How does noncommutative music theory explain the inverse of the Dirac Operator for Alain Connes?

So Fields Medalist Alain Connes states in his music theory lecture that the inverse of the spinor states is finite. So the spinor states is the noncommutative phase harmonics as the 5th dimension that is non-local. So I didn't realize this inverse he refers to is actually the noncommutative version of the Pythagorean Theorem (which, of course, originated from music theory).... So the inverse is the square root solution of the Pythagorean Theorem based on the discrete numbers being noncommutative.

Previously I had made this reference connection:

 Replacing the Pythagorean knotted rope by a spin-half fermionic Dirac propagator for the quantum surveyor

Now I could almost visualize this as music harmonics being noncommutative. So I started thinking about the music theory aspect, just as Alain Connes does as well in his music lecture. Then I remembered the solution - since the doubling of 1 as the octave, 2 then has 3 as noncommutative creating the new 1 as F, so that F is then doubled to create 4/3 in the same ratio to the original octave as 1/2. So 2/3 is C to F that is noncommutative to 3/2 as C to G but the 3 as F is doubled to 4/3 to be in the same "finite" materialistic "octave" or string as C to C or 1 to 1 as 2 (doubling).

So what would this look like visually in terms of the Pythagorean Theorem?

Well at any rate - this is what the actual spin-half Pythagorean Theorem equation looks like!

 http://noncommutativegeometry.blogspot.com/2007/08/harmonic-mean.html

So that is from Alain Connes directly. Not exactly what you learn in high school is it! That is the Pythagorean "knotted rope" as the spin-half noncommutative propagator.

 Essentially there is a transfer in algebra as pure time of zero dimension geometry (a subset of the complex plane), that then resonates into spatial non-local noncommutative phase, as diameter. And in fact there is no "zero" of geometry but instead the eternal emerging of geometry from noncommutative phase.

We know the deep beauty of music is precisely this noncommutative ratio to the "ONE" - as the subharmonic compared to overtone - is the Perfect Fifth as F to C and then as C to G. This is the secret power of blues music and Indian music theory recognizes this as the secret power of raga music. Connes calls this the triple spectral (frequency) of 2, 3, infinity.

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/DiscoveringGravity.htm

This is an excellent overview of the connection between Kepler and Newton. But what doesn't get mentioned, of course, is that Newton got his inverse square law directly from music harmonics (of Archytas/Plato) and Kepler, of course, was relying on Pythagorean harmonics. This is why Kepler realized number was "male" and "female" and Kepler was against the "closed solution" of the Golden Ratio. So Kepler still saw geometry as transcendent without the irrational numbers as a precise "unit" solution.

So this 1933 pdf math article is an excellent overview on the attempts by mathematicians to plug holes in the logic of "continuity" and "irrational" number - of course noncommutative phase is not mentioned.




So his argument is rebutted by the argument I cite of Sayward and Hugly (pdf link).
It's a fascinating logical paradox that noncommutative phase logic solves.

But here's where the juicy tidbit comes in. Noncommutative algebra of Connes still relies on the process of measurement in a "pure time" state before spacetime exists - as a conceptual illusion of the scientist (detached from reality). This then is "applied" to the experiment being measured. In other words the "measurement problem" still exists in the quantum realm.

Only music as meditation RESOLVES this logical paradox of science! At least science is now acknowledging the logical paradox! By the way - the above "image"  is mirrored by Boethius - whom Borzacchini notes - has confusion about whether to consider the "points" as number or the geometric length as "number." The issue is - what is the "unit" being measured. The "unit" is this conceptual illusion of a zero dimensional pure algebra. It was Plato who argued that "twoness" as a symmetric Unit was before number as geometry and therefore logically resolved this paradox. No - that is not true.