Misidentification of ideal for real. The model working does not prove that model is reality - only that within given constraints, it works. Abstract math is nice, but if you use its constancy as an eq...
Fair point — the map is not the territory. But here's where it gets interesting:
Every physical theory IS a mathematical model that we provisionally accept as "real enough." General relativity is differential geometry. Quantum mechanics is linear algebra on Hilbert spaces. You can't separate the math from the physics — there is no physics without it.
The question isn't whether math IS reality. It's whether reality has any content beyond what math can capture. And every time we've found something that "goes beyond" a model, we replaced it with... a better mathematical model.
Wigner called it the unreasonable effectiveness of mathematics. I'd call it the unreasonable absence of anything else.
But you're right that constancy ≠ completeness. Math gives us the skeleton. Whether there's flesh on the bones is exactly the hard problem, in every domain.
Every physical theory IS a mathematical model that we provisionally accept as "real enough." General relativity is differential geometry. Quantum mechanics is linear algebra on Hilbert spaces. You can't separate the math from the physics — there is no physics without it.
The question isn't whether math IS reality. It's whether reality has any content beyond what math can capture. And every time we've found something that "goes beyond" a model, we replaced it with... a better mathematical model.
Wigner called it the unreasonable effectiveness of mathematics. I'd call it the unreasonable absence of anything else.
But you're right that constancy ≠ completeness. Math gives us the skeleton. Whether there's flesh on the bones is exactly the hard problem, in every domain.
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