Monkeys don’t have enough time to write Shakespeare, math confirms

There’s a thought experiment called the “infinite monkey theorem” that says, given an infinite amount of time, a monkey that randomly hits keys on a typewriter will eventually reproduce any body of text, including the complete works of William Shakespeare.

Maybe you’ve heard of this before? The thought experiment is meant to illustrate the principles of probability and how chance can lead to unexpected outcomes. It’s even been referenced in popular culture, from The Simpsons to The Hitchhiker’s Guide to the Galaxy.

However, according to a new study, that would take an incredibly long time to happen — far longer than the expected lifespan of the universe. In other words, it’s basically impossible for a monkey to actually type out Shakespeare’s works by mere random keystrokes.

Mathematicians Stephen Woodcock and Jay Falletta from University of Technology Sydney (UTS) decided to investigate the theorem in the context of our finite universe:

“The infinite monkey theorem assumes an infinite amount of time or an infinite number of monkeys. We decided to look at the probability that a given sequence of letters would be written by a finite number of monkeys within the expected lifetime of the universe.”

In the study, the researchers assumed a keyboard with 30 keys that included all letters and common punctuation marks. They used both a single monkey and the current global population of about 200,000 chimpanzees, and calculated a productive typing rate of one key per second until the universe ceases to exist.

The results showed that it’s possible (about a 5 percent chance) for a single chimpanzee to type the word “bananas” in its lifetime. But even with all the chimpanzees together, it’s near impossible that they would write the entire works of Shakespeare (about 884,647 words) before the universe ends in 10¹⁰⁰ years. (Yes, that’s 1 followed by 100 zeros.)

The researchers concluded that it’s unlikely that monkey labor could ever be used as a realistic method of producing complex written works, even if they wrote faster or there were more chimpanzees.