising a division called right action. Under the Five Precepts ethical code, `{{transliteration|sa|upāsaka}}`{=mediawiki} and `{{transliteration|sa|upāsikā}}`{=mediawiki} lay followers should abstain from sexual misconduct, while `{{transliteration|sa|[[bhikkhu]]}}`{=mediawiki} and `{{transliteration|sa|[[bhikkhuni]]}}`{=mediawiki} monastics should practice strict chastity.
### Taoism
The Five Precepts of the Taoist religion include \"no sexual misconduct\", which is interpreted as prohibiting extramarital sex for lay practitioners and marriage or sexual intercourse for monks and nuns.
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# Chastity
## Government
In Iran, women are required to wear hijabs as part of that society\'s efforts to enforce chastity. In 2023 the Ministry of Culture and Islamic Guidance announced a new bill titled the Protection of the Culture of Chastity and Hijab Law, expanding its former sections from 15 to 70
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# Electromagnetic coil
An **electromagnetic coil** is an electrical conductor such as a wire in the shape of a coil (spiral or helix). Electromagnetic coils are used in electrical engineering, in applications where electric currents interact with magnetic fields, in devices such as electric motors, generators, inductors, electromagnets, transformers, sensor coils such as in medical MRI imaging machines. Either an electric current is passed through the wire of the coil to generate a magnetic field, or conversely, an external *time-varying* magnetic field through the interior of the coil generates an EMF (voltage) in the conductor.
A current through any conductor creates a circular magnetic field around the conductor due to Ampere\'s law. The advantage of using the coil shape is that it increases the strength of the magnetic field produced by a given current. The magnetic fields generated by the separate turns of wire all pass through the center of the coil and add (superpose) to produce a strong field there. The greater the number of turns of wire, the stronger the field produced. Conversely, a *changing* external magnetic flux induces a voltage in a conductor such as a wire, due to Faraday\'s law of induction. The induced voltage can be increased by winding the wire into a coil because the field lines intersect the circuit multiple times.
The direction of the magnetic field produced by a coil can be determined by the right hand grip rule. If the fingers of the right hand are wrapped around the magnetic core of a coil in the direction of conventional current through the wire, the thumb will point in the direction the magnetic field lines pass through the coil. The end of a magnetic core from which the field lines emerge is defined to be the North pole.
There are many different types of coils used in electric and electronic equipment.
## Windings and taps {#windings_and_taps}
The wire or conductor which constitutes the coil is called the **winding**. The hole in the center of the coil is called the **core** area or *magnetic axis*. Each loop of wire is called a **turn**. In windings in which the turns touch, the wire must be insulated with a coating of nonconductive insulation such as plastic or enamel to prevent the current from passing between the wire turns. The winding is often wrapped around a *coil form* made of plastic or other material to hold it in place. The ends of the wire are brought out and attached to an external circuit. Windings may have additional electrical connections along their length; these are called **taps**. A winding that has a single tap in the center of its length is called **center-tapped**.
Coils can have more than one winding, insulated electrically from each other. When there are two or more windings around a common magnetic axis, the windings are said to be **inductively coupled** or **magnetically coupled**. A time-varying current through one winding will create a time-varying magnetic field that passes through the other winding, which will induce a time-varying voltage in the other windings. This is called a transformer. The winding to which current is applied, which creates the magnetic field, is called the *primary winding*. The other windings are called *secondary windings*.
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# Electromagnetic coil
## Magnetic core {#magnetic_core}
Many electromagnetic coils have a magnetic core, a piece of ferromagnetic material like iron in the center to increase the magnetic field. The current through the coil magnetizes the iron, and the field of the magnetized material adds to the field produced by the wire. This is called a **ferromagnetic-core** or **iron-core coil**. A ferromagnetic core can increase the magnetic field and inductance of a coil by hundreds or thousands of times over what it would be without the core. A **ferrite core coil** is a variety of coil with a core made of ferrite, a ferrimagnetic ceramic compound. Ferrite coils have lower core losses at high frequencies.
- A coil with a core which forms a closed loop, possibly with some narrow air gaps, is called a **closed-core** coil. By providing a closed path for the magnetic field lines, this geometry minimizes the magnetic reluctance and produces the strongest magnetic field. It is often used in transformers.
- A common form for closed-core coils is a **toroidal core** coil, in which the core has the shape of a torus or doughnut, with either a circular or rectangular cross section. This geometry has minimum leakage flux and radiates minimum electromagnetic interference (EMI).
- A coil with a core which is a straight bar or other non-loop shape is called an **open-core** coil. This has lower magnetic field and inductance than a closed core, but is often used to prevent magnetic saturation of the core.
A coil without a ferromagnetic core is called an **air-core coil**. This includes coils wound on plastic or other nonmagnetic forms, as well as coils which actually have empty air space inside their windings.
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# Electromagnetic coil
## Types of coils {#types_of_coils}
Coils can be classified by the frequency of the current they are designed to operate with:
:\**Direct current* or *DC* coils or electromagnets operate with a steady direct current in their windings
:\**Audio-frequency* or *AF* coils, inductors or transformers operate with alternating currents in the audio frequency range, less than 20 kHz
:\**Radio-frequency* or *RF* coils, inductors or transformers operate with alternating currents in the radio frequency range, above 20 kHz
Coils can be classified by their function:
### Electromagnets
Electromagnets are coils that generate a magnetic field for some external use, often to exert a mechanical force on something. or remove existing background fields. A few specific types:
:\*Solenoid - an electromagnet in the form of a straight hollow helix of wire
:\*Motor and generator windings - iron core electromagnets on the rotor or stator of electric motors and generators which act on each other to either turn the shaft (motor) or generate an electric current (generator)
:\*\*Field winding - an iron-core coil which generates a steady magnetic field to act on the armature winding.
:\*\*Armature winding - an iron-core coil which is acted on by the magnetic field of the field winding to either create torque (motor) or induce a voltage to produce power (generator)
:\*Helmholtz coil, Maxwell coil - air-core coils which serve to cancel an external magnetic field
:\*Degaussing coil - a coil used to demagnetize parts
:\*Voice coil - a coil used in a moving-coil loudspeaker, suspended between the poles of a magnet. When the audio signal is passed through the coil, it vibrates, moving the attached speaker cone to create sound waves. The reverse is used in a dynamic microphone, where sound vibrations intercepted by something like a diaphragm physically transfer to a voice coil immersed in a magnetic field, and the coil\'s terminal ends then provide an electric analog of those vibrations.
### Inductors
Inductors or reactors are coils which generate a magnetic field which interacts with the coil itself, to induce a back EMF which opposes changes in current through the coil. Inductors are used as circuit elements in electrical circuits, to temporarily store energy or resist changes in current. A few types:
:\*Tank coil - an inductor used in a tuned circuit
:\*Choke - an inductor used to block high frequency AC while allowing through low frequency AC or DC.
:\*Loading coil - an inductor used to add inductance to an antenna, to make it resonant, or to a cable to prevent distortion of signals.
:\*Variometer - an adjustable inductor consisting of two coils in series, an outer stationary coil and a second one inside it which can be rotated so their magnetic axes are in the same direction or opposed.
:\*Flyback transformer - Although called a transformer, this is actually an inductor which serves to store energy in switching power supplies and horizontal deflection circuits for CRT televisions and monitors
:\*Saturable reactor - an iron-core inductor used to control AC power by varying the saturation of the core using a DC control voltage in an auxiliary winding.
:\*Inductive ballast - an inductor used in gas-discharge lamp circuits, such as fluorescent lamps, to limit the current through the lamp.
### Transformers
*Main article: Transformer*
A transformer is a device with two or more magnetically coupled windings (or sections of a single winding). A time varying current in one coil (called the primary winding) generates a magnetic field which induces a voltage in the other coil (called the secondary winding). A few types:
:\*Distribution transformer - A transformer in an electric power grid which transforms the high voltage from the electric power line to the lower voltage used by utility customers.
:\*Autotransformer - a transformer with only one winding. Different portions of the winding, accessed with taps, act as primary and secondary windings of the transformer.
:\*Toroidal transformer - the core is in the shape of a toroid. This is a commonly used shape as it decreases the leakage flux, resulting in less electromagnetic interference.
:\*Induction coil or trembler coil - an early transformer which uses a vibrating interrupter mechanism to break the primary current so it can operate off of DC current.
:\*\*Ignition coil - an induction coil used in internal combustion engines to create a pulse of high voltage to fire the spark plug which initiates the fuel burning.
:\*Balun - a transformer which matches a balanced transmission line to an unbalanced one.
:\*Bifilar coil - a coil wound with two parallel, closely spaced strands. If AC currents are passed through it in the same direction, the magnetic fluxes will add, but if equal currents in opposite directions pass through the windings the opposite fluxes will cancel, resulting in zero flux in the core. So no voltage will be induced in a third winding on the core. These are used in instruments and in devices like Ground Fault Interrupters. They are also used in low inductance wirewound resistors for use at RF frequencies.
:\*Audio transformer - A transformer used with audio signals. They are used for impedance matching.
:\*\*Hybrid coil - a specialized audio transformer with 3 windings used in telephony circuits to convert between two-wire and four-wire circuits
### Electric machines {#electric_machines}
Electric machines such as motors and generators have one or more windings which interact with moving magnetic fields to convert electrical energy to mechanical energy. Often a machine will have one winding through which passes most of the power of the machine (the \"armature\"), and a second winding which provides the magnetic field of the rotating element ( the \"field winding\") which may be connected by brushes or slip rings to an external source of electric current. In an induction motor, the \"field\" winding of the rotor is energized by the slow relative motion between the rotating winding and the rotating magnetic field produced by the stator winding, which induces the necessary exciting current in the rotor.
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# Electromagnetic coil
## Types of coils {#types_of_coils}
### Transducer coils {#transducer_coils}
thumb\|upright=0.7\|The sensor coil of a metal detector. These are coils used to translate time-varying magnetic fields to electric signals, and vice versa. A few types:
:\*Sensor or pickup coils - these are used to detect external time-varying magnetic fields
:\*Inductive sensor - a coil which senses when a magnet or iron object passes near it
:\*Recording head - a coil which is used to create a magnetic field to write data to a magnetic storage medium, such as magnetic tape, or a hard disk. Conversely it is also used to read the data in the form of changing magnetic fields in the medium.
:\*Induction heating coil - an AC coil used to heat an object by inducing eddy currents in it, a process called induction heating.
:\*Loop antenna - a coil which serves as a radio antenna, to convert radio waves to electric currents.
:\*Rogowski coil - a toroidal coil used as an AC measuring device
:\*Musical instrument pickup - a coil used to produce the output audio signal in an electric guitar or electric bass.
:\*Flux gate - a sensor coil used in a magnetometer
:\*Magnetic phonograph cartridge - a sensor in a record player that uses a coil to translate vibration of a needle to an audio signal in playing vinyl phonograph records.
There are also types of coil which don\'t fit into these categories
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# Cardiology diagnostic tests and procedures
The **diagnostic tests in cardiology** are methods of identifying heart conditions associated with healthy vs. unhealthy, pathologic heart function.
## Bedside
### History
Obtaining a medical history is always the first \"test\", part of understanding the likelihood of significant disease, as detectable within the current limitations of clinical medicine. Yet heart problems often produce no symptoms until very advanced, and many symptoms, such as palpitations and sensations of extra or missing heart beats correlate poorly with relative heart health *vs* disease. Hence, a history alone is rarely sufficient to diagnose a heart condition.
### Auscultation
*Auscultation* employs a stethoscope to more easily hear various normal and abnormal sounds, such as normal heart beat sounds and the usual heart beat sound changes associated with breathing versus heart murmurs.
## Laboratory
### Blood tests {#blood_tests}
A variety of *blood tests* are available for analyzing cholesterol transport behavior, HDL, LDL, triglycerides, lipoprotein little a, homocysteine, C-reactive protein, blood sugar control: fasting, after eating or averages using glycated albumen or hemoglobin, myoglobin, creatine kinase, troponin, brain-type natriuretic peptide, etc. to assess the evolution of coronary artery disease and evidence of existing damage. A great many more physiologic markers related to atherosclerosis and heart function are used and being developed and evaluated in research.
+------------------------+----------------------+---------------+------------+
| Test Name | Lower/normal risk | High risk | Cost \$US\ |
| | | | (approx) |
+========================+======================+===============+============+
| | | | |
+------------------------+----------------------+---------------+------------+
| Total Cholesterol | \<200 mg/dL | \>240 mg/dL | |
+------------------------+----------------------+---------------+------------+
| LDL-C | \<100 mg/dL | \>160 mg/dL | \$150\* |
+------------------------+----------------------+---------------+------------+
| HDL-C | \>60 mg/dL | \<40 mg/dL | |
+------------------------+----------------------+---------------+------------+
| Triglyceride | \<150 mg/dL | \>200 mg/dL | |
+------------------------+----------------------+---------------+------------+
| Blood Pressure | \<120/80 mmHg | \>140/90 mmHg | |
+------------------------+----------------------+---------------+------------+
| | | | |
+------------------------+----------------------+---------------+------------+
| C-reactive protein | \<1 mg/L | \>3 mg/L | \$20 |
+------------------------+----------------------+---------------+------------+
| Fibrinogen | \<300 mg/dL | \>460 mg/dL | \$100 |
+------------------------+----------------------+---------------+------------+
| Homocysteine | \<10 μmol/L | \>14 μmol/L | \$200 |
+------------------------+----------------------+---------------+------------+
| Fasting Insulin | \<15 μIU/mL | \>25 μIU/mL | \$75 |
+------------------------+----------------------+---------------+------------+
| Ferritin | male 12--300 ng/mL\ | | \$85 |
| | female 12--150 ng/mL | | |
+------------------------+----------------------+---------------+------------+
| Lipoprotein(a) - Lp(a) | \<14 mg/dL | \>19 mg/dL | \$75 |
+------------------------+----------------------+---------------+------------+
| Coronary calcium scan | \<100 | \>300 | \$250--600 |
+------------------------+----------------------+---------------+------------+
: **Cardiology diagnostic tests**
(\*) due to the high cost, LDL is usually calculated instead of being measured directly\
source: Beyond Cholesterol, Julius Torelli MD, 2005 `{{ISBN|0-312-34863-0}}`{=mediawiki}
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# Cardiology diagnostic tests and procedures
## Electrophysiology
### Electrocardiogram
*Electrocardiography* (ECG/EKG in German vernacular. Elektrokardiogram) monitors electrical activity of the heart, primarily as recorded from the skin surface. A 12 lead recording, recording the electrical activity in three planes, anterior, posterior, and lateral is the most commonly used form. The ECG allows observation of the heart electrical activity by visualizing waveform beat origin (typically from the sinoatrial or SA node) following down the bundle of HIS and ultimately stimulating the ventricles to contract forcing blood through the body. Much can be learned by observing the QRS morphology (named for the respective portions of the polarization/repolarization waveform of the wave, P,Q,R,S,T wave). Rhythm abnormalities can also be visualized as in slow heart rate bradycardia, or fast heart rate tachycardia.
### Fasegram
A *Fasegraphy* allows expanding the system of Electrocardiography diagnostic features, based on the evaluation of the speed characteristics of the process, and thereby increasing the sensitivity and specificity of ECG-diagnostics.
Fasegraphy allows determining the initial features of changes in the cardiac muscle, even on a single-channel ECG, which are underestimated in traditional ECG diagnostics.
### Holter monitor {#holter_monitor}
A *Holter monitor* records a continuous EKG rhythm pattern (rarely a full EKG) for 24 hours or more. These monitors are used for suspected frequent rhythm abnormalities, especially ones the wearer may not recognize by symptoms. They are more expensive than event monitors.
### Event monitor {#event_monitor}
An *event monitor* records short term EKG rhythm patterns, generally storing the last 2 to 5 minutes, adding in new and discarding old data, for 1 to 2 weeks or more. There are several different types with different capabilities. When the wearer presses a button on the monitor, it quits discarding old and continues recording for a short additional period. The wearer then plays the recording, via a standard phone connection, to a center with compatible receiving and rhythm printing equipment, after which the monitor is ready to record again. These monitors are used for suspected infrequent rhythm abnormalities, especially ones the wearer does recognize by symptoms. They are less expensive than Holter monitors.
### Cardiac stress testing {#cardiac_stress_testing}
*Cardiac stress testing* is used to determine to assess cardiac function and to disclose evidence of exertion-related cardiac hypoxia. Radionuclide testing using thallium or technetium can be used to demonstrate areas of perfusion abnormalities. With a maximal stress test the level of exercise is increased until the person\'s heart rate will not increase any higher, despite increased exercise. A fairly accurate estimate of the target heart rate, based on extensive clinical research, can be estimated by the formula 220 beats per minute minus patient\'s age. This linear relation is accurate up to about age 30, after which it mildly underestimates typical maximum attainable heart rates achievable by healthy individuals. Other formulas exist, such as that by Miller (217 - (0.85 × Age)) and others. Achieving a high enough heart rate at the end of exercise is critical to improving the sensitivity of the test to detect high grade heart artery stenosis. High frequency analysis of the QRS complex may be useful for detection of coronary artery disease during an exercise stress test.
### Electrophysiology study {#electrophysiology_study}
The electrophysiology study or EP study is the end all of electrophysiological tests of the heart. It involves a catheter with electrodes probing the endocardium, the inside of the heart, and testing the conduction pathways and electrical activity of individual areas of the heart.
## Medical imaging {#medical_imaging}
Cardiac imaging techniques include coronary catheterization, echocardiogram, intravascular ultrasound, retinal vessel analysis and the coronary calcium scan
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# Chalcolithic
The **Chalcolithic** (`{{IPAc-en|ˈ|k|æ|l|k|ə|ˌ|l|ɪ|θ|ɪ|k}}`{=mediawiki} `{{respell|KAL|kə|LI|thik}}`{=mediawiki}) (also called the **Copper Age** and **Eneolithic**) was an archaeological period characterized by the increasing use of smelted copper. It followed the Neolithic and preceded the Bronze Age. It occurred at different periods in different areas, but was absent in some parts of the world, such as Russia, where there was no well-defined Copper Age between the Stone and Bronze Ages. Stone tools were still predominantly used during this period.
The Chalcolithic covers both the early cold working (hammering) of near pure copper ores, as exhibited by the likes of North American Great Lakes Old Copper complex, from around 6,500 BC, through the later copper smelting cultures. The archaeological site of Belovode, on Rudnik mountain in Serbia, has the world\'s oldest securely dated evidence of copper smelting at high temperature, from c. 5,000 BC. The transition from Copper Age to Bronze Age in Europe occurred between the late 5th and the late `{{nobr|[[3rd millennium BC]].}}`{=mediawiki} In the Ancient Near East the Copper Age covered about the same period, beginning in the late `{{nobr|[[5th millennium BC]]}}`{=mediawiki} and lasting for about a millennium before it gave rise to the Early Bronze Age.
