If you give a monkey a typewriter and enough time, it should eventually be able to bang out the complete works of William Shakespeare. Doesn’t that sound bananas?
This idea is called the Infinite Monkey Theorem and is used to help scientists understand the principles of probability and randomness.
When given an infinite amount of time, a monkey randomly hitting keys on a typewriter can produce the works of Shakespeare entirely by chance, according to the Infinite Monkey Theorem.
However, a new study has found that the theorem is true but is also a bit misleading. It would take much longer than the lifespan of our universe for a typing monkey to randomly produce Shakespeare.
To put that into context, the universe is estimated to last around another 100 trillion years, which is when the last light will go out.
Two mathematicians from the University of Technology Sydney (UTS) wanted to test the theorem using the bounds of our finite universe instead of using endless time and resources.
“The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labor,” said Stephen Woodcock, an associate professor at UTS.
“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.”
For the purposes of the study, the researchers assumed that a keyboard has 30 keys, including all the letters of the English alphabet and common punctuation marks.
LiliGraphie – stock.adobe.com – illustrative purposes only
They did their calculations based on a single monkey and the current global population of about 200,000 chimpanzees.
They also assumed a typing speed of one key per second until the end of the universe in 10 trillion years.
The results showed that there is approximately a five percent chance for a single chimp to type out the word “bananas” in its own lifetime. The average life expectancy for a chimpanzee is 33 years, according to Project Chimps.
But even with all the chimps busy typing away, Shakespeare’s entire works, which consists of about 884,647 words, the odds are still stacked against them.
The finite nature of time and the randomness that is required make it nearly impossible for the monkeys to accomplish the hypothetical task before the universe calls it quits.
“It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labor will ever be a viable tool for developing non-trivial written works,” the study authors said.
“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,” Woodcock said.
The mathematicians’ approach offers a fresh perspective on chance and randomness in a real-world context and challenges people to reconsider these kinds of concepts.
The study was published in the journal Franklin Open.
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