Drew W. Hempel, MA
EcoEcho Cultivation, Minnesota
ecoechocultivation@gmail.com

Professor JohnJoe McFadden, one of the founders of quantum biology, explains the no repeatability paradox is resolved through acoustic quantum phonons:

Coherence in biology seems to be maintained by molecular vibrations. [acoustic phonons] This is why quantum coherence, entanglement and tunneling in biological systems is puzzling, because they are hot, messy, noisy where you wouldn't expect coherence to survive for very long. But it does ... Biology has somehow worked out how to use vibrations, use molecular noise, to maintain, rather than destroy coherence. There's a lot of evidence for that. (McFadden, 2014)

This quantum biology resonance coherence, physicist Pascual Jordan insisted in the 1930s, was amplifying from "intuitive meaning" of "noncommutativity" (Howard, 2013). Quantum physics Professor Basil J. Hiley, the collaborator on David Bohm's extension of de Broglie's noncommutative quantum foundations, makes the same point as Connes:

The mathematics that is necessary to describe the holomovement is a non-commutative algebra and this way of looking at physical processes has a very profound impact on what we mean by the very notion of 'existence'... In the context of the holomovement, any change of the experimental conditions will change the overall structure process. But it must happen in a way that cannot be achieved by using the laws of classical mechanics. It turns out that this feature is beautifully captured by the non-commutative geometry ... Since we started this work, mathematicians have been developing what they call 'non-commutative algebraic geometry' and what one finds is that if we go deeply into this new mathematics, we find that the standard quantum formalism is but a fragment of this new geometry. This is not surprising because the mathematics was inspired by the standard quantum formalism. (Hiley, 2015)

Hiley emphasizes this secret of a newly discovered nonlocal energy: "a new form of inner energy possessed by the particle, organising the flow lines in a novel way and suggesting a 'formative' cause ... quantum phenomena emerged from a non-commutative phase space" (Hiley, 2016). By utilizing the noncommutative phase logic, Hiley distinguishes this new form of "inner energy." Hiley states:

Somehow the 'quantum force' is a 'private' force. It thus cannot be regarded as a distortion of some underlying sub-quantum medium as was originally suggested by de Broglie. It is independent of field intensity, thus fulfilling a precondition for non-locality, and it carries information about the whole experimental arrangement in which the particle finds itself. (Hiley, 1995)

Hiley also makes the connection to music as being noncommutative quantum logic:

To make this clearer let us consider what happens when we are listening to music. We do not perceive the individual notes directly. Rather the notes enter our nervous system in which they are enfolded. There we have a memory of the notes past, and we have an anticipation of the notes to come. It is the tension between the two that creates an active continuous movement in our nervous system which generates our experience of music. In the language we are using, we perceive directly the implicate order and it is only afterwards that we explicate the structure of the score as an intellectual exercise rather than an experience of the music. Indeed, composers experience the sensation of the whole movement before writing the score. The score is then structured in such a way as to stimulate a reaction in the nervous system of the listener that corresponds to the one originally experienced by the composer. Thus what we call consciousness is the unfolding activity of what is enfolded in the nervous system. (Hiley, 2015

Again, just as with Connes, Hiley emphasizes the noncommutativity truth of reality:

The structure that you, that we, were finding was a non-commutative structure; it was the structure that the early guys [of quantum physics] that you had up there were using, but then they went on to operationism because they wouldn't stay with the non-commutative ... non-commutativity to find out what it meant geometrically or what it meant ontologically. (Hiley, 2017)

The parapsychological implications are lurking just under the surface as Hiley recognizes with the connection to nonwestern philosophy: "Then, of course, they thought we'd gone mystically East. But I mean the quantum potential is not a classical force. It's not a classical potential. It's something extraordinary, very strange. It doesn't get propagated, as far as we can find out" (Musser, 2013). And Hiley (2012) states: "Certainly that's [the paranormal] a possibility and that's why people get scared of it."

So as Hiley alludes to, noncommutativity has also been key to explaining the paranormal. Eddie Oshins, working at Stanford Linear Accelerator Center (SLAC), argued that "this property of noncommutivity [sic] in itself might be valuable in some way. My claim, and original idea, has been that this is circumnavigating a T'ai Chi (Yin/Yang) symbol!" (Oshins, 1998). As I'll give more details, Oshins also calls this noncommutativity the basis of "Noi Kung" or paranormal neigong as an example of "quantum psychology." For follow-up analysis see Oshins' collaborator, Math Professor Louis Kauffman, in his article, Noncommutative Worlds, ... "I particularly thank Eddie Oshins" (2004). Oshins passed away in October 2003 but fortunately he had already developed his noncommutative Physics of Tao analysis:

Identification of parallel roots in the development of Taoism in China, and ... by Anaximander [who taught Pythagoras] in Ionia, Greece ... The empirical demonstration of Eddie Oshins' work on self-referential motion and the hunt for psychic torque. (Oshins, n.d.)

