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Comment by tlb | Hacker News Reader

The conjecture that our universe is isomorphic to a CA is absolutely testable. When we find a CA that behaves just like the universe, we'll know it's true. If we find a completely different way of computing it that doesn't map to a CA, we'll know it's false.

Computable physics would be extremely useful. Even with coarse approximations you can only integrate the Schrödinger equation among hundreds of particles. So you can't do accurate computational biochemistry except maybe one small molecule at a time.

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That's not how falsifiability works.

>"If we find a completely different way of computing [the universe]"

We can only compute models of the universe. If a model apparently never contradicts our observations of the universe, then we lazily identify the universe with the model within casual contexts, but we don't actually take that as Absolute Truth. Thus, within appropriate contexts, we might speak as if the "forces" of Newton are actual platonic things, as if the arrows in a freshman physics textbook actually exist and could poke you in the eye. But they don't, they are merely a model.

So, suppose we discover tomorrow a new equation which seems to match all observations, and which we can formally prove transcends CAs. Well, we'll never know whether or not tomorrow we'll find an instance where that new equation breaks down, and has to be replaced by an updated equation which IS computable by CAs. Thus, your supposed "test" is not a test at all.

>Computable physics would be extremely useful. Even with coarse approximations you can only integrate the Schrödinger equation among hundreds of particles

You seem to be confusing "computable" with "efficiently computable" or something. A function can be computable but still be prohibitively expensive to compute.

OK, I agree that finding a non-CA way of computing physics doesn't necessarily rule out a future CA model being better.

Current physics models (integrating the Schrödinger equation) aren't computable even in principle, because they involve infinite continuous vector spaces. So a CA model is a theoretical breakthrough because it's computable, even if it's not efficient.

Numerically integrating the Schrödinger equation scales exponentially in the number of quantum states, while the CAs proposed in NKS only scale with the volume of space, so there is some size of system where it'll beat numerical integration.

> ... Computable physics would be extremely useful.

Yeah, undoubtedly, but that has nothing to do with it being true.

Wolfram doesn't make the case, at all, that it might be true, nor does he suggest any reason a CA might be a better model than the Schroedinger equation, or a way of searching for CA oriented models. The fact that modeling physical equations is difficult on a Turing machine is probably telling you something interesting about nature, rather than telling you to dispose of equations as models of reality.

The whole thing is about as useful as Tipler's idea that God is a supercomputer at the end of the universe. Maybe thought provoking for certain kinds of people, but not helpful at all in the business of figuring out how the universe works, or useful things to do on a computer. It's basically an exotic form of science fiction with a higher than average cognitive load.

> If we find a completely different way of computing it that doesn't map to a CA, we'll know it's false.

This is wrong. You would have to additionally prove that the other thing is the only alternative.

Also, CA is not testable in the sense that the theory of relativity is testable. The latter makes measurable predictions that can be satisfied, the former does not. I can imagine any model - unicorns and fairies included - and say that is behaves like the universe. The only way to falsify my claim is to empirically contradict one of my claims. NKS does not put forth such claims. Not the kind you would build a new CERN for.

A CA model of physics would certainly make measurable predictions, probably including some surprising ones that would suggest experiments to confirm them.

Where do you take your certainess from? If even Stephen Wolfram could not produce such predictions, then I doubt anyone else could. In all likelyhood, it is just not a good physical model.

> This is wrong. You would have to additionally prove that the other thing is the only alternative.

A CA theory of physics would just be math, right? Wouldn't it end up being isomorphic with some mathematical representation, albeit perhaps easier to understand or evaluate in its CA form?

Currently, we only know continuous mathematical models of physics. A CA model would be discrete, so not isomorphic to anything we know.

What if it's discrete but effectively matches what we know in that current mathematical methods correctly approximate it in their respective contexts and resolutions? I mean in the same sense that Newtonian physics approximates Einsteinian physics at low speeds and distances.

Wouldn't a truly non-quantized field or dimension falsify this idea? AFAIK there are none known yet, though there are some (like time) where we don't know.

Yes. But it's hard to prove something is non-quantized. All you can do is measure precisely and say that the quantization must be smaller than X.

There are phenomena that arise from quantization rather than just have discrete levels of x

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