this post was submitted on 08 Dec 2024
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But your citation gives both statements:
"In fact, the monkey would almost surely type every possible finite text an infinite number of times."
and
"The theorem can be generalized to state that any sequence of events that has a non-zero probability of happening will almost certainly occur an infinite number of times, given an infinite amount of time or a universe that is infinite in size."
So when you say the number of times is "unknowable" the actual answer is "almost surely an infinite number of times" no ? Since the probability of that can be calculated as 100%. The mindfuck part is that it is still possible that no monkey at all will type a particular text, even though the probability of that is 0.
The probability that only 2 monkeys will type the text is also still 0, same as 3 monkeys, 4 monkeys, etc. - in fact the probability of any specific finite number of monkeys only typing out the text is still 0 - only the probability of an infinite number of monkeys typing it out is 100% (the probabilities of all possible outcomes, even when infinite, have to sum up to 1 after all)
Basically, if we know "it will almost surely happen" then we also know just as surely (p=1) that it will also happen an infinite number of times (but it might also never happen, although with p=0)