Revisiting the Infinite Monkey Theorem: A Finite Perspective

The Infinite Monkey Theorem posits that a monkey randomly pressing keys on a typewriter for an infinite duration would eventually produce the complete works of Shakespeare purely by chance. This widely recognized thought experiment serves to illustrate concepts of probability and randomness, demonstrating how chance can lead to unexpected outcomes. The idea has permeated popular culture, appearing in works from *The Simpsons* to *Hitchhiker's Guide to the Galaxy* and even trending on TikTok.

However, a new study reveals that the time required for a monkey to randomly generate Shakespeare's works is astronomically large—far beyond the lifespan of our universe. Mathematicians Associate Professor Stephen Woodcock and Jay Falletta from the University of Technology Sydney (UTS) sought to explore the theorem under the constraints of our finite universe.

"The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labor," explains Associate Professor Woodcock. "We aimed to assess the probability of a specific string of letters being typed by a finite number of monkeys within a time frame that aligns with the estimated lifespan of our universe."

Their study, titled *A Numerical Evaluation of the Finite Monkeys Theorem*, was recently published in the peer-reviewed journal *Franklin Open*. For their calculations, the researchers assumed a keyboard with 30 keys, encompassing all letters of the English language and common punctuation. They analyzed scenarios with a single monkey as well as the current global population of approximately 200,000 chimpanzees, with the assumption of a typing speed of one key every second until the estimated end of the universe in about 10^100 years—a staggering figure represented by a 1 followed by 100 zeros.

The findings indicate that while a single chimp has a roughly 5% chance of typing the word 'bananas' in its lifetime, even the combined efforts of all chimps would not suffice to produce Shakespeare's complete works (approximately 884,647 words) before the universe concludes.

The authors note, "It is not plausible that, even with improved typing speeds or a larger chimpanzee population, monkey labor will ever serve as a practical method for generating significant written works." This study situates the theorem alongside other probability puzzles and paradoxes—such as the St. Petersburg paradox, Zeno's paradox, and the Ross-Littlewood paradox—where the concept of infinite resources yields outcomes that diverge from our understanding under finite constraints.

In the age of generative AI, both the Infinite Monkey Theorem and its finite counterpart prompt philosophical considerations about the nature of creativity, meaning, and consciousness, and how these attributes emerge.