A study in the journal *Antiquity* from 2013 reporting the discovery of a tin bronze foil from the Pločnik archaeological site dated to c. 4,650 BC, as well as 14 other artefacts from Bulgaria and Serbia dated to before 4,000 BC, showed that early tin bronze was more common than previously thought and developed independently in Europe 1,500 years before the first tin bronze alloys in the Near East. In Britain, the Chalcolithic is a short period between about 2,500 and 2,200 BC, characterized by the first appearance of objects of copper and gold, a new ceramic culture and the immigration of Beaker culture people, heralding the end of the local late Neolithic.
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# Chalcolithic
## Terminology
The multiple names result from multiple definitions of the period. Originally, the term Bronze Age meant that either copper or bronze was being used as the chief hard substance for the manufacture of tools and weapons. Ancient writers, who provided the essential cultural references for educated people during the 19th century, used the same name for both copper- and bronze-using ages.
The concept of the Copper Age was put forward by Hungarian scientist Ferenc Pulszky in the 1870s, when, on the basis of the significant number of large copper objects unearthed within the Carpathian Basin, he suggested that the previous threefold division of the Prehistoric Age -- the Stone, Bronze and Iron Ages -- should be further divided with the introduction of the Copper Age.
In 1881, John Evans recognized that use of copper often preceded the use of bronze, and distinguished between a *transitional Copper Age* and the *Bronze Age proper*. He did not include the transitional period in the Bronze Age, but described it separately from the customary stone / bronze / iron system, at the Bronze Age\'s beginning. He did not, however, present it as a fourth age but chose to retain the tripartite system.
In 1884, Gaetano Chierici, perhaps following the lead of Evans, renamed it in Italian as the *eneo-litica*, or \"bronze--stone\" transition. The phrase was never intended to mean that the period was the only one in which both bronze and stone were used. The Copper Age features the use of copper, excluding bronze; moreover, stone continued to be used throughout both the Bronze Age and the Iron Age. The part *-litica* simply names the Stone Age as the point from which the transition began and is not another *-lithic* age.
Subsequently, British scholars used either Evans\'s \"Copper Age\" or the term \"Eneolithic\" (or Æneolithic), a translation of Chierici\'s *eneo-litica*. After several years, a number of complaints appeared in the literature that \"Eneolithic\" seemed to the untrained eye to be produced from *e-neolithic*, \"outside the Neolithic\", clearly not a definitive characterization of the Copper Age. Around 1900, many writers began to substitute *Chalcolithic* for Eneolithic, to avoid the false segmentation. The term chalcolithic is a combination of two words- Chalco+Lithic, derived from the Greek words \"khalkos\" meaning \"copper\", and \"líthos\" meaning \"stone\".
But \"chalcolithic\" could also mislead: For readers unfamiliar with the Italian language, *chalcolithic* seemed to suggest another *-lithic* age, paradoxically part of the Stone Age despite the use of copper. Today, *Copper Age*, *Eneolithic*, and *Chalcolithic* are used synonymously to mean Evans\'s original definition of Copper Age.
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# Chalcolithic
## Regions
### Near East {#near_east}
The emergence of metallurgy may have occurred first in the Fertile Crescent.
Lead may have been the first ore that humans smelted, since it can be easily obtained by heating galena.
Possible early examples of lead smelting, supported by the extreme rarity of native lead, include: lead beads, found on Level IX of Chatal/Çatal Hüyük in central Anatolia, though they might be made of galena, cerussite, or metallic lead, and accordingly might or might not be evidence of early smelting; a lead bead, found in a GK59 group test square in the 4th level of Jarmo, dated to the 7th millennium BCE, though it is small enough that its human usage is doubtful; a lead bracelet, found in level XII of Yarim Tepe I, dated to the 6th millennium BC; a small cone-shaped piece of lead, found in the \"Burnt House\" in TT6 at Arpachiyah, dated to the Halaf period or slightly later than the Yarim Tepe bracelet; and more.
Copper smelting is also documented at this site at about the same time period (soon after 6000 BC). However, the use of lead seems to precede copper smelting. Early metallurgy is also documented at the nearby site of Tell Maghzaliyah, which seems to be dated even earlier, and completely lacks pottery.
The Timna Valley contains evidence of copper mining in 7000--5000 BC. The process of transition from Neolithic to Chalcolithic in the Middle East is characterized in archaeological stone tool assemblages by a decline in high quality raw material procurement and use. This dramatic shift is seen throughout the region, including the Tehran Plain, Iran. Here, analysis of six archaeological sites determined a marked downward trend in not only material quality, but also in aesthetic variation in the lithic artefacts. Fazeli & Coningham use these results as evidence of the loss of craft specialisation caused by increased use of copper tools.
The Tehran Plain findings illustrate the effects of the introduction of copper working technologies on the in-place systems of lithic craft specialists and raw materials. Networks of exchange and specialized processing and production that had evolved during the Neolithic seem to have collapsed by the Middle Chalcolithic (c. 4500--3500 BC) and been replaced by the use of local materials by a primarily household-based production of stone tools.
Arsenical copper or bronze was produced in eastern Turkey (Malatya Province) at two ancient sites, Norşuntepe and Değirmentepe, around 4200 BC. According to Boscher (2016), hearths or natural draft furnaces, slag, ore, and pigment had been recovered throughout these sites. This was in the context of Ubaid period architectural complexes typical of southern Mesopotamian architecture. Norşuntepe site demonstrates that some form of arsenic alloying was indeed taking place by the 4th millennium BC. Since the slag identified at Norşuntepe contains no arsenic, this means that arsenic in some form was added separately.
### Europe
A copper axe found at Prokuplje, Serbia contains the oldest securely dated evidence of copper-making, c. 5500 BC (7,500 years ago). The find in June 2010 extends the known record of copper smelting by about 800 years, and suggests that copper smelting may have been invented in separate parts of Asia and Europe at that time rather than spreading from a single source. In Britain and central and northern Europe a Chalcolithic period has never been defined. However, copper artefacts have been found in archaeological groups. Copper artefacts found in northern Germany and Denmark date from between 4000 and 3300 BC, with most finds dating from 3500 - 3300 BC. They belong to the Funnel Beaker group. The copper was mined in Serbian mines, as researchers from Kiel have recently discovered.
Knowledge of the use of copper was far more widespread than the metal itself. Many European archaeological Cultures used stone axes modeled on copper axes, even with moulding carved in the stone, such as the Battle Axe culture or the late Funnel Beaker Culture. Ötzi the Iceman, who was found in the Ötztal Alps in 1991 and whose remains have been dated to about 3300 BC, was found with a Mondsee copper axe.
Examples of Chalcolithic cultures in Europe include Vila Nova de São Pedro and Los Millares on the Iberian Peninsula. Pottery of the Beaker people has been found at both sites, dating to several centuries after copper-working began there. The Beaker culture appears to have spread copper and bronze technologies in Europe, along with Indo-European languages. In Britain, copper was used between the 25th and `{{nobr|22nd centuries BC}}`{=mediawiki}, but some archaeologists do not recognise a British Chalcolithic because production and use was on a small scale.
### South Asia {#south_asia}
Ceramic similarities between the Indus Valley Civilisation, southern Turkmenistan, and northern Iran during 4300--3300 BC of the Chalcolithic period suggest considerable mobility and trade.
The term \"Chalcolithic\" has also been used in the context of the South Asian Stone Age.
In Bhirrana, the earliest Indus civilization site, copper bangles and arrowheads were found. The inhabitants of Mehrgarh in present-day Pakistan fashioned tools with local copper ore between 7000 and 3300 BC.
The Nausharo site was a pottery workshop in province of Balochistan, Pakistan, that dates to 4,500 years ago; 12 blades and blade fragments were excavated there. These blades are 12 - long, 1.2 - wide, and relatively thin. Archaeological experiments show that these blades were made with a copper indenter and functioned as a potter\'s tool to trim and shape unfired pottery. Petrographic analysis indicates local pottery manufacturing, but also reveals the existence of a few exotic black-slipped pottery items from the Indus Valley.
In India, Chalcolithic culture flourished in mainly four farming communities -- Ahar or Banas, Kayatha, Malwa, and Jorwe. These communities had some common traits like painted pottery and use of copper, but they had a distinct ceramic design tradition. Banas culture (2000--1600 BC) had ceramics with red, white, and black design. Kayatha culture (2450--1700 BC) had ceramics painted with brown colored design. Malwa culture (1900--1400 BC) had profusely decorated pottery with red or black colored design. Jorwe culture (1500--900 BC) had ceramics with matte surface and black-on-red design.
Pandu Rajar Dhibi (2000--1600 BC) is a Chalcolithic site in the eastern part of the Indian subcontinent. It is located on the south bank of Ajay River in West Bengal. Blackware, painted Koshi ware, pottery, various ornaments made of pearl and copper, various types of tools, pieces of fabric woven from Shimul cotton thread, human and various animal skeletons, burnt clay fragments have been found at the site.
In March 2018, archaeologists had discovered three carts and copper artifacts including weapons dating to 1800 BC in Sanauli village of Uttar Pradesh. The artifacts belongs to Ochre Coloured Pottery culture.
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# Chalcolithic
## Regions
### Pre-Columbian Americas {#pre_columbian_americas}
In the Archaeology of the Americas, a five-period system is conventionally used which does not include metal ages, though metalworking technology did precede European contact in some areas.
Andean civilizations in South America appear to have independently invented copper smelting.
The term \"Chalcolithic\" is also applied to American civilizations that already used copper and copper alloys thousands of years before Europeans immigrated. Besides cultures in the Andes and Mesoamerica, the Old Copper complex mined and fabricated copper as tools, weapons, and personal ornaments in an area centered in the upper Great Lakes region (present-day Michigan and Wisconsin).
The evidence of smelting or alloying that has been found in North America is subject to some dispute and a common assumption by archaeologists is that objects were cold-worked into shape. Artifacts from some of these sites have been dated to 6500--1000 BC, making them some of the oldest Chalcolithic sites in the world. Some archaeologists find artifactual and structural evidence of casting by Hopewellian and Mississippian peoples to be demonstrated in the archaeological record.
### East Asia {#east_asia}
In the 5th millennium BC copper artifacts start to appear in East Asia, such as in the Jiangzhai and Hongshan cultures, but those metal artifacts were not widely used during this early stage.
Copper manufacturing gradually appeared in the Yangshao period (5000--3000 BC). Jiangzhai is the only site where copper artifacts were found in the Banpo culture. Archaeologists have found remains of copper metallurgy in various cultures from the late fourth to the early third millennia BC. These include the copper-smelting remains and copper artifacts of the Hongshan culture (4700--2900) and copper slag at the Yuanwozhen site. This indicates that inhabitants of the Yellow River valley had already learned how to make copper artifacts by the later Yangshao period.
### Sub-Saharan Africa {#sub_saharan_africa}
In the region of the Aïr Mountains, Niger, independent copper smelting developed between 3000 and 2500 BC. The process was not in a developed state, indicating smelting was not foreign. It became mature about 1500 BC
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# Called to Common Mission
**Called to Common Mission** (**CCM**) is an agreement between The Episcopal Church (ECUSA) and the Evangelical Lutheran Church in America (ELCA) in the United States, establishing full communion between them. It was ratified by the ELCA in 1999, the ECUSA in 2000, after the narrow failure of a previous agreement. Its principal author on the Episcopal side was theological professor J. Robert Wright. Under the agreement, they recognize the validity of each other\'s baptisms and ordinations. The agreement provided that the ELCA would accept the historical episcopate and the \"threefold ministry\" of bishop - priest (or pastor) - deacon with respect to ministers of communicant churches serving ELCA congregations; the installation of the ELCA presiding bishop was performed through the laying on of hands by Lutheran bishops in the historic episcopate. This provision was opposed by some in the ELCA, which after its founding merger in 1988, held a lengthy study of the ministry which was undertaken with divided opinions. In response to concerns about the meaning of the CCM, synod bishops in the ELCA drafted the Tucson resolution which presented the official ELCA position. It made clear that there is no requirement to ordain deacons or accept their ministry. It also provided assurance that the ELCA did not and was not required by CCM to change its own theological stance.
Lutheran churches of Scandinavian origin, such as the Church of Sweden and Church in Kenya, affirm apostolic succession and are in the historical episcopate; nevertheless, some within the ELCA argued that the historical episcopate would contradict the doctrine that the church exists wherever the Word of God is preached and sacraments are practiced. The traditional ELCA doctrine is affirmed by the Tucson resolution. Others objected on the grounds that adopting the Episcopalian / Anglican view on priestly orders and hierarchical structure was contrary to the Evangelical Lutheran concept of the \"priesthood of all believers\", which holds that all Christians stand on equal footing before God. They argued that the Old Covenant required a priest to mediate between God and humanity, but that New Covenant explicitly abolishes the need for priestly role by making every Christian a priest with direct access to God\'s grace. The Tucson resolution explained that the ELCA had not adopted the Episcopal view, but ECUSA or Reformed ordinands accepted by ELCA congregations would follow ELCA practice. Still others objected because of the implied directive that the use of a lay presidency would be abolished. This was a particular issue for rural congregations that periodically \"called\" a congregation member to conduct communion services consecrating the elements (of bread and wine for service) in the interim period or with the absence of ordained clergy (pastor). The Tucson resolution explicitly affirmed the continued use of lay ministry
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# Context menu
A **context menu** (also called **contextual**, **shortcut**, and **pop up** or **pop-up** **menu**) is a menu in a graphical user interface (GUI) that appears upon user interaction, such as a right-click mouse operation. A context menu offers a limited set of choices that are available in the current state, or context, of the operating system or application to which the menu belongs. Usually the available choices are actions related to the selected object. From a technical point of view, such a context menu is a graphical control element.
## History
Context menus first appeared in the Smalltalk environment on the Xerox Alto computer, where they were called *pop-up menus*; they were invented by Dan Ingalls in the mid-1970s.
Microsoft Office v3.0 introduced the context menu for copy and paste functionality in 1990. Borland demonstrated extensive use of the context menu in 1991 at the Second Paradox Conference in Phoenix Arizona. Lotus 1-2-3/G for OS/2 v1.0 added additional formatting options in 1991. Borland Quattro Pro for Windows v1.0 introduced the Properties context menu option in 1992.
## Implementation
Context menus are opened via various forms of user interaction that target a region of the GUI that supports context menus. The specific form of user interaction and the means by which a region is targeted vary:
- On a computer running Microsoft Windows, macOS, or Unix running the X Window System, clicking the secondary mouse button (usually the right button) opens a context menu for the region that is under the mouse pointer.
- For quickness, implementations may additionally support hold-and-release selection, meaning the pointer is held down and dragged, and released at desirable menu entry.
- On systems that support one-button mice, context menus are typically opened by pressing and holding the primary mouse button (this works on the icons in the Dock on macOS) or by pressing a keyboard/mouse button combination (e.g. Ctrl-mouse click in Classic Mac OS and macOS). A keyboard alternative for macOS is to enable Mouse keys in Universal Access. Then, depending on whether a laptop or compact or extended keyboard type is used, the shortcut is `{{keypress|Function}}`{=mediawiki}+`{{keypress|Ctrl}}`{=mediawiki}+5 or `{{keypress|Ctrl}}`{=mediawiki}+5 (numeric keypad) or `{{keypress|Function}}`{=mediawiki}+`{{keypress|Ctrl}}`{=mediawiki}+i (laptop).
- On systems with a multi-touch interface such as MacBook or Surface, the context menu can be opened by pressing or tapping with two fingers instead of just one.
```{=html}
<!-- -->
```
- Some cameras on smartphones for example recognize a QR code when a picture is taken. Then a pop-up appears if you want to \'open\' the QR content. This could be anything like a website or to configure your phone to connect to Wi-Fi. See image.
- On some user interfaces, context menu items are accompanied by icons for quicker recognition upon navigation.
- Context menus can also have a top row of icons only for quick access to most frequently used options.
Windows mouse click behavior is such that the context menu doesn\'t open while the mouse button is pressed, but only opens the menu when the button is released, so the user has to click again to select a context menu item. This behavior differs from that of macOS and most free software GUIs.
- In Microsoft Windows, pressing the Application key or Shift+F10 opens a context menu for the region that has focus.
Context menus are sometimes hierarchically organized, allowing navigation through different levels of the menu structure. The implementations differ: Microsoft Word was one of the first applications to only show sub-entries of some menu entries after clicking an arrow icon on the context menu, otherwise executing an action associated with the parent entry. This makes it possible to quickly repeat an action with the parameters of the previous execution, and to better separate options from actions.
### X Window Managers {#x_window_managers}
The following window managers provide context menu functionality:
- Awesome
- IceWM---middle-click and right-click context menus on desktop, menu bar, title bars, and title icon
- olwm
- openbox
- sawfish
## Usability
Context menus have received some criticism from usability analysts when improperly used, as some applications make certain features *only* available in context menus, which may confuse even experienced users (especially when the context menus can only be activated in a limited area of the application\'s client window).
Context menus usually open in a fixed position under the pointer, but when the pointer is near a screen edge the menu will be displaced - thus reducing consistency and impeding use of muscle memory. If the context menu is being triggered by keyboard, such as by using Shift + F10, the context menu appears near the focused widget instead of the position of the pointer, to save recognition efforts.
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# Context menu
## In documentation {#in_documentation}
Microsoft\'s guidelines call for always using the term *context menu*, and explicitly deprecate *shortcut menu*
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# Cuitláhuac
**Cuitláhuac** (`{{IPA|es|kwiˈtlawak|-|Cuitlahuac1.ogg}}`{=mediawiki}, `{{audio|Kuitlawatsin.ogg|modern Nahuatl pronunciation}}`{=mediawiki}) (c. 1476 -- 1520) or **Cuitláhuac** (in Spanish orthography; *Cuitlāhuac*, `{{IPA|nah|kʷiˈt͡ɬaːwak}}`{=mediawiki}, honorific form: **Cuitlahuatzin**) was the 10th *Huey Tlatoani* (emperor) of the Aztec city of Tenochtitlan for 80 days during the year Two Flint (1520). He is credited with leading the resistance to the Spanish and Tlaxcalteca conquest of the Mexica Empire, following the death of his kinsman Moctezuma II.
