Editing Infinite monkey theorem (section)

==Applications and criticisms==

===Evolution===
[[Image:Thomas Henry Huxley - Project Gutenberg eText 16935.jpg|thumb|upright|[[Thomas Huxley]] is sometimes misattributed with proposing a variant of the theory in his debates with [[Samuel Wilberforce]].]]
In his 1931 book ''The Mysterious Universe'', Eddington's rival [[James Hopwood Jeans|James Jeans]] attributed the monkey parable to a "Huxley", presumably meaning [[Thomas Henry Huxley]]. This attribution is incorrect.<ref name="Padmanabhan2005">{{cite journal |first=Thanu |last=Padmanabhan |title=The dark side of astronomy |journal=Nature |volume=435 |pages=20–21 |year=2005 |doi=10.1038/435020a |issue=7038|bibcode=2005Natur.435...20P |doi-access=free }} {{cite book |author=Platt, Suzy |title=Respectfully quoted: a dictionary of quotations |year=1993 |publisher=Barnes & Noble |isbn=0-88029-768-9 |pages=[https://archive.org/details/respectfullyquot00suzy/page/388 388–389] |url-access=registration |url=https://archive.org/details/respectfullyquot00suzy/page/388 }}</ref> Today, it is sometimes further reported that Huxley applied the example in a [[1860 Oxford evolution debate|now-legendary debate]] over [[Charles Darwin]]'s ''[[On the Origin of Species]]'' with the Anglican Bishop of Oxford, Samuel Wilberforce, held at a meeting of the [[British Association for the Advancement of Science]] at Oxford on 30 June 1860. This story suffers not only from a lack of evidence, but the fact that in 1860 the typewriter was [[Typewriter#History|not yet commercially available]].<ref name="Rescher2006">{{Cite book |last=Rescher |first=Nicholas |url=https://books.google.com/books?id=_NSBWYdDDAoC |title=Studies in the Philosophy of Science: A Counterfactual Perspective on Quantum Entanglement |date=2006 |publisher=Ontos Verlag |isbn=978-3-11-032646-8 |pages=103 |language=en}}</ref>

Despite the original mix-up, monkey-and-typewriter arguments are now common in arguments over evolution. As an example of [[Christian apologetics]] Doug Powell argued that even if a monkey accidentally types the letters of ''Hamlet'', it has failed to produce ''Hamlet'' because it lacked the intention to communicate. His parallel implication is that natural laws could not produce the information content in [[DNA]].<ref name="Powell2006">{{cite book |last=Powell |first=Doug |title=Holman Quicksource Guide to Christian Apologetics |year=2006 |publisher=Broadman & Holman | isbn = 0-8054-9460-X |pages=60, 63}}</ref> A more common argument is represented by Reverend [[John F. MacArthur]], who claimed that the genetic mutations necessary to produce a tapeworm from an amoeba are as unlikely as a monkey typing Hamlet's soliloquy, and hence the odds against the evolution of all life are impossible to overcome.<ref name="MacArthur2003">{{cite book |first=John |last=MacArthur |title=Think Biblically!: Recovering a Christian Worldview |year=2003 |publisher=Crossway Books |isbn=1-58134-412-0 |pages=78–79}}</ref>

[[Evolutionary biology|Evolutionary biologist]] [[Richard Dawkins]] employs the typing monkey concept in his book ''[[The Blind Watchmaker]]'' to demonstrate the ability of [[natural selection]] to produce biological [[complexity]] out of random [[mutation]]s. In a simulation experiment Dawkins has his [[weasel program]] produce the Hamlet phrase ''METHINKS IT IS LIKE A WEASEL'', starting from a randomly typed parent, by "breeding" subsequent generations and always choosing the closest match from progeny that are copies of the parent with random mutations. The chance of the target phrase appearing in a single step is extremely small, yet Dawkins showed that it could be produced rapidly (in about 40 generations) using cumulative selection of phrases.  The random choices furnish raw material, while cumulative selection imparts information.  As Dawkins acknowledges, however, the weasel program is an imperfect analogy for evolution, as "offspring" phrases were selected "according to the criterion of resemblance to a ''distant ideal'' target."  In contrast, Dawkins affirms, evolution has no long-term plans and does not progress toward some distant goal (such as humans).  The weasel program is instead meant to illustrate the difference between [[non-random]] cumulative selection, and [[random]] single-step selection.<ref name="Dawkins1996">{{cite book |last=Dawkins |first=Richard |year=1996 |title=The Blind Watchmaker |publisher=W.W. Norton & Co. |isbn=0-393-31570-3 |pages=[https://archive.org/details/blindwatchmaker0000dawk/page/46 46–50] |url=https://archive.org/details/blindwatchmaker0000dawk/page/46 }}</ref>  In terms of the typing monkey analogy, this means that ''Romeo and Juliet'' could be produced relatively quickly if placed under the constraints of a nonrandom, Darwinian-type selection because the [[fitness function]] will tend to preserve in place any letters that happen to match the target text, improving each successive generation of typing monkeys.

