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The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type or create a particular chosen text, such as the complete works of William Shakespeare. In this context, "almost surely" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rather, it is a vivid metaphor for an abstract device that produces a random sequence of letters ad infinitum. The theorem illustrates the perils of reasoning about infinity by imagining a vast but finite number, and vice versa. The probability of a monkey typing a given string of text as long as, say, Hamlet is so infinitesimally tiny that, were the experiment conducted, the chance of it actually occurring during a span of time of the order of the age of the universe is minuscule but not zero.

Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's Metaphysics and Cicero's De natura deorum, through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics. Various Christian apologetics on the one hand, and Richard Dawkins on the other, have argued about the appropriateness of the monkeys as a metaphor for evolution.

Today, popular interest in the typing monkeys is sustained by numerous appearances in literature, television and radio, music, and the Internet. A "Monkey Shakespeare Simulator" website got as far as 24 characters with "RUMOUR. Open your ears; ". In 2003 a humorous experiment was performed with six Sulawesi crested macaques, but their literary contribution was five pages consisting largely of the letter S, besides attacking and defecating on the keyboard. Researchers concluded that the infinite monkey theorem does not apply to real monkeys; despite their entertaining methods, they make poor random number generators, as well as needing to be fed.

Solution

Direct proof

The infinite monkey theorem is straightforward to prove. If two events are statistically independent, meaning neither affects the outcome of the other, then the probability of both happening equals the product of the probabilities of each one happening on its own. For example, if the chance of rain in Sydney on a particular day is 0.3 and the chance of an earthquake in San Francisco on that day is 0.008, the chance of both happening on that same day is 0.3 × 0.008 = 0.0024.

Suppose the typewriter has 50 keys, and the word to be typed is "banana". Typing at random, the chance that the first letter typed is b is 1/50, as is the chance that the second letter typed is a, and so on. These events are independent, so the chance of the first six letters matching banana is

(1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50).

For the same reason, the chance that the next 6 letters match banana is also (1/50), and so on.

From the above, the chance of not typing banana in a given block of 6 letters is 1 − (1/50). Because each block is typed independently, the chance X_n of not typing banana in any of the first n blocks of 6 letters is

${\displaystyle X_{n}=\left(1-{\frac {1}{50^{6}}}\right)^{n}.}$

As n grows, X_n gets smaller. For an n of a million, X_n is 99.99%, but for an n of 10 billion X_n is 53% and for an n of 100 billion it is 0.17%. As n approaches infinity, the probability X_n approaches zero; that is, by making n large enough, X_n can be made as small as one likes.

The same argument shows why at least one of infinitely many monkeys will (almost surely) produce a text as quickly as it would be produced by a perfectly accurate human typist copying it from the original. Of course, the rest of the infinite number of monkeys will produce something else while the human typist will produce only the correct text. In this case X_n = (1 − (1/50)) where X_n represents the probability that none of the first n monkeys types banana correctly on their first try. When we consider 100 billion monkeys, the probability falls to 0.17%, and as the number of monkeys n increases to infinity the value of X_n — the probability of the monkeys failing to reproduce the given text — decreases to zero. This is equivalent to stating that the probability that one or more of an infinite number of monkeys will produce a given text on the first try is 100%, or that it is almost certain they will do so.

Infinite strings

The two statements above can be stated more generally and compactly in terms of strings, which are sequences of characters chosen from some finite alphabet:

• Given an infinite string where each character is chosen uniformly at random, any given finite string almost surely occurs as a substring at some position (and indeed, infinitely many positions).
• Given an infinite sequence of infinite strings, where each character of each string is chosen uniformly at random, any given finite string almost surely occurs as a prefix of one of these strings (and indeed, as a prefix of infinitely many of these strings in the sequence).

Both follow easily from the second Borel-Cantelli lemma. For the second theorem, let E_k be the event that the kth string begins with the given text. Because this has some fixed nonzero probability p of occurring, the E_k are independent, and the below sum diverges,

${\displaystyle \sum _{i=1}^{\infty }P(E_{k})=\sum _{i=1}^{\infty }p=\infty ,}$

the probability that infinitely many of the E_k occur is 1. The first theorem is shown similarly; one can divide the random string into nonoverlapping blocks matching the size of the desired text, and make E_k the event where the kth block equals the desired string.

