Thursday, September 11, 2008

King Wen sequence

The ''I Ching'' , or “Yì Jīng” ; also called “Classic of Changes” or “Book of Changes” is one of the oldest of the Chinese classic texts. The book is a symbol system used to identify order in chance events. The text describes an ancient system of cosmology and philosophy that is intrinsic to ancient Chinese cultural beliefs. The cosmology centres on the ideas of ''the dynamic balance of opposites'', ''the evolution of events as a process,'' and ''acceptance of the inevitability of change'' . In cultures and modern East Asia, the ''I Ching'' is sometimes regarded as a system of divination. The classic consists of a series of symbols, rules for manipulating these symbols, poems, and commentary.

Implications of the title

* 易 , while as a verb it implies “to change“ or 'to exchange/substitute one thing for another'.
* 經 here means “classic ”, derived from its original meaning of “regularity” or “persistency”, implying that the text describes the which will not change throughout the flow of time. This same character was later appropriated to translate the Sanskrit word 'sūtra' into Chinese in reference to Buddhist scripture. In this sense the two concepts, in as much as they mean 'treatise,' 'great teaching,' or 'canonical scripture,' are equivalent.

The ''I Ching'' is a "reflection of the universe in miniature." The word "I" has three meanings: ease and simplicity, change and transformation, and invariability. Thus the three principles underlying the ''I Ching'' are the following:
# ''Simplicity'' - the root of the substance. The fundamental law underlying everything in the universe is utterly plain and simple, no matter how abstruse or complex some things may appear to be.
# ''Variability'' - the use of the substance. Everything in the universe is continually changing. By comprehending this one may realize the importance of flexibility in life and may thus cultivate the proper attitude for dealing with a multiplicity of diverse situations.
# ''Persistency'' - the essence of the substance. While everything in the universe seems to be changing, among the changing tides there is a persistent principle, a central rule, which does not vary with space and time.
::— 易一名而含三義:易簡一也;變易二也;不易三也。 commented on by Zheng Xuan in his writings ''Critique of I Ching'' and ''Commentary on I Ching'' of Eastern Han Dynasty.


Traditional view

Traditionally it was believed that the principles of the ''I Ching'' originated with the mythical Fu Xi . In this respect he is seen as an early culture hero, one of the earliest legendary rulers of China , reputed to have had the 8 revealed to him supernaturally. By the time of the legendary 2194 BCE–2149 BCE, the trigrams had supposedly been developed into 64 hexagrams , which were recorded in the scripture Lian Shan . ''Lian Shan'', meaning “continuous mountains” in Chinese, begins with the hexagram , which depicts a ''mountain'' mounting on another and is believed to be the origin of the scripture's name.

After the traditionally recorded Xia Dynasty was overthrown by the Shang Dynasty, the hexagrams are said to have been re-deduced to form Gui Cang , and the hexagram became the first hexagram. ''Gui Cang'' may be literally translated into “return and be contained”, which refers to ''earth'' as the first hexagram itself indicates. At the time of Shang's last king, Zhou Wang, King Wen of Zhou is said to have deduced the hexagram and discovered that the hexagrams beginning with revealed the rise of . He then gave each hexagram a description regarding its own nature, thus Gua Ci .

When King Wu of Zhou, son of King Wen, toppled the Shang Dynasty, his brother Zhou Gong Dan is said to have created Yao Ci to clarify the significance of each horizontal line in each hexagram. It was not until then that the whole context of ''I Ching'' was understood. Its philosophy heavily influenced the literature and government administration of the Zhou Dynasty .

Later, during the time of Spring and Autumn , Confucius is traditionally said to have written the Shi Yi , a group of commentaries on the ''I Ching''. By the time of Han Wu Di of the Western Han Dynasty , ''Shi Yi'' was often called ''Yi Zhuan'' , and together with the ''I Ching'' they composed ''Zhou Yi'' . All later texts about ''Zhou Yi'' were explanations only, due to the classic's deep meaning.

