is the fact that, while the metric dimension of F is zero,
I emailed Alain Connes - as usual - no response.
https://www.alainconnes.org/docs/book94bigpdf.pdf
We say that qi s zero almost everywhere iff q◦λi s so
OK so it is just time-frequency with NO wavelength. So also it has exponential growth as octave equivalence of pitch. So this is why it has a geometric dimension of zero. BECAUSE it is noncommutative then it is not "contained" into space.
But - how does the "rate" as exponential affect this? Clearly it is due to the time-frequency Fourier transformation? The Uncertainty rate?
I asked my former music professor private tutor - from high school music training. He said he's read Alain Connes as per music - I sent him the latest "Music of Shapes" lecture. Then I asked him about this zero dimension of geometry from music theory claim of Connes. No response. haha.
Much more concrete work will be needed to implement this idea but as we shallhttps://alainconnes.org/docs/einsymp.pdf
see shortly the \e®ective geometry" of space-time coming from the nuance between
QED and the standard model is also described as a product of the form (14) of the
standard euclidean geometry by a zero dimensional noncommutative space.
the
zero dimensional geometry (Af ;Hf ;Df )
OK so that is the Quantum Sphere.
where "f" stands for finite.
So the "D" is the noncommutative phase of the "inner fluctuations" of noncommutative phase of the Dirac Operator. So it's future and past time noncommutative to frequency energy.
H is the infinite Hilbert Space.
Duality between shapes and spectra. The music of shapes. A. Connes ... Towards a musical shape. 1 ... The inner fluctuations of the metric are given by. D → DA.
So... lots of papers on the "inner fluctuations"
The spectral action in noncommutative geometry naturally implements an ultraviolet cut-off, by counting the eigenvalues of a (generalized) Dirac operator lower than an energy of unification. Inverting the well known question "how to hear the shape of a drum ?", we ask what drum can be designed by hearing the truncated music of the spectral action ? This makes sense because the same Dirac operator also determines the metric, via Connes distance. The latter thus offers an original way to implement the high-momentum cut-off of the spectral action as a short distance cut-off on space. This is a non-technical presentation of the results of arXiv:1305.2605
I'm just trying to stick to the music model.
the asymptotic expansion
So that's the same as the exponential growth of the music octaves.
Reversing the well known question on how to retrieve the shape of a drum from its vibration modes, our point here is to understand what drum can one design from hearing the spectral action ? We have shown in [8]that the answer is not obvious, and asks for a careful discussion on the nature of the points of the“cut-off drum”. We report here some of these results, in a non technical manner.
I guess the issue here is that the de Broglie wavelength creates an infinity rest mass for the electron - due to the equivalence or inversion of momentum and frequency (whether it's relativistic or quantum). And so... the noncommutative phase then "cuts" off the infinities by containing the geometry?
Why not just show a Taiji symbol to make it all easier for us? haha.
Funny enough, both French and Italian languages have very close words for time (temps/tempo) and temperature (température/temperatura). Could they be physically closely related, as real and imaginery parts of a complex number? Do algebra have periods
https://laurent-duval.blogspot.com/2010/07/time-is-simplest-non-commutative-thing.html
In the book Triangle of Thoughts (American Mathematical Society,2001) Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger discuss the interrelationships among Mathematics, Physics, and Philosophy. In Chapter 8, they say:
"... A.C. - ... I am trying to use a mathematical model that allows me to conceive of time in a way that is more fruitful and more individually satisfying than this dreadfully one-dimensional time upon which we inscribe our existence and which I find profoundly distasteful. ...
The first example that comes to mind ... is Kronecker's foliation,a straight line that winds at an irrational angle around a torus of very high dimension. ... most of the points of reference allowing us to feel and monitor time are cyclical rhythms ... There are a huge number of rhythms, each of which is a variable windingaround in a circle. ... the multiple periods that, not being necessarily commensurate, allow us to imaging intuitive time as a high dimensional torus. There are as many dimensions as there a recyclical times ... Of course this can be compared to the linear physical time winding around this torus, if we trace the path of an individual. ...
M.P.S. - ... I wonder whether the simple problem of the coexistence of individual polycyclic time with its socialization is not virtually insoluble from the start.
A.C. - Not necessarily. These multiple cycles originate in a biological periodicity, which is common to a huge number of individuals. ... it is geographic proximity that imposes consistency and that causes the diverse parameters to be in phase within a particular society. Whenever the number of cyclical parameters is reduced, the "vital space" available to an individual is reduced. ...It has been observed that Anglo-Saxon societies are much more dependent on an affine time than are Mediterranean civilizations,which are much more familiar with polycyclic time. ... In Spanish literature, the individual's naive time is not one-dimensional, but rather a return time - return of the sun, of the moon - a time inwhich the accumulation associated with aging is not experienced in a drab bureaucratic manner.
