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Comment by Aardwolf | Hacker News Reader

The theorem is called "infinite monkey theorem". That means infinite amount of time. A googol years is not infinite, it's infinite times smaller than that. In an infinite amount of time they will write Shakespeare works (if they type randomly enough and not with some bias like never typing certain combinations of letters)

Also, at least the article could have said what the actual probability is then? Are we talking 1e-500, 1e-1000000, 1 / googolplex, or what?

EDIT: of the above examples 1e-1000000 is the closest I think (in order of magnitude of exponent), based on something like 30^5000000 divided through some amount of years assuming ~5 characters per word. So perhaps "If every atom in the universe was a universe in itself" won't get us there, but recursively repeat that process a million times and we do get there

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Reverse Gellman effect: you witness pedants in your own domain surgically tear down a harmless puff piece and immediately know this must be happening 24/7 in every other domain where fun is modestly attempted

Yes, but the theorem is meant to explain what can happen in the universe over long time scales.

The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.

Perhaps not in our observable universe, but in the space of all possible physics that could take place and / or beyond the observable universe if it actually is infinitely big there, perhaps it can? (as in, anything can happen, there will be copies of the Earth with subtle differences somewhere there, Boltzmann brains appearing purely out of quantum fluctuations, etc...)

I don't think I've ever heard anyone use the infinite monkey example outside of theoretical mathematics; I'm sure someone has, but when I've heard it, it was to describe regular distribution of random.

I think it's a very bizarre thing for these mathematicians to act like they discovered something that I don't think anyone really disputed.

> Yes, but the theorem is meant to explain what can happen in the universe over long time scales.

I never understood it that way. I always interpreted it as a fun way to explain the mathematical truth that no matter how low a probability is, as long as it is technically above 0, the event it describes WILL eventually occur given enough time/trials/etc.

I can't see anybody ever interpreting it as a statement about the real, actual, universe. Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side. Surely people can separate the mathematical ideal/concept from constraints of physical reality.

Have you heard of a Boltman Brain? It's the kind of absurdity that happens when people think seriously about this in the real, actual universe.

https://en.wikipedia.org/wiki/Boltzmann_brain

> the event it describes WILL eventually occur given enough time/trials/etc.

What's the meaning of writing WILL with capitals, and then saying "nobody is talking about the real, actual universe"? What is the value of certainty about what WILL happen in hypothetical universes?

> What is the value of certainty about what WILL happen in hypothetical universes?

Talking about something that would take greater than 1 googol years in our universe has about as much value as talking about something that would take 1 googol years in our universe.

In other words, the fact that something might probably occur right before the heat death of the universe, rather than after, isn't particularly useful either. For that matter, there's about an equal value in talking about something probably "only" a trillion years out, either.

> Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side.

That's a nice thought, but that's giving the average person too much credit when it comes to probability. In my experience, most people's understanding of probability is very poor. For example, few people truly understand the concept of independent events.

Most people believe that after flipping 10 heads in a row, the probability of tails on the next flip is much higher.

I'm sure you could convince a rational individual that the assymetry of the coin makes 50/50 impossible. But I doubt that the average person has ever really considered it.

"Infinite monkeys" would produce Shakespeare and every other book, document, and all future possible book and document in the amount of time equal to the number of letters in the book and the typing rate of a monkey. It wouldn't take an infinite amount of time. :)

Yes, I always imagined this being just a silly exercise in pulling out a finite outcome from infinity. It’s not meant to be provable or disprovable, just hard to comprehend because we cannot think in infinite terms.

Relatedly, I wrote an essay that covers this a few years back: https://medium.com/@beadey.teigh/typewriters-29309c8e3b71

Yeah, I might be naive, since they're professional mathematicians and I'm not, but their conclusion feels like saying that they "tested" the concept of infinity and found that it's simply unreachable. To me, the infinite monkey theorem is an abstract idea and not something that needs to be "tested", though it's certainly fun to run the numbers.

Reminds me of Archimedes calculating the number of grains of sand to fill the universe

They didn't "test" the concept of infinity. They said that the results of the infinite monkey theorem are well known, and they wanted to see what happens in the finite case.

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