Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram Sequence
by Richard S Cook
University of California, Berkeley: STEDT Monograph Series, Vol. 5, 2006
paperback, 660 pages
Order through Lulu
It seems fitting that a linguist, someone attentive to how patterns combine to produce meaning, would tackle the great puzzle of the Yijing’s hexagram order. The hexagram order, often referred to as the “King Wen order” is the traditional arrangement found in almost all Yijing books; other orders include the Mawangdui order (see I Ching translated by Edward Shaughnessy) and the Zagua order (the Yijing’s Tenth Wing).
Dr. Richard Cook’s Classical Chinese Combinatorics makes use of mathematical theories of Fibonacci, Pythagoros, the Golden Mean, among others. He proposes organizing hexagram by “classes” such as gender (female, male, neuter) based on quantity of yin and yang lines in a hexagram. He uses these theories to try to uncover deeper layers of organization to the traditional hexagram sequence. The merits of Cook’s theories await analysis by those with deeper mathematical skills; in lieu, we offer the publisher’s description:
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.
Cook is a linguist associated with the large, ongoing project The Sino-Tibetan Etymological Dictionary and Thesaurus (STEDT) at the University of California, Berkeley. This project began in 1987 with the goal of creating “an etymological dictionary of Proto-Sino-Tibetan (PST), the ancestor language of the large Sino-Tibetan language family. This family includes Chinese, Tibetan, Burmese, and over 200 other languages spoken in South and Southeast Asia.” Cook’s prior work has been in developing Chinese language software, including ancient scripts.
Preview pages, including an abstract, can be viewed at this link. The price of the book, $64 (the symbolism is not lost on us), puts it beyond all but the most serious Yijing students, however copies can be found also in various libraries.
For a deeper analysis of Cook’s theories, we refer the reader to a recent review written by József Drasny for Yijing Dao, which can be read here. Drasny, a retired engineer in Hungary, has created his own interesting theories, including a three-dimensional “Yi-globe.”
Classical Combinatrics is a challenging read, but contains a number of interesting ideas.