zmgsabst 21 hours ago

Mathematics is a human language. It being a formal language doesn’t change that.

Further, it’s not objective: you’re choosing the basis which causes the complexity, but any particular structure can be made simple in some basis.

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  • hackinthebochs 21 hours ago

    Mathematical notation is a human invention, but the structure that mathematics describes is objective. The choice of basis changes the absolute number of terms, but the relative magnitude of terms for a more or less disordered state is generally fixed outside of degenerate cases.

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    • zmgsabst 20 hours ago

      The structure that most words describe is objective, so you haven’t distinguished math as a language. (Nor is mathematics entirely “objective”, eg, axiom of choice.) And the number of terms in your chosen language with your chosen basis isn’t objective: that’s an intrinsic fact to your frame.

      The complexity of terms is not fixed — that’s simply wrong mathematically. They’re dependent on our chosen basis. Your definition is circular, in that you’re implicitly defining “non-degenerate” as those which make your claim true.

      You can’t make the whole class simplified at once, but for any state, there exists a basis in which it is simple.

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      • hackinthebochs 19 hours ago

        This is getting tedious. The point about mathematics was simply that it carries and objectivity that natural language does not carry. But the point about natural language was always a red-herring; not sure why you introduced it.

        >You can’t make the whole class simplified at once

        Yes, this is literally my point. The further point is that the relative complexities of two systems will not switch orders regardless of basis, except perhaps in degenerate cases. There is no "absolute" complexity, so your other points aren't relevant.

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