The old adage says that if you give an infinite number of monkeys an infinite amount of time to press random keys on a typewriter, one of them will eventually type the complete works of William Shakespeare.

This concept, known as the infinite monkey theorem, suggests that, given infinite time and random chance, any sequence of text, including something as complex as Shakespeare’s catalog, would eventually be produced .

The theorem “owes its name to mathematician Émile Borel, who used animals metaphorically to illustrate his theory of probability in 1913,” according to Manon Bischoff, a theoretical physicist and editor at Spektrum, a sister publication of Scientific American, who says that The ideas behind the theorem are much older, however. In ancient times, the Roman philosopher and politician Marcus Tullius Cicero wrote that one could “believe that if a large quantity of the twenty-one letters, composed of either or, or of any other matter, were thrown to the ground, they would fall in such an order that they would legibly form (the epic poem) the Annals of Ennius (But) I doubt fortune could make (even) one. single verse.'”

However, according to a new article in Franklin Open reviewthere is not enough time left in the entire lifetime of the universe for all the chimpanzees alive today to write the works of the bard.

“The long-established result of the infinite monkey theorem is correct, but misleading,” the University of Technology Sydney researchers wrote in the paper. “Generating non-trivial text within the lifetime of our universe is almost certainly impossible.”

The “heat death” of the universe is a theory of how the universe will and is expected to end as a result of the gradual dispersal of energy as the universe continues to expand into billions and billions of years. Eventually, the universe will reach a state where no usable energy remains and all matter will be uniformly distributed, reaching maximum entropy.

The delay for this to happen should be greater than 10¹⁰⁰ years. The Universe is currently estimated to be only about 13.8 billion years old, or 1.38 x 10¹⁰ years, we still have an unimaginably long time to go.

However, according to the new paper, that might not yet be long enough for an infinite number of monkeys to randomly perform Shakespeare’s works.

“The infinite monkey theorem only considers the infinite limit, either with an infinite number of monkeys or with an infinite period of monkey work,” said Stephen Woodcock, co-author of the study and associate professor at the University of Technology Sydney, in a statement.

“We decided to examine the probability of a given string of letters being typed by a finite number of monkeys over a finite period of time, consistent with estimates of the lifespan of our universe,” he said .

In the study, the researchers calculated the probability that a given string of characters would be typed by one of a finite number of monkeys. They assumed that the keyboard contained 30 keys of English characters and punctuation marks, a finite number of 200,000 monkeys (based on the current chimpanzee population), and a typing rate of one key per monkey per second for the rest of the life of the universe.

They found that using these assumptions, it is extremely unlikely that all 884,647 words of Shakespeare’s works would be typed before the heat death of the universe.

“Given plausible estimates of the lifetime of the universe and the number of possible monkey typists available, this still leaves huge differences between the resources available and those required for the generation of non-trivial texts,” the researchers wrote. authors.

In fact, there’s only a 5% chance that any of the chimpanzees will manage to type the single word “bananas” in their own lifetime.

“This discovery places the theorem among other probabilistic puzzles and paradoxes – such as the St. Petersburg paradox, Zeno’s paradox, and the Ross–Littlewood paradox – where using the idea of ​​infinite resources yields results which don’t match what we get when we consider the constraints of our universe,” Woodcock said.

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References

Woodcock, S. and Falletta, J. (2024). A numerical evaluation of the finite monkey theorem. Franklin Open, 100171.