By the way, I read for some time ago the claim that Hippasus was not even temporary of Pythagoras. I am disappointed: it was so nice story;-).

There are indeed two manners to see numbers. The physicist’s way is rather primitive but practical: number has just real magnitude and representation involves topology via limiting procedure.

Number theorist sees their anatomy and in this framework sqrt(2) is whose square produces 2: could one define sqrt(2) operationally using realizing squaring operation and its inverse physically without bringing in topology and limiting procedure? What comes in mind that p-adic length scale hypothesis gives fundamental length scales as proportional to sqrt(p):s.

The values of Zeta (zeta(n) are used as basis in advanced calculations of Feynman diagrams: this is a really elegant manner to do precise numerics by bringing the magnitudes in only at the last step.

And could one efine roots of unity “operationally” via corresponding symmetries, which would be exact symmetries of dark matter at corresponding level of hierarchy (that is those of field body consisting of magnetic flux tubes related by Z_n rotational symmetry ). Nature would have done what is impossible to us! Exact symmetry would play a key role also in the physical representation of numbers.

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