Review: Cook’s Classical Chinese Combinatrics

Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram Sequence

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
ISBN: 9780944613443
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.


Review: Cheng Yi’s Yi River Commentary of the Book of Changes

The Yi River Commentary on the Book of Changes
by Cheng Yi, edited and translated by L. Michael Harrington
Introduction by L. Michael Harrington and Robin R. Wang
Yale University Press, 2019
ISBN: 9780300218077
Hardcover, 576 pages
$85 USD

Cheng Yi (1033–1107) lived during the Song dynasty, and was one of the era’s great thinkers. His Yijing commentary greatly influenced subsequent generations. Understanding the Yijing was important, but difficult, it was by then already a 2000-year-old book. Translator L. Michael Harrington, a professor of philosophy, gives a succinct overview of Cheng Yi’s thoughts and his influence on subsequent generations, including our own. He notes an important feature of Cheng’s commentary, that it offers full discussion of the hexagram components, rather than the snippets of explanation and terse definitions common to other commentaries. In addition, Cheng Yi creates a “coherent conceptual structure: the principle that governs the interaction between different capacities and functions in any state of affairs.”

The Yi River Commentary is an excellent companion to I Ching editions of Richard Wilhelm (translated by Cary Baynes), and Wang Bi (translated by Richard John Lynn). These are all dependable translations that introduce readers to particular strains of Yijing interpretations. In Cheng’s presentation, we can, in particular, see the roots of Richard Wilhelm’s work eight centuries later, both using a “teaching voice” that seeks to engage the student in depth.

Translating the Yijing is a difficult task, and Harrington clearly describes methods used in his effort to see the Yijing through Cheng’s eyes. He explains translation choices, as well. One interesting choice, for example, is the name “Ebb” for Hexagram 59 渙, which is “Dispersion/Dissolution” in the classic Wilhelm/Baynes I Ching. Harrington includes an introduction (written with colleague Robin Wang), notes on Cheng’s quotations of other material, extensive glossary, and a thorough index.

Avid Yijing readers will undoubtedly want to compare this translation of Cheng Yi’s work to others. Harrington’s is a model of transparency, detailing sources, methodology, and what material is included. Another English translation of Cheng Yi, by Thomas Cleary, is titled I Ching: The Tao of Organization. As with his other Yijing translations, The Taoist I Ching, The Buddhist I Ching, and I Ching Mandalas  (all from Shambhala Books) Cleary has succeeded in his effort to reach an educated popular audience. However, in each translation, he offers little clarity about his source material or methods, and, in this particular case, interpolates modern ideas (e.g., sociology). In addition, Cleary severely edited the original material, leaving out what Harrington estimates to be more than half of Cheng’s comments, in particular, on the Ten Wings as related to each hexagram. An interested reader would have to do their own comparative reading of the original to figure out what Cleary included or omitted, and what of Cheng’s text is actually quotes of other material. Harrington, in contrast, includes thorough information, greatly enriching the reading experience.

The Yi River Commentary is a well-made book physically, with a sturdy hardcover binding, though it weighs in at over two pounds. Unfortunately, the price for this book is set for libraries and specialists, not for the average Yijing reader, who would undoubtedly find this book of interest. The book is missing two key items for general readers: a hexagram finding chart and instructions for how to use the Yijing. Fortunately, these are easily found elsewhere (see our Basics page for such).

The Yi River Commentary is highly recommended for Yijing readers who enjoy pondering the deeper meaning of this ancient book and what it meant to the philosophers of imperial China, and for those readers who may be interested in the sources of modern interpretations.


Review: Book of Changes: The Original Core of the I Ching by Lars Bo Christensen

Book of Changes: The Original Core of the I Ching
by Lars Bo Christensen
CreateSpace 2015
paperback, 392 pages
ISBN-13: 978-1508848400
audio edition available
Excerpt available as
I Ching: The Core Kindle Edition

The Book of Changes by Lars Bo Christensen is a compendium of material suitable for close study of the Zhouyi. The book has discussion of the historical backdrop of the Zhouyi, including selections from the Zuozhuan, one of the earliest texts that mentions the Zhouyi. Hexagrams are presented in Chinese with English translation and concordance, including discussion of the meanings of specific characters that allows the reader to follow Christensen’s thought process. Frequently occurring characters are  provided in a separate glossary.

The Zhouyi translation is repeated at the end of the book, for easy access for divination purposes, along with the author’s terse summary of hexagrams and line meanings. Instructions are given for yarrow stalks and coins. (It should be noted that, taking advantage of the flexibility of self-publishing, the author has since issued I Ching: The Core Kindle Edition, described as a “simpler and more handy alternative” aimed at general readers who may not be as interested in his in-depth analysis of the Chinese text.)

This translation is helpful for anyone exploring details of the core Zhouyi text, and can be used in conjunction with Richard Rutt’s Zhouyi, Richard Kunst’s thesis notes (available online), Stephen Field’s Duke of Zhou Changes, Bradford Hatcher’s online I Ching works, and Edward Shaughnessy’s many books on the Yi. As a concordance, it draws from much prior scholarship and is much more topic- and era-specific than earlier Riitsima/Karcher concordances.

The book has a few problems in editing and formatting. One is that in the solo translation in the back, the paired hexagrams are not on facing pages. This is unfortunate, as Christensen has some important discussion of the pairings in an earlier chapter, and it would have been helpful to be able to compare the hexagram pairs without having to turn pages. Another puzzling choice: the Zuozhuan section is supplied in Chinese, with Christensen’s English summary and comments, but without full translation.

Overall, the Book of Changes: The Original Core of the I Ching is a good choice for the serious student of the Zhouyi; the tools it provides will help readers take an even closer look at the text, even if they do not have specialized language training.