The math-music proof by Alain Connes is found starting on page 385 to
388 in this pdf. https://www.its.caltech.edu/~matilde/coll-55.pdf Noncommutative Geometry, Quantum Fields and Motives
Alain Connes
Matilde
Marcolli
https://elixirfield.blogspot.com/2022/02/my-newly-published-article-on-viewzone.html
for quote screenshots from the Connes book - just scroll down.
Thanks to Dr. Ruth E. Kastner for her positive feedback and interest in
my research via our correspondence. We have a lot of common interests
and she is on the record considering that her relativistic transactional
interpretation of quantum physics or RTI - does enable the potential of
paranormal phenomenon.
What I'm doing - as Dr. Kastner described herself as "paranormally
challenged" in her video interview - is explaining how a person can
"train" in paranormal abilities via the secret of the noncommutative
music theory that Alain Connes explains.
The comparison of Kastner and Connes also better explains and corroborates my own music-meditation claim from the rational Pythagorean ratios, proving that Connes does rely on this and not just the equal-tempered logarithms (as some might try to incorrectly claim about Connes). haha. Math Professor Luigi Borzacchini calls this a "cognitive prejudice" or cognitive error to disregard the music theory origins of the symmetric irrational number magnitude math called the "Greek Miracle" from Archytas defining the octave as a geometric mean squared - thereby developing the concept of a geometric irrational number continuum in Western modern science. I recently discovered a NEW quote from Math Professor Borzacchini in his professor math forum discussions:
"The "quadrivium" is based on a double opposition: the first between
multiplicity ("poson", arithmetic+music) and magnitude
("peelikotes", geometry+astronomy), the second inside both pairs between
rest and motion, but even maybe between theory and model. This last
aspect can be another "divination", but in the above Archytas' fragment
(and in other his arithmetical-musical fragments) the approach to the
music/arithmetic connection is model-driven, whereas in Philolaus' ones
the approach is in 'intrinsic' and 'numerologic' (I can try, if needed,
to give some supports to these statements)." And in the same comment he states: Greeks employed 'numbers' for geometrical measures, but even the numerical system opposed "numbers" (usually on base 10) and "parts" (usually on base 12) There are a lot of examples of the base-12 employed by Babylonians, Greeks and Romans for their pantheon or musical or measuring systems,
even sometimes with an autonomous system of numerical graphical
representation (as in Vitruvius), there is the Greek abacus quoted by
Heath in the first pages of his "Greek Mathematics" with its double
system of division (5 for integers, 6 for parts), but the best is, in my
opinion, the history of Athens' organization, as performed by Clistenes,
Pericles, etc. and 'sublimated' in Plato's "Laws", where base 12 appears
throughout when there is a whole to divide and base 10 when there is a
group to build. (The easiest and trivial rationale could be the base-12
in astronomy in the passage from the lunar to the solar calendar, and
the base-10 in hands-counting.)"
http://archives.math.utk.edu/hypermail/historia/apr99/0134.html
So this brings us precisely back to the Plutarch quote that I discussed with Borzacchini about how the 9/8 music ratio from the squaring of 3/2 and "halving" back into the same octave as 9/8 could then not be doubled and halved as an arithmetic mean of 17 or any other rational number. Therefore Osiris was identified with 17 as the three days AFTER the Full Moon when the full moon energy stopped but Osiris was also identified with the height of the triangle based on the squaring of the lengths for geometric mean as a Pythagorean triangle. So this is the key issue from the conversion of the Lunar calendar as synchronized to the music theory of the 12 notes as noncommutative phase for the psychic "yin qi" energy to be built up BEFORE the transfer of the yang qi into the Yuan Qi as the yang qi is the "Single Perfect Fifth" based on the noncommutative time-frequency phase shift.
So also it is cited by Cartwight and proven empirically that if the fundamental frequency is removed for a sound along with the Perfect Fifth overtone as the harmonic - while keeping the higher harmonics and then a phase shift occurs by subtracting the higher harmonics by an all equal language - if the time phase was defined by the spatial geometric mean wavelength then the fundamental frequency should not change. The total difference solution remains the same due to the equality of the phase shift difference for the subtraction of the harmonics YET the fundamental frequency is perceived to change! This is further confirmation that the fundamental frequency is based on absolute pitch as the noncommutative time-frequency.
It also explains as Dr. Daniel Levitin discovered: when diff people globally sing Happy Bday they maintain the same absolute pitch!
Back to Borzacchini:
On the Greek troubles about continuity and infinite I can give some evidence. The best is
Archimedes' lemma (for the area of the parabola's segment) where he substantially discovers the sum of the geometrical series, but is not able to assert it.
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