... My assertion is that the one-dimensional model of time is too reductive for individual time. ... I am going to propose a model for you to examine. The universe in which you are located ... is that of language. ... I would say "the universe of words," simply to give it a name. ... I ...propose a ... definition of the "Self." ... It is simply the discrete information coded in the reproducible genetic information. The Universal Self is this immense genealogical tree that we are part of... I consider myself to be a sort of translation, a material realization, of this abstract Self, through its interaction with physical reality. ...
M.P.S. - ... There is the consciousness of time, but there is also the consciousness of consciousness of time, which is not the same thing. ... I have reservations about the problem of language, because there are realities that are not verbal, such as music. ...
A.C. - All the same, music is transmissible and reproducible. It resembles a language. ... like a language it is written, spoken, and transmitted. ... I am fascinated by the relation between the usual model of time and the sequential nature of written language. This writing is perfectly adapted to associative algebra in the sense that the associativity condition simply means that a product of elements of an associative algebra can be written without the encumbrance of parentheses. ... Commutativity does not hold, but since sequential writing preserves the order of the terms of a product, it is perfect for handling non-commutativity. ...
a non-commutative algebra naturally engenders a one-parameter group of automorphisms that makes it evolve, that makes it rotate in such a way that the passage from xy to yx corresponds to what evolution yields for the purely imaginary value t = sqrt(-1) of the parameter t of the evolution group. We must ... introduce evolution only after choosing a state in the algebra, but the evolution obtained is modified only by inner automorphisms and these are in a certain sense invisible. Here, I believe, is the key link that Hamilton sought between time and algebra. ...
M.P.S. - Is musical notation sequential?
A.C. - I don't think so. Musical notation allows several themes tobe developed simultaneously. Several melodies can coexist and a dialogue can be established in the same instant; polyphony is a dialogue that is simultaneous, not sequential. In this sense, I think that music is an outline of a language that is inscribed in a multi-dimensional not sequential framework; it is a language that,except for certain musicians, cannot be effectively used as a means of communicating factual data ...
There are people who are capable of listening to an opera and hearing several voices at once. This is what made Victor Hugo jealous of Giuseppe Verdi.
M.P.S. - But you cannot compare the impressions that different people have when they listen to music.
A.C. - Not yet. ...
M.P.S. - ... Alain, you are sketching an image of evolving humanity: why do you believe it is evolving rather than static.?
A.C. - I can easily imagine the time when writing was never read silently, when it was transmissible only by reading aloud, so an oral reader was required. ... The time when one bought a book and read it silently came later. ...
Music in its current stage is analogous to oral reading: at this stage, the text can be transmitted only by the emission of sounds.
I claim there is another stage beyond this. I remember having heard the conductor Solti explain how he prepared for a concert. ...he simply took the score and holed up in a room where he would spend hours reading the score in silence.
M.P.S. - ... In other words, you conceive of the possibility of music that exists only in written form ...
A.C. - ... and 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 ...
M.P.S. - Silent reading must have begun in the 11th or 12thcentury, in Benedictine convents, so that the monks would not make too much noise reading. Little by little, people reached the stage of internalized reading. ... We know at what point people began to be taught to read directly by internalizing. It is a very curious phenomenon.
A.C. - Reading one voice is easy; reading a page of polyphony, as does a conductor, is much more difficult. ... music is still at the primitive stage, much more primitive than spoken language.
A.L. - Music is as old as language. ... social polycyclic time seems to me to be much more complicated.
A.C. - And it could be formalized by music.
M.P.S. - ... according to you, we can assume that the evolution of language can serve as a model for music. ... language begins with poetry rather than grammar; euphony plays a big role here.
A.C. - ... I sincerely believe that music is at its very beginnings, like language when it was at the stage of euphony. 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 ...
the problem of adaptation ... has to be resolved in order for usto understand quantum correlation and interrelation which we discussed earlier, and which are fundamentally schizoid in nature.
https://www.tony5m17h.net/musPhys.html
So I'm realizing that Alain Connes doesn't quite get it. He thinks that Orchestration as multiple spacetimes is the KEY to what he is saying about a higher dimensional noncommutative geometry.
So he is actually denigrating oral cultures that used real noncommutative phase music scales of natural numbers.
I knew this before but he's just so close - yet so far. He is the only scientist to acknowledge the real truth of music theory. Yet he still defines it as based on language - notice here he differentiates Latin language from AngloSaxon language based on the meaning of time.
No comments:
Post a Comment