Comment by hackinthebochs
Comment by hackinthebochs a day 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.
I didn’t introduce it, you did — by positing that formal language is more objective, as you’ve again done here. My original point was that mathematics is human language.
> The further point is that the relative complexities of two systems will not switch orders regardless of basis, except perhaps in degenerate cases.
Two normal bases: Fourier and wavelet; two normal signals: a wave and an impulse.
They’ll change complexity between the two bases despite everything being normal — the wave simple and impulse complex in Fourier terms; the wave complex and impulse simple in wavelet terms.
That our choice of basis makes a difference is literally why we invented wavelets.