Math Prof Lou Kauffman's noncommutative Pythagorean Theorem proof is published as quantum negentropy

Math Professor Louis Kauffman sent me a screen shot of this Pythagorean noncommutative proof when I contacted him, January 5th, at 10:03 pm and he replied at 10:18 pm (also CCing our conversation to a music-math scientist). Kauffman's noncommutative Pythagorean proof is now published!
The next morning Professor Kauffman sent me this message:
The paper I sent is new, but it contains insights already published. Here is a longer version.
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).
Well looks like I have some studying to do. haha. I just sent math professor Louis Kauffman another email. I first contacted him in regards to Eddie Oshins who collaborated with Kauffman. Oshins realized the truth of reality is noncommutativity as the secret of Neigong alchemy for internal martial arts training - while Oshins worked at Stanford Linear Accelerator Center.
So my goal is to continue the work of Oshins - and Kauffman has continued this noncommutative math analysis.
Thanks to Professor Kauffman for sending me that noncommutative Pythagorean math proof! The one I had been thinking of is this:
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
Kauffman responded in part re the standard Pythagorean Theorem:
" But just before that, we have entered an infinite loop of deduction. Thus the assumption of Sqrt(2) irrational leads to an oscillation back and forth between P and Q and in that sense is a relative of i = -1/i.
Best,
Lou K."
Thanks! I had not seen that paper yet - it must be from that book?
Of course my own take is from noncommutative music theory and Alain Connes and Eddie Oshins as meditation.
I'll study this more - I'm submitting a paper to the Journal of Scientific Exploration - on noncommutative music model of the paranormal.
thanks,
drew
"Looking at the oscillation between +1 and −1, we see that there are naturally
two phase-shifted viewpoints. We denote these two views of the oscillation by
[+1, −1] and[−1, +1]. These viewpoints correspond to whether one regards
the oscillation at time zero as starting with +1 or with −1. See Figure 29. We
shall let the word iterant stand for an undisclosed alternation or ambiguity
between +1 and −1. There are two iterant views: [+1, −1] and [−1, +1] for
the basic process we are examining. Given an iterant [a, b], we can think of
[b, a] as the same process with a shift of one time step. The two iterant views,
[+1, −1] and [−1, +1], will become the square roots of negative unity, i and
−i."

[voidisyinyangvoidisyinyang]

For Aristotle, two things cannot be in the same place at the same time and still be two. Place is what makes the difference, what helps us to distinguish this here from that there. In Plato’s version, “so long as the two things are different, neither can ever come to be in the other in such a way that the two should become at once one and the same thing, and two.” For Plato, that in which things come to be (i.e., space-chora, the matrix of becoming) serves to keep the sensible and intelligible realms separate — sensible beings are spatially instantiated copies of the Forms.

Notice that they are dealing with different ideas of the ontological. Aristotle is concerned with sensible beings and materiality, while Plato’s preoccupations tend towards the otherworldly Forms. But whatever their disagreements, they come together in their thinking difference in terms of this twoness. The presocratic philosophers already organized natural phenomenal according to elemental opposites (e.g., fire and water), but this binary opposition is codified in, and as, ontological difference, which is the difference between two."
Aristotle says this can not be true since the number 2 is not unique to any particular form and so Form Numbers can not exist. Form Numbers contradicts number as a comparable unit non-differentiated abstraction.

As Aristotle points out you can have two units come into existence at the same time and therefore are not "non-comparable units." Yes this is the secret of noncommutative phase!

Also Aristotle states the concept of Form Numbers implies "equalization of unequals" which conflicts with "non-comparability" of units.

[voidisyinyangvoidisyinyang]

. Once this is available, the relationship between Fermion algebra and Clifford
algebra (as we have outlined it above) comes forward and the paradox to be resolved is
i = -1/i,
the analogue in ordinary arithmetic of the truth value paradox in logic.
In Section 4, we take a wider view and outline the historical emergence of algebra, pointing out that
temporal and non-commutative interpretations came late in the sequence of events, and that the reader
will be able to see that our temporal interpretations of Fermion and Clifford algebras are a jump from
the historical progression and yet related to it in important ways. It is also important to realize that the
square root of minus one first appeared as a commutative entity, but in our temporal jump it first appears
in a Clifford algebraic and non-commutative context."

[EnvironmentalCoffeehouse]

How can math be a perspective when it is at the root of so much?