Former Hampshire College quantum mechanics Professor Lawrence Domash also identified the noncommutative music model when he wrote on paranormal yoga meditation:

The macroscopic analog of stimulated emission (alluded to before in connection with the mantra) ... the role of the mantra ... to electrically correlate and quiet millions of neurons ... in such a way that a latent biophysical phase correlation at a quantum macromolecular level is permitted to manifest itself among them ... due directly to the non-commutative properties of the field operators. (Domash, 1975, pp. 659-663)

Harold Atmanspacher (2014) has emphasized "Non-Commutative Operations in Consciousness Studies: For reasons easy to understand, non-commuting operations must be expected to be the rule rather than the exception for operations on mental systems." Atmanspacher follows up:

There are two major extraphysical directions in which non-commuting operations, the basis of complementarity, have been applied in the past 20 years. One of them refers to fertile new insights in psychology and cognitive science ... and other cognitive processes using quantum concepts. (Atmanspacher, 2016)

Music resonance is often recognized as of crucial significance in science (i.e., the "music logarithmic spiral" concept key to Philosopher of Science Professor Oliver L. Reiser's UN thinktank work). Philosopher of Science Sir Karl Popper wrote:

This means that, as in Kepler, it is resonance - and thus harmony and dissonance - which govern the world ... Kepler's Harmony of the World acquired scientific status only with Louis de Broglie and Erwin Schrödinger ... Wave optics, in turn, takes its orientation from musical theory, from the theory of acoustical vibrations and waves, resonance and dissonance. But in this theory Kepler and his doctrine of harmony - Hence Pythagoras in the end - plays a decisive role. (Popper, 1999, p. 75)

Nobel Physicist Louis de Broglie considered his Law of Phase Harmony as his greatest discovery, based on the Pythagorean insight that as a particle goes towards the speed of light the quantum frequency increases while, paradoxically time also gets bigger (slows down) due to relativity. Logically this proves there must be a reverse time and negative frequency energy that is in phase harmony and guiding the particle from the future. From the invariance of light as the observer, a superluminal phase wave guides, from the future, the space ship (our brains):

[Image Source: http://mc1soft.com/papers/deBroglie/deBroglie_moving.gif ]

Professor Yakir Aharonov's entangled reverse time photon weak measurements have empirically corroborated what's now called the de Broglie-Bohm model. Professor Basil Hiley reveals that "the Bohm approach has its origins in non-commutative algebra" (Hiley, 2018) and continues:

Energy is the thing that is non-local ... you could use the formalism to measure these things locally they're called weak measurements ... we're not supposed to say anything about what happens between the [quantum double] slits and the screen remember yeah, but we can actually construct the momentum, we can actually draw little vector diagrams, and we can construct the trajectories with this new [weak] method of dealing with things ... in fact, quantum processes are organic so already we're beginning to say that maybe this is where we can get into biology ... therefore we must change our view of reality and this is the important point about changing our view of reality to get in to see how mind works...

Implicate order is algebraic ... more important it's in the brain, there already, the order is in the brain; you're trying to make it explicit ... and music, and also, in music, you actually, you anticipate; you've got the memory of the past anticipating the future and that is inside you, so you are actually experiencing the implicate order directly through music ... it's in the algebraic structure that it's a much clearer way of seeing what is going on then; it ties directly with non-commutativity and therefore you're developing a non-commutative geometry ... the process is going on whether we're there or not; it's got nothing to do with us. (Hiley, 2021)

[Image Source: http://iopscience.iop.org/article/10.1088/1367-2630/15/7/073022 ]

Yakir Aharonov corroborates Hiley's interpretation: "Alternatively, in the Heisenberg picture, the particle has both a definite location and a nonlocal modular momentum that can 'sense' the presence of the other slit and therefore, create interference" (Aharonov, 2017). Dr. Juliana Brooks (2009) revealed this error of quantum physics as directly from the standards of measurement units for Planck's Constant:

The photon, as historically defined, is a time dependent packet of energy, based on the arbitrary measurement time of one second ... An arbitrary one second energy increment cannot be a truly indivisible and elementary particle of nature ... The variable for measurement time was relegated to an invisible existence as a hidden variable, with an implicit and fixed value of "one second." ... Planck thereafter adopted the methods of Wilhelm Wien to convert the experimental black-body data, from time dependent energy measurements to energy density measurements seemingly "independent" of time.

