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: Richard Smith on the I Ching

The I Ching: A Biography
Richard J. Smith
Princeton University Press, 2012
ISBN 978-0691145099
Hardcover, 304 pp.
Fathoming the Cosmos and Ordering the World
The Yijing (I Ching, or Classic of Changes) and Its Evolution in China
Richard J. Smith
University of Virginia Press, 2008, 2018 (paper)
Paper, 416 pp.
ISBN 9780813940465
Mapping China and Managing the World: Culture, Cartography and Cosmology in Late Imperial Times
Routledge, 2012
Paper, 288 pp.

Richard Smith, a professor of Chinese history from Rice University in Texas, has written several outstanding books about the Yijing that will be of interest to readers looking to learn about where the Yijiing came from, what it meant, and how it spread around the world.

The first, Fathoming the Cosmos and Ordering the World: The Yijing (I Ching, or Classic of Changes) and Its Evolution in China is an in-depth look at almost every aspect of the Yijing: how it was used and by whom, the schools of thought that used and extended its meaning,  how its use evolved, the key personalities who wrote about it, and how it came to have such a global impact. Fathoming the Cosmos is a key starting point for any English-language Yijing research. Even a cursory look through it will demonstrate that dozens more volumes could easily be written on Yijing topics. The book has recently been reissued in paperback. In a companion volume, The I Ching: A Biography, Smith revisits the material of Fathoming the Cosmos, reworking it to create a volume for a general audience. Both books have thorough notes, indexes, and bibliographies.


Smith is author of several other highly regarded books that look at aspects of imperial Chinese history, culture, ritual, and ordering of the world. Fortunetellers and Philosophers: Divination in Traditional Chinese Society (1991) was his first foray into the Yijing, and also looked at topics such as fengshui, mediums, and face-reading.

Smith’s recent book, Mapping China and Managing the World (2013) revises a number of his lectures and articles. Several of these, updated into full chapters, are directly about the Yijing. “The Languages of the Yijing and the Representation of Reality,” is a thorough overview of Yijing studies. “Divination in the Qing” shows how involved the Qing dynasty rulers were with Yijing study and divination (remembering that the Qing themselves were Manchurians, not Chinese), while “Jesuit Interpretations of the Yijing in Global Perspective” covers the intriguing and complex interactions between European Christians and the Chinese during that dynasty. Smith’s introduction to the book also provides a good summary of current questions and issues about Chinese studies in general, and explains how he came to be interested in the Yijing. Central to this was comprehending that the Yijing is deeply connected with all aspects of Chinese culture and society.

Richard Smith’s books are excellent resources for anyone wishing to trace the Yijing’s history, whether for a class paper or for personal enrichment.

Analog Morals, Modern Tech

Image result for smartphone“As arrogant occupants of 21st-century Earth, who can rightly boast of creating exciting innovations, like the computer, talking paint, and the margarita blender, it serves us to believe we’re also the more enlightened generation.

….Alas, ethically and morally speaking, we moderns are merely the new models, not the better ones….”

Read this interesting article by Jim Blasingame about our human condition here. He mentions the I Ching as an important “analog” ancient source of wisdom.

Portraits of Fortunetellers

fortunetellerHong Kong is home to many fortunetellers. This article presents “The Fortune Market” a collection of portraits by photographer Kris Vervaeke of fortunetellers next to a Daoist temple.

“The fortune tellers have different backgrounds,” Vervaeke explained. “For some the job is passed on from each generation to the next within a family. Others learn it from a Master or through other means. The future of the shops is uncertain, however, as finding someone interested to take over is getting more and more difficult.” He also added that the rise of online fortune telling puts the physical institutions’ futures in jeopardy.

Divination in China Thesis

cropped-yi-hex-29-30-laiA new PhD dissertation related to the I Ching is available, “Divination And Deviation: The Problem Of Prediction And Personal Freedom In Early China” by Yunwoo Song, from the University of Pennsylvania. This interesting dissertation explores ancient methods and meaning of divination in early China through early imperial times. The dissertation can be viewed at UPenn’s site.



