a name that can be named is not the constant name

It is interesting to see how hypertext has gone from being a grand possibility to a never-finished chore. --Ted Nelson

[the tao/dao that can be told . . .] [tai chi] [book of change] [book of sand] [end of the internet]

Wednesday, March 03, 2010


Homework: Computer Emulations of the Yarrow Stalk Method

Whatever else the I Ching/Yijing (the Book of Change) might be, it is one of the oldest surviving examples of a hypertext document. The central core of this ancient Chinese text is a series of sixty-four six line images, referred to as hexagrams. Each of the six lines can be broken/yin or unbroken/yang. Each line can be young/stable/unchanging or old/moving/changing.

Each hexagram has a text associated with it. Traditionally these texts are ascribed to King Wen (~1165-1115 B.C.E.). King Wen is also traditionally credited with arranging the sequence of the hexagrams as they appear in the text. Each of the lines also has an associated text. According to tradition, these texts were written by one of King Wen's sons, the Duke of Zhou/Chou. This earliest strata of the text is known as Zhouyi, The Changes of Zhou/Chou. (The historical/critical approach to the study of the Book of Change has suggested other possibilities for the origin of the text.) The oldest layer of commentary, the Ten Wings, together with the Zhouuyi comprise the basic text of the Book of Change. Commentaries and interpretations have proliferated in great number ever since.

A particular hexagram is selected by a process of manipulating a bundle of fifty stalks of yarrow (or milfoil), or by tossing three coins. (There are many other methods, but these two are the most commonly employed.) The text relating to the resulting hexagram is read. Usually a passage from Xiang Zhuan , the third and forth wings, which explains the hexagram in terms of its component trigrams, is also read. If the hexagram includes changing/moving lines, the text associated with these lines is also consulted. As lines of the prevailing hexagram change, a new hexagram (depicting the emerging situation) is formed. The text of the second hexagram is considered as well.

The Book of Change is usually approached in one of two ways. Scholars of the Chinese language study it as an ancient text and either try to recover the “original meaning” of the text or investigate what the text meant to readers in various historical periods. Other folks use it as a tool for contemplating what might be a favorable course of action in a particular situation. There have always been people who have considered the Book of Change as a predictive prognosticator, a fortune teller, a magic eight ball with 4096 possible responses. However, most folks who find the Book of Change a helpful aid to decision making understand it not as describing the future, but as a tool for exploring the texture and structure of the present moment . The moment is understood as experiential, lived time, as distinguished from the instant of abstract, calculated punch clock time of physics and train schedules. The Book of Change is momentous, rather than instantaneous. Sometimes the calming ritual of manipulating the yarrow stalks can help clarify the mind even before the text is consulted.

Before the establishment of the Zhou/Chou Dyansty, the rulers of the Shang Dynasty (c. 16th-11th century BCE) consulted bone oracles . Animal bones or tortoise shells were heated until they cracked and the cracks were interpreted. The interpretation (and sometimes subsequent events) were inscribed on the bone or shell in pictographs known as Oracle Script . This is the earliest known form of writing in the Chinese language.

Although the Zhou/Chou yarrow oracle displaced the Shang bone/shell oracle, there is evidence of the influence of the earlier method in the text of the Book of Change. One example is found at hexagram 41, line 5 . One legend relates that a numerical chart related to the eight trigrams was revealed to Emperor Yu on the back of a tortoise which crawled out of the River Lou. (Swetz 9-12). The Shang tradition of oracular pronouncements may have influenced the text of the Book of Change.

Before the I Ching/Yijing appeared in a form we would recognize as a book, the text was inscribed on strips of bamboo which were strung together with a piece of leather. Legend asserts that Confucius studied the Book of Change so intently that he wore out its leather bindings three times (Cheng Man-Ch'ing 144). Tradition has ascribed Confucius as the author of the Ten Wings, the earliest commentaries. Although there is no real evidence for this attribution, The Book of Change is one of the Five Classics of the Confucian canon (Nylan 202-252).

