Over a sufficiently long period of time, could a monkey randomly typing on a typewriter (or on a keyboard, to be more contemporary) write HamletShakespeare's play? This “infinite monkey theorem” is true, but it wouldn't come true until the universe dies, according to a new study.
By virtue of this theorem, a monkey randomly pressing the keys of a keyboard, for an infinite time, would eventually succeed in rewriting all of Shakespeare's works, and this, only by luck.
This wild hypothesis helps us understand the principles of probability and chance, and how luck can lead to unexpected results. The idea in question has been referenced in many works of popular culture, such as the television series The Simpsonsthe novels of Galactic Guideor even on the digital platform TikTok.
To assess the feasibility of this theorem, two researchers from the University of Technology Sydney, Associate Professor Stephen Woodcock and Jay Falletta, both mathematicians, decided to rely on the limits of our finite universe.
“This theorem only takes into account infinite limits, i.e. an unlimited number of monkeys, or an infinite writing time,” explains Professor Woodcock.
“We wanted to examine the probability that a given series of letters would be typed by a limited number of monkeys, all within a fixed period of time, based on estimates for the lifespan of our universe,” he said. he added.
The research is published in Franklin Open.
To achieve their goals, the researchers imagined a keyboard with 30 keys, that is to say all the letters of the English alphabet, as well as the usual punctuation marks.
In addition to performing the calculations with a single monkey typing, the study authors also used the global population of chimpanzees, approximately 200,000 individuals, and assumed that the typing rate was touch per second, until the end of the universe, in approximately 10^100 years.
The results indicate that it is possible, with about a 5% probability, that a single monkey would type the word “banana” before its own death. However, even with all the chimpanzees put to work, Shakespeare's entire work, 884,647 words in English, will likely never be typed before the universe dies.
“It is not plausible, even by accelerating the speed of typing or increasing the number of chimpanzees, that monkeys will one day be a viable tool for developing meaningful written works,” write the authors, in a humorous tone. .
“This theorem joins others based on the idea of infinite resources, and which give results that do not fit with the constraints of our universe,” adds Professor Woodcock.
