Thanks for the lecture quote. Question: Did you insert the bracketed words -- "[frequency]" next to the word "spectrum"? Alain Connes seems to be talking about the spectra of operators, not of waves. Because such spectra are capable of being discrete and continuous.
I was taking that from the following (Connes, A. Noncommutative geometry and reality. J. Math Phys, 34(3) 1995, pp. 6194-6231.):
I haven't read the paper, it isn't what I'm working on right now, and would require a lot of digging for me. But it doesn't appear to displace or call untrue the use of Riemannian geometry where the length scales are appropriate, it includes Riemannian geometry (if I had to guess, not having read more than the intro, Riemannian geometry emerges as the model for the continuous part of the spectra of non-commuting operators).
So let me quote what you said:
Now let's go back to Connes:Because such spectra are capable of being 1) discrete and 2) continuous.
, the amazing fact is that exactly time is emerging from the noncommutivity. You think that these variables do not commute, first of all it is that they don't commute so you can have the 1) discrete variable that coexists with the 2) continuous variable. What you find out after awhile is that the origin of time is probably quantum mechanical and its coming from the fact that thanks to noncommutativity ONLY that one can write the time evolution of a system
So the operators are actually two different frequencies at the same time that have noncommutative phase.
My background is actually music studies - and I started out doing University level music training while I was in high school - doing private studies with a former University professor. This was after I had also done intensive piano training starting at age 5.
So I realized this secret of the noncommutative phase - but I did not have the mathematical concepts to explain it. I was calling it "complementary opposite ratios."
Now let's go back to Connes again on music theory. Here's what you are stating:
Here is Connes:Riemannian geometry emerges as the model for the continuous part of the spectra
Their spectrum is SO DENSE that it appears continuous but it is not continuous.... It is only because one drops commutativity that variables with a continuous range can coexist with variables with a countable range
So you say you'd have to do a lot of digging - actually there is a short overview of the implications of noncommutative geometry for science - here:
Now you say - it's not what you're working on.
Yes hardly anyone is "working" on noncommutative geometry.
But does anyone really have a choice?
Let's see what Connes states again:
passing to noncommutative spaces forces one to rethink about most of our familiar notions
OK so I realize it may not be what you're working on now but we're just talking about the truth of reality - no big deal.
.
So you ask me whether the Dirac spectrum refers to frequency or not.It's a rather delicate thing....There is a very strange mathematical fact.
Connes repeatedly also uses frequency - stating the Dirac Operator has a scale that is modeled by acoustic systems, with music theory providing the formal language for the model.You really are in a different world, then the world of geometry, which we all like because we all like to draw pictures and think in a geometric manner. So what I am going to explain is a very strange way to think about geometry, from this point of view, which is quite different from drawing on the blackboard
Why? Because music theory is actually noncommutative!!
Now notice - you may not have noticed this - but he reverses his logarithmic math - between 2 to the 12th and 3 to the 19th and then 2 to the 19th and 3 to the 12th!
So when I inserted frequency I used brackets - but that is from Connes - using parenthesis for spectrum as the frequency scale.the scale (spectrum) which consists of all positive integer powers qn for the real number q=2 to the 12th∼3 to the 19th.
,
So how he REVERSED the frequency ratios - why? Because the PHASE is noncommutative. In other words the EAR perceives the same Perfect Fifth Pitch while the frequency is reversed. So that 2/3 is the Perfect Fifth as C to F subharmonic frequency while 3/2 is also the Perfect Fifth as C to G overtone harmonic.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
This basic empirical truth was COVERED UP in order to CREATE the commutative symmetry math system of normal Western math-science!!
So now let's look at what "Eigen-Frequency" means for the Dirac Operator....
giving the eigen-frequencies of the spinors that can live on that spacetime.
