The problem with physics is that everyone is searching for deep philosophical meaning. Just don't: the Nature doesn't owe you any meaning. It doesn't care at all about a bunch of carbon polymers that for some reason tricked itself into thinking it is the center of the universe.
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Mathematics was crafted by humans to be the thing that marvelously works; would be a shame if it finally didn't.
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but the applicability yo nature need not be true, and yet it is
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But the world (Nature) isn’t mathematical. Mathematics are just inventions we use to represent the world’s patterns. Furthermore, most of mathematics aren’t effective to represent any given branch of the world. Sometimes, none of mathematics is, and a new one has to be invented.
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i agree.. i don't see how that changes anything
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Nature is mathematical much like the human hand has 5 fingers. It just doesn't care to describe itself as thus. But a tiny human subset of Nature is inclined to focus it's gaze long enough to detect and infer patterns and assign values to them. That's a good thing
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A perhaps more powerful move is to appeal to the success of science (what philosophers call the “no miracles argument) and try to make an inference from success —> truth.
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But you’re right that there’s something there. One way of posing this is to ask “how do we explain that the tools we use (like maths) work so well? Is it because we’re carving nature at the joints? If not, what’s going on?” and other things of that sort.
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