Probabilities

Ignoring punctuation, spacing, and capitalization, a monkey typing letters uniformly at random has one chance in 26 of correctly typing the first letter of Hamlet. It has one chance in 676 (26 times 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only one chance in 26 = 19,928,148,895,209,409,152,340,197,376, roughly equivalent to the probability of buying 4 lottery tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. Say the text of Hamlet contains 130,000 letters (it is actually more, even stripped of punctuation), then there is a probability of one in 3.4×10 to get the text right at the first trial. The average number of letters that needs to be typed until the text appears is also 3.4×10.

For comparison purposes, there are only about 10 atoms in the observable universe and only 4.3 x 10 seconds have elapsed since the Big Bang. Even if the universe were filled with monkeys typing for all time, their total probability to produce a single instance of Hamlet would still be less than one chance in 10. As Kittel and Kroemer put it, "The probability of Hamlet is therefore zero in any operational sense of an event…", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers." This is from their textbook on thermodynamics, the field whose statistical foundations motivated the first known expositions of typing monkeys.

History

Statistical mechanics

In one of the forms in which probabilists now know this theorem, with its "dactylographic" monkeys, appeared in Émile Borel's 1913 article "Mécanique Statistique et Irréversibilité" (Statistical mechanics and irreversibility)., and in his book "Le Hasard" in 1914. His "monkeys" are not actual monkeys; rather, they were a vivid 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:

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.

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.

Origins and "The Library of Babel"

In a 1939 essay entitled "The Library of Babel", 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 position and ordering. The Greek philosopher compares this to the way that a tragedy and a comedy consist of the same "atoms", i.e., alphabetic characters. Three centuries later, Cicero's De natura deorum (On the Nature of the Gods) argued sarcastically against the atomist worldview:

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 Annals of Ennius. I doubt whether fortune could make a single verse of them.

Borges follows the history of this argument through Blaise Pascal and Jonathan Swift, 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:

Everything would be in its blind volumes. Everything: the detailed history of the future, Aeschylus' The Egyptians, the exact number of times that the waters of the Ganges have reflected the flight of a falcon, the secret and true nature 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 theorem, the unwritten chapters of Edwin Drood, those same chapters translated into the language spoken by the Garamantes, the paradoxes Berkeley invented concerning Time but didn't publish, Urizen's books of iron, the premature epiphanes of Stephen Dedalus, which would be meaningless before a cycle of a thousand years, the Gnostic Gospel of Basilides, the song 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.

Applications

Evolution

In his 1931 book The Mysterious Universe, Eddington's rival James Jeans attributed the monkey parable to a "Huxley", presumably meaning Thomas Henry Huxley. This attribution is incorrect. Today, it is sometimes further reported that Huxley applied the example in a now-legendary debate over Charles Darwin's 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 in June 30, 1860. This story suffers not only from a lack of evidence, but the fact that in 1860 the typewriter itself had yet to emerge. Primates were still a sensitive topic for other reasons, and the Huxley-Wilverforce debate did include byplay about apes: the bishop asked whether Huxley was descended from an ape on his grandmother's or his grandfather's side, and Huxley responded something to the effect that he would rather be descended from an ape than from someone who argued as dishonestly as the bishop.

Despite the original mix-up, monkey-and-typewriter arguments are now common in arguments over evolution. For example, Doug Powell argues as a Christian apologist 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. A more common argument is represented by John MacArthur, who claims 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.

Evolutionary biologist Richard Dawkins employs the typing monkey concept in his 1986 book The Blind Watchmaker to demonstrate the abilities of natural selection in producing biological complexity out of random mutations. In the simulation experiment he describes, Dawkins has his Weasel program produce the Hamlet phrase METHINKS IT IS LIKE A WEASEL by typing random phrases but constantly freezing those parts of the output which already match the goal. The point is that random string generation merely serves to furnish raw materials, while selection imparts the information.

A different avenue for rejecting 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:

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.

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 metazoan genome in this other sense: both have "combinatorial, hierarchical structures" that greatly constrain the immense number of combinations at the alphabet level.

Literary theory

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

…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…

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

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.

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…." Gérard Genette dismisses Goodman's argument as begging the question.

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?

Random number 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 August 4, 2004: After the group had worked for 42,162,500,000 billion billion years, one of the "monkeys" typed, “VALENTINE. Cease toIdor:eFLP0FRjWK78aXzVOwm)-‘;8.t . . ." The first 19 letters of this sequence can be found in "The Two Gentlemen of Verona". Other teams have reproduced 18 characters from "Timon of Athens", 17 from "Troilus and Cressida", and 16 from "Richard II".