Inner perturbations in noncommutative geometry - Walter van Suijlekom
by WD van Suijlekom - 2014 - Related articles
(joint with Ali Chamseddine and Alain Connes). May 15, 2014 ... A. ChamseddineGravity from Dirac Eigenvalues
by G Landi - 1997 - Cited by 39 - Related articles
We study a variant of the Connes-Chamseddine spectral action ... of the Dirac operator
D de ned on the spacetime geometry described by g(x). Thus, the general
idea is to describe spacetime geometry by giving the eigen-frequencies.Alain Connes | Institut des Hautes Études Scientifiques, Bures-sur ...
Alain Connes of Institut des Hautes Études Scientifiques, Bures-sur-Yvette (IHÉS) ... We give a detailed study of Dirac operators with Dirichlet boundary ...... of a given frequency traverses the path between two points which takes the least time.
Noncommutative Geometry Alain Connes
by A Connes - Cited by 6950 - Related articles
Alain Connes ... Riemannian Manifolds and the Dirac Operator. 555 ..... sults of spectroscopy forced Heisenberg to replace the classical frequency group of the.
and so Connes uses FORCED again:
The noncommutativity can be measured through the concept of commutator defined as follows
![\displaystyle \boxed{[ X , D ] = X D - D X = \frac{i}{2 \pi}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cboxed%7B%5B+X+%2C+D+%5D+%3D+X+D+-+D+X+%3D+%5Cfrac%7Bi%7D%7B2+%5Cpi%7D%7D&bg=ffffff&fg=7c705e&s=0 "\displaystyle \boxed{[ X , D ] = X D - D X = \frac{i}{2 \pi}}")
This relation is very similar to the usual quantum mechanical expression ![[ X , P ] = \frac{i h}{2 \pi}](https://s0.wp.com/latex.php?latex=%5B+X+%2C+P+%5D+%3D+%5Cfrac%7Bi+h%7D%7B2+%5Cpi%7D&bg=ffffff&fg=7c705e&s=0 "[ X , P ] = \frac{i h}{2 \pi}")
.
.https://mathematicalgarden.wordpress.com/2010/06/15/heisenberg-inequality-on-the-real-line/
No, that wasn't really quoting what I said because I meant, and said, "discrete and continuous".
Spectra of (closed) operators on a Hilbert space have 3 parts: The resolvent, the discrete spectrum, and the continuous spectrum. So I really did mean "discrete and continous" as in a spectrum that includes both. In particular, if you have a self-adjoint operator, it's spectrum is real, and if it is not commutative, the commutation operator gives an uncertainty like the Heisenberg uncertainty principle. These spectra don't have to have anything to do with frequencies, it is when they are Fourier spectra that they correspond to such, which is where the name came from -- why they are called spectra. In this case, they are the eigenfunctions of the operator, and the best analogy is to the eigenvalues of a matrix (If a matrix has determinant not zero, you can find a coordinate system in which it is a diagonal matrix and the eigenvalues are the elements on the diagonal).
Good to know, I do find your stuff inspiring for mental images. My background, with respect to this stuff is mathematics, spec. dynamical systems and chaos, and I have undergrad and a little grad physics.
I suppose that's true, but not what I meant. I have an erstwhile professional now retired interest in some differential geometry topics, the Ricci equation and anisotropic diffusion. There's some overlap with Connes' subject matter, but only some. I do sometimes read stuff about string theory, but not in any mathematical depth. And I do have my own use for discretization in my topic, which is why I thanked you for the references.
It actually refers to the spectrum of the Dirac operator. The Dirac operator is the formal square root of the Laplace-Beltrami operator (so that actually is something I get to use from time to time). But like I said, because some operators have spectra that are related to frequency, they are all called spectra as an analogy to light spectra. That one, because it's related to the Laplace operator, whose spectrum is Fourier eigenfunctions which really are frequencies as in frequency domain, is easier to picture as frequencies than most operators in general.
Connes' point in relating everything to music is to try to make everyone intuit the notion of noncommutative geometry as easily as they can intuit other geometries. Because he wants to end the dichotomous thinking about classical v. quantum physics and think of the whole as one physics.
