Over the last couple of days I have realized that the laws of physics are rather more complex than they seem. The lovely equations like G = 8πT and F = Gmm′/r2 (with a different G in the two equations) seem to be an iceberg most of which is submerged in the icy waters of the foundations of mathematics where the foundational concepts of real analysis and arithmetic are defined in terms of axioms.
This has a curious consequence. We might think that F = Gmm′/r2 is much simpler than F = Gmm′/r2 + Hmm′/r3 (where H is presumably very, very small). But if we fill out each proposal with the foundational mathematical structure, the percentage difference in complexity will be slight, as almost all of the contribution to complexity will be in such things as the construction of real numbers (say, via Dedekind cuts).
Perhaps, though, the above line of thought is reason to think that real analysis and arithmetic are actually fundamental?
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