Calling all mathematically-minded Yeeks (that’s Yi Geeks) – there is a new monograph available from Berkeley:
STEDT Monograph 5: Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram Sequence
Richard S. Cook
The first and most enigmatic of the Chinese classics is the Book of Changes, and the reasoning behind its binary hexagram sequence remained an unsolved mystery for some 3,000 years (according to the tradition ascribing it to King Wen of Zhou, d. -11th c.). This Monograph resolves the classical enigma: Richard Cook provides a comprehensive analysis of the hexagram sequence, showing that its classification of binary sequences demonstrates knowledge of the convergence of certain linear recurrence sequences (LRS; Pingala -5th c.?, Fibonacci 1202) to division in extreme and mean ratio (DEMR, the “Golden Section†irrational; Pythagoras -6th c.?, Euclid -4th c.). It is shown that the complex hexagram sequence encapsulates a careful and ingenious demonstration of the LRS/DEMR relation, that this knowledge results from general combinatorial analysis, and is reflected in elements emphasized in ancient Chinese and Western mathematical traditions. This copiously illustrated 656-page volume presents a detailed introduction of the classical problem, an overview and in-depth derivation of the solution, an extensive terminological glossary, and computer source code formalizing all aspects of the derivations. The conclusion of this work situates the major findings in larger historical context.
ISBN 0-944613-44-6
656 pages
soft cover: $100.00 + shipping and handling
hard cover: (special order)
If this sounds like the kind of thing you could relate to, the monograph is available from here.
Wow! So Richard Cook finally wrote a book about it. Great! I remember Richard from the old Hexagram-8 forum. The only other people I can think of that remembers him is Chris Lofting and perhaps Midaughter and Chris Gait. He’s a really good guy and with strong opinions. Very knowledgeable. Actually, I think he was a member of Clarity way back at the beginning (I just Google him and a 2001 Clarity thread came up…)
I remember to be amazed by Richard when he said that his doctoral thesis was based on the etymology of a single Chinese character (I can’t remember now which one was it).
The price of the monograph is steep but I’ll consider it.
L
The Clarity thread is here:
http://www.onlineclarity.co.uk/friends/archive/index.php/t-2693.html
Thanks!
Hm – there is also
http://linguistics.berkeley.edu/~rscook/html/writing.html
which says ‘online version coming soon’. Sounds promising…
Thanks for the link! I used to have and lost it. Is in my Del.icio.us now.
L
Googling, I found this thread, and thought you all might want to know that Dr. Cook’s monograph _Classical Chinese Combinatorics_ is now available online. Their new webstore looks like it’s still in development … but there are sample pages from the book there now, enough to give you an idea of just how important this book is for Yi Jing studies. The Series Editor’s preface (by Prof. James Matisoff, leading American Sino-Tibetanist) is there, along with the table of contents, sample figures, complete author’s Preface, and Acknowledgments. Cook spent 23 years working on this book! If you study The Book of Changes, this is truly essential reading. Get your local library to buy a copy, if the academic book price seems too high: you’ll want to buy your own later! Cook is the leading American Sinologist, and lectured on this subject to Chinese Yi Jing experts in Taiwan last summer, at Academia Sinica and Taiwan National University. This is serious stuff, far beyond what English readers usually get. Somone above mentions one of Cook’s earlier books: actually, that amazing book was not his PhD thesis, but something he wrote before doing his PhD. You can see that info here.
Oh crumbs. Thank you very much for the link. It looks seriously fascinating – but it also looks as though it’d take more than a dusty 19-year-old ‘O’ level maths to make head or tail of the whole thing, doesn’t it?
Hilary, The basic idea of the book is really quite simple, and Cook really seems to aim at making this accessible to everyone. There is an extensive Glossary in the book, that explains everything. For sure, this book is not a light read: it is the kind of thing people will read and re-read and re-re-read for years to come! It’s no mistake that the Hexagram Sequence went unexplained for 3,000 years! But this book seems so important for the history of Eastern and Western mathematics, it ought to have a big impact beyond Yi Jing studies and Chinese history. What can I say? I’ve read it, and it’s fascinating! I think he should put more preview pages online, since the really great parts are not there yet! The color front cover of the book is there now, but the color back cover is just extraordinary, and not online yet, as far as I can tell! That color figure alone is well worth the price. I hope he makes that available as a large poster, and I’ve emailed him to say so! it would look great on my wall.
Here is a for-free treatment of this very issue
by a Dutch writer:
http://www.fourpillars.net/pdf/kingwen.pdf
Pretty cool, isn’t it ?
Very, very cool indeed. I’ve written about it before.
Note also a “magic squares” graphic derivation:
http://www.magichypercubes.com/Encyclopedia/i/IChingPaper.pdf
and
http://www.magichypercubes.com/Encyclopedia/i/SquareBase8.pdf
-KenD
Thanks for the links!
Connections between King-Wen Sequence, 64 DNA Codons (and 20 Aminoacids), Benjamin Franklin’s Magic Square of 8 and Tzolkin’s Mayan Calendar are explained in Jose Arguelle’s book: “Earth Ascendig: an Illustrated Treatise on the Law Governing Whole Systems”.
Note:
– Benjamin Franklin’s Magic Square of 8 rows and columns add up to 260 (Tzolkin’s days);
– Benjamin Franklin’s Magic Square of 8 numerical pattern leads to a geometrical shape slightly different from that in base eight (similar to DNA double helix);
-The link between King-Wen sequence and Benjamin Franklin’s Magic Square of 8 numerical pattern is semantic and not mathematical.
Best regards.
Thank you for the reference 🙂