https://www.youtube.com/watch?v=DaXkyxTZB58&lc=UgytF0EKPQdGwiRziOB4AaABAg.9eNF7HSlGBO9ePHU-v5r4K
So basically ever since Plato and the Pythagorean Theorem aka the "power axiom set" almost all math is based on "commutative geometry" as Fields Medal math professor Alain Connes points out. Essentially this is what we learn in high school - and also stems from Zero as "negative infinity" for a materialist idealism philosophy of the geometric continuum. In math this is called "incommensurability" since as Roger Penrose (and other math professors point out like Luigi Borzacchini) - there is no "one to one" correspondence between number and geometry in certain mathemathatical logic paradoxes.
So as Penrose points out, based on Godel's Incompleteness Theorem, "understanding" at its primary level is not a calculation and thus can not be expressed in an algorithm or function. So Alain Connes uses music theory to explain noncommutativity but Connes calls this "primitive time" while Penrose calls it "fundamental time" and math professor Louis Kauffman calls it "primoridal time."
Most people assume that complex numbers are also commutative geometry but as Kauffman points out in fact the imaginary number as the square root of negative one is from an algebraic process that is inherently noncommutative. So when we make a measurement this in itself causes a shift in time and so there really is no symmetric rest frame that relativity relies on. Nobel Physicist Louis de Broglie also figured this out - that there is no symmetric rest frame for a measurement - as Martin van der Mark has emphasized in his recent youtube uploads.
So when people learn music theory it is mainly by rote. Mathematics, as Borzacchini points out, actually originates from music theory. So for example the square root of two first originated from the major 2nd music interval as 9/8 that is cubed to the Tritone (that splits the Perfect Fourth and Perfect Fifth). So the 9/8 originates from the squaring of 3/2 to 9/4 which is then "halved" back into the octave. But there is an earlier understanding of this origin - that Alain Connes in his "Music of Shapes" lecture on youtube calls, "Two, Three, Infinity...." as the basic understanding of noncommutativity.
What happened, as Professor Richard McKirahan revealed in a recent - maybe 10 years ago? - paper on Philolaus - that Philolaus to develop the first use of "magnitude" as a mathematical irrational geometry number - from music theory - flipped his lyre around! So by "flipping" his musical instrument around Philolaus was able to cover up the reversal of the time-frequency resonance. Essentially the music theory assumes a "zero" point in space but noncommutativity is stating that even at the zero point of Time there already is a future and past overlapping!
If you watch Alan Guth's recent debate with Roger Penrose (on youtube) - Guth emphasizes that at T-Naught or the zero point of time there is a quantum wave function already. This is how Guth argues for the inflationary phase of the universe since if you can create energy faster than the Time-Frequency Uncertainty or the Fourier Uncertainty that is the linear operator of changing time into frequency and vice versa then you can create energy from "nothing" at the Planck quantum scale (the average energy of light based on frequency).
So Alan Guth is arguing for the standard quantum assumption that at Time Naught there is a symmetric rest frame (in quantum physics it's the Poisson Bracket that Dirac used from its earlier use in Maxwell's mathematics) - so the Poisson Bracket converts the inner cross products of the matrices. What is fascinating about Noncommutativity is that as Penrose emphasizes the quantum nonlocality is "seemingly" or "apparently" random but as Alain Connes points out the inner cross products of the matrices are discrete rational numbers again most simply modeled as Two, Three, Infinity from music theory! so in fact just because they are not observable as an external measurement assuming a symmetric spatial rest frame (and thus are apparently random to mainstream science) - this does not mean that the inner cross products of the future and past overlapping via the 1/2 spin, modeled by the 2 x 2 matrices with imaginary time do not exist!!
We can logically infer their existence and even experimentally verify the nonlocal entanglement by doing the "weak measurement" entangled photon "Negaparticle" research, as shown by the Yakir Aharonov research group. (there is a paper showing that in fact those Weak Measurement experiments are actually noncommutative). Hiley refers to those experiments in the email reply. So my background is music theory and thus I realized this noncommutative truth from my study of music and I called it "complementary opposites" as the secret harmonization of reality. In fact it also explains nonwestern meditation as alchemy!
