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Monkeys given infinite time would probably get carpal tunnel or form a labor union before typing out Shakespeare. (lemmy.world)
submitted 2 years ago by to c/showerthoughts@lemmy.world
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[–] 12 points 2 years ago* (last edited 2 years ago) (4 children)

Well no. You can try to count every real number forever and you will miss infinitely many still. Some infinites are larger than others, hence I do not see any reason why "infinite time" would cover "every possibility happening". On the other hand, if you do have a mathematical proof you could refer to, I would be most grateful.

EDIT: To write out my example, let us consider a machine that picks a random number between 3 and 4 every second. Then there is every second a nonzero chance that this machine (assuming true and not pseudo randomness) will pick, say pi. The range of numbers picked constitute the image of a function from the whole numbers to the real numbers (up to isomporphism), which cannot be surjective. Hence there are numbers not picked even though there was a > 0 chance of picking them every second for an infinite time.

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  • [–] 11 points 2 years ago

    Then there is every second a nonzero chance that this machine (assuming true and not pseudo randomness) will pick, say pi.

    No. The probability of picking any particular number from a uniform distribution is 0.

    On the contrary, since the works of Shakespeare are a finite string over a finite alphabet (I can formalize this argument if you want), the probability of typing them out after some fixed large number of keystrokes is some nonzero number 𝑝. With 𝑛 monkeys, the probability that at least one will type out the works is 1 − (1 − 𝑝)ⁿ, which goes to 1 as 𝑛 → ∞.

    Now, you are right that this does not mean that the works are guaranteed to be typed out. However, it has probability 1, so it’s mathematically “almost certain”.

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  • [–] 5 points 2 years ago (2 children)

    I hear what you are saying and agree. I never took the monkey Shakespeare theory seriously. It sounded a bit too poppy and quite honestly the guy that told me was a douche and pronounced giblets wrong. But as a theory you could get anything in a long enough time span and infinite amount of resources. Why or how that matters? Well I just don't see it.

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  • [–] 3 points 2 years ago* (last edited 2 years ago) (1 child)

    Of course I am not denying that anything possible could happen. That is contradictory to the assumption it was possible in the first place. What I am saying is just that not all that is possible will happen, even if given an infinite time to do so.

    EDIT: Unfortunately, given a setup like this the math says monkey Shakespeare will almost surely happen due to there only being finite variations.

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