Showerthoughts

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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. A showerthought should offer a unique perspective on an ordinary part of life.

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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 9 months ago by solid_matt@lemmy.world to c/showerthoughts@lemmy.world

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[–] xigoi@lemmy.sdf.org 11 points 9 months 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”.