I thus finished my master's degree by doing nonwestern meditation and so, just as Olivier Costa de Beauregard argued, as the protege of Louis de Broglie, the truth of reality is inherently precognitive consciousness from the future - as this reverse time, negative frequency energy. We can listen to the source of the energy up to ten times faster than Fourier Uncertainty and thus achieve quantum coherence via the ultrasound Hypersonic Effect in music - as my research details. Essentially the 2/3 as the Perfect Fifth is C to F as the Undertone and C to G as the overtone or 3/2 and thus logically it is noncommutative as an eternal energy harmonization process.
The "one" is not a materialistic rest frame that is symmetric to the octave or 2 - that Western music theory assumes with the Harmonic Series, etc. Rather the "one" is coherent biophoton laser light that is turned around to access the supermomentum source energy of light as the virtual photon energy. Just as Gerard 't Hooft points out in his "Light is Heavy" article - all matter is inherently made of light but doe to this inherent 1/2 spin there is a supermomentum to light (or relativistic mass) that is a newly discovered "causal force" as Professor Basil J. Hiley calls it. You can read my free research for more details - see my channel link.
yeah Philolaus was not supposed to write down the teachings but rather the real student is supposed to do five years of silence while just listening to Pythagoras. This is a cave meditation - and only then can the teacher be seen. So what Philolaus did is derive the Perfect Fourth by flipping his Lyre around using the "Greater Perfect System" or double octave.
So Philolaus argued that the music tuning is just the ratios and not the actual frequency and thus the order is commutative and symmetric. So he did this by ignoring the fact that the Overtone Series requires the root tonic as the 1 to have the denominator be maintained as the same pitch resonance of the 1. So therefore 4/3 as the Harmonic Series Perfect Fifth (G to C) is not actually the same root tonic! This is only proven by LISTENING to the source of the one rather than just a visual measurement. Philolaus relied on the double octave of 6:8:9:12 so that the Perfect Fifth is 12 to 8 but the Perfect Fourth is 8 to 6 derived from a new root tonic of 4/3 based on a 0 to 8 "scale" or root tonic instead of a 0 to 12 scale or root tonic.
If you listen to Alain Connes "Music of Shapes" lectures that I quote from and explain in my book - he emphasizes that the two note chord is noncommutative while the scale as the octave is commutative. Connes then relates this principle back to Von Neumann's Type III quantum factorization based on the inner cross products of the matrices as noncommutative discrete numbers. So what Connes is stating is that the two-spin Dirac Operator (that Penrose relies on) has an inverse Dirac Propagator for the 1/2 spin as a "chord" or "cord" - a "line element."
So this is derived from a spectralizaton of frequency and time. In other words in stead of thinking of distance as a geometric length based on the symmetric continuum - the distance between two "zero points" in spacetime is from a Primitive time that is noncommutative time-frequency and it is also nonlocal. So this means you compare the 2/3 and the 3/2 with the 1 as the octave. The "1" as the root tonic changes what the scale or octave invariance is - depending on what time-frequency is being measurement.
What Philolaus did is flip his lyre around so that the 6/8 as 3/4 has a different root tonic but then it can be ADDED to the 8/12 as 3/2 and thus creates the very first logarithmic irrational geometry ratio!! So people learn in basic music theory that the Perfect Fifth PLUS the Perfect Fourth = the octave and this is derived from 3/2 x 4/3 = 12/6 or 2 as the octave. But again it covers up the fact that 2/3 is actually from the 8 as the undertone Perfect Fifth that is then doubled as 8/6 or 4/3 with a different root tonic of 0 to 8. So in basic music theory of the overtone series the 3/2 is allowed since it creates the logarithmic equation. So 3/2 is C to G as the overtone for 3/2 plus 4/3 = 2.
But the 4/3 is actually from the undertone as 2/3 that is then doubled based on a new root tonic! So the truth of the music theory is an infinite noncommutative time-frequency energy. For example in nonwestern music theory like in Indian music theory the "three gunas" as the oldest philosophy of India is from music theory. So if you listen to a drone and the Perfect fourth is the higher note of the root tonic - this actually creates a NEW root tonic as the octave below the Perfect fourth. The empirical truth is that the Perfect Fourth is never a natural overtone of the root tonic - but this is the lie created by Philolaus to claim that G to C is the Perfect Fourth in the scale when in fact it is C to F as 6/8 while 8/12 is C to G as 3/2.
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