The first translations of the Book of Change into a Western language were Latin versions make by Jesuit missionaries to China (Rutt 60-68). Western fascination with the digital structure of Book of Change began when a Jesuit missionary, Joachim Bouvet, provided Gottfried Leibniz with a diagram of the hexagrams. Leibniz saw a correspondence between these hexagrams and the binary numeration system he was developing.

According to Tom Van Vleck: “The first computer implementation of this ancient text that I am aware of was done in the early 60s on CTSS by C. Tillman. It is documented in the Second Edition CTSS Manual, section AJ.11.03, dated 9/24/65. The program was called ORACLE” which ran on an IBM 7094 at MIT. Some distributions of Unix included an I Ching/ Yi jing program in the games tree.

Since these early efforts, numerous computerized versions of the I Ching/ Yi jing have been implemented. This discussion will examine three web sites which emulate the yarrow stalk method of casting a hexagram. Instructions for the yarrow stalk method can be found on pages 721-723 of the Wilhelm/Baynes translation. On the web, the instructions that Gia-fu Feng (translator of one of the most popular English versions of the Tao Te Ching ) imparted to his wife, Jane English, are available at her Earth Heart website.

Emulating a coin toss, randomizing a heads or tails outcome, is a fairly elementary programming exercise. By repeating the process with three coins six times it is possible to indicate a hexagram. Many I Ching/Yi jing web site use this approach to provide an inquiry with a single hexagram and its associated text. Including moving/changing lines which produce a second hexagram is somewhat more complicated.

A complication arises when it is understood that the statistical probabilities of the yarrow stalk method are not the same as those of the three coin method:

old yang Yarrow: 3/16 Coins: 1/8 (stable)
young yang Yarrow: 7/16 Coins:3/8 (moving)
young yin Yarrow: 5/16 Coins:3/8 (stable)
old yin Yarrow: 1/16 Coins: 1/8 (moving)

(Huang , 64, 68)

YarrowStalk.ORG is a website developed by Ralph Abraham who is a Professor Emeritus of Mathematics at the University of California Santa Cruz. His many interests include investigations into the relationship between Renaissance magic and the emergence of the scientific method (http://www.biroco.com/kaos/lodge.pdf pp. 34-49). This semester he is teaching a class in the Digital Arts and New Media MFA Program, DANM 221: Mathematics the Arts.

The simple interface of YarrowStalk.ORG provides a significant amount of information about the Book of Change, including Prof. Abraham’s understanding of the text in terms of chaos theory. The instructions for “Simulation of the YSO” (Yarrow Stalk Oracle) indicates that one should “Click on the postage stamp once, you get one hyperline. Write it down for the bottom line, then repeat five times.” The “postage stamp” is a rudimentary graphic image portraying 49 yarrow stalks being divided into two groups (fig. 1). The stalks in the picture do not move, but returning to the graphic from the previous page shows them in a somewhat different configuration.

Clicking on the image reveals, not a hexagram line, but what appears to be a cgi script. Considering the instructions provided, this appears to be an unintended feature. Since I have no experience with cgi, I have no understanding of what it required to have a cgi script run rather than being displayed. Although I have no understanding of cgi vocabulary, anyone with some knowledge of programming who had any interest in how a math professor approached the problem of emulating the yarrow stalk probabilities in 1999 might be able to learn something here. Prof. Abraham indicates that YarrowStalk.ORG is not his top priority, but he continues to work on it as time allows.

Russell Cottrell is a psychiatrist at the Chico, California V.A. Outpatient Clinic. His website includes sections on his military medical career, photography, genealogy, instruction in ancient Greek, a fractal mandala generator, a Celtic calendar, and also Virtual Yarrow Stalks. Dr. Cottrell describes his approach:

"Most automated I Ching programs and scripts operate via computer-generated random numbers. This is not unlike the flip of a coin, which is how many people consult the I Ching. But the yarrow stalk method, in addition to an element of randomness, involves a volitional act on the part of the user, in the division of the stalks into two groups. The Virtual Yarrow Stalks I Ching seeks to duplicate this by having the user click on a group of virtual yarrow stalks of varying widths. Done without conscious effort, this is much closer to using real yarrow stalks than is instructing the computer to generate numbers."