Modernist view

In the past 50 years a “Modernist” history of the ''I Ching'' has been emerging, based on context criticism and research into Shang and Zhou dynasty oracle bones, as well as Zhou bronze inscriptions and other sources . These reconstructions are dealt with in a growing number of books, such as '''', by S. J. Marshall, and Richard Rutt's ''Zhouyi: The Book of Changes'', .

Scholarly works dealing with the new view of the Book of Changes include doctoral dissertations by Richard Kunst and Edward Shaughnessy and a 2008 study by Richard J. Smith. These and other scholars have been helped immensely by the discovery, in the 1970s, by Chinese archaeologists, of intact Han dynasty era tombs in Mawangdui near Changsha, Hunan province. One of the tombs contained more or less of the ''I Ching'', the ''Dao De Jing'' and other works, which are mostly similar yet in some ways diverge significantly from the “received”, or traditional, texts preserved historically.

The tomb texts include additional commentaries on the ''I Ching'', previously unknown, and apparently attributed to Confucius. All of the Mawangdui texts are many centuries older than the earliest known attestations of the texts in question. When talking about the evolution of the Book of Changes, therefore, the Modernists contend that it is important to distinguish between the traditional history assigned to texts such as the ''I Ching'' , assignations in commentaries which have themselves been canonized over the centuries along with their subjects, and the more recent scholarly history aided by modern linguistic textual criticism and archaeology.

Many hold that these perspectives are not necessarily mutually exclusive, but, for instance, many Modernist scholars doubt the actual existence of Fuxi, or think Confucius had nothing to do with the Book of Changes, and contend that the hexagrams came before the trigrams. Modern scholarship comparing poetic usage and formulaic phrasing in this book with that in ancient bronze inscriptions has shown that the text cannot be attributed to King Wen or Zhou Gong, and that it likely was not compiled until the late Western Zhou, perhaps ca. the late 9th century BCE.

Rather than being the work of one or several legendary or historical figures, the core divinatory text is now thought to be an accretion of Western Zhou divinatory concepts. As for the Shi Yi commentaries traditionally attributed to Confucius, scholars from the time of the 11th century A.D. scholar Ouyang Xiu onward have doubted this, based on textual analysis, and modern scholars date most of them to the late Warring States period , with some sections perhaps being as late as the Western Han period .


The text of the ''I Ching'' is a set of predictions represented by a set of 64 abstract line arrangements called '''' . Each hexagram is a figure composed of six stacked horizontal lines , where each line is either , or . With six such lines stacked from bottom to top there are 26 or 64 possible combinations, and thus 64 hexagrams represented.

The hexagram diagram is conceptually subdivided into two three-line arrangements called ''trigrams'' . There are 23, hence 8, possible trigrams. The traditional view was that the hexagrams were a later development and resulted from combining the two trigrams. However, in the earliest relevant archaeological evidence, groups of numerical symbols on many Western Zhou bronzes and a very few Shang oracle bones, such groups already usually appear in sets of six. A few have been found in sets of three numbers, but these are somewhat later. Note also that these numerical sets greatly predate the groups of broken and unbroken lines, leading modern scholars to doubt the mythical early attributions of the hexagram system.

Each hexagram represents a description of a state or process. When a hexagram is cast using one of the traditional processes of , each of the yin or yang lines will be indicated as either ''moving'' , or ''fixed'' . Moving lines will change to their opposites, that is “young” lines of the other type -- old yang becoming young yin, and old yin becoming young yang.

The oldest method for casting the hexagrams, using yarrow stalks, is a ''biased'' random number generator, so the possible answers are not equiprobable. While the probability of getting either yin or yang is equal, the probability of getting old yang is three times greater than old yin.

The yarrow stalk method was gradually replaced during the Han Dynasty by the three coins method. Using this method the imbalance in generating old yin and old yang was eliminated. There is no theoretical basis for indicating what should be the optimal probability basis of the old lines versus the young lines. Of course, the whole idea behind this system of divination is that the oracle will select the appropriate answer, regardless of the probabilities.

