Well, they wouldn’t write it instantly - in the best case, they would start writing it instantly, and finish in optimal time. However, it’s possible that no monkey would actually write it on the first try - we’d have to get into some complex predictions on monkey brains and physiology, it’s possible that with their brains and muscle structure they wouldn’t go for the kinds of character sequences to produce Hamlet, perhaps changing up patterns enough to produce something more random only after a certain amount of time.
Depending on how you formulate the experiment, it could be that no monkey could finish it before physiologically having to take a break or something, returning to specific patterns afterwards that would render it impossible for it to finish writing Hamlet, and thus no monkey would ever write Hamlet in a continuous string of characters, from start to end.
But yeah, if we just say they’re typing completely random characters without pause forever, yup, infinity dictates some fraction of monkeys would immediately be on the right track and finish writing as soon as possible, for anything you can think of.
That only is true with limited amounts of monkeys. A million might not do it in the first try, but an infinite amount would mean one of those monkeys at least would do it first try. Which monkey that is is just as absurd as asking when it will happen when we use infinite time instead.
Is the point of these logic memes to illustrate the properties of infinity or to prove a point about what can or cant be done though?
I think we’re looking too deep into what is really meant to be a simple thought experiment. Entertaining the discussion, however, if the occurrence of a monkey to type, say Hamlet, on the first try, is not physiologically possible for the mind and body of a monkey, it will never happen on the first try by any monkey even with infinite monkeys as it is not within the realm of possibilities. Infinity just means every possible outcome will occur, but anything outside of the realm of possibilities is still impossible and won’t happen no matter how many instances are attempted.