## Biography
Cuitláhuac was the eleventh son of the ruler Axayacatl and a younger brother of Moctezuma II, the late Emperor of Tenochtitlan, who died during the Spanish occupation of the city. His mother\'s father, also called Cuitlahuac, had been ruler of Iztapalapa, and the younger Cuitláhuac also ruled there initially. Cuitláhuac was an experienced warrior and an adviser to Moctezuma, warning him not to allow the Spaniards to enter Tenochtitlan. Hernán Cortés imprisoned both Moctezuma and Cuitláhuac. Cortes had to leave the city in order to meet a Spanish force sent by Diego Velasquez, Spanish governor of Cuba. Following the massacre of Aztec elites when Cortés was away from Tenochtitlan, the Mexica besieged the Spanish and their indigenous allies. Cuitláhuac was released on the pretense to reopen the market to get food to the invaders. Moctezuma was stoned to death after trying to tell his people to withdraw from the battle between the Aztecs and the Spanish, and Cuitláhuac was elected *tlatoani* following the flight of the Spaniards and their allies from Tenochtitlan on June 30, 1520. Some sources claim he was serving in that role even before Moctezuma\'s death.
Cuitláhuac was ritually married to Moctezuma\'s eldest daughter, a ten- or eleven-year-old girl, who later was called Isabel Moctezuma.
Cuitláhuac ruled just 80 days, perhaps dying from smallpox that had been introduced to the New World by an African suffering from the disease who was part of Pánfilo de Narváez\'s expedition to capture Cortés. However, he played a really important role in the Aztec empire, and was best known for leading the Aztec resistance against the Spanish invaders. The early sources do not explicitly say from what he succumbed. Immediately after Cuitláhuac\'s death, Cuauhtémoc was made the next *tlatoani*.
## Legacy
The modern Mexican municipality of Cuitláhuac, Veracruz and the Mexico City Metro station Metro Cuitláhuac are named in honor of Cuitláhuac. The asteroid 2275 Cuitláhuac is also named after this ruler.
There is an Avenue in Mexico City Called Cuitláhuac (Eje 3 Norte) that runs from Avenue Insurgentes to Avenue Mexico-Tacuba and that is part of an inner ring; also many streets in other towns and villages in Mexico are so called
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# Cross section (physics)
In physics, the **cross section** is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted `{{math|''σ''}}`{=mediawiki} (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
When two discrete particles interact in classical physics, their mutual **cross section** is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic spheres that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as electromagnetism or gravity, their scattering cross section is generally larger than their geometric size.
When a cross section is specified as the differential limit of a function of some final-state variable, such as particle angle or energy, it is called a **differential cross section** (see detailed discussion below). When a cross section is integrated over all scattering angles (and possibly other variables), it is called a **total cross section** or **integrated total cross section**. For example, in Rayleigh scattering, the intensity scattered at the forward and backward angles is greater than the intensity scattered sideways, so the forward differential scattering cross section is greater than the perpendicular differential cross section, and by adding all of the infinitesimal cross sections over the whole range of angles with integral calculus, we can find the total cross section.
Scattering cross sections may be defined in nuclear, atomic, and particle physics for collisions of accelerated beams of one type of particle with targets (either stationary or moving) of a second type of particle. The probability for any given reaction to occur is in proportion to its cross section. Thus, specifying the cross section for a given reaction is a proxy for stating the probability that a given scattering process will occur.
The measured reaction rate of a given process depends strongly on experimental variables such as the density of the target material, the intensity of the beam, the detection efficiency of the apparatus, or the angle setting of the detection apparatus. However, these quantities can be factored away, allowing measurement of the underlying two-particle collisional cross section.
Differential and total scattering cross sections are among the most important measurable quantities in nuclear, atomic, and particle physics.
With light scattering off of a particle, the **cross section** specifies the amount of optical power scattered from light of a given irradiance (power per area). Although the cross section has the same units as area, the cross section may not necessarily correspond to the actual physical size of the target given by other forms of measurement. It is not uncommon for the actual cross-sectional area of a scattering object to be much larger or smaller than the cross section relative to some physical process. For example, plasmonic nanoparticles can have light scattering cross sections for particular frequencies that are much larger than their actual cross-sectional areas.
## Collision among gas particles {#collision_among_gas_particles}
thumb\|upright=1.5\|**Figure 1.** In a gas of particles of individual diameter `{{math|2''r''}}`{=mediawiki}, the cross section `{{math|''σ''}}`{=mediawiki}, for collisions is related to the particle number density `{{math|''n''}}`{=mediawiki}, and mean free path between collisions `{{math|''λ''}}`{=mediawiki}.
In a gas of finite-sized particles there are collisions among particles that depend on their cross-sectional size. The average distance that a particle travels between collisions depends on the density of gas particles. These quantities are related by
: $\sigma = \frac{1}{n \lambda},$
where
: is the cross section of a two-particle collision (SI unit: m^2^),
: is the mean free path between collisions (SI unit: m),
: is the number density of the target particles (SI unit: m^−3^).
If the particles in the gas can be treated as hard spheres of radius `{{math|''r''}}`{=mediawiki} that interact by direct contact, as illustrated in Figure 1, then the effective cross section for the collision of a pair is
: $\sigma = \pi \left(2r\right)^2$
If the particles in the gas interact by a force with a larger range than their physical size, then the cross section is a larger effective area that may depend on a variety of variables such as the energy of the particles.
Cross sections can be computed for atomic collisions but also are used in the subatomic realm. For example, in nuclear physics a \"gas\" of low-energy neutrons collides with nuclei in a reactor or other nuclear device, with a cross section that is energy-dependent and hence also with well-defined mean free path between collisions.
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# Cross section (physics)
## Attenuation of a beam of particles {#attenuation_of_a_beam_of_particles}
If a beam of particles enters a thin layer of material of thickness `{{math|d''z''}}`{=mediawiki}, the flux `{{math|Φ}}`{=mediawiki} of the beam will decrease by `{{math|dΦ}}`{=mediawiki} according to
: $\frac{\mathrm d \Phi}{\mathrm d z} = -n \sigma \Phi,$
where `{{math|''σ''}}`{=mediawiki} is the total cross section of *all* events, including scattering, absorption, or transformation to another species. The volumetric number density of scattering centers is designated by `{{math|''n''}}`{=mediawiki}. Solving this equation exhibits the exponential attenuation of the beam intensity:
: $\Phi = \Phi_0 e^{-n \sigma z},$
where `{{math|Φ<sub>0</sub>}}`{=mediawiki} is the initial flux, and `{{math|''z''}}`{=mediawiki} is the total thickness of the material. For light, this is called the Beer--Lambert law.
## Differential cross section {#differential_cross_section}
Consider a classical measurement where a single particle is scattered off a single stationary target particle. Conventionally, a spherical coordinate system is used, with the target placed at the origin and the `{{math|''z''}}`{=mediawiki} axis of this coordinate system aligned with the incident beam. The angle `{{math|''θ''}}`{=mediawiki} is the **scattering angle**, measured between the incident beam and the scattered beam, and the `{{math|''φ''}}`{=mediawiki} is the azimuthal angle.
:
The impact parameter `{{math|''b''}}`{=mediawiki} is the perpendicular offset of the trajectory of the incoming particle, and the outgoing particle emerges at an angle `{{math|''θ''}}`{=mediawiki}. For a given interaction (coulombic, magnetic, gravitational, contact, etc.), the impact parameter and the scattering angle have a definite one-to-one functional dependence on each other. Generally the impact parameter can neither be controlled nor measured from event to event and is assumed to take all possible values when averaging over many scattering events. The differential size of the cross section is the area element in the plane of the impact parameter, i.e. `{{math|d''σ'' {{=}}`{=mediawiki} *b* d*φ* d*b*}}. The differential angular range of the scattered particle at angle `{{math|''θ''}}`{=mediawiki} is the solid angle element `{{math|dΩ {{=}}`{=mediawiki} sin *θ* d*θ* d*φ*}}. The differential cross section is the quotient of these quantities, `{{math|{{sfrac|d''σ''|dΩ}}}}`{=mediawiki}.
It is a function of the scattering angle (and therefore also the impact parameter), plus other observables such as the momentum of the incoming particle. The differential cross section is always taken to be positive, even though larger impact parameters generally produce less deflection. In cylindrically symmetric situations (about the beam axis), the azimuthal angle `{{math|''φ''}}`{=mediawiki} is not changed by the scattering process, and the differential cross section can be written as
: $\frac{\mathrm{d} \sigma}{\mathrm{d}(\cos \theta)} =\int_0^{2\pi} \frac{\mathrm{d} \sigma}{\mathrm{d} \Omega} \,\mathrm{d}\varphi$.
In situations where the scattering process is not azimuthally symmetric, such as when the beam or target particles possess magnetic moments oriented perpendicular to the beam axis, the differential cross section must also be expressed as a function of the azimuthal angle.
For scattering of particles of incident flux `{{math|''F''<sub>inc</sub>}}`{=mediawiki} off a stationary target consisting of many particles, the differential cross section `{{math|{{sfrac|d''σ''|dΩ}}}}`{=mediawiki} at an angle `{{math|(''θ'',''φ'')}}`{=mediawiki} is related to the flux of scattered particle detection `{{math|''F''<sub>out</sub>(''θ'',''φ'')}}`{=mediawiki} in particles per unit time by
: $\frac{\mathrm d \sigma}{\mathrm d \Omega}(\theta,\varphi) = \frac{1}{n t \Delta\Omega} \frac{F_\text{out}(\theta,\varphi)}{F_\text{inc}}.$
Here `{{math|ΔΩ}}`{=mediawiki} is the finite angular size of the detector (SI unit: sr), `{{math|''n''}}`{=mediawiki} is the number density of the target particles (SI unit: m^−3^), and `{{math|''t''}}`{=mediawiki} is the thickness of the stationary target (SI unit: m). This formula assumes that the target is thin enough that each beam particle will interact with at most one target particle.
The total cross section `{{math|''σ''}}`{=mediawiki} may be recovered by integrating the differential cross section `{{math|{{sfrac|d''σ''|dΩ}}}}`{=mediawiki} over the full solid angle (`{{math|4π}}`{=mediawiki} steradians):
: $\sigma = \oint_{4\pi} \frac{\mathrm d \sigma}{\mathrm d \Omega} \, \mathrm d \Omega = \int_0^{2\pi} \int_0^\pi \frac{\mathrm d \sigma}{\mathrm d \Omega} \sin \theta \, \mathrm d \theta \, \mathrm d \varphi.$
It is common to omit the \"differential\" qualifier when the type of cross section can be inferred from context. In this case, `{{math|''σ''}}`{=mediawiki} may be referred to as the *integral cross section* or *total cross section*. The latter term may be confusing in contexts where multiple events are involved, since \"total\" can also refer to the sum of cross sections over all events.
The differential cross section is extremely useful quantity in many fields of physics, as measuring it can reveal a great amount of information about the internal structure of the target particles. For example, the differential cross section of Rutherford scattering provided strong evidence for the existence of the atomic nucleus.
Instead of the solid angle, the momentum transfer may be used as the independent variable of differential cross sections.
Differential cross sections in inelastic scattering contain resonance peaks that indicate the creation of metastable states and contain information about their energy and lifetime.
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# Cross section (physics)
## Quantum scattering {#quantum_scattering}
In the time-independent formalism of quantum scattering, the initial wave function (before scattering) is taken to be a plane wave with definite momentum `{{math|''k''}}`{=mediawiki}:
: $\phi_-(\mathbf r) \;\stackrel{r \to \infty}{\longrightarrow}\; e^{i k z},$
where `{{math|''z''}}`{=mediawiki} and `{{math|''r''}}`{=mediawiki} are the *relative* coordinates between the projectile and the target. The arrow indicates that this only describes the *asymptotic behavior* of the wave function when the projectile and target are too far apart for the interaction to have any effect.
After scattering takes place it is expected that the wave function takes on the following asymptotic form:
: $\phi_+(\mathbf r) \;\stackrel{r \to \infty}{\longrightarrow}\; f(\theta,\phi) \frac{e^{i k r}}{r},$
where `{{math|''f''}}`{=mediawiki} is some function of the angular coordinates known as the scattering amplitude. This general form is valid for any short-ranged, energy-conserving interaction. It is not true for long-ranged interactions, so there are additional complications when dealing with electromagnetic interactions.
The full wave function of the system behaves asymptotically as the sum
: $\phi(\mathbf r) \;\stackrel{r \to \infty}{\longrightarrow}\; \phi_-(\mathbf r) + \phi_+(\mathbf r).$
The differential cross section is related to the scattering amplitude:
: $\frac{\mathrm d \sigma}{\mathrm d \Omega}(\theta, \phi) = \bigl|f(\theta, \phi)\bigr|^2.$
This has the simple interpretation as the probability density for finding the scattered projectile at a given angle.
A cross section is therefore a measure of the effective surface area seen by the impinging particles, and as such is expressed in units of area. The cross section of two particles (i.e. observed when the two particles are colliding with each other) is a measure of the interaction event between the two particles. The cross section is proportional to the probability that an interaction will occur; for example in a simple scattering experiment the number of particles scattered per unit of time (current of scattered particles `{{math|''I''<sub>r</sub>}}`{=mediawiki}) depends only on the number of incident particles per unit of time (current of incident particles `{{math|''I''<sub>i</sub>}}`{=mediawiki}), the characteristics of target (for example the number of particles per unit of surface `{{math|''N''}}`{=mediawiki}), and the type of interaction. For `{{math|''Nσ'' ≪ 1}}`{=mediawiki} we have
: \\begin{align}
I\_\\text{r} &= I\_\\text{i}N\\sigma, \\\\ \\sigma &= \\frac{I\_\\text{r}}{I\_\\text{i}} \\frac{1}{N} \\\\ &= \\text{probability of interaction} \\times \\frac{1}{N}. \\end{align}
### Relation to the S-matrix {#relation_to_the_s_matrix}
If the reduced masses and momenta of the colliding system are `{{math|''m''<sub>i</sub>}}`{=mediawiki}, `{{math|'''p'''<sub>i</sub>}}`{=mediawiki} and `{{math|''m''<sub>f</sub>}}`{=mediawiki}, `{{math|'''p'''<sub>f</sub>}}`{=mediawiki} before and after the collision respectively, the differential cross section is given by`{{clarify|reason=This section is an uncontextualized leap. We have jumped, without announcement, from the Schrödinger PDE for a wave in a potential to the language of QFT for two particles colliding.|date=September 2016}}`{=mediawiki}
: $\frac{\mathrm d\sigma}{\mathrm d\Omega} = \left(2\pi\right)^4 m_\text{i} m_\text{f} \frac{p_\text{f}}{p_\text{i}} \bigl|T_{\text{f}\text{i}}\bigr|^2,$
where the on-shell `{{math|''T''}}`{=mediawiki} matrix is defined by
: $S_{\text{f}\text{i}} = \delta_{\text{f}\text{i}} - 2\pi i \delta\left(E_\text{f} - E_\text{i}\right) \delta\left(\mathbf{p}_\text{i} - \mathbf{p}_\text{f}\right) T_{\text{f}\text{i}}$
in terms of the S-matrix. Here `{{math|''δ''}}`{=mediawiki} is the Dirac delta function. The computation of the S-matrix is the main goal of the scattering theory.
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# Cross section (physics)
## Units
Although the SI unit of total cross sections is m^2^, a smaller unit is usually used in practice.
In nuclear and particle physics, the conventional unit is the barn b, where 1 b = 10^−28^ m^2^ = 100 fm^2^. Smaller prefixed units such as mb and μb are also widely used. Correspondingly, the differential cross section can be measured in units such as mb/sr.
When the scattered radiation is visible light, it is conventional to measure the path length in centimetres. To avoid the need for conversion factors, the scattering cross section is expressed in cm^2^, and the number concentration in cm^−3^. The measurement of the scattering of visible light is known as nephelometry, and is effective for particles of 2--50 μm in diameter: as such, it is widely used in meteorology and in the measurement of atmospheric pollution.
The scattering of X-rays can also be described in terms of scattering cross sections, in which case the square ångström is a convenient unit: 1 Å^2^ = 10^−20^ m^2^ = `{{val|10000|u=[[picometre|pm]]<sup>2</sup>}}`{=mediawiki} = 10^8^ b. The sum of the scattering, photoelectric, and pair-production cross-sections (in barns) is charted as the \"atomic attenuation coefficient\" (narrow-beam), in barns.
## Scattering of light {#scattering_of_light}
For light, as in other settings, the scattering cross section for particles is generally different from the geometrical cross section of the particle, and it depends upon the wavelength of light and the permittivity, shape, and size of the particle. The total amount of scattering in a sparse medium is proportional to the product of the scattering cross section and the number of particles present.
In the interaction of light with particles, many processes occur, each with their own cross sections, including absorption, scattering, and photoluminescence. The sum of the absorption and scattering cross sections is sometimes referred to as the attenuation or extinction cross section.
: $\sigma = \sigma_\text{abs} + \sigma_\text{sc} + \sigma_\text{lum}.$
The total extinction cross section is related to the attenuation of the light intensity through the Beer--Lambert law, which says that attenuation is proportional to particle concentration:
: $A_\lambda = C l \sigma,$
where `{{math|''A<sub>λ</sub>''}}`{=mediawiki} is the attenuation at a given wavelength `{{math|''λ''}}`{=mediawiki}, `{{math|''C''}}`{=mediawiki} is the particle concentration as a number density, and `{{math|''l''}}`{=mediawiki} is the path length. The absorbance of the radiation is the logarithm (decadic or, more usually, natural) of the reciprocal of the transmittance `{{mathcal|T}}`{=mediawiki}:
: $A_\lambda = -\log \mathcal{T}.$
Combining the scattering and absorption cross sections in this manner is often necessitated by the inability to distinguish them experimentally, and much research effort has been put into developing models that allow them to be distinguished, the Kubelka-Munk theory being one of the most important in this area.
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# Cross section (physics)
## Scattering of light {#scattering_of_light}
### Cross section and Mie theory {#cross_section_and_mie_theory}
Cross sections commonly calculated using Mie theory include efficiency coefficients for extinction $Q_\text{ext}$, scattering $Q_\text{sc}$, and Absorption $Q_\text{abs}$ cross sections. These are normalized by the geometrical cross sections of the particle $\sigma_\text{geom} = \pi a^2$ as $Q_\alpha = \frac{\sigma_\alpha}{\sigma_\text{geom}}, \qquad \alpha = \text{ext}, \text{sc}, \text{abs}.$ The cross section is defined by
:
\\sigma\_\\alpha = \\frac{W\_\\alpha}{I\_{\\text{inc}}} where $\left[W_\alpha \right] = \left[ \text{W} \right]$ is the energy flow through the surrounding surface, and $\left[I_{\text{inc}}\right] = \left[ \frac{\text{W}}{\text{m}^2} \right]$ is the intensity of the incident wave. For a plane wave the intensity is going to be $I_{\text{inc}} = |\mathbf{E}|^2 / (2 \eta)$, where $\eta = \sqrt{\mu \mu_0 / (\varepsilon \varepsilon_0)}$ is the impedance of the host medium.
