Stephen Wolfram

They were doing things that were as sophisticated as they did when their rules were much more complicated.

So it didn't look like this idea, oh, to get sophisticated computation, you have to build something with very sophisticated rules.

That idea didn't seem to pan out.

And instead, it seemed to be the case that sophisticated computation was completely ubiquitous, even in systems with incredibly simple rules.

And so that led to this thing that I call the principle of computational equivalence, which basically says when you have a system that follows rules of any kind, then whenever the system isn't doing things that are in some sense obviously simple,

then the computation that the behavior of the system corresponds to is of equivalent sophistication.

So that means that when you kind of go from the very, very, very simplest things you can imagine, then quite quickly you hit this kind of threshold above which everything is equivalent in its computational sophistication.

Not obvious that would be the case.

I mean, that's a science fact.

Well, my guess is that they all blend together.

But we don't know that for sure yet.

I mean, this, you know, I should say, I said rather glibly that the principle of computational equivalence is sort of a science fact.

Yes.

I was using air quotes for the science fact.

Just to talk about that for a second, the thing is that it has a complicated epistemological character, similar to things like the second law of thermodynamics, the law of entropy increase.

What is the second law of thermodynamics?

Is it a law of nature?

Is it a thing that is true of the physical world?

Is it something which is mathematically provable?

Is it something which happens to be true of the systems that we see in the world?