Wednesday, February 16, 2022

Why the Noncommutative secret to the Pythagorean scale tuning of Alain Connesd debunks the papers of Meijer Dirk F, et. al.

So someone has been debating me - based on the research group of this paper here - that has similar research to my own

 https://elixirfield.blogspot.com/2019/12/dirk-k-f-meijer-needs-to-study-orthodox.html

I had already critiqued their research and contacted them some three years ago.

OK Now I see they have a new paper out based on this noncommutative secret as "5D symmetry breaking" - all get to it later. 

 The claim by this research group is that Alain Connes is only using the equal-tempered music scale and not the Pythagorean scale. Why is this claim being made so insistently in a "private" discussion I've had with this person? The reason is what math professor Luigi Borzacchini calls a cognitive bias or error that is a symmetric geometry bias and thus a "deep pre-established disharmony."

So it's also then been claimed that I don't do any original research. If that were true then how could I have critiqued the research of Richard McKirahan? haha. I have pointed out the noncommutative change of the root tonic due to the Perfect Fourth being a "phantom tonic." This was known to me because of my music training experience that is proven to increase the corpus callosum.

So I had that realization at a young age - as I mentioned to someone recently on my youtube upload... and ever since high school I have pursued the same concept. So the idea that it is not "my own" is hilarious - because nonlocality is actually the impersonal formless awareness and that is the concept that is pursued.

OK so let's return back to the tuning claim.  https://en.wikipedia.org/wiki/Pythagorean_tuning

So the whole point of Connes is that the exponentiation is noncommutative when the order is reversed.

As I point out in my paper (NOW newly published! thanks Gary) - giving the example that (3/2) squared is not the same as 2 to the (3/2).

So we can see that the Pythagorean scale thus relies on a combination of the inverse exponentiation against the exponentiation - and thus it is noncommutative.

The claim against me is that the Pythagorean scale is only rational and thus only commutative. Using rational numbers does not mean something is only commutative.

This has been my point all along that the Perfect Fifth is inverted as the Perfect Fourth and thus noncommutative but also that the Perfect Fourth is derived from a different octave!

That's the key issue that really irks the person who is holding the octave sacred as a symmetric "twoness" from Platonic philosophy. haha.

So they just have not studied the music theory enough. 9/8 cubed approximates the square root of two. I give the references. Clearly the Pythagorean tuning was based on the idea of trying to achieve the equal-tempered tuning as irrational magnitude - in the fake teaching of Philolaus and Plato that is.

More later....

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."

So that's what I explain in the article.

So the time-frequency is the 5th dimension as the Pythagorean rational numbers whereas the "approximation" to the logarithms using the 2 to (1/19th) and 3 to the (1/12) - is the three dimensional two-sphere that is noncommutative also. So it also has a geometric dimension of zero just as with the "infinite spiral of fifths" from Pythagoras and Daoist tuning.... and the "three gunas" of India, etc. (by etc. I mean the research of Dr. Victor Grauer tracing this around the world)...

So the person debating with me is insisting that the Pythagorean scale is not at all like the equal-tempered or ET scale. So https://arxiv.org/pdf/1909.06259.pdf as with this example the noncommutative ratio of 3 to the (1/19th) is NOT given whereas Connes emphasizes this noncommutative inversion of the exponentiation just as with the original Pythagorean scale.


So Connes is referring to the rational number approximation of the actual irrational numbers and he's emphasizing that those rational discrete ratios are still noncommutative just as with the original Pythagorean ratios.

So correct it can never hold true but what is not pointed out again is the Noncommutativity logic such that it is 3 to the (1/19th) as 2 to the (1/12th) with the inverse 2 to the 19th and 3 to the 12th as the original Pythagorean exponentiation "comma."

So what is missing from this is the noncommutative rational approximation of 3 to the (7/19)... that equals:

1.49893056299

So Connes is point is that the "convergence" of the Pythagorean  noncommutativity is the real key to the equal-tempered approximation.

citing:

The Sounds of Music : Science of Musical Scales II -- Western Classical

Sushan Konar

 

For example, if it is in dimension 3, it will be y = x to the 1/3, okay, but here, it's not at all a thing that is round like a parabola like that ... This is something that pffuiittt! ... that gets up in the air like that. And what it tells you is that the object in question must be of dimension 0. So you say to yourself, "an object of dimension 0, What does it mean? etc. Well ...

