Editing Infinite monkey theorem (section)

==History==

===Statistical mechanics===
In one of the forms in which probabilists now know this theorem, with its "dactylographic" [i.e., typewriting] monkeys ({{langx|fr|singes dactylographes}}; the French word ''singe'' covers both the monkeys and the apes), appeared in [[Émile Borel]]'s 1913 article "''Mécanique Statique et Irréversibilité''" (''Static mechanics and irreversibility''),<ref name=":0">{{Cite journal |last=Borel |first=Émile |date=1913 |title=La mécanique statique et l'irréversibilité |url=https://hal.science/jpa-00241832 |journal=Journal de Physique Théorique et Appliquée |language=fr |volume=3 |issue=1 |pages=189–196 |doi=10.1051/jphystap:019130030018900 |issn=0368-3893 |quote=Concevons qu'on ait dressé un million de singes à frapper au hasard sur les touches d'une machine à écrire et que […] ces singes dactylographes travaillent avec ardeur dix heures par jour avec un million de machines à écrire de types variés. […] Au bout d'un an, [leurs] volumes se trouveraient renfermer la copie exacte des livres de toute nature et de toutes langues conservés dans les plus riches bibliothèques du monde.}}</ref> and in his book "Le Hasard" in 1914.<ref name="Borel1914">{{cite book |author=Borel |first=Émile |url=https://books.google.com/books?id=Kmm4vgEACAAJ&q=frapper |title=La hasard |publisher=Félix Alcan |year=1914 |location=Paris |page=164 |language=fr-FR }} [https://archive.org/details/lehasard00boreuoft/page/164 Alt URL]</ref> His "monkeys" are not actual monkeys; rather, they are a metaphor for an imaginary way to produce a large, random sequence of letters. Borel said that if a million monkeys typed ten hours a day, it was extremely unlikely that their output would exactly equal all the books of the richest libraries of the world; and yet, in comparison, it was even more unlikely that the laws of statistical mechanics would ever be violated, even briefly.

The physicist [[Arthur Eddington]] drew on Borel's image further in ''The Nature of the Physical World'' (1928), writing:

{{blockquote|If I let my fingers wander idly over the keys of a typewriter it might happen that my screed made an intelligible sentence. If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules returning to one half of the vessel.<ref name="Arthur1928">{{cite book | author=Arthur Eddington | title=The Nature of the Physical World: The Gifford Lectures | url=https://archive.org/details/natureofphysical00eddi | publisher=Macmillan | location=New York | year=1928 | page=[https://archive.org/details/natureofphysical00eddi/page/72 72] | isbn=0-8414-3885-4}}</ref><ref name='Arthur1927'>{{cite web | url = http://www.giffordlectures.org/Browse.asp?PubID=TPNOPW&Volume=0&Issue=0&ArticleID=6 | title = Chapter IV: The Running-Down of the Universe | access-date = 2012-01-22 | last = Eddington | first = Arthur | work = The Nature of the Physical World 1926–1927: The [[Gifford Lectures]] | url-status = dead | archive-url = https://web.archive.org/web/20090308150708/http://www.giffordlectures.org/Browse.asp?PubID=TPNOPW&Volume=0&Issue=0&ArticleID=6 | archive-date = 2009-03-08 }}</ref>}}

These images invite the reader to consider the incredible improbability of a large but finite number of monkeys working for a large but finite amount of time producing a significant work and compare this with the even greater improbability of certain physical events. Any physical process that is even less likely than such monkeys' success is effectively impossible, and it may safely be said that such a process will never happen.<ref name="KK" /> It is clear from the context that Eddington is not suggesting that the probability of this happening is worthy of serious consideration. On the contrary, it was a rhetorical illustration of the fact that below certain levels of probability, the term ''improbable'' is functionally equivalent to ''impossible''.