A website entitled The Monkey Shakespeare Simulator, launched on July 1, 2003, contained a Java applet that simulates 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 million billion billion billion monkey-years" to reach 24 matching characters:

RUMOUR. Open your ears; 9r"5j5&?OWTY Z0d…

Due to processing power limitations, the program uses 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 "detects a match" (that is, the RNG generates a certain value or a value within a certain range), the simulator simulates the match by generating matched text.

Questions about the statistics describing how often an ideal monkey should type certain strings can motivate practical tests for random number generators as well; these range from the simple to the "quite sophisticated". Computer science professors George Marsaglia and Arif Zaman report that they used to call such tests "overlapping m-tuple tests" in lecture, 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.

Real monkeys

Primate behaviorists Cheney and Seyfarth remark that real monkeys would indeed have to rely on chance to have any hope of producing Romeo and Juliet. Unlike apes and particularly chimpanzees, the evidence suggests that monkeys lack a theory of mind and are unable to differentiate between their own and others' knowledge, emotions, and beliefs. Even if a monkey could learn to write a play and describe the characters' behavior, it could not reveal the characters' minds and so build an ironic tragedy.

In 2003, lecturers and students from the University of Plymouth MediaLab Arts course used a £2,000 grant from the Arts Council to study the literary output of real monkeys. They left a computer keyboard in the enclosure of six Sulawesi Crested Macaques in Paignton Zoo in Devon in England for a month, with a radio link to broadcast the results on a website. One researcher, Mike Phillips, defended the expenditure as being cheaper than reality TV and still "very stimulating and fascinating viewing".

Not only did the monkeys produce nothing but five pages consisting largely of the letter S, the lead male began by "bashing the hell out of" the keyboard with a stone, and the monkeys continued by urinating and defecating on it. The zoo's scientific officer remarked that the experiment had "little scientific value, except to show that the 'infinite monkey' theory is flawed". Phillips said that the artist-funded project was primarily performance art, and they had learned "an awful lot" from it. He concluded that monkeys "are not random generators. They're more complex than that. … They were quite interested in the screen, and they saw that when they typed a letter, something happened. There was a level of intention there."

Popular culture

The infinite monkey theorem, or some version thereof, appears in novels, short stories, plays, a radio program, television programs in various genres, graphic novels, stand-up comedy routines, musical works, and the Internet.

Literature

• Jonathan Swift's Gulliver's Travels (1782) anticipates the central idea of the theorem, depicting a professor of the Grand Academy of Lagado who attempts to create a complete list of all knowledge of science by having his students constantly create random strings of letters by turning cranks on a mechanism (Part three, Chapter five): although his intention was more likely to parody Ramon Llull.
• In "Inflexible Logic" by Russell Maloney, a short story that appeared in The New Yorker in 1940, the protagonist felt that his wealth put him under an obligation to support the sciences, and so he tested the theory. His monkeys immediately set to work typing, without error, classics of fiction and nonfiction. The rich man was amused to see unexpurgated versions of Samuel Pepys's diaries, of which he owned only a copy of a bowdlerised edition.
• Jorge Luis Borges' "The Library of Babel" depicts a library which contains books consisting of every single possible permutation of characters. The narrator notes that every great work of literature is contained in the library; but these are outnumbered by the flawed works (which are themselves vastly outnumbered by works of pure gibberish).
• In the one-act play Words, Words, Words by David Ives, three monkeys named Milton, Swift, and Kafka have been confined to a cage by a scientist until they can write Hamlet.
• In a humorous short story "Been a Long, Long Time" by R. A. Lafferty, an angel is punished by having to proofread all the output text until some future time (after trillions of Universes have been created and died) when the monkeys produce a perfect copy of Shakespeare's works.
• In Tom Stoppard's play Rosencrantz & Guildenstern Are Dead, one character says, "If six monkeys..." and then cannot continue, as the characters are actually within Hamlet, one possible topic of this rule. He then finishes the sentence on a different topic.
• Michael Ende's The Neverending Story included a chapter in which some persons play a game with some dice with alphabetic characters carved on the faces. Rules are not clear but supposedly the dice are thrown and the results of them are the words, which are then collected. Sometimes, a coherent word or sentence will be formed and eventually all the stories of the world will appear in this game.
• In J.M. Coetzee's novel Elizabeth Costello Elizabeth Costello's son John thinks: "Sleep, he thinks, that knits up the ravelled sleeve of care. What an extraordinary way of putting it! Not all the monkeys in the world picking away at typewriters all their lives would come up with those words in that arrangement."
• In Jim Cowan's short story "The Spade of Reason", the main character seeks to find meaning in the universe through text randomly generated through various means; the original program he uses to do so is something he dubs the "Motorola Monkey".
• In the Hitchhiker's Guide to the Galaxy, Arthur, while under the effects of the Infinite Improbability Drive, discovers an infinite number of monkeys and tells Ford of their intentions; " want to talk to us about this new script for Hamlet they've worked out."