[Image Source: Chinese Philosophy Professor Patrick Edwin Moran (who started out in physics at Stanford):
https://upload.wikimedia.org/wikipedia/commons/5/52/Why_Planck_Constant_not_energy.jpg ]

Juliana Brooks does not understand the noncommutative phase logic of Alain Connes but as Connes emphasizes: "The current definition which using the speed of light as a conversion factor is expressed in terms of inverse-frequencies rather than wavelength" (Connes, 2009). Remember that it is precisely the discrete inverse frequency as undertone of 2/3 that also reveals the noncommutative mathematical structure in Pythagorean music theory.

De Broglie's protégé, Olivier Costa de Beauregard, a member of Princeton's Institute of Advanced Study, argued this asymmetric time from the future, due to negative frequency, proved the paranormal is, de facto, real. Costa de Beauregard calls this process a "factlike time asymmetry" or retrodiction of "negative frequencies" with time-frequency noncommutativity as a macroscopic measurement. Psychokinesis originates from precognition as a protoconsciousness organizing information will power (Costa de Beauregard, 1978). The CIA "released" the Costa de Beauregard paper from classified status in 2000, with all the paranormal references underlined:

Finally, what would the phenomenology of advanced waves, ... and information as organizing power look like? Exactly to what parapsychologists call precognition and/or psychokinesis. Logically these phenomena should show up, no less than thermodynamical progressing fluctuations - which indeed they are = (Costa de Beauregard, 1978, emphasis in original)

Alain Connes makes this negentropic noncommutative quantum connection to music:

xy is not necessarily equal to yx ... from xy to yx corresponds to what evolution yields for the purely imaginary value t = √-1 ... inner automorphisms and these are in a sense invisible ... the link between time and thermodynamics ... it is very difficult to escape the one-dimensional model of time ... language is a prisoner of sequential writing ... Several melodies can coexist and a dialogue can be established in the same instant ... Music is an outline of a language that is inscribed in a multi-dimensional, not sequential framework. (Connes et al., 2001, p. 168)

[Image Source: https://math.stackexchange.com/questions/1040202/
prove-the-automorphism-given-by-phi-leftg-right-leftg-1-rightt-is-n ]

Aharonov also implies the paranormal power of this reverse time truth:

Not only will they have the opposite charge, but they will also have the opposite mass. The gravitational field that they produce here will be the same as a gravitational field of a negative mass. This is weak value, and you can check it experimentally if you can do the experiment. (Aharonov, 2016)

Citing Connes, math Professor Micho Durdevich confirms the Pythagorean noncommutative quantum paranormal protoconsciousness:

On the other hand, the ancient Pythagorean musical scales naturally lead to a simple quantum circle ... will be quantum (noncommutativity of the algebra V) ... However, even in this case there is a highly non-commutative world of higher order collectivity algebras B(n). This can be used to capture the geometry of rotations, like those appearing in the classical Pythagorean octave versus perfect fifth considerations. (Durdevich, 2015)

The Secret of the Sect:
A Deep 'Preestablished Disharmony'

Math Professor Luigi Borzacchini reveals that the true music origins of Western science were a "secret of the sect" that is "shocking" and "really astonishing." (Bozacchini, 2007) For the orthodox ancient Pythagoreans, as Borzacchini (2007) points out, "We can suppose that the Quadrivium in its earlier Pythagorean version did not know any discrete/continuous opposition." I will return below to this noncommutative discrete/continuous connection. "Music ever since antiquity and until 17th century was a sort of 'open wound' of the relationship between discrete and continuous, between arithmetic and geometry" (Borzacchini, 2011).

Pythagoreans discovered, "that the chief musical intervals are expressible in simple mathematical ratios between the first four integers. This single discovery would account naturally for all the most characteristic of Pythagorean doctrines" (Kirk & Raven, 1964, p. 229). The footnote mentions that the Pythagoreans practiced purification of the body and soul by medicine of music based on reciprocity of opposites.