A different avenue for exploring the analogy between evolution and an unconstrained monkey lies in the problem that the monkey types only one letter at a time, independently of the other letters. Hugh Petrie argues that a more sophisticated setup is required, in his case not for biological evolution but the evolution of ideas:

{{blockquote|In order to get the proper analogy, we would have to equip the monkey with a more complex typewriter. It would have to include whole Elizabethan sentences and thoughts. It would have to include Elizabethan beliefs about human action patterns and the causes, Elizabethan morality and science, and linguistic patterns for expressing these. It would probably even have to include an account of the sorts of experiences which shaped Shakespeare's belief structure as a particular example of an Elizabethan. Then, perhaps, we might allow the monkey to play with such a typewriter and produce variants, but the impossibility of obtaining a Shakespearean play is no longer obvious. What is varied really does encapsulate a great deal of already-achieved knowledge.<ref name="Blachowicz1998">As quoted in {{cite book |first=James |last=Blachowicz |title=Of Two Minds: Nature of Inquiry |year=1998 |publisher=SUNY Press |isbn=0-7914-3641-1 |page=109}}</ref>}}

[[James W. Valentine]], while admitting that the classic monkey's task is impossible, finds that there is a worthwhile analogy between written English and the [[metazoa]]n genome in this other sense: both have "combinatorial, hierarchical structures" that greatly constrain the immense number of combinations at the alphabet level.<ref name="Valentine2004">{{cite book |first=James |last=Valentine |title=On the Origin of Phyla |year=2004 |publisher=University of Chicago Press |isbn=0-226-84548-6 |pages=77–80}}</ref>

=== Zipf's law ===
[[Zipf's law]] states that the frequency of words is a power law function of its frequency rank:<math display="block">\text{word frequency} \propto \frac{1}{(\text{word rank} + b)^a}</math>where <math>a, b</math> are real numbers. Assuming that a monkey is typing randomly, with fixed and nonzero probability of hitting each letter key or white space, then the text produced by the monkey follows Zipf's law.<ref>{{Cite journal |last1=Conrad |first1=B. |last2=Mitzenmacher |first2=M. |date=July 2004 |title=Power laws for monkeys typing randomly: the case of unequal probabilities |url=https://ieeexplore.ieee.org/document/1306541 |journal=IEEE Transactions on Information Theory |volume=50 |issue=7 |pages=1403–1414 |doi=10.1109/TIT.2004.830752 |s2cid=8913575 |issn=1557-9654}}</ref>

===Literary theory===
[[R. G. Collingwood]] argued in 1938 that art cannot be produced by accident, and wrote as a sarcastic aside to his critics,

{{blockquote|...&nbsp;some ... have denied this proposition, pointing out that if a monkey played with a typewriter ... he would produce ... the complete text of Shakespeare. Any reader who has nothing to do can amuse himself by calculating how long it would take for the probability to be worth betting on. But the interest of the suggestion lies in the revelation of the mental state of a person who can identify the 'works' of Shakespeare with the series of letters printed on the pages of a book&nbsp;...<ref name="Sclafani1975">p.&nbsp;126 of ''The Principles of Art'', as summarized and quoted by {{cite journal |first=Richard J. |last=Sclafani |title=The logical primitiveness of the concept of a work of art |journal=British Journal of Aesthetics |year=1975 |volume=15 |issue=1 |doi=10.1093/bjaesthetics/15.1.14 |page=14}}</ref>}}

[[Nelson Goodman]] took the contrary position, illustrating his point along with Catherine Elgin by the example of Borges' "[[Pierre Menard, Author of the Quixote]]",

{{blockquote|What Menard wrote is simply another inscription of the text. Any of us can do the same, as can printing presses and photocopiers. Indeed, we are told, if infinitely many monkeys ... one would eventually produce a replica of the text. That replica, we maintain, would be as much an instance of the work, ''Don Quixote'', as Cervantes' manuscript, Menard's manuscript, and each copy of the book that ever has been or will be printed.<ref name="John2004">{{cite book |editor1=John, Eileen |editor2=Dominic Lopes |title=The Philosophy of Literature: Contemporary and Classic Readings: An Anthology |year=2004 |publisher=Blackwell |isbn=1-4051-1208-5 |page=96}}</ref>}}

In another writing, Goodman elaborates, "That the monkey may be supposed to have produced his copy randomly makes no difference. It is the same text, and it is open to all the same interpretations.&nbsp;..." [[Gérard Genette]] dismisses Goodman's argument as [[begging the question]].<ref name="Genette1997">{{cite book |first=Gérard |last= Genette |title=The Work of Art: Immanence and Transcendence |url=https://archive.org/details/workofart00gene |url-access=registration |year=1997 |publisher=Cornell UP |isbn=0-8014-8272-0}}</ref>

For [[Jorge J. E. Gracia]], the question of the identity of texts leads to a different question, that of author. If a monkey is capable of typing ''Hamlet'', despite having no intention of meaning and therefore disqualifying itself as an author, then it appears that texts do not require authors. Possible solutions include saying that whoever finds the text and identifies it as ''Hamlet'' is the author; or that Shakespeare is the author, the monkey his agent, and the finder merely a user of the text. These solutions have their own difficulties, in that the text appears to have a meaning separate from the other agents: What if the monkey operates before Shakespeare is born, or if Shakespeare is never born, or if no one ever finds the monkey's typescript?<ref name="Gracia1996">{{cite book |last=Gracia |first=Jorge |title=Texts: Ontological Status, Identity, Author, Audience |year=1996 |publisher=SUNY Press |isbn=0-7914-2901-6 |pages=1–2, 122–125}}</ref>

