 "Scientists have rejected the 'Infinite Monkey Theorem' labelling it as “misleading” within the confines of the finite universe. Representational Image")
A fascinating concept in probability theory, the Infinite Monkey Theorem posits that a monkey, if given unlimited time and a typewriter, could randomly type the complete works of William Shakespeare.
This thought experiment is often cited as a metaphor to explain chance, randomness, and the possibility of unlikely events given infinite time.
However, a new study conducted by mathematicians from Australia’s University of Technology Sydney (UTS) has brought a realistic lens to this theory, revealing just how improbable it truly is when we consider our universe’s limitations.
Finite limits, Infinite improbability
In an attempt to re-evaluate the Infinite Monkey Theorem, UTS mathematicians Stephen Woodcock and Jay Falletta looked at the concept of the Finite Monkeys Theorem.
Their study, published in Franklin Open, challenges the traditional notion by applying practical, finite conditions: a set number of chimpanzees typing over the projected lifespan of the universe, estimated at one googol years (that’s 1 followed by 100 zeros).
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The researchers simulated conditions where each chimp types one key per second on a keyboard with 30 keys (the English alphabet plus common punctuation marks). While theoretically possible, Woodcock and Falletta found that the likelihood of typing even one coherent phrase — let alone all of Shakespeare’s works — was astronomically low.
“The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labour,” explained Woodcock. “We decided to look at the probability of a given string of letters being typed by a finite number of monkeys within a finite time period consistent with estimates for the lifespan of our universe.”
The odds: Bananas in a chimp’s lifetime
One of the study’s intriguing findings centered around the probability of a monkey randomly typing the word “bananas” within its average 33-year lifespan. The chances were calculated to be only about 5 per cent for a single chimp.
When extrapolated to the current global chimpanzee population of roughly 200,000, this probability remains extraordinarily slim — even with every chimp typing continuously until the universe ends. As Woodcock humorously told New Scientist, “It’s not even like one in a million. If every atom in the universe was a universe in itself, it still wouldn’t happen.”
In fact, typing just one random sentence, such as “I chimp, therefore I am,” would have a probability of one in 10 million billion billion — virtually impossible given any realistic timeframe.
Shakespeare’s works vs. the Heat death of the universe
The researchers approached this thought experiment with another real-world consideration: the universe’s projected “heat death,” a state in which the universe continues to expand and cool until all energy is used up, estimated to occur in roughly 100 trillion years.
Even with every monkey working continuously at one key per second, the researchers concluded that it would still be impossible for this vast typing workforce to produce the 884,647 words contained in Shakespeare’s canon before the universe’s heat death.
“This finding places the theorem among other probability puzzles and paradoxes — such as the St. Petersburg paradox, Zeno’s paradox, and the Ross-Littlewood paradox — where using the idea of infinite resources gives results that don’t match up with what we get when we consider the constraints of our universe,” said Woodcock, highlighting the paradoxical nature of the Infinite Monkey Theorem when faced with real-world limitations.
Only in theory, not a practical scenario
The UTS study isn’t the first attempt to probe the Infinite Monkey Theorem. In an earlier trial, six Sulawesi crested macaques were given access to a computer for four weeks, but the results were predictably chaotic.
The monkeys produced only five pages of text, consisting mainly of the letter “S.” The results underscored the difficulty of creating even basic words, let alone the poetic complexity of Shakespearean prose.
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While the Infinite Monkey Theorem remains a thought-provoking model in probability, Woodcock and Falletta’s findings has highlighted its impracticality in the finite world we inhabit. Their study encourages us to view the theorem as a theoretical puzzle rather than a feasible scenario.
Despite its mathematical basis, the study concludes, “It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labour will ever be a viable tool for developing non-trivial written works.”