In a study recently published in the peer-reviewed journal 'Franklin Open,' Australian mathematicians Professor Stephen Woodcock and Jay Falletta from the University of Technology Sydney have explored the feasibility of the Infinite Monkey Theorem under finite conditions. The researchers concluded that even if all 200,000 chimpanzees typed a letter a second until the end of the universe in 100 trillion years, they would have no chance of replicating Shakespeare's works.
The 'Infinite Monkey Theorem' is a mathematical thought experiment related to the principles of probability and randomness. It posits that a monkey randomly pressing keys on a typewriter for an infinite amount of time could eventually produce the complete works of William Shakespeare. The theorem has been around for over a century, though its origin remains unclear, with some believing the general idea dates back to Aristotle.
Woodcock's team examined 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 the universe. They introduced a new condition by limiting the time allotted to perform the task to approximately the lifespan of our universe, using the 'heat death' of the universe as the time limit. Practical concerns, like feeding the monkeys or their survival as the Sun expands, were ignored in the study.
The researchers assumed that the current number of chimpanzees, approximately 200,000, would remain constant for the lifetime of the universe, defined as one googol years—a one followed by 100 zeros. They also assumed that each chimpanzee would press one key per second for every second of the day and that the lifespan of each chimpanzee would be just over 30 years.
Using these assumptions, the researchers calculated that among these randomly typing chimpanzees, there is only a 5% chance that a simple word like 'banana' will appear in the lifetime of one chimpanzee. For reference, one chimp typing on a 30-key keyboard would have a 5% chance of writing the word "bananas" within their lifetime. Woodcock explained: "By the time you get to the size of a full book, the probability of producing that sentence decreases by billions of times."
"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," Woodcock said. He further elaborated: "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."
The researchers challenged the Infinite Monkey Theorem by reviewing it under a finite period of time and a finite number of monkeys, illustrating how infinite time could make the improbable probable. Woodcock added: "Even if every atom in our known universe were a universe of its own on the scale of our universe, we would have almost no chance of seeing even just a short book, before the end of the universe."
Woodcock and co-author Jay Falletta concluded that the same chimpanzees are unlikely to type even a short children's story of 1,800 words by the end of the universe. Despite varying the parameters, the researchers calculated that even with this vast number of chimpanzees, success in recreating Shakespeare's works remained practically impossible.
"Even with more chimpanzees typing faster, it is not reasonable to expect their work to produce any meaningful written content beyond trivial sequences," the study stated. After analyzing the data, the researchers concluded that the universe would end long before the monkeys could inadvertently type out the complete works of Shakespeare. Even trivial phrases would take an eternity for the monkeys to type.
While the situation seems dire, there may be hope for the monkeys. Chris Banerjee, who was not involved in the study, explained: "The universe is very vast, and there is room for many more chimpanzees to live here on Earth. According to some cosmic theories, there may be infinite space or an infinite number of universes."
Banerjee noted: "If we accept the possibility of these infinite worlds, then the success of the monkeys in reproducing Shakespeare is 'an ultimate certainty,' as the Infinite Monkey Theorem states." However, in the context of our finite universe and resources, the study provides evidence that chimpanzees will not be able to replicate Shakespeare's works, even after a googol years.
This finding places the theorem among other probability puzzles and paradoxes, highlighting the distinction between theoretical infinites and practical finites. Woodcock stated: "This finding places the theorem among other probability puzzles and paradoxes. 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."
Despite this, primates have demonstrated some very human intellectual traits recently. Over the summer, scientists found that chimpanzees "are capable of" producing sounds that mimic words they hear from people. This finding dispels prior scholarship that stipulated speech was beyond chimpanzees' "neural circuitry."
Sources: The Scottish Sun, The Sun, CNN Arabic, New York Post, BBC
This article was written in collaboration with generative AI company Alchemiq