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Elsevier

Franklin Open

Volume 9, December 2024, 100171
Franklin Open

A numerical evaluation of the Finite Monkeys Theorem

Author links open overlay panelStephen Woodcock ^a, Jay Falletta ^b
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Highlights

  * *
    The long-established result of the Infinite Monkeys Theorem is
    correct, but misleading.
  * *
    Non-trivial text generation during the lifespan of our universe
    is almost certainly impossible.
  * *
    The Finite Monkeys case shows there will never be sufficient
    resources to generate Shakespeare.

Abstract

The Infinite Monkeys Theorem has long-established the eventual
certainty of the complete works of William Shakespeare being
reproduced by a monkey randomly pressing keys on a typewriter. This
only considers the infinite limit, with either an infinite number of
monkeys and/or an infinite time period of monkey labour. Here, we
consider the Finite Monkeys Theorem and look at the probability of a
given string being typed by one of a finite number of monkeys within
a finite time allocation consistent with estimates for the lifespan
of our universe. We also calculate the expected number of keystrokes
until a target string would first be produced. Given the expected
time until the heat death of the universe, we demonstrate that the
widely-accepted conclusion from the Infinite Monkeys Theorem is, in
fact, misleading in our finite universe. As such, this places the
theorem in a class of probabilistic problems or paradoxes, including
the St. Petersburg paradox, Zeno's dichotomy paradox and the
Ross-Littlewood paradox wherein the infinite-resource conclusions
directly contradict those obtained when considering limited
resources, however sizeable.

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Keywords

Infinity
Thought experiment
Combinatorics
Monkeys
Probability
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(c) 2024 The Author(s). Published by Elsevier Inc. on behalf of The
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