===Simulated and limited conditions===
In 1979, [[William R. Bennett Jr.]], a profesor of [[physics]] at [[Yale University]], brought fresh attention to the theorem by applying a series of computer programs.  Dr. Bennett simulated varying conditions under which an imaginary monkey, given a keyboard consisting of twenty-eight characters, and typing ten keys per second, might attempt to reproduce the sentence, "To be or not to be, that is the question."  Although his experiments agreed with the overall conclusion that even such a short string of words would require many times the current age of the universe to reproduce, he noted that by modifying the statistical probability of certain letters to match the ordinary patterns of various languages and of Shakespeare in particular, seemingly random strings of words could be made to appear.  But even with several refinements, the English sentence closest to the target phrase remained gibberish: "TO DEA NOW NAT TO BE WILL AND THEM BE DOES DOESORNS CAI AWROUTROULD."<ref>{{cite journal|date=March 6, 1979|author=Boyce Rensberger|title=Computer Says Monkeys Couldn't Write 'Hamlet'—At Least Not So Far|journal=[[The New York Times]]|url=https://www.nytimes.com/1979/03/06/archives/computer-says-monkeys-couldnt-write-hamlet-at-least-not-so-far.html}}</ref>

===Random document generation===
The theorem concerns a [[thought experiment]] which cannot be fully carried out in practice, since it is predicted to require prohibitive amounts of time and resources. Nonetheless, it has inspired efforts in finite random text generation.

One computer program run by Dan Oliver of Scottsdale, Arizona, according to an article in ''[[The New Yorker]]'', came up with a result on 4&nbsp;August 2004: After the group had worked for 42,162,500,000&nbsp;billion billion monkey-years, one of the "monkeys" typed, "<samp>VALENTINE. Cease toIdor:eFLP0FRjWK78aXzVOwm)-‘;8.t</samp>" The first 19&nbsp;letters of this sequence can be found in "The Two Gentlemen of Verona". Other teams have reproduced 18&nbsp;characters from "Timon of Athens", 17 from "Troilus and Cressida", and 16 from "Richard II".<ref name="ja">{{cite magazine |url=http://www.newyorker.com/arts/critics/books/2007/04/09/070409crbo_books_acocella?currentPage=all |last=Acocella |first=Joan |title=The typing life: How writers used to write |magazine=[[The New Yorker]] |date=9 April 2007}} – a review of {{cite book |title=The Iron Whim: A fragmented history of typewriting |publisher=Cornell University Press |year=2007 |first=Darren |last=Wershler-Henry}}</ref>

A website entitled ''The Monkey Shakespeare Simulator'', launched on 1&nbsp;July 2003, contained a [[Java applet]] that simulated a large population of monkeys typing randomly, with the stated intention of seeing how long it takes the virtual monkeys to produce a complete Shakespearean play from beginning to end. For example, it produced this partial line from ''[[Henry IV, Part 2]]'', reporting that it took "2,737,850&nbsp;million billion billion billion monkey-years" to reach 24 matching characters:
:<samp>RUMOUR. Open your ears; 9r"5j5&?OWTY Z0d</samp>

Due to processing power limitations, the program used a probabilistic model (by using a [[random number generator]] or RNG) instead of actually generating random text and comparing it to Shakespeare. When the simulator "detected a match" (that is, the RNG generated a certain value or a value within a certain range), the simulator simulated the match by generating matched text.<ref>{{cite web |url=http://io9.gizmodo.com/5809583/the-story-of-the-monkey-shakespeare-simulator-project |title=The story of the Monkey Shakespeare Simulator Project |last1=Inglis-Arkell |first1=Esther |date=June 9, 2011 |website=io9 |publisher=gizmodo |access-date=24 February 2016}}</ref>

===Testing of random-number generators===
{{main|Diehard tests}}
Questions about the statistics describing how often an ideal monkey is [[expected value|expected]] to type certain strings translate into [[Randomness tests|practical tests for random-number generators]]; these range from the simple to the "quite sophisticated". Computer-science professors [[George Marsaglia]] and [[Arif Zaman]] report that they used to call one such category of tests "overlapping m-[[tuple]] tests" in lectures, since they concern overlapping m-tuples of successive elements in a random sequence. But they found that calling them "monkey tests" helped to motivate the idea with students. They published a report on the class of tests and their results for various RNGs in 1993.<ref name="Marsaglia1993">
{{Cite journal |last1=Marsaglia |first1=George |last2=Zaman |first2=Arif |year=1993 |title=Monkey tests for random number generators |journal=Computers & Mathematics with Applications |publisher=Elsevier, Oxford |volume=26 |issue=9 |pages=1–10 |doi=10.1016/0898-1221(93)90001-C |issn=0898-1221 |doi-access=free}}
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