The point makes a chord between two notes [of the quantum drum]....The two eigenfunctions will be nonzero, ...if you look carefully at the two shapes [isospectral but not isomorphic] It is impossible to make a chord because the corresponding eigenfunction only means to 1 of the 2 pieces So it is zero in the other piece [and vice versa]. So this chord will not be possible. Now if you understand this example, you understand the finite invariant which is behind the scene, which is allowing you to reconstruct the geometry from the spectrum....Our geometric point will emerge by correlation between different frequencies. A point in the space will actually give you the correlation between the different frequencies. That is how we shall think about the point. It is not enough to give the scale [of the spectrum] but you also have to give which chords are possible.
"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...."
Alain Connes on Music youtube lecture
So as I point out in my expose of Philolaus - by using the double octave then the frequency 2 is made into a geometric mean as the square of the Devil's Interval as 9/8 cubed, by hiding the noncommutative phase. So then to get the frequency 4/3 for the first symmetric math logarithmic equation - the order of infinity had to be reversed with 0 to 12 (negative infinity is zero) as 12 to 0 so that 8:6 became the frequency of wavelength 6/8 or 3/4 of 0 to 8 which is 2/3 wavelength of 12 as the frequency 3/2 of 6:8:9:12. So then 12 to 6 is 2/1 frequency with 0 to 6 as 1/2 wavelength. So that the root tonic of frequency 1 was previously 0 to 8 for 6/8 wavelength as 4/3 frequency while 8 was the 3/2 frequency of 2/3 wavelength of root tonic 1 frequency of 0 to 12. So that 8 as 2/3 wavelength became the NEW root tonic of 1 for the octave as 4/3.
So Philolaus can not use 12:9 as 4/3 frequency with 3/4 wavelength since the music interval based on the scale will be a smaller geometric magnitude to the octave, meaning it will be G to C (octave) as the Perfect Fourth while 12:8 as 3/2 frequency from the octave as 12 is 2/3 as the Perfect Fifth frequency of F to C (octave). So instead for the Perfect Fourth the frequency of 8/6 has to be used as 6/8 wavelength of root tonic 6 to 12 wavelength octave, with 6/8 as 3/4 of root tonic 0 to 8!! So that the subharmonic of 12 as 6/8 is actually 2/3 of 12 but at the octave 6 it is 4/3 of 0 to 6 as frequency while the wavelength is 0 to 12. So that the octave frequency and wavelength are switched around from 6 to 12. This enables the subharmonic frequency of root tonic 0 to 8 as 3/4 wavelength to not be the 2/3 wavelength of 0 to 12 as 8/12. And so then:
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.
And so the Bait and Switch that covered up noncommutative phase - by flipping the Lyre around - emerged.
But Alain Connes rediscovered the truth that Zero geometric dimension is actually, as a physical point, as cover up of noncommutative phase that is pure time-frequency inversion as quantum entanglement!!
From Dr. David Muesham (of Troll Dance fame)
Into the 20th century, Burr and Northrup studied the role of bioelectric signals in embryonic development and regeneration5, and in the 1940s, Marsh and Beams made the remarkable discovery that applying electric fields of different polarities to flatworms (planaria) could change the direction of regeneration6. Significant steps forward were also made by Robert Becker, who mapped the bioelectric potentials associated with growth and repair processes, and found that regeneration could be enhanced by applying electricity to wound sites at the wound when there was a negative potential outside the amputation stub11. Robert Becker popularized these and other advances in our understanding of the role of electric and magnetic fields in healing and regeneration in the 1985 publication in of The Body Electric 12. In the 1970s, it was found that EMFs could promote bone repair7, and later, a seminal series or research by Colin McCaig showed that electric potentials naturally arising in wounds were critical for healing and regeneration8, and a variety of therapeutic uses of EMFs have been developed, including bone and soft tissue repair9,10.
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Levin has shown that patterns of bioelectric signaling constitute “…an autonomous layer of control not reducible to a biochemical or genetic account of cell state”13. In a recent review dedicated to Robert Becker, Kelly McLaughlin and Michael Levin point towards the future, noting that, “The ability of bioelectric signaling to direct cell behavior has been described in the literature for over a century, yet only recently are we gaining sufficient insight about mechanisms and global dynamics to enable biomedicine to unlock this valuable information”14.
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For example, Jain teachings describe the interaction of the soul’s consciousness with the karmic field, producing emanations known as adhyavasāya which interact with a subtle body called the tejas sarir (“fiery body”) which supports mental and physical health, and are described in a manner resembling modern descriptions of electromagnetic fields15. Similarly, the Vedic concept of the energetic body known as prānamayakoṣa, and the Tibetan Buddhist description of a subtle body known as the “vajra body” (Sanskrit:vajradeha; Tibetan: sku rdorje or rdo rje lus) refer to a network of invisible energy channels that guide bodily functions15
- Levin M. Endogenous bioelectrical networks store non-genetic patterning information during development and regeneration. J Physiol. 2014 Jun 1;592(11):2295-305.
- McLaughlin KA, Levin M. Bioelectric signaling in regeneration: Mechanisms of ionic controls of growth and form. Dev Biol. 2018 Jan 15;433(2):177-189.
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