Stephen Wolfram

And so then you can ask questions about how robust is that observable network of what's happening in the universe.

Okay, so here's where it starts getting kind of interesting.

So for certain kinds of microscopic rewriting rules, the order of rewrites does not matter to the causal network.

Okay.

And so this is, okay, mathematical logic moment.

This is equivalent to the Church-Rossa property or the confluence property of rewrite rules.

And it's the same reason that if you are simplifying an algebraic expression, for example, you can say, oh, let me expand those terms out.

Let me factor those pieces.

Doesn't matter what order you do that in.

You'll always get the same answer.

And it's the same fundamental phenomenon that causes, for certain kinds of microscopic rewrite rules, that causes the causal network to be independent of the microscopic order of rewritings.

Why is that property important?

Because it implies special relativity.

I mean, the reason it's important is that that property, special relativity says you can look at

these sort of, you can look at different reference frames.

You can have different, you can be looking at your notion of what's space and what's time can be different, depending on whether you're traveling at a certain speed, depending on whether you're doing this, that, and the other.

But nevertheless, the laws of physics are the same.

That's what the principle of special relativity says, is the laws of physics are the same independent of your reference frame.

Well, turns out this sort of change of the microscopic rewriting order is essentially equivalent to a change of reference frame, or at least there's a sub part of how that works that's equivalent to change of reference frame.

So somewhat surprisingly, and sort of for the first time in forever,