Monkeys and Shakespeare: A Lesson in Probability

Researchers reveal that not even the combined typing efforts of all the world's chimpanzees could replicate Shakespeare's writings, challenging long-held beliefs about infinity.

Two Australian mathematicians have cast significant doubt on the "infinite monkey theorem," which posits that a monkey randomly pressing keys on a typewriter would eventually type out the complete works of Shakespeare, if given infinite time. The theorem has served as a thought experiment for illustrating concepts of probability and randomness, but a recent peer-reviewed study by Stephen Woodcock and Jay Falletta from Sydney has overturned this notion, suggesting the reality is far harsher.

Their findings indicate that the time needed for a monkey to reproduce Shakespeare's plays, sonnets, and poems exceeds the lifespan of the entire universe. This revelation suggests that while theoretically correct, the theorem can be misleading. The researchers extended their investigation by estimating the typing potential of the global chimpanzee population, roughly 200,000.

Even if every chimp typed one key per second until the universe faces its end, their collective efforts would still fall short of producing the Bard's extravagant body of work. The odds are depleting: a single chimp stands a mere 5% chance of typing the word "bananas" during its lifetime, and the likelihood of formulating a random sentence like "I chimp, therefore I am" is approximately one in 10 million billion billion, according to the study's calculations.

The authors assert that the conclusion implies monkeys will never be a viable source for creating serious literary works, even with theoretical advances in typing speed or population growth. Their research relies on commonly accepted theories concerning the universe's long-term fate, specifically the so-called heat death theory, which proscribes that the universe will relentlessly expand and cool until life and matter cease to exist.

“Considering the constraints of our universe, this finding places the theorem alongside various probability puzzles and paradoxes where infinite resources yield unrealistic outcomes,” said Associate Prof Woodcock in a statement regarding their work. This study has prompted a re-evaluation of how we consider infinity in relation to creativity and randomness.