Hi Terry: Thanks for your response. Alain Connes is
correct. You just need to study him more. You ask some good questions
but try to think deeper. He points out that noncommutative phase is MORE
DENSE than real numbers. So we are talking about "before" and "after"
real numbers. Here are some other quotes for you to consider.
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.
Professor Fabio Bellissima
there would be m and n integers such that (2:3)n = (1:2)m, that is, 3n = 2m+n, which is impossible, since the left term is odd and the right is even.
Dr. Oscar Abdounor
3/2 x 4/3 = 2 (geometric mean
squared).
log(3:2×4:3)=log(2:1)
log(3:2)+log(4:3)=log(2:1)
A Truman State University
review on Scriba, Christoph J. “Mathematics and music.” (Danish) Normat 38 (1990), no. 1, 3–17, 52.
“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.”
Alan C. Bowen, "The Minor Sixth (8:5) in Early Greek Harmonic Science," The American Journal of Philology, 1978.
To put the same thing in another way, we have just identified the frequency ratio 1.5 with the interval of a [perfect] fifth, although our table gave the value as 1.4983. The difference is only small – 1.13 parts in a thousand – but by the time we have taken the twelve steps needed to pass completely around the clock-face, it has been multiplied twelvefold into the difference of 13.6 parts in a thousand, which represents the aforesaid difference in pitch of almost a quarter of a semitone. When this is allowed for, the true clock-face is that shown in fig. 55; it extends to infinity in both directions and all simplicity has disappeared.” Sir James Jeans book Science and Music, (Dover Publications, 1968), p. 166
So Sir James Jeans is DIVIDING 1.5 by 1.4983 to get 1.001335 which is 1.33 parts in a thousand in contrast to 1.0136 being 13.6 parts in a thousand. But this is assuming that 2/3 is also NOT the Perfect Fifth. In other words the Ditonic Comma assumes you can not just multiply but also "halve" the Perfect Fifth back into the octave - thereby "losing" or hiding this multiplying factor!!
Philolaus identified the komma [531441 : 524288 aka the Ditonic Comma] with the unit, 1
note that all is geometric magnitude so that 12:8 (3/2) plus 8:6 (4/3) = 2/1 as geometric magnitude from the double octave. This has to use 0 to 8 as one "root tonic" for 6/8 wavelength as 4/3 frequency and then 0 to 12 as the other root tonic for 12/8 frequency as 3/2 with 8/12 wavelength. This is called the "phantom tonic" in music theory since the Perfect Fourth can not be created from the harmonic series as 3 does not go into 2 from 1 as the root tonic denominator. In other words the root tonic changes due to complementary opposites.
And so the use of "zero" is to create the geometric mean as logarithm by covering up the noncommutative phase. So at "zero" energy there is STILL a noncommutative phase quantum energy. Professor Richard McKirahan:
So you have 8 to the 6th power and 9 to the 6th power (531441) so that the 9 is equated to 3/2 squared as 9/4 halved to 9/8 with the 9 being 3 squared and so 9 to the 6th = 3 to the 12th.
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 [as geometric magnitude not wavelength!!] with the length 8 to 6, [as geometric magnitude, not wavelength!!] we get the length 12 to 6, which corresponds to the ratio 2:1.
We are told that 6:8:9:12 is just multiplying (1:4/3:3/2:2) times 6 but in actually 9/8 is assuming that 3/2 is also the geometric mean squared.
So then you get 6 whole tones as 9/8 - being greater than the octave by the so-called Pythagorean Comma. But again this is not the original Pythagorean Comma! This already assumes the octave is a geometric mean squared definition - not the number 2 as a doubling.
So you have 8 to the 6th power and 9 to the 6th power (531441) as the secret of the Ditonic Comma as the fake Pythagorean Comma due to geometric mean. From Euclid and earlier from Philolaus and Archytas as 8 to the 6th compared to 9 to the 6th which assumes that the starting root tonic "frequency" as the 1 is 8 to the 6th which is already from assuming the Perfect Fifth is squared!