What I hope one day is that we will find the noncommutative sphere in Nature and one will be able to use it as a musical instrument and it will be a wonderful instrument because it will never detune." (Connes, 2011)

Richard L. Crocker (1963). Pythagorean Mathematics and Music. The Journal of Aesthetics and Art Criticism, 22(2), 189–198. doi:10.2307/427754  

So this refers to Philolaus and again is covering up the noncommutative origin of how Philolaus "fit" the Perfect Fourth into the scale.

 

 And yet is it precisely this noncommutative infinity of the "coordinates" of time and frequency that Connes is emphasizing as the hidden mathematical structure "behind the scenes" all the time....

9/8= 32/23

So when we "cube" 9/8 as approximating the square root of two then we are revealing the secret Noncommutative Pythagorean Theorem due to the noncommutative phase of the negative and positive frequency ratios that requires a "third" imaginary negative frequency axis as the Bloch Sphere or Two-sphere that is the noncommutative quantum sphere.

Math Professor Louis Kauffman will soon have his noncommutative Pythagorean Theorem derivation published. He sent it to me as I had inferred the solution already and so I contacted him....


So this is their reference for the Pythagorean scale.

This never deals with the fact that the process of the geometric magnitude from ratios was first created from the music tuning. The subtraction by division thus required a double octave in order to hide the fact that the noncommutative "product of factors" was based on changing the root tonic.

To find a power of a product, find the power of each factor and then multiply.

So if we JUST use the 2 to the (1/12) for the equal-tempered tuning then we LOSE the noncommutative Pythagorean secret of the discrete ratios.

This is Connes key point.

OK NOW back to the "new" December 2021 paper based on the critique I sent them a few years ago...

My experience with Science Publishing Group was while evaluating one of their publications, the American Journal of Modern Physics, as being reliable enough to support citations in wikipedia. So far, our consensus has been "not."

The editorial board of the American Journal of Modern Physics had, when I first checked, 30 members, of which two actually lived and worked in the United States (curiously, one said he worked at Fermilab).

Since then, their editorial board has contracted to 22 members, the Fermilab guy having left that august company, leaving a member of the Chemistry and Biochemistry Department at Texas Tech as the only member of the Editorial Board of the American Journal of Modern Physics domiciled in the United States of America.

I notice now that their submission guidelines are password-protected, probably because when they were public, the "manuscript handling fee" was US$380, not counting reprint charges. And there are now articles in the American Journal of Modern Physics.
Earthshaking articles questioning the very foundations of physics as it's currently understood by rubes like Stephen Hawking and Steven Weinberg.

Right - so it's in one of those fake online science journals and hence their inability to truly engage with the noncommutative music theory that Connes understands!

So 2 to the 84th approximates 3 to the 53rd as 2 to the (31/53) = 1.49994

So that is a much closer rational approximation then 2 to the (7/12) =1.498 based on 2 to the 19th=3 to the 12th. Again with the difference due to the Perfect Fifth as the noncommutative transposition as Connes points out.

p. 27 in 

Music and Mathematics: From Pythagoras to Fractals

 

 https://math.stackexchange.com/questions/3381629/what-is-the-fastest-algorithm-for-finding-the-natural-logarithm-of-a-big-number/3383716#3383716

 So the fact that Archytas and Philolaus were using the geometric mean method - first codified by Archytas but first practiced by Philolaus, thereby proves that "their" Pythagorean scale was an early convergent method leading to the rational approximation as the later equal-tempered scale.

What Philolaus did was cover up the noncommutative truth that Alain Connes (and myself) later revealed as the truth of the Pythagorean meditation practice, the same as qigong!

OK now back to the fake "symmetry breaking" claims.

 

 So what they don't notice is that Planck's Constant hides the noncommutative phase, as I point out.

 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 ]

 Meijer D K F and Wong K-W, (2021). Scale-invariant Symmetry Breaking of a Musical Master-code from a 5-D Superfluid Sub-Quantum Space Is Instrumental in the Fabric of Reality, Life Conditions and Cosmic Consciousness. https://www.researchgate.net/publication/355702550_Scale-invariant_Symmetry_Breaking_of_a_Musical_Master-code_from_a_5-D_Superfluid_Sub-Quantum_Space_Is_Instrumental_in_the_Fabric_of_Reality_Life_Conditions_and_Cosmic_Consciousness

So I just debunked that paper along with the following one it's based on.

Oops!

This whole error is from not studying music theory close enough!

No wonder the person "hiding" with a fake name and "pretending" to have a music Ph.D. that they refused to tell me anything about - was so irate with my research. I just debunked about a dozen of their papers. haha. Oops!


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