The main approach is based on the following. Firstly, we construct an imaginary sphere of radius $r$ (surface $A$) around the particle (the scatterer). The net rate of electromagnetic energy crosses the surface $A$ is
:
W\_\\text{a} = - \\oint_A \\mathbf{\\Pi} \\cdot \\hat{\\mathbf{r}} dA where $\mathbf{\Pi} = \frac{1}{2} \operatorname{Re} \left[ \mathbf{E}^* \times \mathbf{H} \right]$ is the time averaged Poynting vector. If $W_\text{a} > 0$ energy is absorbed within the sphere, otherwise energy is being created within the sphere. We will not consider this case here. If the host medium is non-absorbing, the energy must be absorbed by the particle. We decompose the total field into incident and scattered parts $\mathbf{E} = \mathbf{E}_\text{i} + \mathbf{E}_\text{s}$, and the same for the magnetic field $\mathbf{H}$. Thus, we can decompose $W_a$ into the three terms $W_\text{a} = W_\text{i} - W_\text{s} + W_{\text{ext}}$, where
:
W\_\\text{i} = - \\oint_A \\mathbf{\\Pi}\_\\text{i} \\cdot \\hat{\\mathbf{r}} dA \\equiv 0, \\qquad W\_\\text{s} = \\oint_A \\mathbf{\\Pi}\_\\text{s} \\cdot \\hat{\\mathbf{r}} dA, \\qquad W\_{\\text{ext}} = \\oint_A \\mathbf{\\Pi}\_{\\text{ext}} \\cdot \\hat{\\mathbf{r}} dA. where $\mathbf{\Pi}_\text{i} = \frac{1}{2} \operatorname{Re} \left[ \mathbf{E}_\text{i}^* \times \mathbf{H}_\text{i} \right]$, $\mathbf{\Pi}_\text{s} = \frac{1}{2} \operatorname{Re} \left[ \mathbf{E}_\text{s}^* \times \mathbf{H}_\text{s} \right]$, and $\mathbf{\Pi}_{\text{ext}} = \frac{1}{2} \operatorname{Re} \left[ \mathbf{E}_s^* \times \mathbf{H}_i + \mathbf{E}_i^* \times \mathbf{H}_s \right]$.
All the field can be decomposed into the series of vector spherical harmonics (VSH). After that, all the integrals can be taken. In the case of a **uniform sphere** of radius $a$, permittivity $\varepsilon$, and permeability $\mu$, the problem has a precise solution. The scattering and extinction coefficients are $Q_\text{sc} = \frac{2}{k^2a^2}\sum_{n=1}^\infty (2n+1)(|a_{n}|^2+|b_{n}|^2)$ $Q_\text{ext} = \frac{2}{k^2a^2}\sum_{n=1}^\infty (2n+1)\Re(a_{n}+b_{n})$ Where $k = n_\text{host} k_0$. These are connected as $\sigma_\text{ext} = \sigma_\text{sc} + \sigma_\text{abs} \qquad \text{or} \qquad Q_\text{ext} = Q_\text{sc} + Q_\text{abs}$
### Dipole approximation for the scattering cross section {#dipole_approximation_for_the_scattering_cross_section}
Let us assume that a particle supports only electric and magnetic dipole modes with polarizabilities $\mathbf{p} = \alpha^e \mathbf{E}$ and $\mathbf{m} = (\mu \mu_0)^{-1}\alpha^m \mathbf{H}$ (here we use the notation of magnetic polarizability in the manner of Bekshaev et al. rather than the notation of Nieto-Vesperinas et al.) expressed through the Mie coefficients as $\alpha^e = 4 \pi \varepsilon_0 \cdot i \frac{3 \varepsilon}{2 k^3} a_1, \qquad \alpha^m = 4 \pi \mu_0 \cdot i \frac{3 \mu}{2 k^3} b_1.$ Then the cross sections are given by $\sigma_{\text{ext}} = \sigma_{\text{ext}}^{\text{(e)}} + \sigma_{\text{ext}}^{\text{(m)}} =
\frac{1}{4\pi \varepsilon \varepsilon_0} \cdot 4\pi k \Im(\alpha^e) +
\frac{1}{4\pi \mu \mu_0} \cdot 4\pi k \Im(\alpha^m)$ $\sigma_{\text{sc}} = \sigma_{\text{sc}}^{\text{(e)}} + \sigma_{\text{sc}}^{\text{(m)}} =
\frac{1}{(4\pi \varepsilon \varepsilon_0)^2} \cdot \frac{8\pi}{3} k^4 |\alpha^e|^2 +
\frac{1}{(4\pi \mu \mu_0)^2} \cdot \frac{8\pi}{3} k^4 |\alpha^m|^2$ and, finally, the electric and magnetic absorption cross sections $\sigma_{\text{abs}} = \sigma_{\text{abs}}^{\text{(e)}} + \sigma_{\text{abs}}^{\text{(m)}}$ are $\sigma_{\text{abs}}^{\text{(e)}} = \frac{1}{4 \pi \varepsilon \varepsilon_0} \cdot 4\pi k \left[ \Im(\alpha^e) - \frac{k^3}{6 \pi \varepsilon \varepsilon_0} |\alpha^e|^2\right]$ and $\sigma_{\text{abs}}^{\text{(m)}} = \frac{1}{4 \pi \mu \mu_0} \cdot 4\pi k \left[ \Im(\alpha^m) - \frac{k^3}{6 \pi \mu \mu_0} |\alpha^m|^2\right]$
For the case of a no-inside-gain particle, i.e. no energy is emitted by the particle internally ($\sigma_{\text{abs}} > 0$), we have a particular case of the Optical theorem $\frac{1}{4\pi \varepsilon \varepsilon_0} \Im(\alpha^e) + \frac{1}{4\pi \mu \mu_0} \Im(\alpha^m) \geq \frac{2 k^3}{3} \left[ \frac{|\alpha^e|^2}{(4\pi \varepsilon \varepsilon_0)^2} + \frac{|\alpha^m|^2}{(4\pi \mu \mu_0)^2} \right]$ Equality occurs for non-absorbing particles, i.e. for $\Im(\varepsilon) = \Im(\mu) = 0$.
### Scattering of light on extended bodies {#scattering_of_light_on_extended_bodies}
In the context of scattering light on extended bodies, the scattering cross section, `{{math|''σ''<sub>sc</sub>}}`{=mediawiki}, describes the likelihood of light being scattered by a macroscopic particle. In general, the scattering cross section is different from the geometrical cross section of a particle, as it depends upon the wavelength of light and the permittivity in addition to the shape and size of the particle. The total amount of scattering in a sparse medium is determined by the product of the scattering cross section and the number of particles present. In terms of area, the *total cross section* (`{{math|''σ''}}`{=mediawiki}) is the sum of the cross sections due to absorption, scattering, and luminescence:
$$\sigma = \sigma_\text{abs} + \sigma_\text{sc} + \sigma_\text{lum}.$$
The total cross section is related to the absorbance of the light intensity through the Beer--Lambert law, which says that absorbance is proportional to concentration: `{{math|''A<sub>λ</sub>'' {{=}}`{=mediawiki} *Clσ*}}, where `{{math|''A<sub>λ</sub>''}}`{=mediawiki} is the absorbance at a given wavelength `{{math|''λ''}}`{=mediawiki}, `{{math|''C''}}`{=mediawiki} is the concentration as a number density, and `{{math|''l''}}`{=mediawiki} is the path length. The extinction or absorbance of the radiation is the logarithm (decadic or, more usually, natural) of the reciprocal of the transmittance `{{mathcal|T}}`{=mediawiki}:
: $A_\lambda = - \log \mathcal{T}.$
#### Relation to physical size {#relation_to_physical_size}
There is no simple relationship between the scattering cross section and the physical size of the particles, as the scattering cross section depends on the wavelength of radiation used. This can be seen when looking at a halo surrounding the Moon on a decently foggy evening: Red light photons experience a larger cross sectional area of water droplets than photons of higher energy. The halo around the Moon thus has a perimeter of red light due to lower energy photons being scattering further from the center of the Moon. Photons from the rest of the visible spectrum are left within the center of the halo and perceived as white light.
### Meteorological range {#meteorological_range}
The scattering cross section is related to the meteorological range `{{math|''L''<sub>V</sub>}}`{=mediawiki}:
: $L_\text{V} = \frac{3.9}{C \sigma_\text{scat}}.$
The quantity `{{math|''Cσ''<sub>scat</sub>}}`{=mediawiki} is sometimes denoted `{{math|''b''<sub>scat</sub>}}`{=mediawiki}, the scattering coefficient per unit length.
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# Cross section (physics)
## Examples
### Elastic collision of two hard spheres {#elastic_collision_of_two_hard_spheres}
The following equations apply to two hard spheres that undergo a perfectly elastic collision. Let `{{math|''R''}}`{=mediawiki} and `{{math|''r''}}`{=mediawiki} denote the radii of the scattering center and scattered sphere, respectively. The differential cross section is
:
\\frac{d\\sigma}{d\\Omega} = \\frac{R\^2}{4}, and the total cross section is
:
\\sigma\_\\text{tot} = \\pi \\left(r + R\\right)\^2. In other words, the total scattering cross section is equal to the area of the circle (with radius `{{math|''r'' + ''R''}}`{=mediawiki}) within which the center of mass of the incoming sphere has to arrive for it to be deflected.
### Rutherford scattering {#rutherford_scattering}
In Rutherford scattering, an incident particle with charge `{{math|''q''}}`{=mediawiki} and energy `{{math|''E''}}`{=mediawiki} scatters off a fixed particle with charge `{{math|''Q''}}`{=mediawiki}. The differential cross section is
:
\\frac{d \\sigma}{d \\Omega} = \\left(\\frac{q \\, Q}{16\\pi\\varepsilon_0 E \\sin\^2(\\theta/2)} \\right)\^2 where $\varepsilon_0$ is the vacuum permittivity. The total cross section is infinite unless a cutoff for small scattering angles $\theta$ is applied. This is due to the long range of the $1/r$ Coulomb potential.
### Scattering from a 2D circular mirror {#scattering_from_a_2d_circular_mirror}
The following example deals with a beam of light scattering off a circle with radius `{{math|''r''}}`{=mediawiki} and a perfectly reflecting boundary. The beam consists of a uniform density of parallel rays, and the beam-circle interaction is modeled within the framework of geometric optics. Because the problem is genuinely two-dimensional, the cross section has unit of length (e.g., metre). Let `{{math|''α''}}`{=mediawiki} be the angle between the light ray and the radius joining the reflection point of the ray with the center point of the mirror. Then the increase of the length element perpendicular to the beam is
: $\mathrm dx = r \cos \alpha \,\mathrm d \alpha.$
The reflection angle of this ray with respect to the incoming ray is `{{math|2''α''}}`{=mediawiki}, and the scattering angle is
: $\theta = \pi - 2 \alpha.$
The differential relationship between incident and reflected intensity `{{math|''I''}}`{=mediawiki} is
: $I \,\mathrm d \sigma = I \,\mathrm dx(x) = I r \cos \alpha \,\mathrm d \alpha = I \frac{r}{2} \sin \left(\frac{\theta}{2}\right) \,\mathrm d \theta = I \frac{\mathrm d \sigma}{\mathrm d \theta} \,\mathrm d \theta.$
The differential cross section is therefore (`{{math|dΩ {{=}}`{=mediawiki} d*θ*}})
: $\frac{\mathrm d \sigma}{\mathrm d \theta} = \frac{r}{2} \sin \left(\frac{\theta}{2}\right).$
Its maximum at `{{math|''θ'' {{=}}`{=mediawiki} π}} corresponds to backward scattering, and its minimum at `{{math|''θ'' {{=}}`{=mediawiki} 0}} corresponds to scattering from the edge of the circle directly forward. This expression confirms the intuitive expectations that the mirror circle acts like a diverging lens. The total cross section is equal to the diameter of the circle:
: $\sigma = \int_0^{2 \pi} \frac{\mathrm d \sigma}{\mathrm d \theta} \,\mathrm d \theta = \int_0^{2 \pi} \frac{r}{2} \sin \left(\frac{\theta}{2}\right) \,\mathrm d \theta = 2 r.$
### Scattering from a 3D spherical mirror {#scattering_from_a_3d_spherical_mirror}
The result from the previous example can be used to solve the analogous problem in three dimensions, i.e., scattering from a perfectly reflecting sphere of radius `{{math|''a''}}`{=mediawiki}.
The plane perpendicular to the incoming light beam can be parameterized by cylindrical coordinates `{{math|''r''}}`{=mediawiki} and `{{math|''φ''}}`{=mediawiki}. In any plane of the incoming and the reflected ray we can write (from the previous example):
: \\begin{align}
r &= a \\sin \\alpha,\\\\ \\mathrm dr &= a \\cos \\alpha \\,\\mathrm d \\alpha, \\end{align} while the impact area element is
: $\mathrm d \sigma = \mathrm d r(r) \times r \,\mathrm d \varphi = \frac{a^2}{2} \sin \left(\frac{\theta}{2}\right) \cos \left(\frac{\theta}{2}\right) \,\mathrm d \theta \,\mathrm d \varphi.$
In spherical coordinates,
: $\mathrm d\Omega = \sin \theta \,\mathrm d \theta \,\mathrm d \varphi.$
Together with the trigonometric identity
: $\sin \theta = 2 \sin \left(\frac{\theta}{2}\right) \cos \left(\frac{\theta}{2}\right),$
we obtain
: $\frac{\mathrm d \sigma}{\mathrm d \Omega} = \frac{a^2}{4}.$
The total cross section is
: $\sigma = \oint_{4 \pi} \frac{\mathrm d \sigma}{\mathrm d \Omega} \,\mathrm d \Omega = \pi a^2
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# Christian mythology
`{{Christianity|expanded=hide}}`{=mediawiki} `{{Mythology}}`{=mediawiki} **Christian mythology** is the body of myths associated with Christianity. The term encompasses a broad variety of legends and narratives, especially those considered sacred narratives. Mythological themes and elements occur throughout Christian literature, including recurring myths such as ascending a mountain, the *axis mundi*, myths of combat, descent into the Underworld, accounts of a dying-and-rising god, a flood myth, stories about the founding of a tribe or city, and myths about great heroes (or saints) of the past, paradises, and self-sacrifice.
Various authors have also used it to refer to other mythological and allegorical elements found in the Bible, such as the story of the Leviathan. The term has been applied to myths and legends from the Middle Ages, such as the story of Saint George and the Dragon, the stories of King Arthur and his Knights of the Round Table, and the legends of the *Parsival*. Multiple commentators have classified John Milton\'s epic poem *Paradise Lost* as a work of Christian mythology. The term has also been applied to modern stories revolving around Christian themes and motifs, such as the writings of C. S. Lewis, J. R. R. Tolkien, Madeleine L\'Engle, and George MacDonald.
Over the centuries, Christianity has divided into many denominations. Not all of these denominations hold the same set of sacred traditional narratives. For example, the books of the Bible accepted by the Roman Catholic Church and the Eastern Orthodox churches include a number of texts and stories (such as those narrated in the Book of Judith and Book of Tobit) that many Protestant denominations do not accept as canonical.
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# Christian mythology
## Attitudes
Christian theologian and professor of New Testament, Rudolf Bultmann wrote that:
> The cosmology of the New Testament is essentially mythical in character. The world is viewed as a three storied structure, with the earth in the center, the heaven above, and the underworld beneath. Heaven is the abode of God and of celestial beings -- the angels. The underworld is hell, the place of torment. Even the earth is more than the scene of natural, everyday events, of the trivial round and common task. It is the scene of the supernatural activity of God and his angels on the one hand, and of Satan and his demons on the other. These supernatural forces intervene in the course of nature and in all that men think and will and do. Miracles are by no means rare. Man is not in control of his own life. Evil spirits may take possession of him. Satan may inspire him with evil thoughts. Alternatively, God may inspire his thought and guide his purposes. He may grant him heavenly visions. He may allow him to hear his word of succor or demand. He may give him the supernatural power of his Spirit. History does not follow a smooth unbroken course; it is set in motion and controlled by these supernatural powers. This æon is held in bondage by Satan, sin, and death (for \"powers\" is precisely what they are), and hastens towards its end. That end will come very soon, and will take the form of a cosmic catastrophe. It will be inaugurated by the \"woes\" of the last time. Then the Judge will come from heaven, the dead will rise, the last judgment will take place, and men will enter into eternal salvation or damnation.
### Myths as traditional or sacred stories {#myths_as_traditional_or_sacred_stories}
In its broadest academic sense, the word *myth* simply means a traditional story. However, many scholars restrict the term \"myth\" to sacred stories. Folklorists often go further, defining myths as \"tales believed as true, usually sacred, set in the distant past or other worlds or parts of the world, and with extra-human, inhuman, or heroic characters\".
In classical Greek, *muthos*, from which the English word *myth* derives, meant \"story, narrative.\" By the time of Christ, *muthos* had started to take on the connotations of \"fable, fiction,\" and early Christian writers often avoided calling a story from canonical scripture a \"myth\". Paul warned Timothy to have nothing to do with \"godless and silly myths\" (*bebēthous kai graōdeis muthous)*. This negative meaning of \"myth\" passed into popular usage. Some modern Christian scholars and writers have attempted to rehabilitate the term \"myth\" outside academia, describing stories in canonical scripture (especially the Christ story) as \"true myth\"; examples include C. S. Lewis and Andrew Greeley. Several modern Christian writers, such as C. S. Lewis, have described elements of Christianity, particularly the story of Christ, as \"myth\" which is also \"true\" (\"true myth\"). Others object to associating Christianity with \"myth\" for a variety of reasons: the association of the term \"myth\" with polytheism, the use of the term \"myth\" to indicate falsehood or non-historicity, and the lack of an agreed-upon definition of \"myth\". As examples of Biblical myths, Every cites the creation account in Genesis 1 and 2 and the story of Eve\'s temptation.
Christian tradition contains many stories that do not come from canonical Christian texts yet still illustrate Christian themes. These non-canonical Christian myths include legends, folktales, and elaborations on canonical Christian mythology. Christian tradition has produced a rich body of legends that were never incorporated into the official scriptures. Legends were a staple of medieval literature. Examples include hagiographies such as the stories of Saint George or Saint Valentine. A case in point is the historical and canonized Brendan of Clonfort, a 6th-century Irish churchman and founder of abbeys. Round his authentic figure was woven a tissue that is arguably legendary rather than historical: the *Navigatio* or \"Journey of Brendan\". The legend discusses mythic events in the sense of supernatural encounters. In this narrative, Brendan and his shipmates encounter sea monsters, a paradisal island and a floating ice island and a rock island inhabited by a holy hermit: literal-minded devotés still seek to identify \"Brendan\'s islands\" in actual geography. This voyage was recreated by Tim Severin, suggesting that whales, icebergs and Rockall were encountered.
