The “infinite monkey theorem” posits a scenario where, given endless time, a monkey hitting random keys on a typewriter would eventually type out any text, including the complete works of Shakespeare. This idea highlights the relationship between randomness and probability, demonstrating that, theoretically, randomness can produce any outcome if given infinite possibilities. Widely recognized and referenced in popular culture, this thought experiment has appeared in everything from The Simpsons to The Hitchhiker’s Guide to the Galaxy. Yet, while intriguing in theory, the practicality of such a feat happening within a finite period is another question entirely.
Mathematicians Stephen Woodcock and Jay Falletta from the University of Technology Sydney (UTS) set out to re-examine this theorem, focusing on its feasibility within the limits of the known universe. Their study doesn’t assume infinite time or an endless number of monkeys but rather examines the probability of achieving coherent text with a realistic number of monkeys over the universe’s expected lifespan. “We wanted to see how likely it is that a sequence of letters could be written by a finite number of monkeys before the end of the universe,” Woodcock explained. Using a hypothetical 30-key keyboard containing letters and punctuation, they modeled scenarios for both a single monkey and the global chimpanzee population, assuming each could type one keystroke per second.
Their findings showed that, within a chimpanzee’s lifetime, there is a slight—5%—chance that one could type the word “bananas.” However, even with the combined efforts of all 200,000 chimpanzees on Earth, the likelihood of typing out the full works of Shakespeare, which amount to roughly 884,647 words, remains infinitesimally small. In fact, the researchers estimate that achieving this feat before the universe’s projected end (around 10^100 years) is virtually impossible.
Ultimately, this study underlines the enormous improbability of random typing producing complex literary compositions within any practical timeframe. The experiment reinforces that, despite the appeal of the infinite monkey theorem as a thought experiment, such randomness isn’t a viable method for creating complex texts under the constraints of a finite universe. The team’s conclusion serves as a reminder that while theoretical probability allows for virtually any outcome, the realities of time and resource limitations make achieving structured works through random actions far beyond reach.