Let me review your teaching me - which I appreciate.
You state:
then you state:eigenfunctions of the operator
then you state:the eigenvalues of a matrix
OK now let's go back to noncommutative geometry.Fourier eigenfunctions which really are frequencies
Now as I mentioned - Connes' most recent publication is an actual music composition. So perhaps that would be the most enlightening.
So first we go back to the Connes' quote I posted. YOu are claiming he is using music as an analogy. I am claiming that the music theory is directly the model of the Dirac Operator.
Here is what Connes states:
andAnd it could be formalized by music
So if you watch the lecture - Connes actually composes music that is the quantum spectrum and vice versa.Due to the exponential growth of this [music frequency] spectrum, it cannot correspond to a familiar shape but to an object of dimension less than any strictly positive number. As explained in the talk, there is a beautiful space which has the correct spectrum: the quantum sphere of Poddles, Dabrowski, Sitarz, Brain, Landi et all. ... We experiment in the talk with this spectrum and show how well suited it is for playing music.
andGeometry would no longer be dependent on coordinates, it would be spectral
OK so the way he is talking about music is very different than it is normally understood. Sir James Jeans came close to this understanding in his book "Science and Music" - but otherwise you do not find this definition of music ANYWAY in Western science.Musical shape has geometric dimension zero... You think you are in bad shape because all the shapes we know ...but this is ignoring the noncommutative work. This is ignoring quantum groups. There is a beautiful answer to that, which is the quantum sphere... .There is a quantum sphere with a geometric dimension of zero
So Connes is interchanging the word "spectrum" with acoustic "scale."The Dirac Operator itself has a scale, so it's a spectrum....a "universal scaling system," manifests itself in acoustic systems....
OK so now let's go back to the terms you used:
Eigenfunction and Eigenvalue.
But a term you did not use is?
So this is what Connes is talking about.giving the eigen-frequencies of the spinors that can live on that spacetime.
OK so that's what you're referring to. But what does Connes state about the "square-root"?The Dirac operator is a 'square-root' of the Laplacian, so that its spectrum ..
So there is a difference between the square root and the spin structure.when I talk about the Dirac Operator, there is a square root, and this square root, when you take a square root there is an ambiguity. And the ambiguity that is there is coming from the spin structure
The spin structure is the eigen-frequencies that are noncommutative phase.
OK so do you see that this is the level "below" the Dirac Operator?You have matrices which are given by a noncommutative space.....time emerges from noncommutativity...To have a geometry you need to have an inverse space and a Dirac Operator...The inverse space of the finite space is 5 dimensional... the phase space of a microscopic system is actually a noncommutative space and that is what is behind the scenes all the time.
So you did not use the term eigen-frequencies because these are noncommutative phase frequencies - not the same as Fourier frequency (which does not use time and frequency at the same noncommutative phase as the 5th dimension).Thus, the general idea is to describe spacetime geometry by giving the eigen-frequencies.
So these are also called the Spectral Triplets by Connes - meaning 3 frequencies that are noncommutative.a given frequency traverses the path between two points which takes the least time.
To quote Connes again:
So Connes whole work is just building on Heisenberg - replacing what most scientists consider to be frequency with in fact the empirically true definition of frequency that is ALSO found in Daoist Harmonics and Orthodox Pythagorean harmonics - it is noncommutative phase as the 5th dimension that is non-local at "zero" time.spectroscopy forced Heisenberg to replace the classical frequency group of the.
Yes this was also first discovered by Louis de Broglie - the truth "father" of relativistic quantum physics:
The noncommutative geometry of Zitterbewegung
by M Eckstein - 2016 - Cited by 8 - Related articles
Oct 31, 2016 - over, it lies at the heart of Connes' theory of noncommutative geometry [3, 4], which ... frequency of the 'trembling motion' of a single Dirac fermion
In this case, they are the eigenfunctions of the operator, and the
best analogy is to the eigenvalues of a matrix (If a matrix has
determinant not zero, you can find a coordinate system in which it is a
diagonal matrix and the eigenvalues are the elements on the diagonal).