Folktales form a major part of non-canonical Christian tradition. Folklorists define folktales (in contrast to \"true\" myths) as stories that are considered purely fictitious by their tellers and that often lack a specific setting in space or time. Christian-themed folktales have circulated widely among peasant populations. One widespread folktale genre is that of the Penitent Sinner (classified as Type 756A, B, C, in the Aarne-Thompson index of tale types); another popular group of folktales describe a clever mortal who outwits the Devil. Not all scholars accept the folkloristic convention of applying the terms \"myth\" and \"folktale\" to different categories of traditional narrative.
Christian tradition produced many popular stories elaborating on canonical scripture. According to an English folk belief, certain herbs gained their current healing power from having been used to heal Christ\'s wounds on Mount Calvary. In this case, a non-canonical story has a connection to a non-narrative form of folklore --- namely, folk medicine. Arthurian legend contains many elaborations upon canonical mythology. For example, Sir Balin discovers the Lance of Longinus, which had pierced the side of Christ. According to a tradition widely attested in early Christian writings, Adam\'s skull lay buried at Calvary; when Christ was crucified, his blood fell over Adam\'s skull, symbolizing humanity\'s redemption from Adam\'s sin.
## Christ
- The Gospel accounts of Jesus Christ, his life and death. Here the narrative is combined by the author with a story of how all Christian theology \"came to be\". For example, the story of Jesus as the \"word\" or \"Logos\" (John 1:1), the Incarnation of the Logos or Son of God as the man Jesus (e.g., Luke 1:35), and Christ\'s atonement for humanity\'s sins (e.g., Matthew 26:28). Important narratives within the Gospel accounts include:
- Christ\'s miraculous conception and birth from the Virgin Mary
- The baptism of Jesus
- Satan\'s temptation of Christ
- The Transfiguration of Jesus
- Parables of Jesus
- The Last Supper
- The death and resurrection of Jesus
- The Ascension
- The Acts of the Apostles -- the story of the Early Christian church, the ministry of the Twelve Apostles and of Paul the Apostle.
- The descent of the Holy Spirit on Jesus\' disciples after the Ascension.
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# Christian mythology
## Eschatology
- The coming of the Antichrist
- The Second Coming
- The resurrection of the dead
- Judgement Day
- The final and total establishment of the Kingdom of God on earth
## Other examples {#other_examples}
Examples of (1) Christian myths not mentioned in canon and (2) literary and traditional elaborations on canonical Christian mythology:
- Versions of Christian mythology used by Gnostic Christianity
- The Valentinian creation myth involving Sophia and the demiurge.
- The Manichaean creation myth.
- The Gnostic accounts of Jesus, some of which present a Docetic view of Jesus; see Gnostic Gospels.
- Literary treatments of Christian canon or theology
- John Milton\'s *Paradise Lost*, which describes Satan\'s rebellion against God and the Fall of Man, and his *Paradise Regained*, which describes Satan\'s temptation of Christ.
- Dante Alighieri\'s *Divine Comedy*, a literary allegory that describes a visit to Hell, Purgatory, and Heaven.
- John Bunyan\'s *Pilgrim\'s Progress*, a Christian spiritual allegory.
- C. S. Lewis\'s *The Pilgrim\'s Regress*, a more modern Christian spiritual allegory.
- According to some interpretations, Aslan\'s role in C. S. Lewis\'s *The Lion, the Witch, and the Wardrobe* allegorically represents Christ\'s death and resurrection (although Lewis denies that the story is a direct allegory; see section on \"Mythopoeia\" above).
- Legends about Christian saints and heroes. Examples include Abgarus of Edessa, John the Dwarf, and Saint George. Legends about saints are commonly called hagiographies. Some such stories are heavily miraculous, such as those found in Jacobus de Voragine\'s *Golden Legend*; others, less so.
- Stories about artifacts such as the Holy Grail, Holy Lance, and Shroud of Turin.
- Names and biographical details supplied for unnamed Biblical characters; see *List of names for the Biblical nameless*
- The legends of King Arthur and Charlemagne as Christian kings, notably the Quest for the Holy Grail.
- Legendary history of the Christian churches, such as the tales from the Crusades or the paladins in medieval romance.
- Legends of the Knights Templar and the Priory of Sion.
- Medieval Christian stories about angels and guardian angels.
- Non-canonical elaborations or amendments to Biblical tales, such as the tales of Salomé, the Three Wise Men, or St. Dismas.
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# Christian mythology
## Connections to other belief systems {#connections_to_other_belief_systems}
### Jewish mythology {#jewish_mythology}
- Cosmogony
- The 7-day creation week narrative (Genesis 1:1---2:3)
- The Eden narrative (Genesis 2:4---3:24)
- Origins
- The Fall of Man: Although the Book of Genesis does not mention original sin, many Christians interpret the Fall as the origin of sin.
- Noah\'s Ark
- The Tower of Babel: the origin and division of nations and languages
- The life of Abraham
- The Exodus of the Hebrews from Egypt
- The Hebrews\' conquest of the Promised Land
- The period of the Hebrew prophets. One example is the apocryphal part of the Book of Daniel (14:1--30; excluded from the Hebrew and Protestant canon) that tells the story of Bel and the dragon.
### Zoroastrianism
Some scholars believe that many elements of Christian mythology, particularly its linear portrayal of time, originated with the Persian religion of Zoroastrianism. Mary Boyce, an authority on Zoroastrianism, writes: `{{blockquote|Zoroaster was thus the first to teach the doctrines of an individual judgment, Heaven and Hell, the future resurrection of the body, the general Last Judgment, and life everlasting for the reunited soul and body. These doctrines were to become familiar articles of faith to much of mankind, through borrowings by Judaism, Christianity and Islam.<ref>Boyce, p. 29</ref>}}`{=mediawiki}
Mircea Eliade believes the Hebrews had a sense of linear time before Zoroastrianism influenced them. However, he argues, \"a number of other \[Jewish\] religious ideas were discovered, revalorized, of systematized in Iran\". These ideas include a dualism between good and evil, belief in a future savior and resurrection, and \"an optimistic eschatology, proclaiming the final triumph of Good\".
The Zoroastrian concepts of Ahriman, Amesha Spentas, Yazatas, and Daevas probably gave rise to the Christian understanding of Satan, archangels, angels, and demons.
### Other connections {#other_connections}
In Buddhist mythology, the demon Mara tries to distract the historical Buddha, Siddhartha Gautama, before he can reach enlightenment. Huston Smith, a professor of philosophy and a writer on comparative religion, notes the similarity between Mara\'s temptation of the Buddha before his ministry and Satan\'s temptation of Christ before his ministry.
In the Book of Revelation, the author sees a vision of a pregnant woman in the sky being pursued by a huge red dragon. The dragon tries to devour her child when she gives birth, but the child is \"caught up to God and his throne\". This appears to be an allegory for the triumph of Christianity: the child presumably represents Christ; the woman may represent God\'s people of the Old and New Testaments (who produced Christ); and the Dragon symbolizes Satan, who opposes Christ. According to Catholic scholars, the images used in this allegory may have been inspired by pagan mythology: `{{blockquote|This corresponds to a widespread myth throughout the ancient world that a goddess pregnant with a savior was pursued by a horrible monster; by miraculous intervention, she bore a son who then killed the monster.<ref>footnote on Revelation 12:1–6 in ''The New American Bible'', St Joseph Edition. The footnote does not specify which pagan myths it means.</ref>}}`{=mediawiki}
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# Christian mythology
## Mythical themes and types {#mythical_themes_and_types}
Academic studies of mythology often define mythology as deeply valued stories that explain a society\'s existence and world order: those narratives of a society\'s creation, the society\'s origins and foundations, their god(s), their original heroes, mankind\'s connection to the \"divine\", and their narratives of eschatology (what happens in the \"after-life\"). This is a very general outline of some of the basic sacred stories with those themes.
### Cosmogonic myths {#cosmogonic_myths}
The Christian texts use the same creation myth as Jewish mythology as written in the Old Testament. According to the Book of Genesis, the world was created out of a darkness and water in seven days. (Unlike a Jew, a Christian might include the miracle of Jesus\' birth as a sort of second cosmogonic event) Canonical Christian scripture incorporates the two Hebrew cosmogonic myths found in Genesis 1:1---2:2 and Genesis 2:4---3:24.
#### Genesis 1:1---2:3 {#genesis_1123}
In the first text on the creation (Genesis 1:1---2:3), the Creator is called *Elohim* (commonly translated simply as \"God\"). He creates the universe over a six-day period, creating a new feature each day: first he creates day and night; then he creates the firmament to separate the \"waters above\" from the \"waters below\"; then he separates the dry land from the water; then he creates plants on the land; then he places the Sun, Moon, and stars in the sky; then he creates swimming and flying animals; then he creates land animals; and finally he creates man and woman together, \"in his own image\". On the seventh day, God rests, providing the rationale for the custom of resting on Sabbath.
#### Genesis 2:4---3:24 {#genesis_24324}
The second creation myth in Genesis differs from the first in a number of important elements. Here the Creator is called *Yahweh elohim* (commonly translated \"Lord God\" or \"LORD God\" (with small caps), although Yahweh is in fact the personal name of the God of Israel and does not literally mean \"Lord\").
This myth begins with the words, \"When the LORD God made the earth and the heavens, and no shrub of the field was yet in the earth, and no plant of the field had yet sprouted, for the LORD God had not sent rain upon the earth ...\" (Genesis 2:4--5 NASB). It then proceeds to describe Yahweh creating a man called Adam out of dust. Yahweh creates the Garden of Eden as a home for Adam, and tells Adam not to eat the fruit of the Tree of Knowledge of Good and Evil in the center of the Garden (next to the Tree of Life).
Yahweh also creates animals, and shows them to man, who names them. Yahweh sees that there is no suitable companion for the man among the beasts, and he subsequently puts Adam to sleep and takes out one of Adam\'s ribs, creating from it a woman whom Adam names Eve.
A talking serpent tempts Eve to eat from the Tree of Knowledge of Good and Evil, and she succumbs, offering the fruit to Adam as well. As a punishment, Yahweh banishes the couple from the Garden and \"placed on the east side of the Garden of Eden the cherubim with a fiery revolving sword to guard the way to the Tree of Life\". The Lord says he must banish humans from the Garden because they have become like him, knowing good and evil (because of eating the forbidden fruit), and now only immortality (which they could get by eating from the Tree of Life) stands between them and godhood:
> \"The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever\" (Genesis 3:22).
Although the text of Genesis does not identify the tempting serpent with Satan, Christian tradition equates the two. This tradition has made its way into non-canonical Christian \"myths\" such as John Milton\'s *Paradise Lost*.
### Ascending the mountain {#ascending_the_mountain}
According to Lorena Laura Stookey, many myths feature sacred mountains as \"the sites of revelations\": \"In myth, the ascent of the holy mountain is a spiritual journey, promising purification, insight, wisdom, or knowledge of the sacred\". As examples of this theme, Stookey includes the revelation of the Ten Commandments on Mount Sinai, Christ\'s ascent of a mountain to deliver his Sermon on the Mount, and Christ\'s ascension into Heaven from the Mount of Olives.
### Axis mundi {#axis_mundi}
Many mythologies involve a \"world center\", which is often the sacred place of creation; this center often takes the form of a tree, mountain, or other upright object, which serves as an *axis mundi* or axle of the world. A number of scholars have connected the Christian story of the crucifixion at Golgotha with this theme of a cosmic center. In his *Creation Myths of the World*, David Leeming argues that, in the Christian story of the crucifixion, the cross serves as \"the *axis mundi*, the center of a new creation\".
According to a tradition preserved in Eastern Christian folklore, Golgotha was the summit of the cosmic mountain at the center of the world and the location where Adam had been both created and buried. According to this tradition, when Christ is crucified, his blood falls on Adam\'s skull, buried at the foot of the cross, and redeems him. George Every discusses the connection between the cosmic center and Golgotha in his book *Christian Mythology*, noting that the image of Adam\'s skull beneath the cross appears in many medieval representations of the crucifixion.
In *Creation Myths of the World*, Leeming suggests that the Garden of Eden may also be considered a world center.
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# Christian mythology
## Mythical themes and types {#mythical_themes_and_types}
### Combat myth {#combat_myth}
Many Near Eastern religions include a story about a battle between a divine being and a dragon or other monster representing chaos---a theme found, for example, in the *Enuma Elish*. A number of scholars call this story the \"combat myth\". A number of scholars have argued that the ancient Israelites incorporated the combat myth into their religious imagery, such as the figures of Leviathan and Rahab, the Song of the Sea, Isaiah 51:9--10\'s description of God\'s deliverance of his people from Babylon, and the portrayals of enemies such as Pharaoh and Nebuchadnezzar. The idea of Satan as God\'s opponent may have developed under the influence of the combat myth. Scholars have also suggested that the Book of Revelation uses combat myth imagery in its descriptions of cosmic conflict.
### Descent to the underworld {#descent_to_the_underworld}
According to David Leeming, writing in *The Oxford Companion to World Mythology*, the harrowing of hell is an example of the motif of the hero\'s descent to the underworld, which is common in many mythologies. According to Christian tradition, Christ descended to hell after his death in order to free the souls there; this event is known as the Harrowing of Hell. This story is narrated in the Gospel of Nicodemus and may be the meaning behind 1 Peter 3:18--22.
### Dying God {#dying_god}
Many myths, particularly from the Near East, feature a God who dies and is resurrected; this figure is sometimes called the \"dying god\". An important study of this figure is James George Frazer\'s *The Golden Bough*, which traces the dying God theme through a large number of myths. The dying God is often associated with fertility. A number of scholars, including Frazer, have suggested that the Christ story is an example of the \"dying God\" theme. In the article \"Dying God\" in *The Oxford Companion to World Mythology*, David Leeming notes that Christ can be seen as bringing fertility, though of a spiritual as opposed to physical kind.
In his 2006 homily for Corpus Christi, Pope Benedict XVI noted the similarity between the Christian story of the resurrection and pagan myths of dead and resurrected gods: \"In these myths, the soul of the human person, in a certain way, reached out toward that God made man, who, humiliated unto death on a cross, in this way opened the door of life to all of us.\"
### Flood myths {#flood_myths}
Many cultures have myths about a flood that cleanses the world in preparation for rebirth. Such stories appear on every inhabited continent on earth. An example is the biblical story of Noah. In *The Oxford Companion to World Mythology*, David Leeming notes that, in the Bible story, as in other flood myths, the flood marks a new beginning and a second chance for creation and humanity.
### Founding myths {#founding_myths}
According to Sandra Frankiel, the records of \"Jesus\' life and death, his acts and words\" provide the \"founding myths\" of Christianity. Frankiel claims that these founding myths are \"structurally equivalent\" to the creation myths in other religions, because they are \"the pivot around which the religion turns to and which it returns\", establishing the \"meaning\" of the religion and the \"essential Christian practices and attitudes\". Tom Cain uses the expression \"founding myths\" more broadly, to encompass such stories as those of the War in Heaven and the fall of man; according to Cain, \"the disastrous consequences of disobedience\" is a pervasive theme in Christian founding myths.
Christian mythology of their society\'s founding would start with Jesus and his many teachings, and include the stories of Christian disciples starting the Christian Church and congregations in the 1st century. This might be considered the stories in the four canonical gospels and the Acts of the Apostles. The heroes of the first Christian society would start with Jesus and those chosen by Jesus, the twelve apostles including Peter, John, James, as well as Paul and Mary (mother of Jesus).
### Hero myths {#hero_myths}
In his influential 1909 work *The Myth of the Birth of the Hero*, Otto Rank argued that the births of many mythical heroes follow a common pattern. Rank includes the story of Christ\'s birth as a representative example of this pattern.
According to Mircea Eliade, one pervasive mythical theme associates heroes with the slaying of dragons, a theme which Eliade traces back to \"the very ancient cosmogonico-heroic myth\" of a battle between a divine hero and a dragon. He cites the Christian legend of Saint George as an example of this theme. An example from the Late Middle Ages comes from Dieudonné de Gozon, third Grand Master of the Knights of Rhodes, famous for slaying the dragon of Malpasso. Eliade writes:
> \"Legend, as was natural, bestowed upon him the attributes of St. George, famed for his victorious fight with the monster. \[\...\] In other words, by the simple fact that he was regarded as a hero, de Gozon was identified with a category, an archetype, which \[\...\] equipped him with a mythical biography from which it was *impossible* to omit combat with a reptilian monster.\"
In the *Oxford Companion to World Mythology*, David Leeming lists Moses, Jesus, and King Arthur as examples of the heroic monomyth, calling the Christ story \"a particularly complete example of the heroic monomyth\". Leeming regards resurrection as a common part of the heroic monomyth, in which the resurrected heroes often become sources of \"material or spiritual food for their people\"; in this connection, Leeming notes that Christians regard Jesus as the \"bread of life\".
In terms of values, Leeming contrasts \"the myth of Jesus\" with the myths of other \"Christian heroes such as St. George, Roland, el Cid, and even King Arthur\"; the later hero myths, Leeming argues, reflect the survival of pre-Christian heroic values---\"values of military dominance and cultural differentiation and hegemony\"---more than the values expressed in the Christ story.
### Paradise
thumb\|upright=1.25\|In illustrations of the Book of Genesis, Pomors often`{{quantify|date=August 2016}}`{=mediawiki} depicted sirins as birds sitting in paradise trees. 1710 Many religious and mythological systems contain myths about a paradise. Many of these myths involve the loss of a paradise that existed at the beginning of the world. Some scholars have seen in the story of the Garden of Eden an instance of this general motif.
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# Christian mythology
## Mythical themes and types {#mythical_themes_and_types}
### Sacrifice
Sacrifice is an element in many religious traditions and often represented in myths. In *The Oxford Companion to World Mythology*, David Leeming lists the story of Abraham and Isaac and the story of Christ\'s death as examples of this theme. Wendy Doniger describes the gospel accounts as a \"meta-myth\" in which Jesus realizes that he is part of a \"new myth \[...\] of a man who is sacrificed in hate\" but \"sees the inner myth, the old myth of origins and acceptance, the myth of a god who sacrifices himself in love\".
### Eucharist
Related to the doctrine of transsubstantiation, the Christian practice of eating the flesh and blood of Jesus Christ during the Eucharist is an instance of theophagy.
