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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 mod
by xamuel 7y ago
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.
- tlb 7y agoOK, 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.