So then http://www.waltervansuijlekom.nl/wp-content/uploads/2014/07/leiden2014.pdf
as I quoted before:
Inner perturbations in noncommutative geometry - Walter van Suijlekom
by WD van Suijlekom - 2014 - Related articles(joint with Ali Chamseddine and Alain Connes). May 15, 2014 ... A. Chamseddine, Alain Connes, WvS. ... Wave numbers on the disc: high frequencies. 50. 100. 150 ... The Dirac operator is a 'square-root' of the Laplacian, so that its spectrum ..
So if you open that pdf - it is explained:
This is what you state above, but the link explains:it is a diagonal matrix
emphasis in the original.Instead of diagonal matrices, we consider block diagonal matrices...
So then the noncommutative block matrice is explained by a 3 block form or 3 x 3 matrix.
So what you describe is then "perturbed" by the block diagonal noncommutative algebra.
So then at each "zero" point of space there is an "inner" or "sub space" that is noncommutative phase.
That subspace or the 5th dimension is then ADDED to the Riemannian space - and THEN you can do the Dirac Operator on it.
There's some overlap with Connes' subject matter, but only some.http://www.alainconnes.org/docs/shapes.pdf
So then if you actually read Connes' "Music of the Spheres" lecture - as a pdf doc - he explains then how the "twisted" Spectral triplet in the subspace at the zero geometric point, then explains the hidden 6 dimensions of string theory. Connes (2018) pdf:
And Connes' inspiration for this was directly the analysis of whether you can HEAR the SHAPE of a DRUM - and the answer is no because the drum can be "isospectral" - the same frequency - but NOT "isomorphic" - the same geometric shape. So that, again, is the same concept applied to the twisted spectral triplet as a bounded diagonal matrice (containing both the Future and the Past overlapping as the chirality of 1/2 spin).
So again this is frequency BEFORE the Fourier Transform frequency that you refer to - or BEFORE the Poisson Bracket that I referred to a few posts above. Connes:
There are three types of notes....What do I mean by possible chords? I mean now that you have eigenfunctions.... The point [zero in space] makes a chord between two notes. When the value of the two eigenfunctions [2, 3, infinity] will be non-zero
http://www.noncommutativegeometry.nl/wp-content/uploads/2013/10/ConnesLeiden.pdf
This gives more details - the pdf is called "The Spectral Model" - by Connes
So that shows the Isospectral by NOT isomorphic (noncommutative phase) of the drum shape that can not be heard. This noncommutative phase music is precise to the quantum origins of reality, Connes:
Connes:
a point of the geometric space "X" can be thought of as a correlation ...which encodes the scalar product at the point between the eigenfunctions of the Dirac operator associated to various frequencies, i.e. eigenvalues of the Dirac operator.
Connes calls it a "twisted" Dirac Operator. So the Spectral Triplet from music theory is what he calls (2, 3, infinity). So no - I'm not at all talking about music as per the usual symmetric Fourier analysis, nor is Connes.
So when I was studying music theory in high school - privately - I just wondered something very simple - why does the Perfect Fifth have to be 3/2 and not 2/3 - or in terms of geometry in music it is C to G and not F to C (subharmonic).
So this was actually the noncommutative phase origin as the 5th dimension that was covered up when the Greek Miracle (the "deep pre-established disharmony") was created.
And so Connes' latest paper is on entropy. The thing is this - we define global warming as entropy based on the solar photon light being of a higher frequency that is absorbed by plants and algae - but then it gets emitted back from the Earth as longer infrared light considered to be entropy. But our science then considers civilization via technology to be Order that is against entropy.
Schroedinger proved that this is wrong, in his book, "What is Life?" And the recent book "Life on the Edge" on quantum biology (2016) goes into this further.