Soon though the "Greek Miracle" of irrational magnitude "alogon" math was achieved through Archytas, Eudoxus and Euclid and promoted, most importantly, through Plato (McClain, 1977). Yet Math Professor Borzacchini (2007) is pointing out that there was an ancient paradox of logic that still has not been solved in the West. "Continuum is not only inexpressible, but also external to the knowledge of reality" and the geometrical continuum can not be proved coincident with the numerical one, that it can not be empirically verified, that the place of the numerical continuum in the transfinite hierarchy is one of the greatest so far open questions, that it is linked to the most disputed axiom of set theory, etc. (Borzacchini, 2007)

Borzacchini is explaining that the "Greek Miracle" of irrational magnitude math created "incommensurability" and, as a syntactic paradigm, has been "marked in its basic principles with a preestablished disharmony, that is even its hidden evolutive principle" (Borzacchini, 1998). Elsewhere Borzacchini elaborates, "there was a deep 'preestablished disharmony' ... this disharmony grounded many logical paradoxes that endure up to the present time" (Borzacchini, 2010).

And so, the true music origins of the irrational magnitude math were originally a "negative judgment paradox" (impossibility of asserting falsity) that had to be covered up. As Borzacchini (2007) points out, "Such paradox forbade speaking about what is not." The earliest known use of Logos, in Heraclitus, refers to it as a fiery creative soul while alogos is when the fiery spirit, now incarnated in the body, becomes too wet (Finkleberg, 2017). This concept for the need of fire to go under water is closely tied to noncommutative alchemical meditation but as Kingsley notes the ancient meaning of wisdom was lost: "By the time of Plato and Aristotle, the doors of understanding were closed" (Kingsley, 1995). Borzacchini (2007) asked, "Why these silences? And why this sudden and radical change? Why the Pythagoreans' silence? The 'secret of the sect'?"

[Image Source: https://whizkidefos.files.wordpress.com/2013/03/tetractys_pyramid.gif?w=382&h=210 ]

In 2001 Borzacchini replied to me with a written letter that my math-music equation was "good," but I had no historical proof that the specific equation had been used.

However, I think I can prove that in the Platonic Academy there was a trace of this earlier approach, with a tight connection between music, numerical means and similarity, and without any reference to geometric figures, such as square or pentagon. (Borzacchini, 2007)

Borzacchini (2007) had postulated a continued proportions music-math clue:

Many authors (Szabo, Knorr, Burkert) have discussed Boethius' text, and all of them have recognized a musical phase in the discovery of incommensurability ... Hence, when he wrote this dialogue, Plato had credibly a good acquaintance with the well-established 'geometric' theory of incommensurability, = The trouble with 17 could be connected not to some geometrical construction, but to the role this number played in the Pythagorean arithmetic, where it was called the "obstacle," because it "broke the proportion of 9/8 in not equal intervals" (Plutarchus 1962, De Iside et Osiride, 367 f).

[Image Source: https://www.academia.edu/16496242/Incommensurability_Music_and_Continuum_a_cognitive_approach._Arch._
For_History_of_Exact_Sciences_61_2007_273-302._http_dx.doi.org_10.1007_s00407-007-0125-0 ]

The Plutarch clue also emphasizes the uneven 9/8 from 17 as tied to the lunar energy cycle of Osiris with Osiris also defined by the Pythagorean triangle. The 12 note scale alchemy music meditation is also based on the lunar cycle. Plato was relying on his collaboration with Archytas who had changed Philolaus' term of subcontrary mean to harmonic mean (Kingsley, 2010, pp. 156-7). Borzacchini argues "it was exactly the possibility of the geometric drawing of a not-existent music interval to foster the development of the Aristotelian idea of continuity" (Borzacchini, 2007). This will be discussed below further: "Archytas says that this was formerly called the sub-contrary mean. Why was it so called? And why was its name changed?" (Makeig, 1981). And: "The term subcontrary may refer to the fact that a tone based on this mean reverses the order of the two fundamental musical intervals in a scale" (Bonar, Khoury and Khoury, 2016).

How I Discovered the Noncommutativity
Paranormal Music Connection is True

I had realized this noncommutative logical error in music when I took my first music theory class taught by my piano teacher in the evening adult class at McPhail Music School in Minneapolis. I was still in high school and soon after began private tutoring with her husband who had been a University of Minnesota music professor. I believed the logical paradox in music proved that Pythagorean universal harmony was true and when I took quantum mechanics as my first physics course, my first year at Hampshire College, taught by Professor Herbert J. Bernstein, I had another "aha!" moment.

Professor Bernstein was teaching us quantum entanglement by his demonstration of the "Dirac Dance" (holding an imaginary wine glass while rotating your arm through 720 degrees and keeping the wine glass held up vertically).

