I finally was able to read Dr. Peter Kingsley's book in full - 2010 - "A Story Waiting to Pierce You"
There's nothing in the book that is inaccurate as far as I can tell - only his promotion of Archytas as a real Pythagorean is I think the big flaw of the book.
Kingsley hasn't done any music theory analysis that I can tell - of Archytas and Pythagorean philosophy yet we know that music was key to understanding the truth of Pythaogrean teaching.
So Kingsley critiques Carl Huffman's understanding of Philolaus and Archytas but two wrongs don't make a right! It appears that just because Huffman was wrong doesn't mean that Kingsley figured out the secret of the Pythagorean music theory.
This secret requires analyzing the music and mathematics - and so I can understand why that is not part of Kingsley's academic focus.
As I noted three years ago - the later Andrew Barker book also did not figure out Philolaus's math.
So really it was Professor Richard McKirahan who explains the math of Philolaus. But McKirahan supports the math without realizing its error.
It's ONLY Alain Connes who realizes the secret truth of the Pythagorean math as noncommutative phase - what I had previously been calling "complementary opposites" for some fifteen years.
http://elixirfield.blogspot.com/2018/04/is-there-right-and-wrong-in-music.html
So here I quote Huffman on his wrong math about Philolaus - actually it is Jordan Bell quoting Huffman. But the Jordan Bell link is now encrypted and inaccessible.
It's just that Kingsley's big point in his 2010 book is that the origin of Pythagorean philosophy is really from Central Asia - and previously he had made the connection to Daoism as well. So if he properly understood the music theory of Pythagorean (Orthodox - not Archytas) - philosophy then he would realize it is the same as Daoism.
I get it - someone's academic specialty is philosophy and translating ancient Greek, etc. and so they don't want to get bogged down in mathematics and music theory. People in academia are required to be specialized - it's unfortunate then that the bigger picture is lost.
http://www.bibliotheca-classica.org/sites/default/files/zhmud_3.pdf
So I had previously critiqued Zhmud's take on the whole issue as well. Turns out he may have the closest angle on it all.
https://ihst.academia.edu/LeonidZhmud
As much as I enjoyed "A Story Waiting to Pierce You" - it seemed to have missed the inner core secret teachings of the Orthodox Pythagoreans.
So that is Carl Huffman
Verdenius, W.J. (1949). Parmenides' Conception of Light. Mnemosyne, 2(1), 116–131.
doi:10.1163/156852549x00131
Amazingly this is better than Peter Kingsley! haha
Wild - a 1942 Ph.D. thesis! Originally in Dutch.
W. J. Verdenius (1947). Notes on the Presocratics. Mnemosyne (Third Series), 13(4), 271–289.
doi:10.2307/4427107
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