Those typing monkeys will never produce Shakespeare's works, mathematicians say

Talented though they may be, monkeys will never type out the complete works of William Shakespeare, or even a short book, a new study suggests.

The Infinite Monkey Theorem is a famous thought experiment that states that a monkey pressing random keys on a typewriter would eventually reproduce the works of the Bard if given an infinite amount of time and/or if there were an infinite number of monkeys.

However, in the study published in the peer-reviewed journal Franklin Open, two mathematicians from Australia’s University of Technology Sydney have rejected this theorem as “misleading” within the confines of our finite universe.

They challenged it by looking at the Finite Monkeys Theorem, in which there is a finite amount of time and a finite number of monkeys.

They took the assumption that the current population of around 200,000 chimpanzees would remain the same over the lifespan of the universe of one googol years (that’s 1 followed by 100 zeros). They also assumed that each chimpanzee would type one key per second for every second of the day, with each monkey having a working lifespan of just over 30 years.

Using these assumptions, the researchers calculated that among these randomly-typing monkeys, there is just a 5% chance that a word as simple as “bananas” would occur in the lifespan of one chimpanzee.

They found that a short sentence such as “I chimp, therefore I am” will “almost certainly never be produced by any currently living chimp,” study co-author and mathematician Stephen Woodcock, an associate professor at the University of Technology Sydney, told CNN on Friday.

“By the time you’re at the scale of a full book, you’re billions of billions of times less likely,” he continued.

Woodcock and co-author Jay Falletta, a senior research consultant at the university, concluded in the study that, even with more chimpanzees or quicker typing, it is “not plausible” that monkey labor will ever be a viable tool for “developing written works of anything beyond the trivial.”

“Even if every atom in our known universe were its own universe on the scale of ours, we would still have pretty much no chance of ever seeing something as long as even a short book,” such as “Curious George,” which is around 1,800 words, “before the end of the universe,” Woodcock told CNN.

“Personally, I think it’s fascinating how misleading the well-established result for the infinite resource case is,” he added. “Yes, it is true that given infinite resources, any text of any length would inevitably be produced eventually. While true, this also has no relevance to our own universe, as ‘reaching infinity’ in resources is not something which can ever happen.”

Interdisciplinary clinician-scientist Chris Banerji, theme lead for Clinical AI at the Alan Turing Institute in London, agrees that monkeys randomly typing Shakespeare’s works is unlikely since the Finite Monkeys Theorem is “correct,” but he told CNN on Friday that the Infinite Monkey Theorem “still holds.”

“While the situation seems dire, there may be hope for the monkeys yet,” said Banerji, who was not involved in the study. “The universe is very large, and there is room for many more chimps than live here on Earth, under some cosmological theories there may even be infinite space or infinitely many universes.”

He said that “if we accept the possibility of these infinite worlds” then “the monkeys’ successful replication of Shakespeare is an ‘eventual certainty,’” as the Infinite Monkey Theorem states. “In the words of the Bard ‘Until I know this sure uncertainty, I’ll entertain the offered fallacy.’”