Theorems are more powerful than laws

Very quick thought/assertion I'm exploring. It came to me several months ago when I watched a Scott Aaronson talk about quantum physics and P vs. NP. He made a joke that "If P and NP were studied by physicists, they would have declared P != NP a physical law and moved on." But P vs. NP is a mathematical question, it's not something we can observe like mass and energy, it's a question of logic, and it seems there should be a mathematical answer (proof). I'm frustrated humanity doesn't have an answer to it, I can't even imagine the frustration people who spend their lives actually trying to answer it must feel.

Laws are easier and lazier and you can guess at them just by opening your eyes. Theorems take a lot of mental work. When we humans discover a new law, we gain power over the universe. But when we discover a new theorem, especially a new way of obtaining theorems as Wiles did for Fermat's Last Theorem, we humans gain power over logic itself. And power over logic is more powerful than power over the universe.

Or is it? I've reconsidered. There is the possibility that the universe, being the ultimate arbiter of experimental results, may provide us humans with a result that crushes the whole notion of logic and proof far more so than Godel's theorems ever did. I think it's highly unlikely, but if it happened, the physicists would declare this new experiment showing a fundamental problem with logic as a law and move on, while logicians and mathematicians would be dumbstruck about what to do next with their lives.

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Posted on 2013-01-16 by Jach

Tags: thought

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