262144 was then used by Aristotle (and Philolaus) as the starting root tonic value so that the octave was then 524288 as 8 to the 6th with the difference to the Perfect Fifth as 3 to the 12th being 531441 from 9 to the 6th. So that is the diatonic scale of 6 notes above the root tonic but with 12 notes - the error keeps multiplying for each note, as Sir James Jeans points out - so you have a quarter note error.
Connes:
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 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 12th∼3 to the 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.
Terry -
notice how Connes FLIPS around the octave and fifth values? That is
because of the equations I just sent you previously - that is why they
are noncommutative. So before the Western scale based on logarithms is
created then 2/3 is C to F subharmonic while 3/2 is C to G overtone
harmonic. This noncommutativity is empirically true but was covered up
by Philolaus and Archytas and then promoted by Plato, etc.
thanks,
drew
Hi Terry: You ask:
If the coherence principle in category theory means that all diagrams commute, then isn't non-commutative algebra incoherent by definition?
This question of yours is answered in my research. It's now
proven that noncommutativity creates nonlocal quantum entanglement which
is also quantum coherency. I'll look it up for you. So I search
noncommutativity on my blog and I get
"...more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole."
and
Recently, Bigatti and Susskind4 have suggested the quantum model in two space dimensions of a charged particle in the plane interacting with a perpendicular magnetic field in the limit the field strength goes to infinity to observe noncommutativity in the plane coordinates.
and
this blogpost is just on Connes. You have to scroll way down to get to the blog post.
So
that was in response to an academic chaos scientist. He said Connes is
talking about the spectra of quantum OPERATORS - not Fourier spectra. So
quantum physics "converts" the operators into Fourier analysis via the
Poisson Bracket (to achieve commutativity).
Connes is stating that noncommutative time-frequency CREATES the Dirac Operators (as the inverse of the Dirac Operator).
So I first quoted Connes in 2006 - from the first book I discovered by him:
https://www.unexplained-mysteries.com › ... › Ancient Mysteries & Alternative History
The argument by Alain Connes is that music transmitted aurally is currently in the same
stage as when people read out loud—as they did until the 12th Century A.D. Connes states that if people could, as conductor Solti did, read music scores and hear multiple texts in their head "
that is inscribed in a time that would no longer be sequential, because a score is a multitude of
chords, a tangle projected onto physical time of course, but that
manifestly evolves in an higher dimensional space, giving rise to a
variability much more pertinent to the description of individual
time."
So Terry - I'm just curious -
have you studied Orchestration? I studied orchestration privately while I
was in high school - from a former University of Minnesota music
professor. So when I read this from Connes I could immediately relate to
the brain-twisting training involved in transposing in real time
several different clefs - onto the piano.
So that is different than the transposition you are referring to - in sequential time.
Alain Connes continues “
And it could be formalized by music.
And it could be formalized by music.
...I think we might succeed in this way to educate the human mind to deal
with polyphonic situations in which several voices coexist, in which
several states coexist, whereas our ordinary logical allows room for only
one. Finally, we come back to the problem of adaptation, which has to be
resolved in order for us to understand quantum correlation and
interrelation which we discussed earlier, and which are fundamentally
schizoid in nature. It is clear that logic will evolve in parallel with
the development of quantum computers, just as it evolved with computer
science. That will no doubt enable us to cross new borders and to better
integrate the mathematical formalism of the quantum world into our
metaphysical system.”
So that is all for now.
I'm
still looking for that noncommtutativity quote about entanglement. And
then I have a blog post on entanglement as quantum coherency.
I
also corresponded with Physics Professor Manfred Euler about this topic
- specifically about listening to time as noncommutative quantum
coherence.
take care,
drew
So the key factor that gets missed in the quantum versus classical debate is the noncommutative component. Normally it is considered to be the Heisenberg Uncertainty Principle based on momentum and position and this is not due to a technical measuring limitation. Rather it is truly based on the order of measurement, hence the debate about consciousness. But what gets missed in all of this is that Schroedinger developed his wave function based on de Broglie's model of wave matter and yet de Broglie developed his analysis as a critique of Einstein's relativity. So Schroedinger just left out the relativity aspect which is the essence of the noncommutativity as based on the order of measurement.
From Professor Stephon Alexander, author of the Jazz of Physics.
Coherence as consciousness.
