Mathematicians have discovered that the infinite monkey theorem is ‘misleading’

The old saying goes that if you give an infinite number of monkeys an infinite amount of time to press random keys on a typewriter, one of them will eventually type out the complete works of William Shakespeare.

This concept, known as the “Infinite Monkey Theorem”, suggests that given infinite time and random chance, any sequence of text will eventually be produced, including something as complex as Shakespeare’s back catalogue.

The theorem “owes its name to the mathematician Émile Borel, who metaphorically used animals to illustrate his theory of probability in 1913,” according to Manon Bischoff, a theoretical physicist and editor of Spektrum, a Scientific American sister publication, who says: However, the ideas behind it theorems are much older. thrown to the ground, they would form in such order as to clearly constitute the (epic poem) “Annals of Ennius.” (But) I doubt that fate could compose (even) one verse of them.”

However, according to a new article in the journal Franklin Open, there is not enough time left in the lifetime of the universe for all the chimpanzees alive today to write the works of the bard.

“The established result of the infinite monkey theorem is correct but misleading,” researchers from the University of Technology Sydney write in the paper. “Non-trivial text generation during the lifetime of our Universe is almost certainly impossible.”

The “heat death” of the Universe is one theory of how the Universe will end and is expected to occur as a result of the gradual dissipation of energy as the Universe continues to expand over trillions and trillions of years. Eventually the Universe will reach a state in which there is no useful energy left and all matter will be evenly distributed, reaching maximum entropy.

According to forecasts, this will happen in 10 years.¹⁰⁰ years. The universe is currently thought to be about 13.8 billion years old, or 1.38 x 10.¹⁰ years, so we have an incomprehensibly long time left.

However, according to a new paper, this may not be enough time for an infinite number of monkeys to randomly obtain Shakespeare’s works.

“The infinite monkey theorem only considers an infinite limit: either an infinite number of monkeys or an infinite period of monkey labor,” study co-author Stephen Woodcock, an associate professor at the University of Technology Sydney, said in a statement.

“We decided to estimate the probability that a given string of letters would be typed by a finite number of monkeys over a finite period of time, consistent with estimates of the lifespan of our universe,” he said.

In the study, the scientists calculated how likely it was that a given string of characters would be typed by one of a finite number of monkeys. They suggested that the keyboard contained 30 keys with English letters and punctuation, a finite number of 200,000 monkeys (based on the current chimpanzee population), and a typing speed of one key per monkey per second for the rest of the life of the universe.

They found that, using these assumptions, it is extremely unlikely that all 884,647 words of Shakespeare’s works will be printed before the heat death of the universe.

“Given plausible estimates of the lifespan of the Universe and the number of possible monkey typists, the difference between the available resources and the resources required for non-trivial text generation still remains orders of magnitude,” the authors write.

In fact, there is only a 5 percent chance that one chimpanzee will even type the single word “bananas” in his or her lifetime.

“This discovery places the theorem among other probabilistic mysteries and paradoxes, such as the St. Petersburg paradox, Zeno’s paradox and the Ross-Littlewood paradox, where using the idea of ​​infinite resources produces results that are not the same as what we get. when we consider the limitations of our universe,” Woodcock said.

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Links

Woodcock, S., & Faletta, J. (2024). Numerical evaluation of the finite monkey theorem. Franklin Open, 100171. https://doi.org/10.1016/j.fraope.2024.100171.