Television and radio

• In The Simpsons episode Last Exit to Springfield, Montgomery Burns has his own room with 1000 monkeys at typewriters, one of which he chastises for mistyping a word in the opening sentence of A Tale of Two Cities — "It was the best of times, it was the blurst of times? You stupid monkey!"
• On The Daily Show, Jon Stewart promised that none of their material would be plagiarized (after a few stories on the subject) because their show would be written by monkeys. A monkey was then shown typing material for the show; Jon was handed the monkey's latest output, only to reject it.
• In June of 2006, The Colbert Report featured a humorous segment on how many monkeys it would take for various works. This was in response to comments made in the news on monkeys typing out the Bible or the Qur'an. According to Colbert, one million monkeys typing for eternity would produce a Shakespeare, ten thousand (drinking) monkeys typing for ten thousand years would produce a Hemingway, and ten monkeys typing for three days would produce a work of Dan Brown.
• In an episode of The Adventures of Jimmy Neutron, Sheen makes a science project that is very similar: He puts a bug in a glass dome, and places it in front of a hungry lizard on a keyboard. The idea is that the lizard will hit the keys with its feet while trying to get the bug, and will eventually write a great American novel.
• An episode of I Am Weasel features a large room filled with several types of monkeys with typewriters who are working on a novel. When Weasel tries to pay them in bananas, they consider it an insult and quit their job, aside from Baboon.
• In an episode of the daytime soap opera Young and the Restless (broadcast February 2, 2007), when Colleen Carlton copies a scramble of letters obtained from the Grugeon Reliquary onto a dry board, Professor Adrian Korbel jokingly asks if she's testing the Infinite Monkey Theorem.
• In the 5th episode of the first season of The Ricky Gervais Show, a radio compilation put out by xfm, comedian Ricky Gervais to explain this theorem to Karl Pilkington, who refused to believe it possible. In attempting to explain the mathematics behind the theorem, Gervais eventually gives up and storms out of the room when, after a long explication by Gervais and Steve Merchant, Karl says "if they haven't even read Shakespeare, how do they know what they're doin?"
• In a sketch in the comedy show Attention Scum (BBC2 2001) Simon Munnery tackles the million monkey theory, his best line is; "the million monkeys were given a million typewriters... why that would be the internet surely?"
• In an episode of the tv-show Titus Christopher Titus states that "If you let Dave hit at a typewriter eventually he would type the word monkey. In fact, he would only type the word monkey. 'Cause that's his favorite word."
• In the Family Guy episode The King is Dead, Lois questions Peter's creativity, to which he replies, "Oh, art-schmart. Put enough monkeys in a room with a typewriter they'll produce Shakespeare.". The screen then cuts to several monkeys in a room, arguing over which flower is most appropriate in the famous line from Romeo and Juliet.

Comics and graphic novels

• In the comic strip Dilbert, Dogbert tells Dilbert that his poem would take "three monkeys, ten minutes".
• The Animal Man comic by Grant Morrison contained an issue including a monkey who typed not only the works of Shakespeare, but comic books as well. The TPB this is included in featured an "infinite" number of Grant Morrisons typing on the cover.
• In one strip of FoxTrot, Peter mentions the monkey theorem to Paige and tells her Jason wrote a program that generates random letters of the alphabet, adding "if it works for 'Hamlet' why not a 'Hamlet' book report?"

Stand-up comedy

• Comedian Bob Newhart has a stand-up routine in which a lab technician monitoring an "infinitely many monkeys" experiment discovered that one of the monkeys has typed "To be, or not to be; that is the gezortenblatt."
• Ross Noble incorporates the theory into his act, saying that he actually has 100,000 monkeys, but unfortunately only one typewriter.

