Terence Tao

Now give me a rate.

Okay, so if I don't have an infinite number of monkeys, but a large finite number of monkeys, how long do I have to wait for Hamlet to come out?

And that's a more quantitative question.

And this is something that you can attack by purely finite methods, and you can use your finite intuition.

And in this case, it turns out to be exponential in the length of the text that you're trying to generate.

And so this is why you never see the monkeys create Hamlet.

You can maybe see them create a four-letter word,

but nothing that big.

And so I personally find once you finalize an infinite statement, it does become much more intuitive and it's no longer so weird.

Yeah.

The downside is that the finalized proofs are just much, much messier.

So the infinite ones are found first, usually, like decades earlier.

And then later on, people finalize them.

Right.

So I think science in general is interaction between three things.

There's the real world.

There's what we observe of the real world, our observations.

and then our mental models as to how we think the world works.

So we can't directly access reality.

All we have are the observations, which are incomplete, and they have errors.