### Transference of evil {#transference_of_evil}
The theological concept of Jesus being born to atone for original sin is central to the Christian narrative. According to Christian theology, by Adam disobeying God in the Garden of Eden, humanity acquired an ingrained flaw that keeps humans in a state of moral imperfection, generally called \"original sin\". According to Paul the Apostle, Adam\'s sin brought sin and death to all humanity: \"Through one man, sin entered the world, and through sin, death\" (Romans 5:12).
According to the orthodox Christian view, Jesus saved humanity from final death and damnation by dying for them. Most Christians believe that Christ\'s sacrifice supernaturally reversed death\'s power over humanity, proved when he was resurrected, and abolished the power of sin on humanity. According to Paul, \"if the many died by the trespass of the one man, how much more did God\'s grace and the gift that came by the grace of the one man, Jesus Christ, overflow to the many\" (Romans 5:15). For many Christians, atonement doctrine leads naturally into the eschatological narratives of Christian people rising from the dead and living again, or immediately entering heaven to join Jesus.
#### Atonement in canonical scripture {#atonement_in_canonical_scripture}
Paul\'s theological writings lay out the basic framework of the atonement doctrine in the New Testament. However, Paul\'s letters contain relatively little mythology (narrative). The majority of narratives in the New Testament are in the Gospels and the Book of Revelation.
Although the Gospel stories do not lay out the atonement doctrine as fully as does Paul, they do have the story of the Last Supper, crucifixion, death and resurrection. Atonement is also suggested in the parables of Jesus in his final days. According to Matthew\'s gospel, at the Last Supper, Jesus calls his blood \"the blood of the new covenant, which will be poured out for the forgiveness of many\" (Matthew 26:28). John\'s gospel is especially rich in atonement parables and promises: Jesus speaks of himself as \"the living bread that came down from heaven\"; \"and the bread that I shall give is My flesh, which I shall give for the life of the world\" (John 6:51); \"Truly, truly, I say to you, unless a grain of wheat falls to the ground and dies, it remains alone; but if it dies, it bears much fruit\" (John 12:24).
#### Atonement in non-canonical literature {#atonement_in_non_canonical_literature}
The sacrifice and atonement narrative appears explicitly in many non-canonical writings as well. For instance, in Book 3 of Milton\'s *Paradise Lost*, the Son of God offers to become a man and die, thereby paying mankind\'s debt to God the Father.
The Harrowing of Hell is a non-canonical myth extrapolated from the atonement doctrine. According to this story, Christ descended into the land of the dead after his crucifixion, rescuing the righteous souls that had been cut off from heaven due to the taint of original sin. The story of the harrowing was popular during the Middle Ages. An Old English poem called \"The Harrowing of Hell\" describes Christ breaking into Hell and rescuing the Old Testament patriarchs. (The Harrowing is not the only explanation that Christians have put forth for the fate of the righteous who died before Christ accomplished the atonement.)
In modern literature, atonement continues to be theme. In the first of C. S. Lewis\'s *Narnia* novels, *The Lion, the Witch and the Wardrobe*, a boy named Edmund is condemned to death by a White Witch, and the magical lion-king Aslan offers to die in Edmund\'s place, thereby saving him. Aslan\'s life is sacrificed on an altar, but returns to life again. Aslan\'s self-sacrifice for Edmund is often interpreted as an allegory for the story of Christ\'s sacrifice for humanity; although Lewis denied that the novel is a mere allegory.
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# Christian mythology
## Mythical themes and types {#mythical_themes_and_types}
### Eschatological myths {#eschatological_myths}
Christian eschatological myths include stories of the afterlife: the narratives of Jesus Christ rising from the dead and now acting as a saviour of all generations of Christians, and stories of heaven and hell. Eschatological myths would also include the prophesies of end of the world and a new millennium in the Book of Revelation, and the story that Jesus will return to earth some day.
The major features of Christian eschatological mythology include afterlife beliefs, the Second Coming, the resurrection of the dead, and the final judgment.
#### Immediate afterlife (heaven and hell) {#immediate_afterlife_heaven_and_hell}
Most Christian denominations hold some belief in an immediate afterlife when people die. Christian scripture gives a few descriptions of an immediate afterlife and a heaven and hell; however, for the most part, both New and Old Testaments focus much more on the myth of a final bodily resurrection than any beliefs about a purely spiritual afterlife away from the body.
Much of the Old Testament does not express a belief in a personal afterlife of reward or punishment:
> \"All the dead go down to Sheol, and there they lie in sleep together--whether good or evil, rich or poor, slave or free (Job 3:11--19). It is described as a region \"dark and deep,\" \"the Pit,\" and \"the land of forgetfulness,\" cut off from both God and human life above (Psalms 6:5; 88:3--12). Though in some texts Yahweh\'s power can reach down to Sheol (Psalms 139:8), the dominant idea is that the dead are abandoned forever. This idea of Sheol is negative in contrast to the world of life and light above, but there is no idea of judgment or of reward and punishment.\"
Later Old Testament writings, particularly the works of the Hebrew prophets, describe a final resurrection of the dead, often accompanied by spiritual rewards and punishments:
> \"Many who sleep in the dust of the earth shall awake. Some shall live forever; others shall be in everlasting contempt. But the wise shall shine brightly like the splendor of the firmament, and those who lead the many to justice shall be like the stars forever\" (Daniel 12:2).
However, even here, the emphasis is not on an immediate afterlife in heaven or hell, but rather on a future bodily resurrection.
The New Testament also devotes little attention to an immediate afterlife. Its primary focus is the resurrection of the dead. Some New Testament passages seem to mention the (non-resurrected) dead experiencing some sort of afterlife (for example, the parable of rich man and Lazarus); yet the New Testament includes only a few myths about heaven and hell. Specifically, heaven is a place of peaceful residence, where Jesus goes to \"prepare a home\" or room for his disciples (John 14:2). Drawing on scriptural imagery (John 10:7, John 10:11--14), many Christian narratives of heaven include a nice green pasture land and a meeting with a benevolent God. Some of the earliest Christian art depicts heaven as a green pasture where people are sheep led by Jesus as \"the good shepherd\" as in interpretation of heaven.
As the doctrines of heaven and hell (and also Catholic purgatory) developed, non-canonical Christian literature began to develop an elaborate mythology about these locations. Dante\'s three-part *Divine Comedy* is a prime example of such afterlife mythology, describing Hell (in *Inferno*), Purgatory (in *Purgatorio*), and Heaven (in *Paradiso*). Nowadays, conceptualizations of hell differ quite widely across various denominations.
#### Second Coming {#second_coming}
The Second Coming of Christ holds a central place in Christian mythology. The Second Coming is the return of Christ to Earth during the period of transformation preceding the end of this world and the establishment of the Kingdom of Heaven on Earth. According to Matthew\'s gospel, when Jesus is on trial before the Roman and Jewish authorities, he claims, \"In the future you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven.\" The legend of the Wandering Jew concerns a Jew who taunted Jesus on the way to the Crucifixion and was then cursed to walk the earth until the Second Coming.
#### Resurrection and final judgment {#resurrection_and_final_judgment}
Christian mythology incorporates the Old Testament\'s prophecies of a future resurrection of the dead. Like the Hebrew prophet Daniel (e.g., Daniel 12:2), the Christian Book of Revelation (among other New Testament scriptures) describes the resurrection: \"The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them; and they were judged, every one of them according to their deeds.\" The righteous and/or faithful enjoy bliss in the earthly Kingdom of Heaven, but the evil and/or non-Christian are \"cast into the lake of fire\".
#### The Kingdom of Heaven on Earth {#the_kingdom_of_heaven_on_earth}
Christian eschatological myths feature a total world renovation after the final judgment. According to the Book of Revelation, God \"will wipe every tear from their eyes, and there will be no more death or mourning, wailing or pain, for the old order has passed away\". According to Old and New Testament passages, a time of perfect peace and happiness is coming:
> \"They will beat their swords into plowshares and their spears into pruning hooks. One nation will not raise the sword against another; nor will they train for war again.\"
Certain scriptural passages even suggest that God will abolish the current natural laws in favor of immortality and total peace:
- \"Then the wolf will be a guest of the lamb, and the leopard will lie down with the kid. The calf and the young lion will browse together, with a little child to guide them. \[...\] There will be no harm or ruin on all my holy mountain, for the earth will be filled with knowledge of the LORD as water fills the sea.\"
- \"On this mountain, \[God\] will destroy the veil that veils all peoples, the web that is woven over all nations: he will destroy Death forever.\"
- \"The trumpet will sound, and the dead will be raised imperishable, and we will be changed.\"
- \"Night will be no more, nor will they need light from lamp or sun, for the Lord God shall give them light, and they shall reign forever and ever.\"
#### Millennialism and amillennialism {#millennialism_and_amillennialism}
When Christianity was a new and persecuted religion, many Christians believed the end times were imminent. Scholars debate whether Jesus was an apocalyptic preacher; however, his early followers, \"the group of Jews who accepted him as messiah in the years immediately after his death, understood him in primarily apocalyptic terms\". Prevalent in the early church and especially during periods of persecution, this Christian belief in an imminent end is called \"millennialism\". (It takes its name from the thousand-year (\"millennial\") reign of Christ that, according to the Book of Revelation, will precede the final world renovation; similar beliefs in a coming paradise are found in other religions, and these phenomena are often also called \"millennialism\")
Millennialism comforted Christians during times of persecution, for it predicted an imminent deliverance from suffering. From the perspective of millennialism, human action has little significance: millennialism is comforting precisely because it predicts that happiness is coming no matter what humans do: \"The seeming triumph of Evil made up the apocalyptic syndrome which was to precede Christ\'s return and the millennium.\"
However, as time went on, millennialism lost its appeal. Christ had not returned immediately, as earlier Christians had predicted. Moreover, many Christians no longer needed the comfort that millennialism provided, for they were no longer persecuted: \"With the triumph of the Church, the Kingdom of Heaven was already present on earth, and in a certain sense the old world had already been destroyed.\" (Millennialism has revived during periods of historical stress, and is currently popular among Evangelical Christians.)
In the Roman Church\'s condemnation of millennialism, Eliade sees \"the first manifestation of the doctrine of \[human\] progress\" in Christianity. According to the amillennial view, Christ will indeed come again, ushering in a perfect Kingdom of Heaven on earth, but \"the Kingdom of God is \[already\] present in the world today through the presence of the heavenly reign of Christ, the Bible, the Holy Spirit and Christianity\". Amillennialists do not feel \"the eschatological tension\" that persecution inspires; therefore, they interpret their eschatological myths either figuratively or as descriptions of far-off events rather than imminent ones. Thus, after taking the amillennial position, the Church not only waited for God to renovate the world (as millennialists had) but also believed itself to be improving the world through human action.
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# Christian mythology
## Mythical themes and types {#mythical_themes_and_types}
### Witches
In the early modern period, distinguished Christian theologians developed elaborated witch mythologies which contributed to the intensification of witch hunts. Major works in Christian demonology, such as Malleus Maleficarum, were dedicated to the implementation of Exodus 22:18 of the Old Testament: \"You shall not permit a sorceress to live.\" The concept of witches\' sabbath was well articulated by the 17th century. Theologian Martin Delrio was one of the first to provide a vivid description in his influential *Disquisitiones magicae*:
> There, on most occasions, once a foul, disgusting fire has been lit, an evil spirit sits on a throne as president of the assembly. His appearance is terrifying, almost always that of a male goat or a dog. The witches come forward to worship him in different ways. Sometimes they supplicate him on bended knee; sometimes they stand with their back turned to him. They offer candles made of pitch or a child\'s umbilical cord, and kiss him on the anal orifice as a sign of homage. Sometimes they imitate the sacrifice of the Mass (the greatest of all their crimes), as well as purifying with water and similar Catholic ceremonies. After the feast, each evil spirit takes by the hand the disciple of whom he has charge, and so that they may do everything with the most absurd kind of ritual, each person bends over backwards, joins hands in a circle, and tosses his head as frenzied fanatics do. Then they begin to dance. They sing very obscene songs in his \[Satan\'s\] honour. They behave ridiculously in every way, and in every way contrary to accepted custom. Then their demon-lovers copulate with them in the most repulsive fashion.
### Legend and folklore {#legend_and_folklore}
- Legendary
- Prester John
- Saint George and the Dragon
- Wandering Jew
#### Legendary creatures {#legendary_creatures}
Numerous legendary creatures are attested in Christian mythology. These include the Behemoth, Leviathan, Angels, Demons, Nephilim, Re\'em, Ziz and dragons.
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# Christian mythology
## Attitudes toward time {#attitudes_toward_time}
According to Mircea Eliade, many traditional societies have a cyclic sense of time, periodically reenacting mythical events. Through this reenactment, these societies achieve an \"eternal return\" to the mythical age. According to Eliade, Christianity retains a sense of cyclical time, through the ritual commemoration of Christ\'s life and the imitation of Christ\'s actions; Eliade calls this sense of cyclical time a \"mythical aspect\" of Christianity.
However, Judeo-Christian thought also makes an \"innovation of the first importance\", Eliade says, because it embraces the notion of linear, historical time; in Christianity, \"time is no longer \[only\] the circular Time of the Eternal Return; it has become linear and irreversible Time\". Summarizing Eliade\'s statements on this subject, Eric Rust writes, \"A new religious structure became available. In the Judaeo-Christian religions --- Judaism, Christianity, Islam --- history is taken seriously, and linear time is accepted. \[...\] The Christian myth gives such time a beginning in creation, a center in the Christ-event, and an end in the final consummation.\"
In contrast, the myths of many traditional cultures present a cyclic or static view of time. In these cultures, all the \"\[important\] history is limited to a few events that took place in the mythical times\". In other words, these cultures place events into two categories, the mythical age and the present, between which there is no continuity. Everything in the present is seen as a direct result of the mythical age:
> \"Just as modern man considers himself to be constituted by \[all of\] History, the man of the archaic societies declares that he is the result of \[only\] a certain number of mythical events.\"
Because of this view, Eliade argues, members of many traditional societies see their lives as a constant repetition of mythical events, an \"eternal return\" to the mythical age:
> \"In *imitating* the exemplary acts of a god or of a mythical hero, or simply by recounting their adventures, the man of an archaic society detaches himself from profane time and magically re-enters the Great Time, the sacred time.\"
According to Eliade, Christianity shares in this cyclic sense of time to an extent. \"By the very fact that it is a religion\", he argues, Christianity retains at least one \"mythical aspect\" --- the repetition of mythical events through ritual. Eliade gives a typical church service as an example:
> \"Just as a church constitutes a break in plane in the profane space of a modern city, \[so\] the service celebrated inside \[the church\] marks a break in profane temporal duration. It is no longer today\'s historical time that is present --- the time that is experienced, for example, in the adjacent streets --- but the time in which the historical existence of Jesus Christ occurred, the time sanctified by his preaching, by his passion, death, and resurrection.\"
Heinrich Zimmer also notes Christianity\'s emphasis on linear time; he attributes this emphasis specifically to the influence of Augustine of Hippo\'s theory of history. Zimmer does not explicitly describe the cyclical conception of time as itself \"mythical\" per se, although he notes that this conception \"underl\[ies\] Hindu mythology\".
Neil Forsyth writes that \"what distinguishes both Jewish and Christian religious systems \[...\] is that they elevate to the sacred status of myth narratives that are situated in historical time\".
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# Christian mythology
## Legacy
### Concepts of progress {#concepts_of_progress}
According to Carl Mitcham, \"the Christian mythology of progress toward transcendent salvation\" created the conditions for modern ideas of scientific and technological progress. Hayden White describes \"the myth of Progress\" as the \"secular, Enlightenment counterpart\" of \"Christian myth\". Reinhold Niebuhr described the modern idea of ethical and scientific progress as \"really a rationalized version of the Christian myth of salvation\".
According to Irwin, from the perspective of the Hebrew Bible (Old Testament), \"history is a tale of progress\". Christianity inherited the Hebrew sense of history through the Old Testament. Thus, although most Christians believe that human nature is inherently \"fallen\" (see original sin) and cannot become perfected without divine grace, they do believe that the world can and will change for the better, either through human and divine action or through divine action alone.
### Political and philosophical ideas {#political_and_philosophical_ideas}
According to Mircea Eliade, the medieval \"Gioacchinian myth \[...\] of universal renovation in a more or less imminent future\" has influenced a number of modern theories of history, such as those of Lessing (who explicitly compares his views to those of medieval \"enthusiasts\"), Fichte, Hegel, and Schelling; and has also influenced a number of Russian writers.
Calling Marxism \"a truly messianic Judaeo-Christian ideology\", Eliade writes that Marxism \"takes up and carries on one of the great eschatological myths of the Middle Eastern and Mediterranean world, namely: the redemptive part to be played by the Just (the \'elect\', the \'anointed\', the \'innocent\', the \'missioners\', in our own days the proletariat), whose sufferings are invoked to change the ontological status of the world\".
In his article \"The Christian Mythology of Socialism\", Will Herberg argues that socialism inherits the structure of its ideology from the influence of Christian mythology upon western thought.
In *The Oxford Companion to World Mythology*, David Leeming claims that Judeo-Christian messianic ideas have influenced 20th-century totalitarian systems, citing the state ideology of the Soviet Union as an example.
According to Hugh S. Pyper, the biblical \"founding myths of the Exodus and the exile, read as stories in which a nation is forged by maintaining its ideological and racial purity in the face of an oppressive great power\", entered \"the rhetoric of nationalism throughout European history\", especially in Protestant countries and smaller nations.
### Christmas stories in popular culture {#christmas_stories_in_popular_culture}
Christmas stories have become prevalent in Western literature and culture.
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# Christian mythology
## The Bible {#the_bible}
### Old Testament {#old_testament}
Mythic patterns such as the primordial struggle between good and evil appear in passages throughout the Hebrew Bible, including passages that describe historical events. A distinctive characteristic of the Hebrew Bible is the reinterpretation of myth on the basis of history, as in the Book of Daniel, a record of the experience of the Jews of the Second Temple period under foreign rule, presented as a prophecy of future events and expressed in terms of \"mythic structures\" with \"the Hellenistic kingdom figured as a terrifying monster that cannot but recall \[the Near Eastern pagan myth of\] the dragon of chaos\".
Mircea Eliade argues that the imagery used in some parts of the Hebrew Bible reflects a \"transfiguration of history into myth\". For example, Eliade says, the portrayal of Nebuchadnezzar as a dragon in Jeremiah 51:34 is a case in which the Hebrews \"interpreted contemporary events by means of the very ancient cosmogonico-heroic myth\" of a battle between a hero and a dragon.
