Hi Professor Kauffman: Your derivation of the imaginary number from
primordial time as an iteration of 1, -1, 1... is tied to the rational
number approximation proof of the Pythagorean Theorem:
From that time on, an absolute periodic proof appears (+1, –1, +1…)
So
the noncommutative Pythagorean theorem is based on the triangle
embedded in a Bloch Sphere such that the square root of two is the
imaginary time factor of the noncommutative pi/4 angle.
If we
assume, as you argue, that the measurement of time is part of the
noncommutative iteration then it reveals the original Pythagorean
rational number proof as containing the noncommutative secret of the
Orthodox or ancient Pythagoreans.
What do you think of that?
thanks,
drew hempel
Response:
Dear Drew Hempel.
I am not sure I know what you mean when you say"So the noncommutative Pythagorean theorem is based on the triangle embedded in a Bloch Sphere such that the square root of two is the imaginary time factor of the noncommutative pi/4 angle.”Do you mean this non-commutative PT? (See included paper below.)
from
https://www.worldscientific.com/doi/abs/10.1142/9789814504782_0001
I can't believe you had already derived the same logic that I inferred intuitively. That's hilarious!! Thanks so much, drew
Dear Divyamaan Sahoo: Please review the attached as I quote
Professor Kauffman and it is a noncommutative music theory argument.
This
paper is a draft that I am revising. Any feedback is greatly
appreciated. I plan to submit it to "Journal of Scientific Exploration"
soon,
thanks,
drew hempel, MA
Louis H. Kauffman . Knot logic and topological quantum computing with majorana fermions. In ``Logic and algebraic structures in quantum computing and information", Lecture Notes in Logic, J. Chubb, J. Chubb, Ali Eskandarian, and V. Harizanov, editors, 124 pages Cambridge University Press (2016).
is the original source of the paper Lou sent me and then he says:
An early paper is Sign and Space.
Sign and Space, In Religious Experience and Scientific Paradigms. Proceedings of
the 1982 IASWR Conference, Stony Brook, New York: Institute of Advanced Study of
World Religions, (1985), 118-164.
Basically I was reading the early Greek rational number proof for the Pythagorean Theorem whereby the greater and lesser solution is an eternal iteration of 1, -1, 1. Immediately I thought of your primordial time iteration argument. I will confess that from my early music training I never accepted the standard Pythagorean Theorem proof. haha.
You probably know that the major 2nd music interval as 9/8 cubed is the square root of 2 approximation and so considered a likely origin. 9/8 though was derived by Philolaus from the Perfect Fifth or 3/2 squared and then reduced back into the same octave scale by half so 9/4 to 9/8. What gets left out of that analysis is what Professor Richard McKirahan discovered when he translated Philolaus. The "lyre" musical instrument was flipped around so that 8 became the new root tonic "one" or 1 - creating 8/6 as 4/3 whereas 8/12 had been the 2/3 wavelength for the 3/2 frequency.
So in music theory this is called the "Phantom Tonic" because the Perfect Fourth is actually NEVER an overtone of the root tonic since the denominator as 3 is not an octave or same pitch root tonic. In other words the Perfect Fourth was created from 2/3 or the Perfect Fifth as the noncommutative phase reverse time - in order to create the "zero point" of the scale origin of the "one" root tonic as a contained two doubling. The traditional music tuning of China and India simply do not try to line up the octaves as the "scale" but rather stick to the empirical truth of music as Sir James Jeans explained in his book, Science and Music, an infinite spiral of fifths that actually is noncommutative and the secret to what Eddie Oshins discovered as Neigong or internal alchemy meditation.
thanks,
drew
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