Infinite monkey theorem
The infinite monkey theorem is a popular misnomer for an idea from Emile Borel's book on probability, published in 1909. The book introduced the concept of "dactylographic monkeys" seated in front of typewriter keyboards and hitting keys at random. Borel exemplified a proposition in the theory of probability called Kolmogorov's zero-one law by saying that the probability is 1 that such a monkey will eventually type every book in France's National Library. Strictly speaking, what Borel was illustrating was only a special case of Kolmogorov's zero-one law, the more general statement of which had not yet been given (Kolmogorov's famous monograph on probability theory was not published until 1933). Subsequent restatements by other people have replaced the National Library with the British Museum and the Library of Congress; a popular retelling says that the monkeys would eventually type Shakespeare's plays.
(The word dactylographic appears in the English translation of Borel's book, and seems to be an Anglicization of a French word for typewriting, but in English, dactylography means the study of fingerprints.)
There need not be infinitely many monkeys; a single monkey who executes infinitely many keystrokes suffices.
The literary notion may have its origin in Jonathan Swift's Gulliver's Travels (1782), part 3, chapter 5, in which a professor of the Grand Academy of Lagado is attempting 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.
It is likely (but certainly not proven) that Emile Borel's use of monkeys and typewriters in his theorem was inspired by an argument used by Thomas Huxley on June 30, 1860. Thomas Huxley held a debate with the Anglican Bishop of Oxford, Samuel Wilberforce held at a meeting of the British Association, Oxford, of which Bishop Wilberforce was a vice-president, and was sparked by the publication of Charles DarwinÃÂÃÂs Origin of Species seven months earlier, in November 1859.
Wilberforce began the debate and, after making several scientific points regarding the plausibility of Darwin's work, concluded with William PaleyÃÂÃÂs argument that a watch implies the existence of a watchmaker, and similarly design in nature implies the existence of a Designer.
Huxley then arose and put forward his now well-known argument that six eternal monkeys or apes typing on six eternal typewriters with unlimited amounts of paper and ink could, given enough time, produce a Psalm, a Shakespearean sonnet, or even a whole book, purely by chance that is, by random striking of the keys.
In the course of his presentation Huxley pretended to find the 23rd Psalm among the reams of written gibberish produced by his six imaginary apes at their typewriters. He went on to make his point that, in the same way, molecular movement, given enough time and matter, could produce Bishop Wilberforce himself, purely by chance and without the work of any Designer or Creator.
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 that theory. (He had heard the British-Museum version.) His monkeys immediately set to work typing classics of fiction and nonfiction. The rich man was amused to see unexpurgated versions of Samuel Pepys' diaries, of which he owned only a copy of a bowdlerized edition.
A similar theme was struck in the story The Library of Babel by Jorge Luis Borges, which contains billions of volumes filled with random strings of characters.
Popular culture references to this theorem include The Simpsons (in one episode, Montgomery Burns has his own room with 1000 dactylographic monkeys, one of which is chastised for mistyping a word in the opening sentence of A Tale of Two Cities) and The Hitchhiker's Guide to the Galaxy (Ford Prefect and Arthur Dent, under the influence of a device that makes highly improbable events occur, are ambushed by an infinite number of monkeys who want their opinion on the monkeys' script for Hamlet). The theorem is also the basis of a one-act play by playwright David Ives called "Words, Words, Words".
Gian-Carlo Rota wrote in a textbook on probability (unfinished when he died):
- "If the monkey could type one keystroke every nanosecond, the expected waiting time until the monkey types out Hamlet is so long that the estimated age of the universe is insignificant by comparison ... this is not a practical method for writing plays. (We cannot resist the temptation to quote from A.N. Whitehead, 'I will not go to infinity'.)"
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2 Pedantic usage note 3 External links |
"The Monkey Shakespeare Simulator" web site, launched on 1 July 2003, contains a Java applet that simulates a large population of monkeys typing randomly, and matches their output against an electronic copy of the plays of Shakespeare, with the stated intention of seeing how long it takes the virtual monkeys to produce a complete Shakespearean play from beginning to end. As of April 2004, matches as long as 15 consecutive letters (or two words) have been recorded. (Note that, since a complete play is the goal, only matches with the opening of each play are checked for; no statistics exist for how often or how well the monkeys' output has matched portions of plays not beginning at the beginning.)Attempts at simulation