According to scholars including Neil Forsyth and John L. McKenzie, the Old Testament incorporates stories, or fragments of stories, from extra-biblical mythology. According to the New American Bible, a Catholic Bible translation produced by the Confraternity of Christian Doctrine, the story of the Nephilim in Genesis 6:1--4 \"is apparently a fragment of an old legend that had borrowed much from ancient mythology\", and the \"sons of God\" mentioned in that passage are \"celestial beings of mythology\". The New American Bible also says that Psalm 93 alludes to \"an ancient myth\" in which God battles a personified Sea. Some scholars have identified the biblical creature Leviathan as a monster from Canaanite mythology. According to Howard Schwartz, \"the myth of the fall of Lucifer\" existed in fragmentary form in Isaiah 14:12 and other ancient Jewish literature; Schwartz claims that the myth originated from \"the ancient Canaanite myth of Athtar, who attempted to rule the throne of Ba\'al, but was forced to descend and rule the underworld instead\".
Some scholars have argued that the calm, orderly, monotheistic creation story in Genesis 1 can be interpreted as a reaction against the creation myths of other Near Eastern cultures. In connection with this interpretation, David and Margaret Leeming describe Genesis 1 as a \"demythologized myth\", and John L. McKenzie asserts that the writer of Genesis 1 has \"excised the mythical elements\" from his creation story.
Perhaps the most famous topic in the Bible that could possibly be connected with mythical origins is the topic of Heaven (or the sky) as the place where God (or angels, or the saints) resides, with stories such as the ascension of Elijah (who disappeared in the sky), war of man with an angel, flying angels. Even in the New Testament Paul the Apostle is said to *have visited the third heaven*, and Jesus was portrayed in several books as going to return from Heaven on a cloud, in the same way he ascended thereto. The official text repeated by the attendees during Roman Catholic mass (the Apostles\' Creed) contains the words \"He ascended into Heaven, and is Seated at the Right Hand of God, The Father. From thence He will come again to judge the living and the dead\".
### New Testament and early Christianity {#new_testament_and_early_christianity}
According to a number of scholars, the Christ story contains mythical themes such as descent to the underworld, the heroic monomyth, and the \"dying god\" (see section above on \"mythical themes and types\").
Some scholars have argued that the Book of Revelation incorporates imagery from ancient mythology. According to the New American Bible, the image in Revelation 12:1--6 of a pregnant woman in the sky, threatened by a dragon, \"corresponds to a widespread myth throughout the ancient world that a goddess pregnant with a savior was pursued by a horrible monster; by miraculous intervention, she bore a son who then killed the monster\". Bernard McGinn suggests that the image of the two Beasts in Revelation stems from a \"mythological background\" involving the figures of Leviathan and Behemoth.
The Pastoral Epistles contain denunciations of \"myths\" (*muthoi*). This may indicate that Rabbinic or Gnostic mythology was popular among the early Christians to whom the epistles were written and that the epistles\' author was attempting to resist that mythology.
The Sibylline oracles contain predictions that the dead Roman Emperor Nero, infamous for his persecutions, would return one day as an Antichrist-like figure. According to Bernard McGinn, these parts of the oracles were probably written by a Christian and incorporated \"mythological language\" in describing Nero\'s return.
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# Christian mythology
## Historical development {#historical_development}
### From Roman Empire to Europe {#from_roman_empire_to_europe}
After Christian theology was accepted by the Roman Empire, promoted by St. Augustine in the 5th century, Christian mythology began to predominate the Roman Empire. Later the theology was carried north by Charlemagne and the Frankish people, and Christian themes began to weave into the framework of European mythologies. The pre-Christian Germanic and Celtic mythology that were native to the tribes of Northern Europe were denounced and submerged, while saint myths, Mary stories, Crusade myths, and other Christian myths took their place. However, pre-Christian myths never went entirely away, they mingled with the (Roman Catholic) Christian framework to form new stories, like myths of the mythological kings and saints and miracles, for example (Eliade 1963:162--181). Stories such as that of Beowulf and Icelandic, Norse, and Germanic sagas were reinterpreted somewhat, and given Christian meanings. The legend of King Arthur and the quest for the Holy Grail is a striking example. The thrust of incorporation took on one of two directions. When Christianity was on the advance, pagan myths were Christianized; when it was in retreat, Bible stories and Christian saints lost their mythological importance to the culture.
### Middle Ages {#middle_ages}
According to Mircea Eliade, the Middle Ages witnessed \"an upwelling of mythical thought\" in which each social group had its own \"mythological traditions\". Often a profession had its own \"origin myth\" which established models for members of the profession to imitate; for example, the knights tried to imitate Lancelot or Parsifal. The medieval trouveres developed a \"mythology of woman and Love\" which incorporated Christian elements but, in some cases, ran contrary to official church teaching.
George Every includes a discussion of medieval legends in his book *Christian Mythology*. Some medieval legends elaborated upon the lives of Christian figures such as Christ, the Virgin Mary, and the saints. For example, a number of legends describe miraculous events surrounding Mary\'s birth and her marriage to Joseph.
In many cases, medieval mythology appears to have inherited elements from myths of pagan gods and heroes. According to Every, one example may be \"the myth of St. George\" and other stories about saints battling dragons, which were \"modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos\". Eliade notes that some \"mythological traditions\" of medieval knights, namely the Arthurian cycle and the Grail theme, combine a veneer of Christianity with traditions regarding the Celtic Otherworld. According to Lorena Laura Stookey, \"many scholars\" see a link between stories in \"Irish-Celtic mythology\" about journeys to the Otherworld in search of a cauldron of rejuvenation and medieval accounts of the quest for the Holy Grail.
According to Eliade, \"eschatological myths\" became prominent during the Middle Ages during \"certain historical movements\". These eschatological myths appeared \"in the Crusades, in the movements of a Tanchelm and an Eudes de l\'Etoile, in the elevation of Fredrick II to the rank of Messiah, and in many other collective messianic, utopian, and prerevolutionary phenomena\". One significant eschatological myth, introduced by Gioacchino da Fiore\'s theology of history, was the \"myth of an imminent third age that will renew and complete history\" in a \"reign of the Holy Spirit\"; this \"Gioacchinian myth\" influenced a number of messianic movements that arose in the late Middle Ages.
### Renaissance and Reformation {#renaissance_and_reformation}
During the Renaissance, there arose a critical attitude that sharply distinguished between apostolic tradition and what George Every calls \"subsidiary mythology\"---popular legends surrounding saints, relics, the cross, etc.---suppressing the latter. The works of Renaissance writers often included and expanded upon Christian and non-Christian stories such as those of creation and the Fall. Rita Oleyar describes these writers as \"on the whole, reverent and faithful to the primal myths, but filled with their own insights into the nature of God, man, and the universe\". An example is John Milton\'s *Paradise Lost*, an \"epic elaboration of the Judeo-Christian mythology\" and also a \"veritable encyclopedia of myths from the Greek and Roman tradition\".
According to Cynthia Stewart, during the Reformation, the Protestant reformers used \"the founding myths of Christianity\" to critique the church of their time.
Every argues that \"the disparagement of myth in our own civilization\" stems partly from objections to perceived idolatry, objections which intensified in the Reformation, both among Protestants and among Catholics reacting against the classical mythology revived during the Renaissance.
### Enlightenment
The philosophes of the Enlightenment used criticism of myth as a vehicle for veiled criticisms of the Bible and the church. According to Bruce Lincoln, the philosophes \"made irrationality the hallmark of myth and constituted philosophy---rather than the Christian *kerygma*---as the antidote for mythic discourse. By implication, Christianity could appear as a more recent, powerful, and dangerous instance of irrational myth\".
Since the end of the 18th century, the biblical stories have lost some of their mythological basis to western society, owing to the scepticism of the Enlightenment, 19th-century freethinking, and 20th century modernism. Most westerners no longer found Christianity to be their primary imaginative and mythological framework by which they understand the world. However other scholars believe mythology is in our psyche, and that mythical influences of Christianity are in many of our ideals, for example the Judeo-Christian idea of an after-life and heaven. The book *Virtual Faith: The Irreverent Spiritual Quest of Generation X* by Tom Beaudoin explores the premise that Christian mythology is present in the mythologies of pop-culture, such as Madonna\'s *Like a Prayer* or Soundgarden\'s *Black Hole Sun.* Modern myths are strong in comic book stories (as stories of culture heroes) and detective novels as myths of good versus evil.
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# Christian mythology
## Historical development {#historical_development}
### Modern period {#modern_period}
Some commentators have categorized a number of modern fantasy works as \"Christian myth\" or \"Christian mythopoeia\". Examples include the fiction of C. S. Lewis, Madeleine L\'Engle, J.R.R. Tolkien, and George MacDonald.
In *The Eternal Adam and the New World Garden*, written in 1968, David W. Noble argued that the Adam figure had been \"the central myth in the American novel since 1830\". As examples, he cites the works of Cooper, Hawthorne, Melville, Twain, Hemingway, and Faulkner
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# Chronicle
A **chronicle** (*chronica*, from Greek *χρονικά* *chroniká*, from *χρόνος*, *chrónos* -- \"time\") is a historical account of events arranged in chronological order, as in a timeline. Typically, equal weight is given for historically important events and local events, the purpose being the recording of events that occurred, seen from the perspective of the **chronicler**. A chronicle which traces world history is a universal chronicle. This is in contrast to a narrative or history, in which an author chooses events to interpret and analyze and excludes those the author does not consider important or relevant.
The information sources for chronicles vary. Some are written from the chronicler\'s direct knowledge, others from witnesses or participants in events, still others are accounts passed down from generation to generation by oral tradition. Some used written material, such as charters, letters, and earlier chronicles. Still others are tales of unknown origin that have mythical status. Copyists also changed chronicles in creative copying, making corrections or in updating or continuing a chronicle with information not available to the original chronicler. Determining the reliability of particular chronicles is important to historians.
Many newspapers and other periodical literature have adopted \"chronicle\" as part of their name.
## Subgroups
Scholars categorize the genre of chronicle into two subgroups: live chronicles, and dead chronicles. A *dead* chronicle is one where the author assembles a list of events up to the time of their writing, but does not record further events as they occur. A *live* chronicle is where one or more authors add to a chronicle in a regular fashion, recording contemporary events shortly after they occur. Because of the immediacy of the information, historians tend to value live chronicles, such as annals, over dead ones.
The term often refers to a book written by a chronicler in the Middle Ages describing historical events in a country, or the lives of a nobleman or a clergyman, although it is also applied to a record of public events. The earliest medieval chronicle to combine both retrospective (*dead*) and contemporary (*live*) entries, is the Chronicle of Ireland, which spans the years 431 to 911.
Chronicles are the predecessors of modern \"time lines\" rather than analytical histories. They represent accounts, in prose or verse, of local or distant events over a considerable period of time, both the lifetime of the individual chronicler and often those of several subsequent continuators. If the chronicles deal with events year by year, they are often called annals. Unlike the modern historian, most chroniclers tended to take their information as they found it, and made little attempt to separate fact from legend. The point of view of most chroniclers is highly localised, to the extent that many anonymous chroniclers can be sited in individual abbeys.
It is impossible to say how many chronicles exist, as the many ambiguities in the definition of the genre make it impossible to draw clear distinctions of what should or should not be included. However, the *Encyclopedia of the Medieval Chronicle* lists some 2,500 items written between 300 and 1500 AD.
## Citation of entries {#citation_of_entries}
Entries in chronicles are often cited using the abbreviation *s.a.*, meaning *sub anno* (under the year), according to the year under which they are listed. For example, \"*ASC* MS A, s.a. 855\" means the entry for the year 855 in manuscript A of the *Anglo-Saxon Chronicle*. The same event may be recorded under a different year in another manuscript of the chronicle, and may be cited for example as \"*ASC* MS D, s.a. 857\".
## English chronicles {#english_chronicles}
The most important English chronicles are the *Anglo-Saxon Chronicle*, started under the patronage of King Alfred in the 9th century and continued until the 12th century, and the *Chronicles of England, Scotland and Ireland* (1577--87) by Raphael Holinshed and other writers; the latter documents were important sources of materials for Elizabethan drama. Later 16th-century Scottish chronicles, written after the Reformation, shape history according to Catholic or Protestant viewpoints.
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# Chronicle
## Cronista
A **cronista** is a term for a historical chronicler, a role that held historical significance in the European Middle Ages. Until the European Enlightenment, the occupation was largely equivalent to that of a historian, describing events chronologically that were of note in a given country or region. As such, it was often an official governmental position rather than an independent practice. The appointment of the official chronicler often favored individuals who had distinguished themselves by their efforts to study, investigate and disseminate population-related issues. The position was granted on a local level based on the mutual agreements of a city council in plenary meetings. Often, the occupation was honorary, unpaid, and stationed for life. In modern usage, the term usually refers to a type of journalist who writes chronicles as a form of journalism or non-professional historical documentation.
### Cronista in the Middle Ages {#cronista_in_the_middle_ages}
Before the development of modern journalism and the systematization of chronicles as a journalistic genre, cronista were tasked with narrating chronological events considered worthy of remembrance that were recorded year by year. Unlike writers who created epic poems regarding living figures, cronista recorded historical events in the lives of individuals in an ostensibly truthful and reality-oriented way.
Even from the time of early Christian historiography, cronistas were clearly expected to place human history in the context of a linear progression, starting with the creation of man until the second coming of Christ, as prophesied in biblical texts.
## Lists of chronicles {#lists_of_chronicles}
- Babylonian Chronicles (loosely-defined set of 25 clay tablets)
- Burmese chronicles
- Cambodian Royal Chronicles (loosely-defined collection)
- List of collections of Crusader sources (most of them chronicles)
- List of Danish chronicles
- List of English chronicles
- List of Hungarian chronicles
- List of Rus\' chronicles
- Muslim chronicles for Indian history
- Chronicles of Nepal
- Serbian chronicles
### Alphabetical list of notable chronicles {#alphabetical_list_of_notable_chronicles}
- *History of Alam Aray Abbasi* -- Safavid dynasty
- *Alamgirnama* -- Mughal Empire
- \'\'Alexandrian World Chronicle - Greek history of the world until 392 AD
- *Altan Tobchi* - Mongol Empire
- *Anglo-Saxon Chronicle* -- England
- *Annales Bertiniani* -- West Francia
- *Annales Cambriae* -- Wales
- *Annales Posonienses* -- Kingdom of Hungary
- *Annales seu cronicae incliti Regni Poloniae* -- Poland
- *Annals of Inisfallen* -- Ireland
- *Annals of Lough Cé* -- Ireland
- *Annals of the Four Masters* -- Ireland
- *Annals of Spring and Autumn* -- China
- *Annals of Thutmose III* -- Ancient Egypt
- *The Annals of the Choson Dynasty* -- Korea
- *Babylonian Chronicles* -- Mesopotamia
- *Anonymous Bulgarian Chronicle* -- Bulgaria
- *Barnwell Chronicle* - England
- *Bodhi Vamsa* -- Sri Lanka
- *Books of Chronicles* attributed to Ezra -- Israel
- *Buranji* -- Ahoms, Assam, India
- *Bychowiec Chronicle* Lithuania
- *Cāmadevivaṃsa* -- Northern Thailand
- *Culavamsa* -- Sri Lanka
- (*Chronica Polonorum*): see *\[\[Gesta principum Polonorum\]\]*
- *Cheitharol Kumbaba* -- Manipur, India
- *Chronica Gentis Scotorum*
- *Chronica Hungarorum* -- History of Hungary
- *Chronica seu originale regum et principum Poloniae* -- Poland
- *Chronicle of 754* - Spain
- *Chronicle (Crònica) by Ramon Muntaner* -- 13th/14th-century Crown of Aragon. Third and longest of the Grand Catalan Chronicles.
- *Chronicle of Finland* (*Chronicon Finlandiae*) by Johannes Messenius -- Finland
- *Chronicle of Fredegar* - France
- *Chronicle of the Slavs* -- Europe
- *Chronicle of Greater Poland* -- Poland
- *Chronicle of Jean de Venette* -- France
- *Chronicle of the Bishops of England* (*De Gestis Pontificum Anglorum*) by William of Malmesbury
- Chronicles of Jerahmeel
- *Chronicle of the Kings of Alba* - Scotland
- *Chronicle of the Kings of England* (*De Gestis Regum Anglorum*) by William of Malmesbury
- *Chronicles of Mann* - Isle of Man
- *Chronicon* of Eusebius
- *Chronicon Scotorum* -- Ireland
- *Chronicon* of Thietmar of Merseburg
- *Chronicon Paschale* - 7th century Greek chronicle of the world
- *Chronicon Pictum* -- History of Hungary
- *Chronographia* -- 11th century History of the Eastern Roman Empire (Byzantium) by Michael Psellos
- *Comentarios Reales de los Incas*
- *Conversion of Kartli* -- Georgia
- Cronaca- Chronicle of Cyprus from the 4th up to the 15th century by Cypriot chronicler Leontios Machairas
- *Cronaca fiorentina* -- Chronicle of Florence up to the end of the 14th Century by Baldassarre Bonaiuti
- *Cronicae et gesta ducum sive principum Polonorum* -- Poland
- *Crónica Mexicayotl* --- History of the Incas
- *Croyland Chronicle* -- England
- *Dawn-Breakers (Nabil\'s Narrative)* -- Baháʼí Faith and Middle East
- *Dioclean Priest\'s Chronicle* -- Europe
- *Dipavamsa* -- Sri Lanka
- *Divan of the Abkhazian Kings* -- Georgia
- *Epic of Sundiata* - West Africa
- *Epitome rerum Hungarorum* -- History of Hungary
- *Eric\'s Chronicle* -- Sweden
- *Eusebius Chronicle* -- Mediterranean and Middle East
- *Fragmentary Annals of Ireland* -- Ireland
- *Froissart\'s Chronicles* -- France and Western Europe
- *Galician-Volhynian Chronicle* -- Ukraine
- *Georgian Chronicles* -- Georgia
- *Gesta Hungarorum* -- History of Hungary
- *Gesta Hunnorum et Hungarorum* -- History of Hungary
- *Gesta Normannorum Ducum* -- Normandy
-
- *Grandes Chroniques de France* -- France
- *General Estoria by Alfonso X* -- c. 1275-1284 Castile, Spain.