As proved by Hawking, had the Universe's entropy increased been reversed, this reversal would be impossible to observe. This is because time orientation of all biological processes (as we show elsewhere in detail) relies solely on entropy's increase.
Avshalom C. Elitzur, Shahar Dolev
Black-Hole Uncertainty Entails An Intrinsic Time Arrow, Dec. 2000
So this claim is incorrect since it assumes that Western left brain /right hand technology perception is the only means to observe reality. But Nonwestern music harmonics that Connes has revealed as the truth of reality - the noncommutative phase as the 5th dimension - can be logically inferred and LISTENED to and this is the secret of Daoist Neigong training, as Eddie Oshins at Stanford Linear Accelerator Center also realized.
What it has to do directly with music has to do with Milnor's theorem that the spectrum of the Laplacian does not in general determine the shape of a manifold (in this case think surface with boundary),
So yes Connes points out that just as in music theory - which is actually noncommutative phase (and so the inability to hear the shape of a drum is just a specific example that proves this point)....
So to quote Connes on what I just quoted you:
One reason for the difficulty of this task is that, as it is well known since the examples of J. Milnor, non-isometric Riemannian spaces exist which have the same spectra (for the Dirac or Laplace Operators).
So yes that it precisely why music provides the "formal logic" to solve the foundation of reality.
Now you are claiming that this foundation that is noncommutative can then just be "embedded" back into commutative symmetric math via the Poisson Bracket. What Connes emphasizes is that renormalization has been wrong because of missing this noncommutative truth as logic. And as the overview video I posted states - noncommutative geometry has to rely on each force of physics having a different noncommutative spacetime.
So basically Western science has been very precise up till now but NOT accurate. Personally I would go for accuracy over precision. And so we've created great entropy AGAINST relativistic quantum biology - the 5th dimension as negenetropy that life relies on. This is what qigong master Yan Xin calls the "virtual information field" that does the qigong healing. Qigong master Zhong, Hongbao calls this secret the "golden key" of superluminal "yin matter."
So in WEstern science we Assume that the foundation of reality is random. Ian Stewart states that in quantum physics this is not necessarily true. Here is how quantum physics professor (previously of Hampshire College where I took quantum mechanics) describes our true perception of reality:
.
..superconductivity within one neuron could become phase coherent with that in an adjoining cell by virtue of quantum tunnelling, and this could be stimulated by the macroscopic analog of stimulated emission (alluded to before in connection with the mantra), that is an AC Josephson effect. ...At a more interesting level, the quantum vacuum state may be said to be empty (of excitation) and yet full in the sense of pure potentiality; it contains "virtual" (unphysical) representatives of all possible modes of matter and excitation in the form of vacuum fluctuations or "virtual particles" (zero-point excitations of each field mode, assigned one-half quanta of energy, due directly to the non-commutative property of the field operators).
So the thing about "listening" is that science has now proven that humans can listen at 10 times faster than Fourier Uncertainty (with time as a linear operator).
Quote
So what a "tone" is - this actually is quite fascinating.
Here we have a square drum or box drum - whether it has "tones" is subjective.
So what the latest studies have found is that if you take a tone to its shortest "length" or period - then the root tonic is perceived to shift up a Perfect Fifth. Again this is because our ears, as physics professor Euler points out - I corresponded with him - our ears act as an acoustic "double slit" experiment. So we hear with noncommutative phase coherence - down to the microsecond wavelength. And the highest pitch we hear externally actually resonates our brain internally as a whole as ultrasound. This is called the HyperSonic Effect - but it's only found in Nonwestern music tuning in a natural acoustics listening environment. Because the Western logarithmic tuning cuts off the natural noncommutative phase resonance.
So as Connes points out...
