According to the Tireless monkey theoremalso known as Infinite monkeys theoremif we left A monkey press the keys of a typewriter at random For an infinite time, sooner or later it would end up typing the entire divine comedy or all the works of Shakespeare. In short, the concept is that having a infinite timethe monkey would constitute all the possible combinations imaginable on the keyboard, and among all these combinations, there will also be the whole Divine comedy.
The first to formulate this theorem speaking of monkeys was, in 1913, the French mathematician Émile Borel according to which:
Having an infinite time available, a monkey that crushes random keys, sooner or later it will end up typing any existing or imaginable text or literary work.
Let’s see why the theorem it works from a mathematical point of view from the chanceand because when we try to put it into practiceperhaps with real monkeys, the theorem fails.
Why does the tireless monkey theorem work?
Let’s start by trying to understand how it is possible that sooner or later a monkey makes up a manuscript by pressing random keys, starting from a simple case.
Let’s imagine we want to write the word Xy with a typewriter who has only two keysthe letter X and the letter Y. In the image below we can see that by crushing the keys:
- 2 times we can write 4 words of 2 letters, of which only one is Xy. There probability of success And 1 out of 4 or the 25%.
- 3 times we can write 8 words of 3 letters, of which half contains Xy. There probability of success he climbed to 50%.
- 4 times we can write 16 words of 4 letters, of which 11 contain xy. Our monkey this time has one probability of 68% to be able to type the word Xy.
In practice, by increasing the number of characters digit, the probability of success increases by approaching more and more 100% and, To put it in mathematician, At the limit it tends 100% when the number of characters tends to infinity.
If we apply the same reasoning to the case of a complete keyboard we can deduce that the monkey, having an infinite time availablesooner or later he will write the divine comedy.
The theorem put into practice: highly unlikely and impossible
But how much how long Can you use a monkey to type an entire novel by pressing random keys? That’s what Australian mathematicians Stephen Woodcock and Jay Falletta asked themselves. The two researchers, assuming that a monkey types a key to the second, calculated that
The probability that a monkey will be able to write the word bananas Over the average life of a monkey is about 5%.
It is not a high probability, but not very low, however Woodcock and Falletta have calculated that it drops drastically if we want the monkey to write the entire novel The planet of the monkeys: in this case the chance Become a decimal number very small With 698814 Zeri after the comma.
The two researchers then wondered how much the situation would improve using a army of 200000 monkeys That type without stopping until the death of our universe, which will be estimated in 10 to 100 years (a number of 100 digits). Also in this case the chance successful are quite low, about 0.0_06% with 15040 zeros after the comma: it is such a small number that it will make any successful concrete hope vanish.
As for the Divine comedy, Instead, the two researchers have not dealt with it, but the text written by Dante is a little longer than the monkeys planet (about 100,000 words, against 80000) and we can deduce that the probability of success is even lower, therefore
And highly improbable that an army of monkeys can write the Divine comedy before the end of our universe.
In short, it seems that the theorem of the tireless monkey does not work so well in concrete reality, and there were also those who tested it, with poor results, with the real monkeys. It is a experiment conducted by the University of Plymouth in which 6 monkeys they managed to produce a Text of a few page compound mainly from the letter s. The text does not contain not even a word of made meaningbut was still published online with the title of Notes Towards The Complete Works of Shakespeare.
So does this theorem work or not? If we pretend to apply it to one concrete and finished reality The theorem is not worth More, this because the transition from the abstract of mathematics to the concrete of the newspaper is almost never painless: in this specific case, when we pass from the abstract to the concrete, we lose at least the possibility of carrying out Infinites of attemptswhich is one of the aspects key to the theorem.
However, if we return to the imaginary world of mathematics everything is possible and, as Borel hypothesized, our monkey, in a sufficiently large time, will really end up writing anything, also this article … and who knows that in reality it has not been written by a monkey?
