Stephen Wolfram

It is a story of a computationally bounded observer trying to observe a computationally irreducible system.

So it's a story of underneath, the molecules are bouncing around.

They're bouncing around in this completely determined way, determined by rules.

And

But the point is that we, as computationally bounded observers, can't tell that there were these sort of simple underlying rules.

To us, it just looks random.

And when it comes to this question about, can you prepare the initial state so that the disordered thing is, you have exactly the right disorder to make something orderly, a computationally bounded observer cannot do that.

we'd have to have done all of this sort of irreducible computation to work out very precisely what this disordered state, what the exact right disordered state is, so that we would get this ordered thing produced from it.

Right.

So it means...

Okay, you can talk about Turing machines, you can talk about computational complexity theory and polynomial time computation and things like this.

There are a variety of ways to make something more precise, but I think it's more useful, the intuitive version of it is more useful, which is basically just to say that how much computation are you going to do to try and work out what's going on?

And the answer is, you're not allowed to do a lot of, we're not able to do a lot of computation.

When we, you know, we've got, you know, in this room, there will be a trillion, trillion, trillion molecules, a little bit less.

Right.

And, you know,

At every moment, every microsecond or something, these molecules are colliding, and that's a lot of computation that's getting done.

And the question is, in our brains, we do a lot less computation every second than the computation done by all those molecules.

if there is computational irreducibility, we can't work out in detail what all those molecules are going to do.

What we can do is only a much smaller amount of computation.