Stephen Wolfram

And that's something that I think I am somewhat hopeful that that will be possible.

Although, you know, as of literally today, if you ask me, I'm confronted with things that I don't understand very well.

Yeah.

My guess is that within, so we didn't talk much about computational irreducibility, but it's a consequence of this principle of computational equivalence.

And it's sort of a core idea that one has to understand, I think, which is, the question is, you're doing a computation, you can figure out what happens in the computation just by running every step in the computation and seeing what happens.

Or you can say, let me jump ahead and figure out, you know, have something smarter that figures out what's going to happen before it actually happens.

And a lot of traditional science has been about that act of computational reducibility.

It's like we've got these equations and we can just solve them and we can figure out what's going to happen.

We don't have to trace all of those steps.

We just jump ahead because we solve these equations.

Okay, so one of the things that is a consequence of the principle of computational equivalence is you don't always get to do that.

Many, many systems will be computationally irreducible in the sense that the only way to find out what they do is just follow each step and see what happens.

Why is that?

Well, if you're saying, well, we, with our brains, we're a lot smarter.

We don't have to mess around like the little cellular automaton going through and updating all those cells.

We can just use the power of our brains to jump ahead.

But if the principle of computational equivalence is right, that's not gonna be correct, because it means that there's us doing our computation in our brains, there's a little cellular automaton doing its computation, and the principle of computational equivalence says these two computations are fundamentally equivalent.

So that means we don't get to say we're a lot smarter than the cellular automaton and jump ahead, because we're just doing computation that's of the same sophistication as the cellular automaton itself.

I understand, but the problem is, to know whether you're right, you have to have some computational reducibility, because we are embedded in the universe.

If the only way to know whether we get the universe is just to run the universe,