The "appears random" or "seemingly random" claim by Penrose is actually based on Penrose now relying on noncommutativity. I'm glad Professor Emeritus Stuart Hameroff emphasized this distinction. If you study Fields Medal Math Professor Alain Connes he explains that the noncommutative appears random since we can only observe it "after the fact" but in actuality the inner cross products of the noncommutative matrices are discrete natural numbers. Connes most easily models these inner cross products by using music theory as what he calls, "two, three, infinity." You might note that this is the same as the "three gunas" of ancient India from music theory with Rajas as the Perfect Fifth or 3/2. So there is a noncommutative music inversion since both 2/3 and 3/2 is the Perfect Fifth but in one case the geometry is C to F as an undertone and the other case is C to G as an overtone. This is emphasized in traditional Indian music tuning. For example if you have a drone with a perfect Fourth the higher interval is actually heard as the root tonic since it does not form a natural overtone to the lower note. This is glossed over in Western music tuning in order to create the symmetric commutative geometry math of irrational numbers. Equal-tempered tuning is the secret origin of irrational numbers as promoted by Plato but he got it from Archtyas and Philolaus. So the Dao is also the same as the "three gunas" with the Yang as the Perfect Fifth. The Single Perfect Yang then relies on the doubling of the 2/3 as the quantum undertone to the Yin as 4/3 or Perfect Fouth (the tamas in Indian Yoga). I have more details in my free research - see my first upload for details. thanks
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