- *Henry of Livona Chronicle* -- Eastern Europe
- *Historia Ecclesiastica* -- Norman England
- *Historia Scholastica* by Petrus Comestor - 12th century France
- *The Historie and Chronicles of Scotland*, Robert Lindsay of Pitscottie
- *História da Província Santa Cruz a que vulgarmente chamamos Brasil* -- Brazil
- *History of the Prophets and Kings* -- Middle East and Mediterranean
- *Hustyn Chronicle* -- Eastern Europe
- *Jami\' al-tawarikh* by Rashid-al-Din Hamadani - Universal history
- *Jans der Enikel* -- Europe and Mediterranean
- *Jerome\'s Chronicle* -- Mediterranean and Middle East
- *Jinakalamali* -- Northern Thailand
- *Joannis de Czarnkow chronicon Polonorum* -- Poland
- *Kaiserchronik* -- Central and southern Europe, Germany
- *Kano Chronicle* -- Nigeria
- *Khulasat-ut-Tawarikh* by Sujan Rai - History of India
- *Khwaday-Namag* - History of Persia
- *Kilwa Chronicle* - East Africa
- *Kojiki* - Japan
- *Lethrense Chronicle* -- Denmark
- *Livonian Chronicle of Henry* -- Livonia
- *Livonian Rhymed Chronicle* -- Livonia
- *Libre dels Feyts* -- Book of the Deeds by James I of Aragon, first of the Grand Catalan Chronicles
- *Madala Panji* -- Chronicle of the Jagannath Temple in Puri, India, related to the History of Odisha
- Mainz Anonymous
- *Mahavamsa* -- Sri Lanka
- *Maronite Chronicle* -- The Levant, anonymous annalistic chronicle in the Syriac language completed shortly after 664.
- *Manx Chronicle* -- Isle of Man
- *Nabonidus Chronicle* -- Mesopotamia
- *Nihon Shoki* - Japan
- *Novgorod First Chronicle* -- Novgorod Republic
- *Nuova Cronica* -- Florence
- *Nuremberg Chronicle*
- *Old Tibetan Chronicle* - History of Tibet
- *Parian Chronicle* - Ancient Greece
- *Paschale Chronicle* -- Mediterranean
- *Pictish Chronicle* - Scotland
- *Primary Chronicle* -- Kievan Rus\'
- *Puranas* -- India
- *Rajatarangini* -- Kashmir
- *Roit and Quheil of Tyme* -- Scotland, Adam Abell
- *Roskildense Chronicle* -- Denmark
- *Royal Frankish Annals* -- Frankish Empire
- *Scotichronicon* -- by the Scottish historian Walter Bower
- *Shahnama-yi-Al-i Osman* by Fethullah Arifi Çelebi -- Ottoman empire (1300 ac -- the end of Sultan Suleyman I\'s reign) which is the fifth volume of it Süleymanname
- *Skibby Chronicle* -- Danish Latin chronicle from the 1530s
- Solomon bar Simson Chronicle
- *Swiss illustrated chronicles* -- Switzerland
- *Timbuktu Chronicles* -- Mali
- *Zizhi Tongjian* -- China
### Rhymed chronicles {#rhymed_chronicles}
Rhymed or poetic chronicles, as opposed to prosaic chronicles, include:
- *Rhymed Chronicle of 1682*
- *Rhymed Chronicle of Armenia Minor*
- *Cronache aquilane* (\"Chronicle of L\'Aquila\"), both in prose and verse form
- *Brabantsche Yeesten* (c. 1315--1351) by Jan van Boendale (continued by an anonymous author)
- *Cornicke van Brabant* (1415) by Hennen van Merchtenen
- *Cronijck van Brabant* (c. 1435--1460), anonymous, until 1430
- *Rhymed Chronicle of Brunswick*
- *Rhymed Chronicle of Cologne* by Gottfried Hagen
- *Chronicle of Dalimil*
- *Danish Rhymed Chronicle*
- *Chronicon Egmundanum*
- *Engelbrekt\'s Chronicle*
- *Erik\'s Chronicle*
- *Rhymed Chronicle of Flanders*, part of the Comburg Manuscript. It is unique as all other surviving Dutch-language chronicles of Flanders were written in prose.
- *Die olde Freesche cronike* (1474), anonymous history of Friesland until 1248
- *Rhymed Chronicle of Gandersheim*
- *Rhymed Chronicle of Holland* by Melis Stoke
- *Karl\'s Chronicle*
- *Rhymed Chronicle of Kastl* (*Kastler Reimchronik*)
- , notorious 17th-century forgery pretending to be written in the 12th century
- *Livonian Rhymed Chronicle*
- *Rhymed Chronicle of Mecklenburg* by Ernest of Kirchberg
- *Chronique métrique de Philippe le Bel* or *Chronique rimée* (1316) by Geoffrey of Paris
- *Chronique rimée* (c. 1250) by Philippe Mouskes
- *New Prussian Chronicle* by Wigand of Marburg
- *Roman de Brut* by Wace
- *Spieghel Historiael* by Jacob van Maerlant
- *Sture\'s Chronicle*
- *Styrian Rhymed Chronicle*
- *Rhymed Chronicle of Utrecht* (c
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# Christine Lavin
**Christine Lavin** (born January 2, 1952) is a New York City--based singer-songwriter and promoter of contemporary folk music. She has recorded numerous solo albums, and has also recorded under the name Four Bitchin\' Babes with three bandmates. She is known for her sense of humor, which is expressed in both her music and her onstage performances. Many of her songs alternate between comedy and emotional reflections on romance.
Lavin worked at Caffe Lena in Saratoga Springs, New York, until Dave Van Ronk convinced her to move to New York City and make a career as a singer-songwriter. She followed his advice and accepted his offer of guitar lessons. She was the original host of *Sunday Breakfast* on WFUV in New York City and a founding member of the Four Bitchin\' Babes when they were formed in 1990.
She is a lifelong astrophysics hobbyist and has included those themes in her music
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# Convolution
In mathematics (in particular, functional analysis), **convolution** is a mathematical operation on two functions $f$ and $g$ that produces a third function $f*g$, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term *convolution* refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity). Graphically, it expresses how the \'shape\' of one function is modified by the other.
Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution $f*g$ differs from cross-correlation $f \star g$ only in that either $f(x)$ or $g(x)$ is reflected about the y-axis in convolution; thus it is a cross-correlation of $g(-x)$ and $f(x)$, or $f(-x)$ and $g(x)$. For complex-valued functions, the cross-correlation operator is the adjoint of the convolution operator.
Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations.
The convolution can be defined for functions on Euclidean space and other groups (as algebraic structures). For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 18 at `{{section link|DTFT|Properties}}`{=mediawiki}.) A *discrete convolution* can be defined for functions on the set of integers.
Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.
Computing the inverse of the convolution operation is known as deconvolution.
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# Convolution
## Definition
The convolution of $f$ and $g$ is written $f * g$, denoting the operator with the symbol $*$. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. As such, it is a particular kind of integral transform:
$$(f * g)(t) := \int_{-\infty}^\infty f(\tau) g(t - \tau) \, d\tau.$$
An equivalent definition is (see commutativity):
$$(f * g)(t) := \int_{-\infty}^\infty f(t - \tau) g(\tau)\, d\tau.$$
While the symbol $t$ is used above, it need not represent the time domain. At each $t$, the convolution formula can be described as the area under the function $f(\tau)$ weighted by the function $g(-\tau)$ shifted by the amount $t$. As $t$ changes, the weighting function $g(t-\tau)$ emphasizes different parts of the input function $f(\tau)$; If $t$ is a positive value, then $g(t-\tau)$ is equal to $g(-\tau)$ that slides or is shifted along the $\tau$-axis toward the right (toward $+\infty$) by the amount of $t$, while if $t$ is a negative value, then $g(t-\tau)$ is equal to $g(-\tau)$ that slides or is shifted toward the left (toward $-\infty$) by the amount of $|t|$.
For functions $f$, $g$ supported on only $[0,\infty)$ (i.e., zero for negative arguments), the integration limits can be truncated, resulting in:
$$(f * g)(t) = \int_{0}^{t} f(\tau) g(t - \tau)\, d\tau \quad \ \text{for } f, g : [0, \infty) \to \mathbb{R}.$$
For the multi-dimensional formulation of convolution, see *domain of definition* (below).
### Notation
A common engineering notational convention is:
$$f(t) * g(t) \mathrel{:=} \underbrace{\int_{-\infty}^\infty f(\tau) g(t - \tau)\, d\tau}_{(f * g )(t)},$$
which has to be interpreted carefully to avoid confusion. For instance, $f(t) * g(t-t_0)$ is equivalent to $(f*g)(t-t_0)$, but $f(t-t_0) * g(t-t_0)$ is in fact equivalent to $(f * g)(t-2t_0)$.
### Relations with other transforms {#relations_with_other_transforms}
Given two functions $f(t)$ and $g(t)$ with bilateral Laplace transforms (two-sided Laplace transform)
$$F(s) = \int_{-\infty}^\infty e^{-su} \ f(u) \ \text{d}u$$
and
$$G(s) = \int_{-\infty}^\infty e^{-sv} \ g(v) \ \text{d}v$$
respectively, the convolution operation $(f * g)(t)$ can be defined as the inverse Laplace transform of the product of $F(s)$ and $G(s)$. More precisely,
$$\begin{align}
F(s) \cdot G(s) &= \int_{-\infty}^\infty e^{-su} \ f(u) \ \text{d}u \cdot \int_{-\infty}^\infty e^{-sv} \ g(v) \ \text{d}v \\
&= \int_{-\infty}^\infty \int_{-\infty}^\infty e^{-s(u + v)} \ f(u) \ g(v) \ \text{d}u \ \text{d}v
\end{align}$$
Let $t = u + v$, then
$$\begin{align}
F(s) \cdot G(s) &= \int_{-\infty}^\infty \int_{-\infty}^\infty e^{-st} \ f(u) \ g(t - u) \ \text{d}u \ \text{d}t \\
&= \int_{-\infty}^\infty e^{-st} \underbrace{\int_{-\infty}^\infty f(u) \ g(t - u) \ \text{d}u}_{(f * g)(t)} \ \text{d}t \\
&= \int_{-\infty}^\infty e^{-st} (f * g)(t) \ \text{d}t.
\end{align}$$
Note that $F(s) \cdot G(s)$ is the bilateral Laplace transform of $(f * g)(t)$. A similar derivation can be done using the unilateral Laplace transform (one-sided Laplace transform).
The convolution operation also describes the output (in terms of the input) of an important class of operations known as *linear time-invariant* (LTI). See LTI system theory for a derivation of convolution as the result of LTI constraints. In terms of the Fourier transforms of the input and output of an LTI operation, no new frequency components are created. The existing ones are only modified (amplitude and/or phase). In other words, the output transform is the pointwise product of the input transform with a third transform (known as a transfer function). See Convolution theorem for a derivation of that property of convolution. Conversely, convolution can be derived as the inverse Fourier transform of the pointwise product of two Fourier transforms.
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# Convolution
## Visual explanation {#visual_explanation}
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---+
| {{ordered list | list_style = margin-left:1.6em;\|Express each function in terms of a dummy variable $\tau.$\|Reflect one of the functions: $g(\tau)$ → $g(-\tau).$\|Add an offset of the independent variable, $t$, which allows $g(-\tau)$ to slide along the $\tau$-axis. If `{{mvar|t}}`{=mediawiki} is a positive value, then $g(t-\tau)$ is equal to $g(-\tau)$ that slides or is shifted along the $\tau$-axis toward the right (toward $+\infty$) by the amount of $t$. If $t$ is a negative value, then $g(t-\tau)$ is equal to $g(-\tau)$ that slides or is shifted toward the left (toward $-\infty$) by the amount of $|t|$.\|Start $t$ at $-\infty$ and slide it all the way to $+\infty$. Wherever the two functions intersect, find the integral of their product. In other words, at time $t$, compute the area under the function $f(\tau)$ weighted by the weighting function $g(t - \tau).$ }} | |
| | | |
| | The resulting waveform (not shown here) is the convolution of functions $f$ and $g$. | |
| | | |
| | If $f(t)$ is a unit impulse, the result of this process is simply $g(t)$. Formally: | |
| | | |
| | : $\int_{-\infty}^\infty \delta(\tau) g(t - \tau)\, d\tau = g(t)$ | |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---+
| In this example, the red-colored \"pulse\", $\ g(\tau),$ is an even function $(\ g(-\tau) = g(\tau)\ ),$ so convolution is equivalent to correlation. A snapshot of this \"movie\" shows functions $g(t - \tau)$ and $f(\tau)$ (in blue) for some value of parameter $t,$ which is arbitrarily defined as the distance along the $\tau$ axis from the point $\tau = 0$ to the center of the red pulse. The amount of yellow is the area of the product $f(\tau) \cdot g(t - \tau),$ computed by the convolution/correlation integral. The movie is created by continuously changing $t$ and recomputing the integral. The result (shown in black) is a function of $t,$ but is plotted on the same axis as $\tau,$ for convenience and comparison. | | |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---+
| In this depiction, $f(\tau)$ could represent the response of a resistor-capacitor circuit to a narrow pulse that occurs at $\tau = 0.$ In other words, if $g(\tau) = \delta(\tau),$ the result of convolution is just $f(t).$ But when $g(\tau)$ is the wider pulse (in red), the response is a \"smeared\" version of $f(t).$ It begins at $t = -0.5,$ because we defined $t$ as the distance from the $\tau = 0$ axis to the *center* of the wide pulse (instead of the leading edge). | | |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---+
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# Convolution
## Historical developments {#historical_developments}
One of the earliest uses of the convolution integral appeared in D\'Alembert\'s derivation of Taylor\'s theorem in *Recherches sur différents points importants du système du monde,* published in 1754.
Also, an expression of the type:
$$\int f(u)\cdot g(x - u) \, du$$
is used by Sylvestre François Lacroix on page 505 of his book entitled *Treatise on differences and series*, which is the last of 3 volumes of the encyclopedic series: *Traité du calcul différentiel et du calcul intégral*, Chez Courcier, Paris, 1797--1800. Soon thereafter, convolution operations appear in the works of Pierre Simon Laplace, Jean-Baptiste Joseph Fourier, Siméon Denis Poisson, and others. The term itself did not come into wide use until the 1950s or 1960s. Prior to that it was sometimes known as *Faltung* (which means *folding* in German), *composition product*, *superposition integral*, and *Carson\'s integral*. Yet it appears as early as 1903, though the definition is rather unfamiliar in older uses.
The operation:
$$\int_0^t \varphi(s)\psi(t - s) \, ds,\quad 0 \le t < \infty,$$
is a particular case of composition products considered by the Italian mathematician Vito Volterra in 1913.
## Circular convolution {#circular_convolution}
When a function $g_T$ is periodic, with period $T$, then for functions, $f$, such that $f * g_T$ exists, the convolution is also periodic and identical to:
$$(f * g_T)(t) \equiv \int_{t_0}^{t_0+T} \left[\sum_{k=-\infty}^\infty f(\tau + kT)\right] g_T(t - \tau)\, d\tau,$$
where $t_0$ is an arbitrary choice. The summation is called a periodic summation of the function $f$.
When $g_T$ is a periodic summation of another function, $g$, then $f*g_T$ is known as a *circular* or *cyclic* convolution of $f$ and $g$.
And if the periodic summation above is replaced by $f_T$, the operation is called a *periodic* convolution of $f_T$ and $g_T$.
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# Convolution
## Discrete convolution {#discrete_convolution}
For complex-valued functions $f$ and $g$ defined on the set $\Z$ of integers, the *discrete convolution* of $f$ and $g$ is given by:
$$(f * g)[n] = \sum_{m=-\infty}^\infty f[m] g[n - m],$$
or equivalently (see commutativity) by:
$$(f * g)[n] = \sum_{m=-\infty}^\infty f[n-m] g[m].$$
The convolution of two finite sequences is defined by extending the sequences to finitely supported functions on the set of integers. When the sequences are the coefficients of two polynomials, then the coefficients of the ordinary product of the two polynomials are the convolution of the original two sequences. This is known as the Cauchy product of the coefficients of the sequences.
Thus when `{{mvar|g}}`{=mediawiki} has finite support in the set $\{-M,-M+1,\dots,M-1,M\}$ (representing, for instance, a finite impulse response), a finite summation may be used:
$$(f * g)[n]=\sum_{m=-M}^M f[n-m]g[m].$$
### Circular discrete convolution {#circular_discrete_convolution}
When a function $g_{_N}$ is periodic, with period $N,$ then for functions, $f,$ such that $f*g_{_N}$ exists, the convolution is also periodic and identical to**:**
$$(f * g_{_N})[n] \equiv \sum_{m=0}^{N-1} \left(\sum_{k=-\infty}^\infty {f}[m + kN]\right) g_{_N}[n - m].$$
The summation on $k$ is called a periodic summation of the function $f.$
If $g_{_N}$ is a periodic summation of another function, $g,$ then $f*g_{_N}$ is known as a circular convolution of $f$ and $g.$
When the non-zero durations of both $f$ and $g$ are limited to the interval $[0,N-1],$ $f*g_{_N}$ reduces to these common forms**:**
The notation $f *_N g$ for *cyclic convolution* denotes convolution over the cyclic group of integers modulo `{{math|''N''}}`{=mediawiki}.
Circular convolution arises most often in the context of fast convolution with a fast Fourier transform (FFT) algorithm.
### Fast convolution algorithms {#fast_convolution_algorithms}
In many situations, discrete convolutions can be converted to circular convolutions so that fast transforms with a convolution property can be used to implement the computation. For example, convolution of digit sequences is the kernel operation in multiplication of multi-digit numbers, which can therefore be efficiently implemented with transform techniques (`{{harvnb|Knuth|1997|loc=§4.3.3.C}}`{=mediawiki}; `{{harvnb|von zur Gathen|Gerhard|2003|loc=§8.2}}`{=mediawiki}).
requires `{{mvar|N}}`{=mediawiki} arithmetic operations per output value and `{{math|''N''<sup>2</sup>}}`{=mediawiki} operations for `{{mvar|N}}`{=mediawiki} outputs. That can be significantly reduced with any of several fast algorithms. Digital signal processing and other applications typically use fast convolution algorithms to reduce the cost of the convolution to O(`{{mvar|N}}`{=mediawiki} log `{{mvar|N}}`{=mediawiki}) complexity.
The most common fast convolution algorithms use fast Fourier transform (FFT) algorithms via the circular convolution theorem. Specifically, the circular convolution of two finite-length sequences is found by taking an FFT of each sequence, multiplying pointwise, and then performing an inverse FFT. Convolutions of the type defined above are then efficiently implemented using that technique in conjunction with zero-extension and/or discarding portions of the output. Other fast convolution algorithms, such as the Schönhage--Strassen algorithm or the Mersenne transform, use fast Fourier transforms in other rings. The Winograd method is used as an alternative to the FFT. It significantly speeds up 1D, 2D, and 3D convolution.
If one sequence is much longer than the other, zero-extension of the shorter sequence and fast circular convolution is not the most computationally efficient method available. Instead, decomposing the longer sequence into blocks and convolving each block allows for faster algorithms such as the overlap--save method and overlap--add method. A hybrid convolution method that combines block and FIR algorithms allows for a zero input-output latency that is useful for real-time convolution computations.
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