Secrets of Philolaus using the Double Octave: Leon Crickmore cracks the noncommutative phase code of the ancients

So then this logic (pdf) ASSUMES that the octave is already "squared" or that time is already inherently a symmetric geometry (pdf) that is contained as infinity!

 LEON CRICKMORE was born in 1932 and educated at King's College, Cambridge, and the University of Birmingham. After working in further education, he became Dean of the Faculty of Arts at the North East London Polytechnic, and later HM Staff Inspector of Music. In the latter role, he was involved in the establishment of music as a subject in the National Curriculum, and of degree courses in the Conservatoires. In 1997 he was awarded an honorary fellowship of the Royal Scottish Academy of Music and Drama. He is married, and has a son and two daughters. https://independent.academia.edu/leoncrickmore

I wonder what John Curtis Franklin thinks of this? He told me he couldn't find any corroboration of Ernest McClain's claims. This paper seems to corroborate it.

A possible Mesopotamian origin for Plato's World Soul

Leon Crickmore

Hermathena

No. 186 (Summer 2009), pp. 5-23

Totally fascinating! but this notation covers up the Noncommutative phase logic:

Notice that 9^-3/2 can be interpreted as (1) The square root of the inverse of 9 cubed, or (2) the inverse of the cube of the square root of 9. Which you decide to use is up to you.

https://xaktly.com/RationalAndNegativeExponents.html AMAZING! Noncommutative? You decide!

There is a larger family of generalized (also called power or Hölder) means to which the above belong. A Hölder mean with power p of a set of numbers is the p-th root of the arithmetic mean of the p-th power of the numbers. If p=1, this gives the arithmetic mean. If p=-1, this gives the harmonic mean. The limit as p goes to 0 yields the geometric mean. The limit as p approaches infinity produces the maximum. The limit as p approaches negative infinity produces the minimum.

http://www.cs.uni.edu/~campbell/stat/pyth.html

So the problem with this claim is that it ignores the noncommutative phase logic.