The conspiracy between nature and number, atom and arithmetic: Fractal Harp = Liar of the Lyre

So my last blog post I was reviewing Aristotle's critique of Plato's theory of Number Forms. I happened upon a very amazing expose. Aristotle made the claim that Plato had an unwritten doctrine of "indeterminate dyad" as an intermediate number. This all gets very complicated very fast and the philosophy is actually quite fascinating. But only if you know how to see the light at the end of the tunnel so to speak. So I'm not gonna repeat that trail of thorns.

But to cut to the chase - I was reading a pdf that reviewed early calculations of approximation square roots. And so I typically avoid "calculating" and instead I focus on concepts and prioritizing meaning. But in this case I had to make a rare exception.

So I cite a pdf called "Approximating Square Roots in Antiquity."

First it confirms that Archytas really did get his geometric mean squared equation from Babylonia.

But then we get to Philolaus and Burkert gives his analysis from Boethius on Philolaus with the final ratio as 531441:524288. But as Andrew Barker points out  - this is not a frequency/wavelength ratio but a geometric magnitude ratio (and Burkert did not realize this!).

It's achieved by subtraction geometric magnitude as logarithms so dividing as inverse multiplication.

In other words that ratio - and this is where I had to do my calculations - I went back to Alain Connes who states

passing to the octave (frequency ratio of 2) and transposition (the perfect fifth is the frequency ratio 3/2), with the approximate value log(3)/ log(2) ∼ 19/12 responsible for the difference between the “circulating temperament” of the Well Tempered
Clavier and the “equal temperament” of XIX century music.

In other words the 12th root of 3 and the 19th root of 2. So then I typed into google to do the caculation for me "2 to the 19th=" And I copy and paste this:

 524288

Which is exactly the same result as above.

So that proves, once again, that in fact Philolaus and Archytas were indeed using irrational numbers from music theory.

O.K. we've known this - although it's still a secret to the masses that this is the source of Western science.

The question is why didn't the Babylonians create an alogon number symbol - and I addressed that in the last blog post - so again I'm not gonna repeat the philosophy of Plato and how Aristotle critiqued it.

The real issue is what Alain Connes realized - this relation actually covers up the noncommutative foundation of reality!

It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative [complementary opposites as yin/yang] nature of the quotient corresponding to the three places {2, 3,∞}. -Alain Connes

O.K. so here's the deal. When Aristotle was critiquing Plato, Aristotle pointed out that Plato could not generate prime numbers from his system of multipling 2s and 3s to generate numbers - again based on adding geometric magnitudes from the "indefinite dyad" as irrational magnitude.

So in my last blog post - again I quoted a philosopher - and he even publishes on alchemy! - but he promotes the lies of Plato - and so he argues that Plato could indeed generate primes. But this is a simplification of the argument - he did not really understand Aristotle.

And he doesn't need to - because Plato indeed could generate the primes from his method - and this, turns out, is what math professor Steve Strogatz called as the Riemann Hypothesis, aka the "Music of the Primes" as a "conspiracy between nature and number, atom and arithmetic."

What is so funny is that I quoted his promo on the interwebs and then the publisher disappeared that promo quote and reissued the book without the "conspiracy" mention. Hilarious! Didn't want me dumbing down their book I guess. haha.

But in fact - if we consider, for example, another math pdf, Jason C. Payne, "Fractal Strings and Number Theory: The Harmonic String and the Prime String" - how do they define a frequency based on a string? As the square root of wavelength!! Hilarious!! http://math.ucr.edu/~lapidus/

So they ASSUME the Archytas definition of frequency. But as I just pointed out - Alain Connes states no, the truth is NONCOMMUTATIVE - not square root of wavelength as frequency!

So what does this mean? That pdf refers to the Dirac Mass point - but so does Alain Connes!

 "There is a fine structure in spacetime, exactly as there is a fine structure in spectrals [frequencies].... The idea is to replace a geometric space with an algebra, as an inverse of the Dirac operator, by sending a wave with a constraint on the vibration of the wave, can not vibrate faster than 1, the commutator of the Dirac Operator is less than 1....The spectrum of the Dirac Operator...space is not simply a manifold but multiplied by a noncommutative finite space. There is behind the scene, there is a square root and when you take a square root there is an ambiguity and the ambiguity that is there is from the spin structure....Finite space which is there is essentially the simplest finite space which has dimension zero, as far as the [frequency] spectrum is concerned...."

 So this does take us back to the last blog post - the point of Aristotle was that number is inherent Cardinal which is to say based on noncommutative phase as Order from Time.

But Plato and Archytas tried to cover this up with their Alogon definition of Apeiron as irrational magnitude. And when math professor Luigi Borzacchini exposed this music theory connection then David Fowler the supposed expert on Platonic mathematics, also tried to cover it up. haha.

So it really is a conspiracy - and in quantum physics it is technically called a conspiracy as the noncommutative quantum phase of spin 1/2 is also quantum entanglement.

So Fractal Strings and Prime Numbers CAN be generated from Plato's irrational number Apeiron, and is the secret of Riemann's Hypothesis but it still doesn't reveal the noncommutative origin of that number from quantum entanglement itself. It took Louis de Broglie to rediscover that secret in math and physics.