Yijing Videos Available Online

Yijing maven Harmen Mesker has produced several Yijing videos that are now available on YouTube on his “YiTube” channel. These videos are introductions to the Yijing in general and specific topics such as the trigrams, embellished occasionally with Mesker’s sly wit. Mesker, who is based in the Netherlands, maintains an informative website, as well.

Book Review: Yijing, Shamanic Oracle

Yijing, Shamanic Oracle of China: A New Book of Change

Richard Bertschinger, translation and commentary
Singing Dragon 2012
Hardcover/ebook, 336 pp.
US $30 / £25.00
ISBN: 978-1-84819-083-2

Yijing, Shamanic Oracle of China is a nicely presented contemplative book. Richard Bertschinger, an acupuncturist and student of  Gia-fu Feng, has done an engaging job of presenting his thoughts about the Yijing. With occasional cross-cultural philosophical comparisons, Bertschinger presents a translation of the core Zhouyi and selected Wings, enhanced with his comments, and including a helpful glossary.

“The Yijing can reveal the seeds of the future, but above all it teaches reverence for those small inklings in the present which determine the science of change. It encourages us all to be alive to the world, and take a stand on destiny.”

Bertschinger’s translation emphasizes finding one’s path. “You can transform those observing below, by observing the causes of your own life. Observe yourself within and contemplate the evens of your own life. At no time neglect to seek the middle path and at all times act properly” (from Hexagram 20).

This is a very accessible Yijing book, drawn from the author’s reading of traditional Chinese texts, accessible to beginners, but meaty enough for experienced users.

I Ching-based Artwork on Display

The Book of Changes: Symbolic Landscapes of the I Ching
On view December 2nd- January 26th
Opening reception: Tuesday, December 5th from 4-6pm
64 works by Elizabeth Nelson inspired by the 64 hexagrams of the I Ching

Elizabeth Nelson is best known for her images of northeastern landscapes. Her work has been shown since the late 1980s and has been presented in juried shows for nearly as long. She is represented by galleries in New York and Vermont and has won commissions for public art. Neither a young nor obscure artist, one can believe her
when she says, “Every so often artists come to the end of what they’re exploring.” They have to ask, “Where do I go from here?” 2012 was one of those periods for Liz. She wanted to transform her work.

In January 2012, she started a series of “Symbolic Landscapes” inspired by the sixty four hexagrams of the I Ching. Incorporating chance even into the procedure, She threw coins to choose a hexagram each time a painting was started and would contemplate the result as she thought or dreamt an image. Her work has always referenced the landscape of northern New England and this new series continued that exploration, but with an interior dimension of symbols and geometric juxtapositions.

A friend showed her the book in the mid 1960s. “The language about the symbols connected so closely to unconscious thoughts I had been having.” She wears divination loosely; there are times she refers to the method frequently and times she puts it aside for years. Liz describes her use as “something I have used in different ways for different questions and in different intensities.”

The discipline of such a project is “very freeing.” Describing the freedom inside of discipline, Liz makes this analogy: “If you’ve cooked a souffle, one that’s followed the rules, and have had some success, then you start changing things.” She applies that thought to painting: “You have to keep pushing the edges of your knowledge and capabilities to grow as an artist. “Completing one idea,” she explains, gives her the “confidence to do a riff on it. It’s a physical skill, among other things. You have to have confidence in your skills; you keep practicing.”
For the first time all 64 of these new paintings will be on exhibit.
Free and open to the public. For more information, please call (802) 533-9075 or visit

Nederlands Dans Theater takes dance inspiration from ancient Chinese shamanic text, the Book of Changes

When Nederlands Dans Theater presents Safe As Houses during their Asian tour this autumn [2017], they will be following on a well-lit path of using the ancient Chinese shamanic text, the I Ching – (also known as the Yijing or in English the Book of Changes – to create an extraordinary modern dance piece.”

The director said, ‘We created a … theatrical space that also dealt with these ideas of the Book of Changes. The idea is that the stage is never still; it’s constantly altering its form. Therefore, the world around it must also go with it.’ ”
The company builds on previous works by such great choreographers as Merce Cunningham.

Read the full article in the South China Post