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The_Duck comments on Mathematics as a lossy compression algorithm gone wild - Less Wrong
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I think when we say that the universe "runs on math," part of what we mean is that we can use simple mathematical laws to predict (in principle) all aspects of the universe. We suspect that there is a lossless compression algorithm, i.e., a theory of everything. This is a much stronger statement than just claiming that the universe contains some predictable regularities, and is part of what makes the Platonic ideas you are arguing against seem appealing.
We could imagine a universe in which physics found lots of approximate patterns that held most of the time and then got stuck, with no hint of any underlying order and simplicity. In such a universe we would probably not be so impressed with the idea of the universe "running on math" and these Platonic ideas might be less appealing.
Yeah, I don't see this as likely at all. As I repeatedly said here, it's models all the way down.
Fair enough. I can see the appeal of your view if you don't think there's a theory of everything. But given the success of fundamental physics so far, I find it hard to believe that there isn't such a theory!
Given that every time we discover something new we find that there are more questions than answers, I find it hard to believe that the process should converge some day.
I don't think that's really true though. The advances in physics that have been worth celebrating--Newtonian mechanics, Maxwellian electromagnetism, Einsteinian relativity, the electroweak theory, QCD, etc.--have been those that answer lots and lots of questions at once and raise only a few new questions like "why this theory?" and "what about higher energies?". Now we're at the point where the Standard Model and GR together answer almost any question you can ask about how the world works, and there are relatively few questions remaining, like the problem of quantum gravity. Think how much more narrow and neatly-posed this problem is compared to the pre-Newtonian problem of explaining all of Nature!