[Image Source: https://www.thedaobums.com/applications/core/interface/imageproxy/imageproxy.php?
img=https://lh3.googleusercontent.com/proxy/OzekFEmmrFNfHovSUSWih2M7AH6utk8tfViPUINFoH8zpI_qU3za
WRvkr42DzYcAIFzX91TjCdcwaKbK6ihfC8hngK7C4Soiqw=s0-d&key=96d221fcb965f6232b9d989784e4085e8c16f1413b413243526f3ad85f94d9a0 ]

It was not until I discovered Fields Medal math Professor Alain Connes 2012 lecture on music theory, posted on youtube, that I realized my concept had been corroborated. I had already tested out my music-math concept by doing intensive paranormal meditation training to finish my University of Minnesota master's degree in 2000. I first read Connes in 2001 but Connes' 2012 Music of Shapes lecture confirmed it truly was the precisely same concept.

Previously, in 1995 I saw a telephone pole poster for qigong master Effie P. Chow doing a qi-lecture demonstration. I was so skeptical that I called up to ask for a "half off" admission fee. When Effie P. Chow agreed, via the lady who answered the phone, I then took my girlfriend with me to St. Mary's University for the evening class paranormal power demonstration. Effie P. Chow said she was filling the room with qi and had us make "qi balls" with our palms facing each other. Sure enough, I felt a very strong magnetic force pushing my hands apart!

As the event was ending and half the people were gone, a University security guard wandered in and stated, "I'm just wondering what's going on in here because the fuse got blown in the room behind you." This was not staged because I did not even hear a response from Effie P. Chow, and I got kind of freaked out. This really got me intrigued to be sure and we soon left.

In 1996 I discovered a book on "biosonics" by Dr. John Beaulieu and it explained how "yang" is the Perfect Fifth and "yin" is the Perfect Fourth in music theory and the "emptiness" is the Octave. Suddenly I realized how the Pythagorean music intervals explained the paranormal! As arising from the Diapason or Taiji of the Wu Chi (the void), "the fourth and fifth work together as yin and yang ... The fifth and the fourth are the basis for the 1-4-5 chordal progressions found throughout music of all cultures" (Beaulieu, 1984, p. 47).

Of course, this was still not the noncommutative secret, but it was enough to go on for me to start calling these ratios "complementary opposites." And the basis of the qigong meditation training was called the "small universe" neidan internal alchemy or "microcosmic orbit," using 12 notes (the 12-note music scale created from the yin-yang energy) or energy nodes along the body, with the eyes closed, as a listening resonance practice. I realized that this meditation of 12 harmonic nodes was a harmonic energy-consciousness transduction training, the same as the "infinite spiral of fifths" as explained by Sir James Jeans in his book Science and Music. Jeans states, "It extends to infinity in both directions and all simplicity has disappeared" (Jeans, 1937).

[Image Source: Sir James Jeans, Science & Music, 1937, Macmillan and Co., Cambridge, England ]

Qigong master Shen Wu (2016) gives us corroboration: "The Chinese "lü" tuning is closest to the ancient Greek tuning of Pythagoras." The Western bias, of course, is that music has to be equal-tempered so that there can be polyphonic harmony. But as Alain Connes emphasizes it is a conductor reading an orchestral score who then is forced to transpose different clefs as noncommutative spacetimes all at the same time - phase harmonized - which is the real example of proper Western polyphonic music. And this same truth applies then to the "double quotient" of the rational discrete fractions that as noncommutative exponents then cause a resonance energy transduction from beyond sound as a mechanical wave into electromagnetic energy and spacetime transformations. That was the traditional meaning of music in its nonwestern context as the "infinite spiral of fifths."

Before the idea of frequency existed, however, the same relation was expressed simply in terms of length, the length of a resonating agent multiplied by 2/3 being equivalent to the frequency multiplied by 3/2. The length of a zither string, then, multiplied by 2/3 gives a note which when struck is a perfect fifth higher than its fundamental. This is the first step (or lü) in a process which evolves an unending spiral of notes. The length of the resonating agent which sounds the perfect fifth is then multiplied by 4/3, the resulting note being a fourth below the perfect fifth. (Needham, 1971, my emphasis)

Later I found confirmation of my hypothesis from a Daoist scholar Pregadio writing on Chinese alchemy: "The twelve-stage sequence also establishes correspondences with other duodenary series: ... the bells and pitch-pipes" (Pregadio, 2015). And then we find Table 6: Sovereign Hexagrams.