Quantum Effects in the Dynamics of Biological Systems, 1983, Lawrence Berkeley National Laboratory, William Bialek (currently Princeton Professor)
Here is the "mystery" that mainstream science is stopped at since it does not understand noncommutative phase mathematics:
A biological rationale for musical consonance (PDF Download Available).
So the key factor that gets missed in the quantum versus classical debate is the noncommutative component. Normally it is considered to be the Heisenberg Uncertainty Principle based on momentum and position and this is not due to a technical measuring limitation. Rather it is truly based on the order of measurement, hence the debate about consciousness. But what gets missed in all of this is that Schroedinger developed his wave function based on de Broglie's model of wave matter and yet de Broglie developed his analysis as a critique of Einstein's relativity. So Schroedinger just left out the relativity aspect which is the essence of the noncommutativity as based on the order of measurement.
From Professor Stephon Alexander, author of the Jazz of Physics.
- . arXiv:1206.6296 [pdf, ps, other]
Phase harmony in de Broglie theory relates a local periodic phenomenon (the 'particle clock') to a periodic propagating field in such a way that relativistic invariance is satisfied. If a similar phenomenon in the cell is relevant it should couple the global oscillation pattern locally with periodic (mechanic, electric, biochemical ???) processes.
Coherence as consciousness.
"Ghost Tones"Sitting in a quiet room, we can hear sounds that cause our eardrums to vibrate by less than the diameter of an atom. ...
Manfred Euler is a Professor Emeritus of Physics at the University of Kiel.
Quantum Effects in the Dynamics of Biological Systems, 1983, Lawrence Berkeley National Laboratory, William Bialek (currently Princeton Professor)
Here is the "mystery" that mainstream science is stopped at since it does not understand noncommutative phase mathematics:
The Nature and Nurture of Musical Consonance (PDF Download Available).
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).
A biological rationale for musical consonance
The basis of musical consonance has been debated for centuries without resolution. Three interpretations have been considered: (i ) that consonance derives from the mathematical simplicity of small integer ratios; (ii) that consonance derives from the physical absence of
interference between harmonic spectra; and (iii) that consonance derives from the advantages of recognizing biological vocalization and human vocalization in particular. Whereas the mathematical and physical explanations are at odds with the evidence that has now accumulated, biology provides a plausible explanation for this central issue in music and audition.
Noncommutativity is source of quantum non-local consciousness
"Non commutativity is the central mathematical concept expressing the uncertainty."
This number theory is the great conundrum of trying to unify ("are we there yet?" googlebook link) noncommutative quantum physics to relativity (pdf link - "you can not visualize noncommutative spaces - you fundamentally cannot.")
but time-frequency uncertainty was already known to be noncommutative
by the Pre-Socratics! This first music harmonic of the Pythagorean
Perfect Fifth as 3/2 is actually noncommutative (C to G is 3/2 as the
Perfect Fifth overtone while C to F is 2/3 as the Perfect Fifth
subharmonic). As quantum consciousness neuroscientist Stuart Hameroff says, ""Change the Music.... Indeed, microtubule
resonant vibrations have been likened to music, specifically anharmonic Indian Raga (Ghosh et al, 2014)....As the Beatles sang, “Take a sad song and make it better”."
resonant vibrations have been likened to music, specifically anharmonic Indian Raga (Ghosh et al, 2014)....As the Beatles sang, “Take a sad song and make it better”."
"Bandyopadhyay and his team will couple microtubule vibrations from active neurons to play Indian musical instruments. Consciousness depends on anharmonic vibrations of microtubules inside neurons, similar to certain kinds of Indian music, but unlike Western music which is harmonic [commutative logarithmic]" Hameroff explains (Science News, 2014)
Hi Terry: I have corresponded also with math professor Louis
Kauffman who collaborated with Eddie Oshins at Stanford Linear
Accelerator Center - on noncommutative logic of martial arts training:
A natural non-commutative algebra arises directly fromarticulation of discrete process and can be regarded as essential information in a Fermion. It isnatural to compare this algebra structure with algebra of creation and annihilation operators thatoccur in quantum field theory
https://www.researchgate.net/publication/326345373_Braiding_Majorana_Fermions_and_the_Dirac_Equation
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