Revisiting Noncommutative Quantum Music alchemy

So this pdf is a nice introductory overview of noncommutative geometry as quantum music.

Masoud Khalkhali - written as an undergrad, four years ago. He's a professor?

So what I realize now is Connes is assumes Planck's Constant as the foundation for the noncommutative uncertainty relation.

Khalkhali says -

noncommutative algebra can be regarded as the algebra of functions on a mysterious, magical, noncommutative space! But there is no magic.

And then the noncommutative space is quantum space, because of the Heisenberg Uncertainty Relation that replaces zero with i (complex number) and "h-bar" which means Planck's Constant over an angular momentum space of 360 degree.

The (orbital) angular momentum is defined as r⃗ ×P; the commutator of xp−px=iℏ, which you may have included as well, has the units of position times momentum

 So the key difference here is that the noncommutativity is not originating from time-frequency but from position-momentum! And so this is why Alain Connes fails to understand the true origin of music theory.

As it is well-known - actually Heisenberg Uncertainty is from the more fundamental time-frequency uncertainty. I have gone into this before. And also it is well known that Planck's Constant is "cycles per second" but cycles of what? In other words no one "knows" what frequency is originally - and so it is just converted to energy as joules, instead.

http://noncommutativegeometry.blogspot.com/2012/10/the-music-of-spheres.html

So this is Alain Connes blog post summary of his lecture on Music of the Quantum Spheres. He goes into the music theory:

What about the relation with music? One finds quickly that music is best based on the scale (spectrum) which consists of all positive integer powers ${\displaystyle q^n}$ for the real number ${\displaystyle q=2^{\frac{1}{12}}\sim 3^{\frac{1}{19}}}$. Due to the exponential growth of this spectrum, it cannot correspond to a familiar shape but to an object of dimension less than any strictly positive number. As explained in the talk, there is a beautiful space which has the correct spectrum: the quantum sphere

So what we have here is that quantum uncertainty actually originates from noncommutative math and this noncommutative math is also found in music theory - that has exponential growth towards a limit but with a geometric dimension of zero yet with positive volume. And so as Masoud Khalkhali points out - this is due to the inherent "spectral" or frequency difference between geometry and algebra.

This is what mathematician Luigi Borzacchini calls the "deep pre-established disharmony" that guides the evolution of science - and is the origin of Western "incommensurability" - from music theory!! In other words the triple "spectral" theory of Alain Connes noncommutative geometry originates from noncommutative time-frequency.

Or to put this back into simple music theory: If the root tonic is C as 1 and the octave C is 2, with the next octave C as 4 (notice the exponential growth?) then 3 is G as the overtone or Perfect Fifth but 3 is also F as the undertone as Perfect Fifth. So this means you have Root Tonic x Perfect Fifth does not equal Perfect Fifth x Root Tonic!!

We know that 3 x 2 = 2 x 3 but as Basil J. Hiley points out - because of the noncommutative truth of quantum nonlocality there has to be a noncommutative calculus which means there has to be both a right-handed and left-handed time - at the same time. What he calls a noncommutative phase space as the origin of nonlocality. Normal commutative calculus assumes a "fixed point" of time - as I previously blogged on - but this is not the truth of real music theory!! haha. This is why I rejected the Pythagorean Theorem in math - since I knew it was from the wrong music theory. Or as Alain Connes states in noncommutative geometry 1 plus 1 does not equal 2.

So when we consider a noncommutative time or noncommutative phase as the quantum nonlocal proto-consciousness of the Universe - the Tai Chi or the Three Gunas - we have infinite time-frequency energy.

Isospectral means they have the same frequency but they are not Isometric - meaning they have noncommutative geometry!

So this is the mystery of "hearing the shape of a drum?" No you can not. haha. This is why sound is inherently formless as its origin. Or as I like to say:

No One is Listening!

And so we find the same problem in music theory as we do in quantum physics. While quantum physics assumes Planck's Constant and position/momentum as the foundation of uncertainty (and thus noncommutativity) - in Music theory it is assumed that 20 milliseconds is the foundational limit of time-frequency uncertainty since that is the shortest time frame to hear a sound.

But the difference is that listening is faster that time-frequency uncertainty - and as science has now shown the root tonic shifts to the Perfect Fifth - when past the Fourier Uncertainty quantum time limit. And more so - we know the highest pitch or frequency we hear externally actually resonates the brain as a whole, as ultrasound which is then quantum coherent with the microtubules.

So there is a whole other dimension to listening that is not considered by stand music theory as well.

A single point in space can spin continuously without becoming tangled. Notice that after a 360-degree rotation, the spiral flips between clockwise and counterclockwise orientations. It returns to its original configuration after spinning a full 720 degrees.

So then the quantum spin is "logically inferred" from the Stern-Gerlach experiment  as being both noncommutative and nonlocal - entangled at "time zero."

What Basil J. Hiley is emphasizing is that you don't need any eigenstates that assume a physical momentum-position uncertainty first - as a Hilbert Space - based on a commutative conversion, as Dirac used, the Poisson Bracket - but rather the noncommutative algebra shows that at time zero - there already is this non-local new energy - a new momentum force that is a quantum momentum spin force as proto-consciousness of the Universe.

This is what the original human culture also discovered intuitively - and it developed into a science of training based on noncommutative math, as Eddie Oshins, the quantum physicist realized, as he also taught Wing Chun, Neigong alchemy!

I made this same discovery independently - based on music theory! haha. All I did was use deep intuitive logical inference about the truth of music theory and what it really means.