The twelve "sovereign hexagrams" (biguas) and their relation to other duodenary series: earthly branches, bells and pitch-pipes, months of the year, and "double hours." (Wang, 2011, page 130)

Most music theorists would dismiss the infinite spiral of fifths as just modal math and thus no different than an "infinite spiral of thirds." The key logical secret missing was noncommutativity. In fact, the Pythagorean simple ratios were dismissed by the time of Galileo as a "coincidence of consonance" phase synchronization error. But that supposed error has now been corroborated:

The most frequently used intervals - the octave, perfect 5th and 4th - correspond to those considered the most consonant by culturally diverse listeners (Bowling & Purves, 2015; Burns, 1999), an observation that is all the more impressive given that the frequency resolution of the human auditory system is sufficient to distinguish hundreds of unique intervals (Parncutt, 1989; Roederer, 2008). (Bowling, et. al., 2017)

Recent science has confirmed the truth of the natural number simple ratio (Bowling and Purves, 2015).

Of the intervals studied (1, 4, 6, 7, 9 semitones), they found that in all cases the evoked potentials were at their highest (in terms of voltage) for two pure tones separated by a perfect fifth (7 semitones) when compared with other intervals. These results provide electrophysiological evidence that matches behavioural preference for simple frequency ratios (Lots & Stone, 2008).

[Image Source: https://cnx.org/resources/ae1c7c3826b3cb1eba187265035b51f5a4142cde/ISI8.png ]

And again:

Until recently, the failure of most musical tuning systems to conform to the mathematics of small integer ratios was grounds for rejecting Pythagoras's proposal that small integer frequency ratios account for the perception of musical consonance and harmonicity [19]. However, recent modelling of the cumulative effects of physiological nonlinearities at each way-station of the ascending auditory pathway has disclosed the presence of 'resonance neighbourhoods' at whole integer ratio spacings on the tonotopic maps of the auditory system [20-22] ... The presence in humans of cultural patterns of musical practice conforming to these subtle resonances in auditory physiology accordingly requires an explanation. (Merker, et al., 2015)

Abdounur (2015) gives us one: "This implicit contradiction ... [noncommutativity] maybe a defense-mechanism of nature against order." Later I discovered this same 12 harmonic nodes as a body-mind meditation paranormal energy transformation taught in India and Tibet and West Asia also - see my Ancient Advanced Acoustic Alchemy self-published free docdroid educational book for details. For example:

The notes of the scale as the energy points of the spine. Ref: Sriranga sadguru in Amaravani. The 24 frets of the (Veena) instrument are analogous to the 24 cartilages in the spinal cord. The number 24 also relates to the 24 syllables in the Vedic Gayatri mantra. (Prasad, 2002)

[Image Source: http://www.salagram.net/sstp-mgpuja3.html ]

So Lui is the character meaning spinal column. ... This character has one more interesting meaning 'frets' (of musical instruments) (1,5,6), the construction of which is similar with that of the spinal column. We should also mention that Chinese musical scale is also called Liu Liu (Jana, 2016 citing Akhmetsafin, 1989)

I met qigong master Chunyi Lin in 1999 when he gave a presentation to my "Spiritual Healing" class for my Liberal Studies master's degree program at University of Minnesota. By this time, I had read Harvard medical doctor David Eisenberg's book Encounters with Qi (1985) and Chunyi Lin looked just like the person in the book who had demonstrated telekinesis. And so, to finish my interdisciplinary Liberal Studies master's degree I did intensive nonwestern meditation training based on my Pythagorean music analysis, through the African Studies department as "self-directed research." Pythagoras was reputed to have trained in Egypt for decades and I had argued that the Platonic "natural law" was inherently racist due to the eugenics of the equal-tempered music theory, as explained by musicologist Ernst McClain's book The Pythagorean Plato.

The necessity of tempering pure intervals, defined by the ratio of integers, is one of the great themes of Plato's Republic. In his allegorical form, "citizens" modeled on the tones of the scale must not demand "exactly what they are owed" but must keep in mind "what is best for the city." (McClain, 1976)

Similarly, economics Professor Michael E. Hudson, who started out his college training in music, pointed out the ideological use of the equal-tempered music theory of Archytas and Plato. "Burkert [1972:441] notes that the harmonic mean discovered in the context of Pythagorean music theory has a major use precisely in approximating the square root" (Hudson, 2000). He continues:

Archytas developed the musical scale into a political metaphor for the scales of justice. What gave music this imagery of social balance and just proportion was the ability of its mathematics of harmonic ("geometric") proportions to serve as an analogy for how inequities of wealth and status rendered truly superior men equal in proportion to their virtue - which tended to reflect their wealth. By this circular logic the wealthy were enabled to rationalize their hereditary dominance over the rest of the population. (Hudson, 2000)

So, the cover up of noncommutativity of Pythagorean philosophy had deep disharmony implications indeed.

