The infinite monkey theorem falls short

Oct. 31 () –

A new study reveals that a typing monkey It would take much longer than the life of our universe to randomly emulate Shakespeareaccording to a revision of the infinite monkey theorem.

This widely known thought experiment (a monkey pressing random keys on a keyboard for an infinite period of time will eventually type any given text) is used to help us understand the principles of probability and randomness, and how chance can lead to unexpected results. The idea has been referenced in pop culturefrom “The Simpsons” to “The Hitchhiker’s Guide to the Galaxy” and on TikTok.

However, the new study reveals that it would take an incredibly enormous amount of time, much longer than the life of our universe, for a typing monkey to randomly produce Shakespeare.

Associate Professor Stephen Woodcock and Jay Falletta of the University of Technology Sydney (UTS), both mathematicians, They decided to examine the theorem using the limits of our finite universe.

“The infinite monkey theorem only considers the infinite limit, either with an infinite number of monkeys or with an infinite time period of work by the monkeys,” he said. in a statement Associate Professor Woodcock.

“We decided to look at the probability of a given string of letters being typed by a finite number of monkeys in a finite period of time consistent with estimates of the lifetime of our universe,” he said.

The study has just been published in the peer-reviewed journal Franklin Open.

For the purposes of numerical analysis, the researchers assumed that a keyboard contains 30 keys that include all the letters of the English language plus common punctuation marks.

In addition to a single monkey, they also did the calculations using the current global population of around 200,000 chimpanzees, and They assumed a fairly productive typing speed of one key per second until the end of the universe in about 10 to 100 years.

The results reveal that it is possible (about a 5% probability) for a single chimpanzee to write the word “bananas” throughout its life. However, even with all the chimpanzees enlisted, the complete works of the Bard – poet of the ancient Celts – (with around 884,647 words) They will almost certainly never be written before the end of the universe.

“It is not plausible that, even with improved writing speeds or an increase in chimpanzee populations, monkey work will ever be a viable tool for developing non-trivial written works,” the authors reflect.

“This finding places the theorem among other probability puzzles and paradoxes, such as the St. Petersburg paradox, the Zeno paradox, and the Ross-Littlewood paradox, in which the use of the idea of ​​infinite resources gives results that do not coincide with what we get when we consider the limitations of our universe,” said Associate Professor Woodcock.

In the era of generative AI, the Infinite Monkey Theorem and its finite version may also challenge readers to consider philosophical questions around the nature of creativity, meaning, and consciousness, and how these qualities ariseaccording to the authors.