Stephen Wolfram

But if you look inside this pattern,

it looks really random.

You look at the center column of cells, and I studied that in great detail, and so far as one can tell, it's completely random.

And it's kind of a little bit like digits of pi.

You know the rule for generating the digits of pi, but once you've generated them, you know, 3.14159, et cetera, they seem completely random.

And in fact, I put up this prize back in, what was it, 2019 or something, for prove anything about the sequence, basically.

People have sent me some things, but I don't know how hard these problems are.

I mean, I was kind of spoiled because in 2007, I put up a prize for determining whether a particular Turing machine that I thought was the simplest candidate for being a universal Turing machine worked.

determine whether it is or isn't a universal Turing machine.

And somebody did a really good job of winning that prize and proving that it was a universal Turing machine in about six months.

And so I didn't know whether that would be one of these problems that was out there for hundreds of years, or whether in this particular case, a young chap called Alex Smith nailed it in six months.

And so with this Rule 30 collection, I don't really know whether these are things that are 100 years away from being able to get, or whether somebody's going to come and do something very clever.

But, you know, this is— And yet you can't.

Yeah, right.

This is the intuitional surprise of computational irreducibility and so on, that even though the rules are simple, you can't tell what's going to happen, and you can't prove things about it.

And I think—so anyway, the thing I started in 1984 or so, I started realizing—

There's this phenomenon that you can have very simple rules, they produce apparently random behavior.

Okay, so that's a little bit like the second law of thermodynamics, because it's like you have this simple initial condition, you can readily see that it's very, you can describe it very easily, and yet it makes this thing that seems to be random.

Now, turns out there's some technical detail about the second order of thermodynamics and about the idea of reversibility.

When you have a movie of two billiard balls colliding, and you see them collide and they bounce off,