Importantly, the note scale is an additive one: we speak of moving up by a certain number of half-steps. On the other hand, at the frequency level, this change is multiplicative. The process of going from an additive measure of length to a multiplicative one leads us to what is arguably the most important function in all of mathematics, the exponential function, and its inverse the logarithm function. (Naiman, n.d.)

Plato changed the PreSocratic meaning of Apeiron or Cosmic Mother Emptiness as nonlocal formless awareness to the Archtyas "Liar of the Lyre" value of the irrational magnitude "alogon." Or as a scholar explained, "Magnitudes have all the characteristics Plato attributes to Apeiron" (Karasmanis, 2011).

In contrast, at the very first class in 1999 when Chunyi Lin walked past me while my eyes were closed, I did a "moving of yin and yang" qigong exercise and he shook his "Shaolin sword fingers" - suddenly I saw bright yellow light and I felt immense love as joy. By the end of my training in 2000, I had what my teacher called an "enlightenment experience" and I saw ghosts, experienced telepathy, telekinesis, and precognition, among other paranormal phenomena. I had proven my hypothesis true to myself and had permanently transformed my body-mind-spirit connection to the Emptiness, what the PreSocratics called the Apeiron or Cosmic Mother via Aeon. I could now feel a permanent magnetic bliss in the center of my brain, even after I stopped meditating for a couple months to see if the sensation would go away. I, too, also experienced a holographic universe, but it was based on noncommutativity, just as Eddie Oshins explained that Karl Pribram's holographic brain model is not accurate. I'll detail this below.

Pythagorean music training also required a meditation deep mind-body transformation (Lebedev, 2017). Chronos was the Orphic name for, according to Pythagoras, the serpent psyche of the Universe, derived from "Time Unbounded" in Iranian Zurvan philosophy - Chronos Aion. Aion was the "procreative fluid with which psyche was identified, the spinal marrow believed to take serpent form" (Onians, 1951). The original source was attributed to the Pythagorean Hippo.

Begotten by a wind ... a breath-soul ... armony ... drawn from the whole body ... gathers in the spinal marrow ... most of it flows from the head ... a Pythagorean quoted, "that the seed ... generative water of the marrow [aka cerebrospinal fluid] ... that breathes through the reproductive organ ... is a drop of the brain containing in itself warm vapour ... the union of the two serpents represent the life complete by the union of the male and female." (Onians, 1951)

[Image Source: https://qph.fs.quoracdn.net/main-qimg-2ac97395c570981a507b18fceefd7cde ]

The Liar of the Lyre: How Archytas and Philolaus covered up the truth of noncommutative paranormal music training

We are told, "It is believed ... because [the Harmonic Mean] produced a division of the octave that the middle tone stood in the most harmonious relationship to the tonic and the octave." (Kullman, 2001). This is just a mathematician not delving into the noncommutative truth that was hidden by the "Greater Perfect" or Double Octave system, as I mentioned early on and will now detail.

Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the consequent or second term, should consult Archytas DK 47 B 2 ... This Fragment requires that the ratios be of this form if the assertions about the three means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1, 3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them. (Bowen, 1978)

In contrast: "Note that these 3 : 2 ratios can be thought of musically as perfect fifths or fourths," a claim that covers up the symmetric "Greek Miracle" commutative logic of Archytas, as Bowen documents (Makeig, 1981). The Perfect Fifth is also C to F, 2/3 to the One as the root tonic but as an undertone while the overtone is C to G, as 3/2 but this was not allowed by Archytas.

However, he [Archytas] noted that the product of the arithmetic mean and the harmonic mean is equal to the square of the geometric mean, so this gave a way of dividing the fifth of 3:2 into the [arithmetic mean] of 5:4 and 6:5. (Scriba, 1990)

So what we have here is the secret music origins of commutative Western math that is the structural or dimensional trajectory of Western science - the expansion of the exponentials as higher dimensions. Once we go into the 5th dimension suddenly we have the noncommutative math of the Matrices but science practices "renormalization" to try to convert such noncommutativity back into the symmetric commutative algebraic geometry math.

