A numerical evaluation of the Finite Monkeys Theorem
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...
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Elsevier
2024-12-01
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| author | Stephen Woodcock Jay Falletta |
| author_facet | Stephen Woodcock Jay Falletta |
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| description | 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. |
| format | Article |
| id | doaj-art-e419c000e00f40a8a81e6988a5e85f50 |
| institution | Kabale University |
| issn | 2773-1863 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
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| spelling | doaj-art-e419c000e00f40a8a81e6988a5e85f502024-12-19T11:03:30ZengElsevierFranklin Open2773-18632024-12-019100171A numerical evaluation of the Finite Monkeys TheoremStephen Woodcock0Jay Falletta1School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, NSW 2007 Australia; Corresponding author.Institute for Sustainable Futures, University of Technology Sydney, Ultimo, NSW 2007 AustraliaThe 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.http://www.sciencedirect.com/science/article/pii/S2773186324001014InfinityThought experimentCombinatoricsMonkeysProbability |
| spellingShingle | Stephen Woodcock Jay Falletta A numerical evaluation of the Finite Monkeys Theorem Franklin Open Infinity Thought experiment Combinatorics Monkeys Probability |
| title | A numerical evaluation of the Finite Monkeys Theorem |
| title_full | A numerical evaluation of the Finite Monkeys Theorem |
| title_fullStr | A numerical evaluation of the Finite Monkeys Theorem |
| title_full_unstemmed | A numerical evaluation of the Finite Monkeys Theorem |
| title_short | A numerical evaluation of the Finite Monkeys Theorem |
| title_sort | numerical evaluation of the finite monkeys theorem |
| topic | Infinity Thought experiment Combinatorics Monkeys Probability |
| url | http://www.sciencedirect.com/science/article/pii/S2773186324001014 |
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