The inquirer is presented with a graphic image representing fifty yarrow stalks, with one removed before the consultation begins. The mouse is moved over the bundle to divide it into two heaps. This action is repeated three times to produce a line. When the hexagram is completed, the changing lines reveal a second hexagram and the associated texts are presented. Only the Judgment and the texts of the moving lines are provided, the basic material from the Zhouyi without the Image from the Xiang Zhuan. Three different translations are offered. This is not the place to explore the texts in great detail, but at this hour I am indeed Exhausted and whenever I try to write there is always Difficulty at the Beginning.

An interesting feature of Virtual Yarrow Stalks is the section which presents thirty-three translations of the text of the Judgment and the first line of hexagrams 3 and 36. This will definitely be a helpful resource if I ever find time to compile a presentation of the Book of Change that would draw upon a different translation for each of the sixty-four hexagrams. This project is not my top priority at the present moment.

S. J. Marshall, the author of The Mandate of Heaven: Hidden History in the I Ching, maintains an elegant web site called Yijing Dao, which includes a review of LiSe Heyboer's web site, Yi Jing, book of sun and moon :

"LiSe Heyboer is one of the few whose interest in the Yijing has inspired her to research the original etymology of the Chinese characters . . . This is an excellent site, and encouraging to any who delve into the Chinese characters themselves. There is a complete translation of the Zhouyi, as well as an ever-expanding selection of essays. Her commentary on her own translation shows great insight, clearly derived from divination experience. Some of the translations are speculative, but based on her study of early graphs."

LiSe credits the yarrow stalk emulation on her Dutch website to Emanuele, who is someone with an Italian yahoo email address. At the beginning of the consultation the inquirer is presented with a beautiful illustration of yarrow in bloom. The yarrow stalks appear as a bundle and are counted off by fours at a speed controlled by the user after they are divided into two groups by clinking on the bundle.

Dr. Cottrell appears to give the user more control over how the bundle is divided, but the process of moving from the division to determining the line is much more detailed on this site. Both as instruction for using physical yarrow stalks and as a computer emulation of the process, this site is the best that I have yet found. The feature which allows the user to control the speed of the process can accommodate someone who is in a hurry, as well as someone who has time to devote to a more contemplative experience.

The text presented is LiSe's translation, which features her interpretation of Oracle Script (fig. 10). A link in the text takes the reader to a glossary of key terms illustrated with Oracle Script . The Wilhelm/Baynes translation is also made available (fig. 12) This assignment is certainly a Turning Point in the unfolding of this course. Hopefully when I Return to class this paper will be completed. What should I write? Fu advises me to “Follow your own road, your own Tao.”

Although the traditional text of the Book of Change can be appreciated as poetry (Huang 33-34), Yi Jing, book of sun and moon includes a section that is even more directly related to the concerns of our course:

“The Yi Lin, Forest of Changes, "written around 25 BCE by Jiao Shi (Jiao Yanshou) or Xu Jun. It has a verse, usually of four x four characters, for every possible change from one hexagram into another” [4096]; “the 'change' is from the hexagram of the particular day, to the hexagram you cast yourself.”

Here is the verse for hexagram 2 changing to hexagram 1:

Valley winds, life energy starts moving
All things come to life
Germinating in great numbers, growing up and nourished
Magnificent leaves in flourishing abundance

Very few of the verses have been translated. Anyone with skill in translation from Chinese to English is invited to participate in this project.

A web search for “i ching yarrow” indicates that there are thousands of pages that could be explored. Of the few I have spent time with, these three are the most interesting. They will keep me busy for quite awhile.

