It turns out that the amount of time needed for a monkey to randomly type out Shakespeare would exceed the lifetime of our universe, as revealed by a recent study.
According to the Infinite Monkey Theorem, a monkey randomly hitting keys on a typewriter for a limitless duration could eventually type out all of Shakespeare’s works purely by chance.
This well-known hypothetical scenario is often used to explain concepts of probability and randomness, illustrating how chance can lead to surprising results. Its concept has appeared in popular culture, including shows like The Simpsons and The Hitchhiker’s Guide to the Galaxy, as well as on platforms like TikTok.
Despite this notion, recent research indicates that the time necessary for a monkey to randomly recreate Shakespeare is unimaginably vast—much longer than the current estimates for the universe’s lifespan. Therefore, while the theorem holds some truth, it can also be quite misleading.
Mathematicians Associate Professor Stephen Woodcock and Jay Falletta from the University of Technology Sydney (UTS) set out to investigate the theorem, focusing on the limitations of our finite universe.
“The Infinite Monkey Theorem assumes infinite variables, like either an endless number of monkeys or infinite time for them to type,” explained Associate Professor Woodcock.
“We aimed to assess the likelihood of a specific sequence of letters being typed by a limited number of monkeys within a finite timeframe, in line with our universe’s estimated lifespan,” he noted.
The serious yet playful study titled A numerical evaluation of the Finite Monkeys Theorem has recently been published in the peer-reviewed journal Franklin Open.
For their calculations, the researchers considered a keyboard with 30 keys, encompassing all letters of the English alphabet along with common punctuation marks.
They simulated scenarios not only for a single monkey but also for the current worldwide population of approximately 200,000 chimpanzees, assuming each typed at a rather swift pace of one key strike per second, continuing until the universe’s estimated end in about (10^{100}) years—a number represented by a 1 followed by 100 zeros.
The study found that while a lone chimp has about a 5% chance of typing the word ‘bananas’ within its lifetime, even with all chimps involved, the entirety of Shakespeare’s works (comprised of around 884,647 words) will almost certainly never be typed before the universe comes to an end.
“It seems unlikely that, even with faster typing or an increased population of chimpanzees, using monkey efforts will prove effective in creating substantial written texts,” the authors reflect.
“This leads us to place the theorem among other probability enigmas and paradoxes—such as the St. Petersburg paradox, Zeno’s paradox, and the Ross-Littlewood paradox—where assuming infinite resources results in conclusions that differ from what we observe when we consider our universe’s constraints,” stated Associate Professor Woodcock.
In the age of generative AI, both the Infinite Monkey Theorem and its finite counterpart challenge us to ponder philosophical questions about creativity, meaning, consciousness, and how these traits come into being.
