There’s an old law of probability often phrased that if an infinite number of monkeys sat at an infinite number of typewriters pressing random keys for an infinite amount of time, they would at some point type out Shakespeare’s Hamlet. The point is that, given a large enough scope of opportunity, things that are very unlikely but not impossible can and do happen.
One of the earliest known expressions of this idea comes from the Roman statesman and philosopher Cicero, although Cicero takes the negative view. He poses the idea as a thought experiment to reject materialist philosophies, like Epicureanism, which held that the world was not created by the gods but was the product of random collisions of matter:
How can anyone look on these things yet convince themselves that certain solid and discrete bodies are carried by force and gravity, and the beautiful and exquisite world is made by the fortuitous arrangement of these bodies? If someone thinks this is possible, I don’t see why they shouldn’t also think that innumerable shapes of the twenty-one letters, made out of gold or whatever material, could be tossed down on the ground so that one could read the words of Ennius’ Annals in them. For myself, I doubt that chance could make a single verse out of them.
Cicero, On the Nature of the Gods 2.93
(My translation)
As unlikely as it is that just tossing letters down on the ground once will yield any comprehensible lines from Ennius’ early Roman historical epic, the infinite monkey theory tells us that if we threw an infinite number of letters an infinite number of times, some verses of Ennius would eventually emerge, not to mention lines from Cicero himself, or any other text that could be written in the Latin alphabet.
One might say that Cicero’s mistake was an insufficiency of monkeys.
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