There have been several arrangements of the trigrams and hexagrams over the ages. The is a circular arrangement of the trigrams, traditionally printed on a mirror, or disk. According to legend, Fu Hsi found the bā gùa on the scales of a tortoise's back. They function rather like a magic square, with the four axes summing to the same value .

The King Wen sequence is the traditional sequence of the hexagrams used in most contemporary editions of the ''I Ching.'' The King Wen sequence has been shown to contain within it a demonstration of advanced mathematical knowledge.


The solid line represents ''yang'', the creative principle. The open line represents ''yin'', the receptive principle. These principles are also represented in a common circular symbol , known as taijitu , but more commonly known in the west as the ''yin-yang'' diagram, expressing the idea of complementarity of changes: when Yang is at top, Yin is increasing, and the reverse.

In the following lists, the trigrams and hexagrams are represented using a common textual convention, horizontally from left-to-right, using '|' for yang and '?' for yin, rather than the traditional bottom-to-top. In a more modern usage, the numbers 0 and 1 can also be used to represent yin and yang, being read left-to-right.

There are eight possible trigrams :

The first three lines of the hexagram, called the ''lower trigram'', are seen as the ''inner aspect'' of the change that is occurring. The ''upper trigram'' , is the ''outer aspect''. The change described is thus the dynamic of the inner aspect relating to the outer situation. Thus, hexagram 04 ?|???| Enveloping, is composed of the inner trigram Gorge, relating to the outer trigram Bound.

Hexagram Lookup Table

The hexagrams

The text of the ''I Ching'' describes each of the 64 hexagrams, and later scholars added commentaries and analyses of each one; these have been subsumed into the text comprising the ''I Ching''.

Each hexagram's common translation is accompanied by the corresponding R. Wilhelm translation, which is the source for the Unicode names.

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The hexagrams, though, are mere mnemonics for the philosophical concepts embodied in each one. The philosophy centres around the ideas of ''balance through opposites'' and ''acceptance of change''.


In Unicode, monograms cover code points U+268A to U+268B, digrams cover code points U+268C to U+268F, trigrams cover code points U+2630 to U+2637, hexagram symbols cover code points U+4DC0 to U+4DFF .

Tai Xuan Jing digrams cover code points U+1D301 to U+1D305, tetragrams cover code points U+1D306 to U+1D356. The monograms cover code points U+1D300 , U+268A , U+268B .


The hexagrams are built from gradations of binary expressions based on yin and yang. They consist of: old yang, old yin, young yang or young yin Yin and yang, while common expressions associated with many schools of classical Chinese culture, are especially associated with the Taoists.

Another view holds that the ''I Ching'' is primarily a ethical or philosophical document. This view is based upon the following:
* The Wings or Appendices are attributed to Confucius.
* The study of the ''I Ching'' was required as part of the Civil Service Exams in the period that these exams only studied Confucianist texts.
* It is one of the Five Confucian Classics.
* It does not appear in any surviving editions of the Daozang.
* The major commentaries were written by Confucianists, or Neo-Confucianists.
* Taoist scripture avoids, even mocks, all attempts at categorizing the world's myriad phenomena and forming a static philosophy.
* Taoists venerate the non-useful. The ''I Ching'' could be used for good or evil purposes.

Both views may be seen to show that the ''I Ching'' was at the heart of Chinese thought, serving as a common ground for the Confucian and Taoist schools. Partly forgotten due to the rise of Chinese Buddhism during the Tang dynasty, the ''I Ching'' returned to the attention of scholars during the Song dynasty. This was concomitant with the reassessment of Confucianism by Confucians in the light of Taoist and Buddhist metaphysics, and is known in the West as Neo-Confucianism. The book, unquestionably an ancient Chinese scripture, helped Song Confucian thinkers to synthesize Buddhist and Taoist cosmologies with Confucian and Mencian ethics. The end product was a new cosmogony that could be linked to the so-called “lost Tao” of Confucius and Mencius.

