A numerical evaluation of the Finite Monkeys Theorem

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.

Keywords

• Infinity
• Thought experiment
• Combinatorics
• Monkeys
• Probability