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Thanks for your reply. >The point is that while X (e.g. the real numbers) can be encoded as Y (e.g. Cauchy sequences), this doesn't mean that X is literally Y.

Thanks for your reply. >The point is that while X (e.g. the real numbers) can be encoded as Y (e.g. Cauchy sequences), this doesn't mean that X is literally Y. In my opinion, a mathematician does not know what the difference between "being literally" and "being encoded as" is - unless you assume that mathematics should aim to be a formal encoding of some pre-existing 'intrinsic reality', in which case what you're doing is physics and not math. In physics, the debate is more open: Is the wave function literally the electron? Or is the wave function just an encoding of the electron, which is the intrinsic real thing? Or is the electron the way we humans perceive the wave function, which is the intrinsic real thing? Anyway this is probably way too theoretical of a debate :)

cgmg 9y ago
> In my opinion, a mathematician does not know what the difference between "being literally" and "being encoded as" is Wrong. The real numbers are literally a Dedekind-complete ordered field. The real numbers are encoded as Cauchy sequences, or as Dedekind cuts. Cauchy sequences are not Dedekind cuts: The former are equivalence classes of sequences. The latter are downward-closed sets without a greatest element. They are literally different objects. Regarding your electron comment, the answer is straightforward: the electron is an excitation of the electron spinor field, nothing more. Fields are more fundamental than particles.