Ever had a discussion with someone when, pushed to their limit, they fall back on the old, "Yeah but you still think 1 plus 1 = 2 right?!!" This happened to me once in the basement of a Marxist-Communist bookstore. I said to the old timer - actually according to Alain Connes of noncommutative geometry 1 plus 1 does not equal 2.!!!
All I remember was a stony silence as the response. haha.
Ever since then I've questioned whether I made that up or not... NOPE - it's right there on the screen!!
1 plus 1 = 1.
2=1.
It sort of easy gave the spectral realization of the zeros of the Riemann Zeta Function as an absorption spectrum. I mean it gave a space first of all, and that space is noncommutative and this was the whole story from the start. So it gave a space, if you want, was a dual, in the sense of a Type 3 to Type 2 relation to the original BC system....
In mathematics, a Bost–Connes system is a quantum statistical dynamical system related to an algebraic number field, whose partition function is related to ...
So what Connes is stating is that we can not state that zero = 1 as that would collapse the field but we can state that 1 plus 1 = 1 due to the noncommutative creation of a zero point from the "double quotient" of the logarithm/exponentials. This is explained in the music theory model or the "type 3 to type 2 system."
http://denisevellachemla.eu/mai12-en.pdf
https://alainconnes.org/wp-content/uploads/NCGspectral.pdf
So the Riemann Zeta Function Zeros are based on time as wavelength that then creates the prime numbers from rational numbers that are noncommutative double quotients.... So that the zero is converted to 1 and 1 plus 1 as noncommutative....
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