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.
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.
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.
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.
Good luck finding them though.
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.
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.