008:173 Topics in digital media: New Media Poetics

Discussion Moderator:
Good essay Steve,

Thanks for posting it here for us to benefit from. I especially got a jolt from the mathematics you included. However more discussion of the Boolean algebra and it's relation to the programming outcomes is needed, in my opinion. This exploration would also give one a way to compare programs as to their similarity to yarrow stalk results. Then of course there is the relationship between divination to probalistic predictions, if one could devise such a connection.

In a dynamically changing universe, how a simpler probability generator like the I Ching even works at all is a thesis in itself. I wish you luck with this and your second paper. I look forward to your efforts, and hope your last three classes are short and smooth.

An interesting aside: watching the opening of the short animation of "The Way," posted on both the wall and group links, I noticed the swirling diagonal yin/yang becomes like a protein blot before settling into the classic bagua. It could easily have added a second ring of trigrams and generated all sixty-four hexagrams and thereby connected the I Ching with the Yin/Yang in a natural progression. I like when disparate theories link up in interesting and intuitive ways. Good essays like yours make these connections apparent.

Peace of good essays
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I am simply overwhelmed by the time and effort that you must have put into this project Steve. Not only is your summary of the I Ching's history of use and multiple remediations comprehensive, it's also very accessible to a laymen such as myself. I especially liked your discussion of the physical act of "tossing" the yarrow stalks, and how this dualism between physicality and textuality influences one's reading. I guess the only thing I feel like I'm missing is an explanation of how the act of remediation has changed our (society's) reception of the I Ching over time? Maybe it hasn't! Regardless, after reading your paper I have a far deeper understanding of what Aarseth is talking about when he discusses the I Ching as a pre-historical version of a "cybertext". And for that I am very grateful.
May 14, 2010 Classmate

I really appreciate your work here with the I Ching. It has consistently intrigued me over the course of the last few days as I have slowly moved through it; gradually reading your paragraphs, following the links, and drifting off into other parts of the web (as I often do). Having been completely unaware of the Book of Change previous to reading your papers, I feel as though they have served as an excellent introduction, as well as bringing about many jumping off point for further investigations. Several points seem to resonate strongly with my own interests in the web, hypertext, etc. and I will try to address them here, despite my own difficulties in unpacking and articulating many of these thoughts myself.

I'll start by admitting that I purchased the Yi Jing iphone app (Flat Earth Studios) to try my hand at casting hexagrams. The app seems to be fairly well designed and offers a few methods for casting (although there is, sadly, no yarrow stalk method). You can tap for an instant hexagram, shake the iphone to flip the coins, or manually manipulate individual coins to generate a particular line. It contains texts in separate tabs for present, changes, and future. While shaking an iphone is certainly not a contemplative process, I found myself increasingly interested in the texts that were produced; they certainly seemed aware of my present situation. While consulting the application about how to begin responding to your paper, it responded with hexagram #27: "Nourishing". Part of the image text reads "An enlightened person is cautious with their words, and regulates carefully what they take in." I don't know how enlightened I am, but here are a couple of the thoughts that I had.

The idea of hypertext emerging from strips of bamboo strung together with a piece of leather is fascinating. It is refreshing to consider these structures that are often viewed as immaterial or disembodied (cyberspace) as being enacted through physical materials. Discussing the I Ching as a physical hypertext reminds me of the web's physical infrastructure, or the notion that there is no such thing as software, only various states of hardware. The dividing of yarrow stocks to consult the I Ching may be the forgotten ancestor to pressing down keys to enter a Google search query. I relish the comparison.

I am also interested in the notion of "exploring the texture and structure of the present moment" both in terms of what emerges textually from the I Ching and the way I relate to and understand surfing the web. Pondering the relationship between these two instances of "searching" seems to give more weight and relevance to each. The I Ching could be a useful tool in mapping out a spiritual relationship with the web and emerging technology (something I have been interested in).

Your papers have brought up numerous things of great interest and relevance to me, I would love to know where this research leads you in the present as well as the future and anywhere else in-between.
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