Professor Alain Connes details this noncommutative secret when he explains,

The ear is only sensitive to the ratio, not to the additivity ... multiplication by 2 of the frequency and transposition, normally the simplest way is multiplication by 3 ... 2 to the power of 19 is almost 3 to the power of 12...time [spacetime] emerges from noncommutativity ... 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 qn for the real number q=2 to the 1/12th~3 to the 1/19th. 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. (Connes, 2012)

There is another way to explain this for the noncommutative ratios to be made more explicit.

This musical property is the counterpart of the principle mathematical characteristic of the Pythagorean diatonic, very Pythagorean indeed, constituted by the fact that each interval of the scale is expressed by the ratios of type 2 to the m divided by 3 to the n or 3 to the m divided by 2 to the n. (Bellissima, 2013

The Pythagorean Comma claim wrongly assumes that the exponentials can be divided back into the octave, via the logic of Archytas, while not acknowledging the noncommutative ratio dynamic. I'll give a hint though, as to what this all means in terms of relativistic quantum biology as alchemical meditation training.: "This means it is a zero-dimensional object! But it has a positive volume!" (Khalkhali, 2014).

For example consider this "standard" music-math analysis:

When we add intervals, what we're actually doing is multiplying ratios. So P5 + P4 = 3/2 * 4/3 = 2/1 = P8. When we subtract intervals we're dividing ratios, which is multiplying by the reciprocal, so P5 - P4 = 3/2 * 3/4 = 9/8 = M2. And P8 - P5 = 2/1 * 2/3 = 4/3 = P4. Since multiplication of ratios is commutative, then addition of intervals is also commutative.

...

Since exponentiation is not commutative, 2 * P5 would be different than P5 * 2; 2 * P5 = 2^(3/2) = 3 radical 2, while P5 * 2 = (3/2)^2 = 9/4 which is a M9 (P8 + M2 = 9/8 * 2/1). However, we're defining our own algebraic system, so we could define * as always placing the integer in the exponent and thus make this commutative. (Cuthbert, 2012)

What the writer doesn't realize is they are repeating the same error as Philolaus who created the commutative math from the wrong music theory! Alain Connes emphasizes that the empirical truth of listening to music as multiplying ratios or exponentials is noncommutative or "not commutative" just as this person admits. Only Connes refuses to just "make up" his own math (of course he could with a Fields Medal, the hardest to get science award). No, Connes is true to the empirical truth of the music listening based on the multiplication of the "double quotient" or inverse ratios: 3 to the 19 as 2 to the 12 or 3 to the (1/12) as 2 to the (1/19). Hence the noncommutativity as explained about - "exponentiation is not commutative."

But since most people don't train in music from a young age as Connes did, which has been proven to increase the corpus callosum that synchronizes the right and left brain, then most just regurgitate the commutative "Liar of the Lyre," as I shall now explain.

Professor Richard McKirahan figured out the secret in his article on Philolaus: "it makes no difference which way we go, the result is the same. This corresponds to the commutative property of addition of numbers" (McKirahan, 2013). A circular argument indeed. The music theory of Philolaus was the first to use the term "magnitude" as a mathematical ratio concept for the Greek Miracle, to create the commutative symmetric math logic. "Historically, the first application of binary logarithms was in music theory" (Rubinstein 2000).

The word translated epogdoic is not a musical term but a mathematical one. An epogdoic ratio is the ratio of 9 to 8. The occurrence of a mathematical term here is unexpected. (McKirahan, 2013)

Math Professor Connes sets us straight: "Why should Nature require some noncommutativity for the algebra? This is very strange. For most people noncommutativity is a nuisance. You see because all of algebraic geometry is done with commutative variables" (Connes, 2012).

What does this really mean in terms of paranormal power? "... knowing the ratios 2:1, 3:2, and 4:3 (which, by the way, is all the early Pythagoreans knew) is not enough to know the nature of the octave; we also need to know what limiters and unlimiteds are in play" (McKirahan, n.d.). In traditional Chinese music tuning or Indian tuning - the octaves do no line up, as Sir James Jeans points out - the empirical truth is an infinite spiral with the octaves or root tonics also changing. McKirahan, following Philolaus, does not allow this.

Can we do something similar with Philolaus's other claim that 3:2 + 4:3 = 2:1? We might think that this would amount to the claim that 12:8 plus 12:9 = 12:6, but this is not an obvious result, since it is immediately not clear how to perform the addition. ... So instead of taking 12:9, which is 3/4 of 12, we take 8:6, which is 3/4 of 8. And so by adding the length 12 to 8 we get the length 12 to 6, which corresponds to the ratio 2:1. (McKirahan, 2013)

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