It's been calculated many times, and yes, it would take an absurdly long amount of time, and that's the point. When dealing with infinities, time is irrelevant, whether you have infinite monkeys or one monkey and infinite time, they will still both do every possible thing a monkey could do.
In fact, infinite monkeys would not only write Hamlet, they would write it instantly, an infinite number of times, and in all possible languages, as well as the possible sequel where Marvel's Blade shows up to fight vampires. Instantly.
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.
100% and you probably know this, so I'm just addin: think of infinity as a sequence of infinite numbers. The number of all the even numbers, that stretch off into infinity, are also infinite. However, that infinite number isn't as big as regular infinity.
You can have different sizes of infinity because when things get that big, the rules change.
Its almost like infinity / 2 = smaller infinity.
No. They proved it would take a finite number of monkeys longer than there is time in the universe. Not sure what the point of that paper was, since the theory involved an infinite number of monkeys.
We were there, monkeys all along. Or we were their monkeys all along. I'm so confused. This sentence makes no sense. My grammar sucks and i can't even work this out.
The whole premise of the analogy is that the typed characters are random, which is why the animal in it is one that doesn't understand written English. The point being that over an infinite amount of time, even totally random typing will, by definition, eventually produce any specified sequence.
OOP doesn't get it, nor does anyone who finds this clever.
It's like writing a joke based on the premise that exercise makes you gain weight. It doesn't, so any joke based on that is going to fall flat, except for people who think it does, lol.