Binary sequence

In his article ''Explication de l'Arithmétique Binaire'' Gottfried Leibniz writes that he has found in the hexagrams a base for claiming the universality of the binary numeral system. He takes the layout of the combinatorial exercise found in the hexagrams to represent binary sequences, so that ?????? would correspond to the binary sequence 000000 and ?????| would be 000001, and so forth.

The binary arrangement of hexagrams is associated with the famous Chinese scholar and philosopher Shao Yung in the 11th century. He displayed it in two different formats, a circle, and a rectangular block. Thus, he clearly understood the sequence represented a logical progression of values. However, while it is true that these sequences do represent the values 0 through 63 in a binary display, there is no evidence that Shao understood that the numbers could be used in computations such as addition or subtraction.

It should be noted that Shao Yung had been attributed with the original Segregation Table of the symbols of the book of changes ''Fu-Hsi Liu-shih-ssu Kua Tzhu Hsu'' from Chu Hsi's Chou I Pen I Thu Shou .

The Symbolic and Numerical Language

The oracular interpretation of the symbolic language based on trigram symbols formed from yang and yin components is well known. However, the inherent numerical language of line change and non-change is relatively unknown.

When the translated text reads "Nine in the beginning means...." this is the equivalent of saying: "When the positive line in the first place is represented by the number 9, it has the following meaning.....". If, on the other hand, the line is represented by the number 7, it is disregarded in interpreting the oracle. The same principle holds for lines represented by the numbers 6 and 8 respectively.

Thus, line transformation or non-transformation can be represented numerically, as follows:

A POSITIVE transforming into a NEGATIVE = 9

A POSITIVE transforming into a POSITIVE = 7

A NEGATIVE transforming into a POSITIVE = 6

A NEGATIVE transforming into a NEGATIVE = 8

This changes the ancient symbolic linear language of the I Ching into a simple numerical language that enables the practitioner to create sixteen numerical codes, which consist of three numbers, from each circular arrangement of eight trigrams.

John C. Compton suggests that these numerical codes represent specific codons of the Genetic Code.


The ''I Ching'' has long been used as an oracle and many different ways coexist to “cast” a reading, i.e., a hexagram, with its dynamic relationship to others. In China the ''I Ching'' had two distinct functions. The first was as a compendium and classic of ancient cosmic principles. The second function was that of divination text. As a divination text the world of the ''I Ching'' was that of the marketplace fortune teller and roadside oracle. These individuals served the illiterate peasantry. The educated Confucian elite in China were of an entirely different disposition. The future results of our actions were a function of our personal virtues. The Confucian literati actually had little use for the ''I Ching'' as a work of divination. In the collected works of the countless educated literati of ancient China there are actually few references to the ''I Ching'' as a divination text. Any eyewitness account of traditional Chinese society, such as S. Wells Williams ''The Middle Kingdom'', and many others, can clarify this very basic distinction. Williams tells us of the ''I Ching'', "The hundred of fortune- tellers seen in the streets of Chinese towns, whose answers to their perplexed customers are more or less founded on these cabala, indicate their influence among the illiterate; while among scholars, who have long since conceded all divination to be vain..."


The Flag of South Korea contains the Taijitu symbol, or ''tàijítú,'' , representing the origin of all things in the universe. The ''taegeuk'' is surrounded by four of the eight trigrams, starting from top left and going clockwise: Heaven, Water, Earth, Fire.

The flag of the Empire of Vietnam used the ''Li'' trigram and was known as ''c? qu? Ly'' because the trigram represents South. Its successor the connected the middle lines, turning it into the Qián trigram. .

Influence on Western culture

The ''I Ching'' has influenced countless Chinese philosophers, artists and even businesspeople throughout history. In more recent times, several Western artists and thinkers have used it in fields as diverse as psychoanalysis, music, film, drama, dance, eschatology, and fiction writing.