Internet culture

• "It is said that if you place a million monkeys in front, of a million keyboards, they will eventually produce the works of Shakespeare. This is simply not true. They cannot even produce an encyclopedia." from Daniel Brandt.
• In 2000, the IETF Internet standards committee's April 1st RFC proposed an "Infinite Monkey Protocol Suite (IMPS)", a method of directing a farm of infinitely many monkeys over the Internet.
• WWDN, the blog of author and actor Wil Wheaton, uses the slogan, "50,000 monkeys at 50,000 typewriters can't be wrong." His witticism won him a Bloggie in 2002 for the category "Best Tagline of a Weblog." Ironically,Mr. Weaton's blog was itself shut down for nine months when someone entering a comment typed a random series of letters which just so happened to be a signal used by his blogging software, causing massive server problems.
• Robert Wilensky once jocularly remarked, "We've all heard that a million monkeys banging on a million typewriters will eventually reproduce the entire works of Shakespeare. Now, thanks to the Internet, we know this is not true." In a similar vein, Mad Magazine stated, "If an infinite number of monkeys typed 24-hours a day on an infinite number of computers, the result would be not unlike an AOL Chatroom."
• Goats, a webcomic illustrated by Jonathan Rosenberg, featured a story line named infinite typewriters where several characters accidentally teleport to an alternate dimension. There they find that this dimension is populated by monkeys with typewriters, presumably typing the scripts of many other dimensions.
• In 2006 the Infinite Monkey Project was launched by predictive text company T9. The Europe-wide project sees users, unknown to each other, text a word of their choosing to the Website. The text message is free and as it continues the words are combined to form lyrics. The lyrics are then made into a song by the Hip Hop artist Sparo which will be released as an album. If any of the tracks becomes a hit the people who texted in the words for the lyrics will receive royalties from the project.
• Uncyclopedia often names its article improvement projects '10,000 Monkeys Typing Hamlet'. Its French counterpart "Desencyclopedie" claims to be completely written by an infinite number of monkeys typing on keyboards.
• Online there is a game mocking the theorem called "Mojo the Monkey", in which a monkey types random keys that show up on the screen. When the monkey types an actual word, you highlight it and save it to the website's server and highscore list.

Music

• The 1979 debut album by Leeds punk rock band the Mekons is called The Quality of Mercy is Not Strnen. Originally released on Virgin Records in the United Kingdom, its cover features a photo of a typing chimp (which, of course, is not a monkey at all).
• In 1983, the Windbreakers, a power-pop band from Mississippi, released an EP called Any Monkey With a Typewriter.
• In 1989, the band Negativland sampled Estus Pirkle on their album Helter Stupid saying, "If you get enough monkeys, enough typewriters, and enough bread, one of them will eventually come up with the King James Version of the Bible!!!" while to chants of "We don't have enough data. We just don't have enough data" said by a Japanese secretary.
• In 2007, Robot Goes Here, an electronic rock band on Infidel Records, recorded The Infinite Monkey Theorem featuring a chorus with the lyrics, "Got a pet monkey down in the basement, chained to a typewriter pounding away, churning out copies of the works of Shakespeare; halfway through Hamlet he wrote me this song."