Oh and this brings me to my big point - the real reason I wanted to do this blog post. I suddenly remembered - now hold on? This Multicultural Math book is on Chinese music tuning - I had cited it before - archived here 

Tito M.Tonietti 

And Yet 
It Is Heard 

Musical, Multilingual and 
Multicultural History 
of the Mathematical Sciences 

2014.

O.K. so if you go to the Chinese tuning section - what does he claim? I quote it on a blog post.

The ratio between Gong and Zhi was 3:2, like the one between do and sol [in the Greek (orthodox) system]; the ratio between Zhi and Shang was 3:4, like the one between re and sol; hence the ratio between Gong and Shang, Shang and Jiao or Zhi and Yu would be 9:8, like the one between do and re, re and mi, or sol and la. However, if we wanted to unroll the circumference along the Western musical scale, the similarities would finish here.

But guess what!!?? This is WRONG! He is projecting the tuning of Philolaus onto the Chinese! That's why he says it is "along the Western scale." NO.

How do I know this? Because I can quote a Chinese language and philosophy professor who did 2 years as a Stanford physics undergrad. So he knows his math as well.

 So Professor Emeritus Patrick Moran is very clear that the Chinese scale ONLY uses the Perfect Fifth and Perfect Fourth JUST LIKE THE ORTHODOX PYTHAGOREAN TUNING. And yes capitol letters does mean shouting on the interwebs. haha.

So just as with the Orthodox Pythagoreans the Chinese did not use 9/8 for each interval - that was Philolaus trying to use Geometric Mean who used 9/8 for each interval!!

And so a math professor just published false info on the Chinese music tuning that is really the secret of alchemy!! And so now we go back to the Fractal Strings and Harmonic String pdf....

When the Dirac point mass is given the length of the string is 1 plus 1/2 plus 1/3 plus 1/4.... as the Harmonic Series with the frequency as the overtones!

But GUESS WHAT IS MISSING? Again Alain Connes clearly states that 2 to 3 is NONCOMMUTATIVE and is the secret behind the Dirac Mass! And Guess what I have pointed out over and over again for the past 10 years!! Music theory explains that you can not derive the Perfect fourth from the harmonic series but you can still have 2/3 as a noncommutative undertone harmonic of the root tonic of 1.

In other words - we LISTEN to this harmonic since it is from BEFORE geometric spacetime as a point of mass is created. That is Alain Connes big point - our brains deceive us into thinking that physical 4D spacetime exists. But if we turn the light around via meditation, as Aristotle, hinted, then the truth of Pythagorean meditation as alchemy is revealed.

DANG!!

 I just discovered a mathematical music error in someone's master's thesis.

Star Music The ancient idea of cosmic music as a philosophical paradox

 I had to do another calculation! Egads!

 The mathematical reason for this is the fact that twelve fifths do not yield the same proportion as six octaves (2)

The difference is 531441:524288, roughly a quarter of a semitone, which is known as the

Pythagorean comma.

 WRONG!!!!!

 Guess what?!! This dude - what's his name? Eduard Heyning.

O.K. so if you do the calculation -
1.01364326477

Is the ratio divided and if you take the ratio of 12 fifths and six octaves the result is:

1.01372125

Not only are they NOT the same number but as I point out above - the CRUCIAL difference is ONE is based on geometric mean as logarithms!!!

 In other words he is not understanding the concept involved and what got covered up - Noncommutative phase.

Dear Eduard Heyning: Thank you for your master's thesis Star music. I also did a Pythagorean master's thesis in 2000 and have since been researching this topic. I would like to share a simple yet radical secret. Philolaus and Archytas used geometric mean to cover up the real truth of Pythagorean alchemy as macrocosmic harmonics. The truth is preserved in Chinese and Indian alchemy and was rediscovered in quantum relativity as noncommutative phase of spin 1/2 entanglement protoconsciousness. O.K. so you have an error in your master's thesis! It's o.k. I had an error in mine as well. haha. You state - and I blogged on the error. Sorry I was a bit melodramatic about it - but you can read my blog for all the secrets of my Pythagorean research. http://ecoechoinvasives.blogspot.com

Essentially you confuse the ratio of the 3 to the 12th divided by 2 to the 19th with the Pythagorean Comma ratio between 7 octaves and 12 perfect fifths. You point out in your foot note that it is multiplied because it is a logarithm as addition - but the Orthodox Pythagorean tuning did not use 9/8!! Only the Octave, Perfect Fifth and Perfect Fourth, just as in India and China. Whereas 9/8 was used by Philolaus based on geometric mean. I have several blog posts on this so you will have to study my blog research.

So essentially for Archytas to have his equation of arithmetic mean x harmonic mean = geometric mean squared he HAS to use 3/2 as arithmetic mean but if C is 1 and the octave C is 2 then G is 3/2 overtone Perfect Fifth but F is 2/3 undertone harmonic as noncommutative phase! This is the truth of real alchemy training that was concealed. I go into more details about it. Joscelyn Godwin also does not know this truth.

It is simple because people don't really think about the mathematical logic. But Alain Connes, top Field Medal math professor, did figure out the truth of music theory being noncommutative as quantum entanglement consciousness of the Universe.

Thanks for your time and I look forward to hearing back to you so we can have some dialog and discussion,

take care and happy Full Moon before the Spring Equinox,

drew hempel, MA

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