When you say that the noncommutative is an "extension" of the commutative - the point I am emphasizing is that Connes use of music as the formal logic of the noncommutative phase is actually based on using "two notes" as frequency. I gave the example already - this is actually from Pythagorean orthodox music tuning - from before Philolaus even (and therefore before Plato and Archtyas). So math professor Luigi Borzacchini proved that in fact Western math originates from the wrong music theory - and is, as he states, the "guiding evolutive principle" of western science. Philosopher of science Oliver L. Reiser called this music drive of western math, the "music logarithmic spiral." A term from Esther Watson (daughter of Thomas Watson) who discussed this research with Einstein.
Here's Connes again:
There is something even simpler which is what happens with a single string. If we take the most elementary shape, which is the interval, what will happen when we make it vibrate, of course with the end points fixed, it will vibrate in a very extremely simple manner. Each of these will produce a sound....When talking about a string it's a straight line. ... They are isospectral [frequency with the same area], even though they are geometrically different....when you take the square root of these numbers, they are the same [frequency] spectrum but they don't have the same chords. There are three types of notes which are different....What do I mean by possible chords? .... The point [zero in space] makes a chord between two notes. When the value of the two eigenfunctions [2, 3, infinity] will be non-zero. ...The corresponding eigenfunctions only leave you one of the two pieces; so if there is is one in the piece, it is zero on the other piece and if it is non-zero in the piece it is zero there...You understand the finite invariant which is behind the scenes which is allowing you to recover the geometry from the spectrum....
Our notion of point will emerge, a correlation of different frequencies...The space will be given by the scale. The music of the space will be done by the various chords. It's not enough to give the scale. You also have to give which chords are possible....The only thing that matters when you have these sequences are the ratios, 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....You see what we are after....it should be a shape, it's spectrum looks like that...We can draw this spectrum...what do you get? ... It goes up exponentially fast...What is the dimension of this space?...It's much much smaller. It's zero...It's smaller than any positive.... Musical shape has geometric dimension zero... You think you are in bad shape because all the shapes we know ...but this is ignoring the noncommutative work. This is ignoring quantum groups. There is a beautiful answer to that, which is the quantum sphere... .There is a quantum sphere with a geometric dimension of zero.
So in other words - it's a kind of unified field theory that also includes integrated humans as living quantum computers. Ian Stewart is part of this research plan also. But - this is something I exposed after finishing my master's degree - and so I dubbed it the "Actual Matrix Plan" - back in 2001. So based on that plan then nuclear radiation is considered to be a type of spiritual evolution that humans need to adapt to - "medical hormesis."
So actually there is a better spin of the Hameroff-Penrose model - put forth by Jack Tuszynski's research team in quantum biology. https://elixirfield.blogspot.com/2019/05/the-chiral-asymmetric-quantum-potential.html
I did a blog post on it - but you have to scroll down past my intro quotes to get to the actual blog post.
https://www.researchgate.net/publication/332530309_Theorising_how_the_brain_encodes_consciousness_based_on_negentropic_entanglement
To get back to Bernstein - he also developed a noncommutative phase technology that is being tested by NASA as nonlocal quantum correlation signals via satellite. So superluminal quantum entanglement signals - but the particular "spin" he puts on it (in contrast to the Chinese) is to utilize a noncommutative phase topology.
So then that quote you were surprised about - I actually sent that to Nobel physicist Brian Josephson - and he thanked me for it. But Josephson, with whom I corresponded, is now focused on acoustic resonance also and is now also studying noncommutative phase math via the colleague of Eddie Oshins (who made the Neigong connection) - math professor Louis Kauffman.
https://elixirfield.blogspot.com/2018/10/the-dirac-dance-and-aharonov-susskind.html
Eddie Oshins makes reference to the Aharonov-Susskind-Bernstein Effect.
However, Bernstein [24J and Aharonov and Susskind [25] argued that this was not necessarily the case under all ...
https://www.youtube.com/watch?v=CYBqIRM8GiY
So essentially Daoist Neigong - as Eddie Oshins realized - is literally a Macroquantum relativistic training via quantum biology. So the body moves of the training - is literally a recreation of the noncommutative phase resonance.
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