Infinite Monkey Theorem


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 a given 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, but a metaphor for an abstract device that produces a random sequence of letters ad infinitum.

Old-Fashioned Typing

The theorem illustrates the perils of reasoning about infinity by imagining a vast but finite number, and vice versa.

The probability of a monkey exactly typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time of the order of the age of the universe is minuscule, but not zero.

“We’ve heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare; now, thanks to the Internet, we know that is not true.” – Robert Wilensky

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