===Origins and "The Total Library"===
In a 1939 essay entitled "The Total Library", Argentine writer [[Jorge Luis Borges]] traced the infinite-monkey concept back to [[Aristotle]]'s ''Metaphysics.'' Explaining the views of [[Leucippus]], who held that the world arose through the random combination of atoms, Aristotle notes that the atoms themselves are homogeneous and their possible arrangements only differ in shape, position and ordering. In ''[[On Generation and Corruption]]'', the Greek philosopher compares this to the way that a tragedy and a comedy consist of the same "atoms", ''i.e.'', alphabetic characters.<ref>Aristotle, ''Περὶ γενέσεως καὶ φθορᾶς'' (''On Generation and Corruption''), 315b14.</ref> Three centuries later, [[Cicero]]'s ''De natura deorum'' (''On the Nature of the Gods'') argued against the [[Epicureanism#Physics|Epicurean atomist]] worldview:

{{Blockquote|Is it possible for any man to behold these things, and yet imagine that certain solid and individual bodies move by their natural force and gravitation, and that a world so beautifully adorned was made by their fortuitous concourse? He who believes this may as well believe that if a great quantity of the one-and-twenty letters, composed either of gold or any other matter, were thrown upon the ground, they would fall into such order as legibly to form the [[Annales (Ennius)|''Annals'' of Ennius]]. I doubt whether fortune could make a single verse of them.<ref>Marcus Tullius Cicero, ''De natura deorum'', 2.37. Translation from ''Cicero's Tusculan Disputations; Also, Treatises On The Nature Of The Gods, And On The Commonwealth'', C. D. Yonge, principal translator, New York, Harper & Brothers Publishers, Franklin Square. (1877). [https://www.gutenberg.org/ebooks/14988 Downloadable text].</ref>}}

Borges follows the history of this argument through [[Blaise Pascal]] and [[Jonathan Swift]],<ref>The English translation of "The Total Library" lists the title of Swift's essay as "Trivial Essay on the Faculties of the Soul". The appropriate reference is, instead: Swift, Jonathan, Temple Scott et al. "A Tritical Essay upon the Faculties of the Mind." The Prose Works of Jonathan Swift, Volume 1. London: G. Bell, 1897, pp. 291-296. [https://archive.org/details/proseworksjonat01berngoog <!-- quote=The Prose Works of Jonathan Swift. --> Internet Archive]</ref> then observes that in his own time, the vocabulary had changed. By 1939, the idiom was "that a half-dozen monkeys provided with typewriters would, in a few eternities, produce all the books in the British Museum." (To which Borges adds, "Strictly speaking, one immortal monkey would suffice.") Borges then imagines the contents of the Total Library which this enterprise would produce if carried to its fullest extreme:

{{Blockquote|Everything would be in its blind volumes. Everything: the detailed history of the future, [[Aeschylus]]' [[The Suppliants (Aeschylus)|''The Egyptians'']], the exact number of times that the waters of [[the Ganges]] have reflected the flight of a falcon, [[Quintus Valerius Soranus|the secret and true name of Rome]], the encyclopedia [[Novalis]] would have constructed, my dreams and half-dreams at dawn on August 14, 1934, the proof of [[Pierre Fermat]]'s [[Fermat's Last Theorem|theorem]], the unwritten chapters of ''[[Edwin Drood]]'', those same chapters translated into the language spoken by the [[Garamantes]], the paradoxes [[George Berkeley|Berkeley]] invented concerning Time but didn't publish, [[Urizen]]'s books of iron, the premature epiphanies of [[Stephen Dedalus]], which would be meaningless before a cycle of a thousand years, the Gnostic [[Gospel of Basilides]], the song [[siren (mythology)|the sirens]] sang, the complete catalog of the Library, the proof of the inaccuracy of that catalog. Everything: but for every sensible line or accurate fact there would be millions of meaningless cacophonies, verbal farragoes, and babblings. Everything: but all the generations of mankind could pass before the dizzying shelves – shelves that obliterate the day and on which chaos lies – ever reward them with a tolerable page.<ref>{{cite magazine |author-link=Jorge Luis Borges |last=Borges |first=Jorge Luis |title=La biblioteca total |trans-title=The Total Library |magazine=Sur |issue=59 |date=August 1939}} republished in {{cite book |translator-link=Eliot Weinberger |translator-first=Eliot |translator-last=Weinberger |title=Selected Non-Fictions |publisher=Penguin |year=1999 |isbn=0-670-84947-2}}</ref>}}

Borges' total library concept was the main theme of his widely read 1941 short story "[[The Library of Babel]]", which describes an unimaginably vast library consisting of interlocking hexagonal chambers, together containing every possible volume that could be composed from the letters of the alphabet and some punctuation characters.