Stephen Wolfram

The thing is that if you know in great detail the position of every molecule in the gas, the entropy is always zero because there's only one possible state.

The configuration of molecules in the gas, the molecules bounce around, they have a certain rule for bouncing around.

There's just one state of the gas evolves to one state of the gas and so on.

But it's only if you don't know in detail where all the molecules are that you can say, well, the entropy increases because the things we do know about the molecules, there are more possible microscopic states of the system consistent with what we do know about where the molecules are.

And so the question of whether... So people...

this sort of paradox in a sense of, oh, if we knew where all the molecules were, the entropy wouldn't increase.

There was this idea introduced by Gibbs in the early 20th century, well, actually the very beginning of the 20th century as a physics professor, an American physics professor, sort of the first distinguished American physics professor at Yale.

And he introduced this idea of coarse-graining.

This idea that, well, these molecules have a detailed way they're bouncing around, but we can only observe a coarse-grained version of that.

But the confusion has been nobody knew what a valid coarse-graining would be.

So nobody knew that whether you could have this coarse graining that very carefully was sculpted in just such a way that it would notice that the particular configurations that you could get from the simple initial condition, they fit into this coarse graining and the coarse graining very carefully observes that.

Why can't you do that kind of very detailed, precise coarse graining?

The answer is because if you are a computationally bounded observer and the underlying dynamics is computationally irreducible, that's what defines possible coarse grainings is what a computationally bounded observer can do.

And it's the fact that a computationally bounded observer is forced to look only at this kind of coarse grained version of what the system is doing.

That's why, and because what's going on underneath

is it's kind of filling out the different possible... You're ending up with something where

the sort of underlying computational irreducibility is, if all you can see is what the coarse-grained result is with a sort of computationally bounded observation, then inevitably there are many possible underlying configurations that are consistent with that.

No, any observer like us.

I don't know, I can't imagine.

Yeah, yeah.