The Picard ManeuverInfinite Monkey Theorem
JackbyDevIf you have an infinite amount of monkeys and they’re all typing truly randomly, then an infinite number of them would get it correct on the first try. Which is sort of weird to think about lol.
ameancowMost people don’t get the thought experiment at all.
I’ve seen 300+ deep comment chains on reddit with people arguing bitterly back and forth if a monkey could even operate a typewriter, and how it’s absolutely impossible to get monkeys to type out a book, etc, etc, etc.
I hate it here.
I think too many people don’t consider the monkey is not supposed to be making decisions, it’s just supposed to be inputting anything, literally anything, on a typewriter.
Like a random value generator, for typewriter keys.
I mean, if they are actually monkeys who don’t know to type, some of them will still press keys once or twice. And if there’s infinite monkeys, they will still type it out.
If you’re talking magical, biologically accurate monkeys, then they will eventually shit out models of every scene of your life, replicated in perfect detail in monkey feces. Not just once, but an infinite number of times, and also in every possible configuration your life may have ever existed in, every choice you could have made. An infinite number of times.
Just because a set is infinite does not mean that it will contain every possible permutation of something. That’s a common thought but a provably untrue one.
For example, there are infinite even numbers, and none of them are 3. Not a single one. If someone claimed that generating infinite even numbers would eventually return a 3, you wouldn’t take them seriously, and rightly so.
But here’s the rub: you can also generate infinite even numbers and never return a 2. Every time you generate an even number, there are infinite numbers that it could be. Even if you don’t allow numbers to repeat, it’s not like you are gonna exhaust the amount of non-2 even numbers.
Just because a set is infinite does not mean that it will contain every possible permutation of something.
So back to the typewriters. You might say that while there are infinite numbers, there are not infinite permutations of a string of characters the length of the works of Shakespeare.
And that’s true.
If you were to say that a string of characters the length of the works of Shakespeare (or longer) could never be repeated exactly, the yes they would type the works of Shakespeare.
But then they wouldn’t be typing randomly.
Randomness repeats. Infinite randomness can repeat infinitely.
And we are not dealing with strings of characters the length of the works of Shakespeare. We’re dealing with strings of characters of infinite length. And there are, in fact, infinite permutations of those.
So… Yeah.
There’s no logical basis for infinite monkeys typing infinitely, producing the works of Shakespeare. Or fecal dioramas or alternate universes or whatever else. Doesn’t hold water.
I disagree and have also done plenty of reading on the topic.
I don’t disagree to say that “you’re wrong and even wild silly things are possible!” but I’m saying that it’s a lot more accurate to say that we don’t know what real-world systems can and cannot do. Your model is from a pure mathematical and physical point of view, which would be correct. But we don’t know if our knowledge of quantum mechanics and physics broadly is even complete (probably not) so I have grown quite fond of the far more succinct answer of “I don’t know.”
Generally people get really invested in this because it either validates or invalidates some belief, mystical or material, about the universe, but I don’t think it’s an answerable question until we find out if infinities can even exist in a tangible way. Most likely not, at least in our limited understanding.