Alain Connes: The Language and Writing of the Universe is spectral frequency in "momentum space."

 The spectral triples are not only relevant at very small distances...but they are also extremely relevant at large distances. And the reason behind that; the way the universe communicates with us is spectrally. The Universe sends us bar codes. These bar codes are the absorption lines in spectrum that we get in very distance galaxies, in very distance stars, etc. The universe has not only a language but a way of writing. It writes in bar codes. Now these bar codes are what exactly present in the spectral triples.

That's why it would be a great step to think of geometry in a spectral manner, kind of a Fourier mode. ..We have to work in a Momentum Space. 

Alain Connes lecture on renormalization

https://mathematicalgarden.wordpress.com/2010/08/05/connes-distance-function/

   The idea introduced by Alain Connes in noncommutative geometry consists of defining a spectral distance from values taken by operator observables rather than from classical coordinates. In this way, the concept of geometrical point is not used, which allows the spectral distance to be applied to both classical and quantum spaces.

I don't pretend to understand the mathematics - but rather I try to understand the concepts behind the mathematics.

This is commonly done by introducing a so called spectral triple (A,H,D) consisting of an algebra A, in the continuum this are the functions of coordinates, a Hilbert space H, the space of spinors on L² and a Dirac operator D, which in the continuum is just the differential on the spinors.
Introduced by Alan Connes it became quickly clear that the spectral triple description is a powerful tool to better understand the particle content of the standard model, which is the biggest success of spectral geometry. Our aim is to better understand the second major use of non commutative geometry, to better understand discretized space-times.

 https://sites.google.com/site/lisaglaserphysics/research/non-commutative-geometry

 

 https://gdenittis.files.wordpress.com/2016/08/chile-i-2016-2.pdf

 

 So of course my approach to understanding this is from music theory. The SAME music theory that Alain Connes also promotes as explaining his model.

Only I made this realization about music theory on my own and then tested it out as nonwestern meditation: It WORKS.

 So in his talk - Connes calls this the Cosmic Galois Group.

So each "point" has the future and past overlapping at zero as nonlocality.

http://www.neverendingbooks.org/the-oracle-on-the-symmetries-of-roots

 

 https://www.mimuw.edu.pl/~pwit/toknotes/toknotes.pdf

 So Connes is asked at the end of his talk by a young student - how does the noncommutative triple spectral measurement then effect the original space or vice versa? Connes says he doesn't know for sure. So this is what they call "irregular singularities."

So there really isn't a "zero space" because the measurement changes the value as a process of spacetime itself.

Meanwhile based on this noncommutative definition of reality then the "renormalization" process has to keep redefining the rest of science as a kind of grand reverse-engineering process.

All I know is that the music theory is the truth of reality - as I discovered on my own and ONLY noncommutative phase  logic has the correct understanding of music theory. haha.