Early Chinese civilization, as with western civilization, accepted various pre-scientific explanations of natural events, and the ''I Ching'' has been cited as an example of this. As a manual of divination it interpreted natural events through readings based on symbols expressed in the trigrams and hexagrams. Thus any observation in nature could be interpreted as to its significance and cause. This might be compared to the practice of basing decisions on the state of animals' livers. While usually sympathetic to the claims of Chinese culture and science, Joseph Needham, in his second volume of ''Science and Civilization in China'' stated: "Yet really they would have been wiser to tie a millstone about the neck of the ''I Ching'' and cast it into the sea."

Abraham states that Confucius' ten commentaries, called the Ten Wings, transformed the ''I Ching'' from a divination text into a "philosophical masterpiece." It was this form of the ''I Ching'' that inspired the Taoists, Chuang Tzu and Lao Tzu. It has influenced Confucians and other philosophers and scientists ever since. However, Helmut Wilhelm in his ''Change/Eight Lectures on the I Ching'', cautions, "It can no longer be said with certainty whether any of the material-and if any, how much-comes from Confucius' own hand" .


*Anthony, Carol K. & Moog, Hanna. ''I Ching: The Oracle of the Cosmic Way''. Stow, Massachusetts: Anthony Publishing Company, Inc., 2002. ISBN 1-890764-00-0. The publisher's internet address is
*Balkin, Jack M. 2002. “The Laws of Change: I Ching and the Philosophy of Life”. New York: Schocken Books. ISBN 0-8052-4199-X
*Benson, Robert G. 2003. ''I Ching for a New Age: The Book of Answers for Changing Times''. New York: Square One Publishers.
*Blofeld, J. 1965. ''The Book of Changes: A New Translation of the Ancient Chinese I Ching''. New York: E. P. Dutton.
* Cornelius, J Edward & Cornelius, Marlene Y? King: A Beastly Book of Changes. ''Red Flame: A Thelemic Research Journal'' 1998. This book contains Aleister Crowley's notes and comments on the Yi Jing.
*Huang, A. 1998. ''The Complete I Ching: the Definitive Translation From the Taoist Master Alfred Huang''. Rochester, N.Y: Inner Traditions.
*Hua-Ching Ni. 1999. ''I Ching: The Book of Changes and the Unchanging Truth''. . Los Angeles: Seven Star Communications.
*Karcher, Stephen, 2002. ''I Ching: The Classic Chinese Oracle of Change: The First Complete Translation with Concordance''. London: Vega Books. ISBN 1-84333-003-2. The publisher can be found at This version manages to pull together a wide variety of sources and interpretations into a coherent, intelligible whole which is generally easier to understand than the Wilhelm/Baynes edition. Especially interesting are its multiple translations of the Chinese words used and the concordance at the end.
*Legge, J. 1964. ''I Ching: Book of Changes''. With introduction and study guide by Ch'u Chai and Winberg Chai. New York: Citadel Press.
*''I Ching, The Classic of Changes'', The first English translation of the newly discovered second-century B.C. Mawangdui texts by Edward L. Shaughnessy, Ballantine, 1996. ISBN 0-345-36243-8.
*. & Baynes, C., 1967. ''The I Ching or Book of Changes,'' With foreword by Carl Jung. 3rd. ed., XIX. Princeton NJ: Princeton University Press .
*Lynn, Richard J. 1994, ''The Classic of Changes, A New Translation of the I Ching as Interpreted by Wang Bi''. New York: Columbia University Press. ISBN 0-231-08294-0
*Wei, Wu 2005. “I Ching, The Book Of Answers” Power Press ISBN 0-943015-41-3 New revised edition, interpreted by Wu Wei. Appears to follow the Wilhelm and Baynes translation real well, leaving out the sometimes confusing mechanics. Would be handy to use in conjunction with Wilhelm and Baynes when divining for the lay person.
*Cheng Yi translated by Cleary, Thomas 1988, 2003. “I Ching: The Book of Change” Shambala Library, Boston, London ISBN 1-59030-015-7

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