Thanks. Wish I had time to follow it up.
| 6:07 PM (1 hour ago) | ||
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27 vids.
| noamchomsky@email.arizona.edu |
Dear Professor Laureate Noam Chomsky: Professor Alain Connes makes a remark that I thought you'd enjoy. I was rereading his remark and your talks on linguistics enabled me to better understand Connes. Connes says,
"Our brain is an incredible...it perceives things in momentum space of the photons we receive and manufactures a mental picture. Which is geometric. But what I am telling you is that I think...that the fundamental thing is spectral [frequency]...and somehow in order to think we have to do this enormous Fourier Transform on geometry. By talking about the "music of shapes" is really a Fourier Transform of shape and the fact that we have to do it in reverse [meaning noncommutative quantum time-frequency uncertainty is transformed into phase-amplitude shape]. This is a function that the brain does amazingly well, because we think geometrically."
So as you emphasize - the origin of thinking is paradoxically before thoughts - and Connes is addressing this paradox by claiming it is solved through noncommutative phase logic that is before geometry (and therefore before thinking).
The above is from his lecture on music theory. I had first contacted you in 2001 regarding my master's thesis that cites your work (and my own activism inspired by your own research). My graduate degree was self-designed in Liberal Studies with the emphasis on sustainability (so I did a lot of activism). haha. My thesis was on music theory as philosophy of science for the foundation of sustainability. I was trying to describe a concept but I didn't understand noncommutative phase logic - (I had never heard of it until I discovered Alain Connes a few years later).
https://www.youtube.com/watch?v=bIziuv-WLMM
his is the music theory lecture by Alain Connes. My upload paper video has more music theory commentary to better explain Connes' lecture. The video is meant to be paused to read the pages of the paper. For a paper version see https://www.academia.edu/41186978/Two_Three_infinity_How_music_is_the_formal_language_of_the_unified_field_theory_The_Noncommutative_Nondualist_and_Nonlocal_Positive_Pressure_Zero_Mass_math_music_model_of_Fields_Medal_math_professor_Alain_Connes
So Connes says it is due to the irrational function of music theory of 2 and 3 that noncommutative time-frequency arises. What he really means is that the continued fraction series of log 2 and log 3 is 1 plus 1 divided by 1.... infinitely. And the "1" as the square of the logarithms is also the square of the Dirac Operator for relativistic quantum mechanics. So the inverse of the square as the propagator is then the noncommutative time-frequency phase (which is also true in music theory)....
So Oshins says how my Quantum Mechanics Professor Bernstein uses Fourier analysis in his article. So I took another look - and a closer read. Very fascinating indeed. A lot is packed into that article!!
His description of the quantum magnetic vector potential as a universal phase shift is fascinating - stating that only Aharonov-Bohm proved this to be true as a real empirical foundation of reality - what Professor Hiley calls a NEW FORCE discovered!!
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