Notes and references

1. This shows that the probability of typing "banana" in one of the predefined non-overlapping blocks of six letters tends to 1. In addition the word may appear across two blocks.
2. Isaac, Richard E. (1995). The Pleasures of Probability. Springer. pp. 48–50. ISBN 038794415X. Isaac generalizes this argument immediately to variable text and alphabet size; the common main conclusion is on p.50.
3. The first theorem is proven by a similar if more indirect route in Gut, Allan (2005). Probability: A Graduate Course. Springer. pp. 97–100. ISBN 0387228330.
4. For any required string of 130,000 letters from the set a-z, the average number of letters that needs to be typed until the string appears is (rounded) 3.4×10, except in the case that all letters of the required string are equal, in which case the value is about 4% more, 3.6×10. In that case failure to have the correct string starting from a particular position reduces with about 4% the probability of a correct string starting from the next position (i.e., for overlapping positions the events of having the correct string are not independent; in this case there is a positive correlation between the two successes, so the chance of success after a failure is smaller than the chance of success in general).
5. ^ Kittel, Charles and Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. p. 53. ISBN 0-7167-1088-9.
6. Émile Borel (1913). "Mécanique Statistique et Irréversibilité". J. Phys. 5e série. 3: 189–196.
7. Arthur Eddington (1928). The Nature of the Physical World: The Gifford Lectures. New York: Macmillan. p. 72. ISBN 0-8414-3885-4.
8. 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). Downloadable text.
9. Borges, Jorge Luis. "La biblioteca total" (The Total Library), Sur No. 59, August 1939. Trans. by Eliot Weinberger. In Selected Non-Fictions (Penguin: 1999), ISBN 0-670-84947-2.
10. Padmanabhan, Thanu (2005). "The dark side of astronomy". Nature. 435: 20–21. Error: Bad DOI specified!. Platt, Suzy; Library of Congress Congressional Research Service (1993). Respectfully quoted: a dictionary of quotations. Barnes & Noble. pp. 388–389. ISBN 0880297689.{{cite book}}: CS1 maint: multiple names: authors list (link)
11. Rescher, Nicholas (2006). Studies in the Philosophy of Science. ontos verlag. p. 103. ISBN 3938793201.
12. Lucas, J. R. (1979). "Wilberforce and Huxley: A Legendary Encounter". The Historical Journal. 22 (2): 313–330. {{cite journal}}: Unknown parameter |month= ignored (help) Also available at , Retrieved on 2007-03-07
13. Powell, Doug (2006). Holman Quicksource Guide to Christian Apologetics. Broadman & Holman. pp. 60, 63. ISBN 080549460X.
14. MacArthur, John (2003). Think Biblically!: Recovering a Christian Worldview. Crossway Books. pp. 78–79. ISBN 1581344120.
15. Dawkins, Richard (1986). The Blind Watchmaker. Oxford UP.
16. As quoted in Blachowicz, James (1998). Of Two Minds: Nature of Inquiry. SUNY Press. p. 109. ISBN 0791436411.
17. Valentine, James (2004). On the Origin of Phyla. University of Chicago Press. pp. 77–80. ISBN 0226845486.
18. p.126 of The Principles of Art, as summarized and quoted by Sclafani, Richard J. (1975). "The logical primitiveness of the concept of a work of art". British Journal of Aesthetics. 15 (1). Error: Bad DOI specified!.
19. John, Eileen and Dominic Lopes, editors (2004). The Philosophy of Literature: Contemporary and Classic Readings: An Anthology. Blackwell. p. 96. ISBN 1-4051-1208-5. {{cite book}}: |author= has generic name (help)CS1 maint: multiple names: authors list (link)
20. Genette, Gérard (1997). The Work of Art: Immanence and Transcendence. Cornell UP. ISBN 0801482720.
21. Gracia, Jorge (1996). Texts: Ontological Status, Identity, Author, Audience. SUNY Press. pp. 1–2, 122–125. ISBN 0-7914-2901-6.
22. Acocella, Joan, "The Typing Life: How writers used to write", The New Yorker, April 9, 2007, a review of The Iron Whim: A Fragmented History of Typewriting (Cornell) 2007, by Darren Wershler-Henry
23. "The Monkey Shakespeare Simulator". Retrieved 2006-06-13. Link inactive as of 2007-02-02.
24. Marsaglia, George and Arif Zaman (1993). "Monkey Tests for Random Number Generators" (PDF). Computers & Mathematics with Applications. 9: 1–10.
25. Cheney, Dorothy L. and Robert M. Seyfarth (1992). How Monkeys See the World: Inside the Mind of Another Species. University of Chicago Press. pp. 253–255. ISBN 0-226-10246-7.
26. ^ "No words to describe monkeys' play". BBC News. 2003-05-09. Retrieved 2007-02-05. {{cite news}}: Check date values in: |date= (help)
27. "Notes Towards the Complete Works of Shakespeare" (PDF). vivaria.net. 2002. Retrieved 2006-06-13.
28. Associated Press (2003-05-09). "Monkeys Don't Write Shakespeare". Wired News. Retrieved 2007-03-02. {{cite news}}: Check date values in: |date= (help)
29. S. Christey (1 April 2000). "RFC 2795: The Infinite Monkey Protocol Suite (IMPS)". Retrieved 2006-06-13.
30. "The articulate monkeys". Computer Music. Retrieved 2006-11-09.
31. "Infinite Monkey Project wants your texts". Pocket-lint. Retrieved 2006-11-09.
32. "The Infinite Monkey Project". Crossfire. Retrieved 2006-11-09.
33. Mojo the Monkey

External links

• Ask Dr. Math article, Aug 1998, Adam Bridge
• The Parable of the Monkeys, a bibliography with quotations

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• Evolution
• Infinity
• Literary theory
• Mathematical theorems
• Monkeys
• Probability theory
• Randomness
• Thought experiments