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What is the Infinite Monkey Theorum?

Mary McMahon
Updated May 23, 2024
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The infinite monkey theorem is a theorem which suggests that if you put a hypothetical monkey in front of a typewriter for an infinite period of time, the monkey will eventually generate the complete works of William Shakespeare. This theory is often referenced in popular culture, and some mathematicians have even attempted analysis to determine whether or not the theory holds true. According to their calculations, Shakespeare need not fear for his reputation; the probability of such an event is very, very close to zero.

You may hear the infinite monkey theorem stated in a number of ways. For example, people may say that the number of monkeys is infinite, and the period of time is unspecified. Shakespeare may also find himself replaced with other notable authors. The idea is to conjure a laughable scene, with a bunch of simians banging away at typewriters to no apparent cause and actually producing something astounding.

Biologists who specialize in primates have suggested that the infinite monkey theorem has a number of flaws, as the monkey or monkeys involved are just as likely to bash the keyboard with a rock, or urinate on it. Monkeys who have been presented with typewriters and keyboards have generally produced works consisting only of one letter, with a few neighboring letters thrown in for variation, illustrating the fact that monkeys cannot, in fact, type randomly.

If you change the monkey to a random output device, the probability of this event is more likely, although not by much. William Shakespeare is a particularly bad example to use, as his work was extremely prolific, and it is somewhat absurd to suggest that it could be produced entirely at random. However, when you have infinity to work with, anything could happen, and if there's one thing certain about probability, it's that probability can be very unpredictable.

Some people use the infinite monkey theorem in criticisms of evolution, suggesting that the mathematics of probability are not in favor for the development of life on Earth, let alone evolution, and therefore the hand of God must have been involved. You may also hear references to this theory in critical reviews of books, suggesting that a band of monkeys could have done better than a lackluster author.

Language & Humanities is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Mary McMahon
By Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a Language & Humanities researcher and writer. Mary has a liberal arts degree from Goddard College and spends her free time reading, cooking, and exploring the great outdoors.

Discussion Comments
By anon74433 — On Apr 02, 2010

Usually this site is good for answers, but I think this one is off the mark.

When dealing with infinity, the question is not if, but when?

Now the when depends on whether there are an infinite number of monkeys, or the monkeys are there for an infinite time period.

If it's the first (an infinite) then not only will there be one monkey who does it, there will be an infinite number of monkeys who do it!

If it is an infinite time period, then because of the rarity, it will take a very long time -- probably longer than the Universe will exist, but it will still happen, and over the course of an infinite years, it will happen an infinite number of times.

no matter how rare it is, infinity / any number = infinity.

By anon59984 — On Jan 11, 2010

Who's to say there aren't other factors involved? For every sheet of paper produced by Random T Monkey, there may be another monkey who looks at it and realized that it could be a way to convey information.

There may be another monkey (or ape, as we're aware that apes are capable of logic and self-realization) who provides feedback to the typist.

In this situation, the acts of typing, reading, and feedback enable the evolution of typing, in the scope of what might be useful to the monkeys or apes. What they produce after some appreciable amount of literary evolution might not exactly look like our language, but they may eventually produce something with the monkey/ape equivalent of an ageless, beautiful, and touching epic novel.

Imagine that, in our own lifetime, we were given typewriters, rather than slowly figured out on our own how to write and read. We learned practically by chance, that leaving markings somewhere to be seen and read by others would lead to the recording of history, and thus, to the advancement of our cultural and socioeconomic evolution.

By being given a tool to record history and convey information to others over a distance and time, we (the monkeys/apes in the example) would have been given a head-start on this entire process.

It's fairly certain that, with feedback, that monkey at the keyboard would have produced something analogous to Shakespeare in a matter of a few hundred generations. --E. Schorr

By anon9367 — On Mar 04, 2008

I just wanted to thank you for a job well done. Thank you. My kids thought I was making up that theorem.

Mary McMahon
Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a...

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