Stephen Wolfram’s Computational Irreducibility

Stephen Wolfram
Some Modern Perspectives on the Quest for Ultimate Knowledge

A good overview about computational irreducibility and how it could affect our quest for ultimate knowledge. Just one example from the paper. Let us imagine that the Universe is governed by just a few simple rules and they are completely determenistic. Yet, as they represent a computationally irreducible system, there is no way to make a shortcut and learn what happens next. Also free will is just a consequence of the computational irreducibility. An interesting thought. So in a way we are in some simulation with simple rules but we cannot predict what happens next. A couple of citations:

Because I’ve seen so many cases where simple rules end up generating immensely rich and complex behavior.

And that’s made me think it’s not nearly so implausible that our whole universe could come from a simple rule.

It’s possible that in my inventory of candidate universes is our very own universe. But we haven’t been able to tell.

Because going from that underlying rule to the final behavior requires an irreducible amount of computational work.

It’s a peculiar situation: we could in a sense already have ultimate knowledge about our universe, yet not know it.

It looks probabilistic because there is a lot of complicated stuff going on that we’re not seeing–notably in the very structure and connectivity of space and time.

But really it’s all completely deterministic.

That somehow knowing the laws of the universe would tell us how humans would act–and give us a way to compute and predict human behavior.

Of course, to many people this always seemed implausible–because we feel that we have some form of free will.

And now, with computational irreducibility, we can see how this can still be consistent with deterministic underlying laws.