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Infinite Monkey Theorem

Contributor(s): Ivy Wigmore

The Infinite Monkey Theorem is a proposition that an unlimited number of monkeys, given typewriters and sufficient time, will eventually produce a particular text, such as Hamlet or even the complete works of Shakespeare.

The reasoning behind that supposition is that, given infinite time, random input should produce all possible output.The Infinite Monkey Theorem translates to the idea that any problem can be solved, with the input of sufficient resources and time. That idea has been applied in various contexts, including software development and testing, commodity computing, project management and the SETI (the Search for Extraterrestrial Intelligence) project to support a greater allocation of resources -- often, more specifically, a greater allocation of low-end resources -- to solve a given problem. The theorem is also used to illustrate basic concepts in probability.

In 2002, researchers at Plymouth University in the United Kingdom tested the theorem with six crested macaques in a cage with a computer. The monkeys hit the machine with a rock and urinated on it; when they typed, it was mainly the letter "s." However, it should be noted that neither the number of monkeys nor the time allowed for the experiment were infinite.

In 2011, American programmer Jesse Anderson created a software-based infinite monkey experiment to test the theorem. Anderson used his own computer, working with Amazon Elastic Compute Cloud (Amazon EC2) and Hadoop. The virtual monkeys were a million small programs generating random nine-character sequences. When any sequence matched a string of Shakespearean text, that string was checked off. The project finished the complete works in 1.5 months.

The Million Monkey Project was mostly just for fun, and did not really replicate the theorem's scenario. Nevertheless, Anderson's methods could potentially be applied to real-world problems, such as DNA sequencing

In the early 20th century, Émile Borel, a mathematician, and Sir Arthur Eddington, an astronomer, used the Infinite Monkey Theorem to illustrate timescales implied within statistical mechanics. In popular culture, the theorem has appeared in many works, including Russell Maloney's short story, "Inflexible Logic," Douglas Adam's "Hitchhiker's Guide to the Galaxy" and an episode of the Simpsons.

The IETF's Network Working Group applied the concept in their Infinite Monkey Protocol Suite (RFC 2795), in one of their famous April 1 documents.

This was last updated in October 2013

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