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I Ching

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The I Ching (Wade-Giles), or “Yì Jīng” (Pinyin); also called “Book of Changes” or “Classic 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 (see Philosophy, below). In Western 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.

I Ching
Traditional Chinese
Simplified Chinese
Hanyu Pinyin Yì Jīng
Literal meaning "Classic of Changes"

Implications of the title

  • 易 (), when used as an adjective, means “easy” or “simple”, while as a verb it implies “to change“ or 'to exchange/substitute one thing for another'.
  • 經 (jīng) here means “classic (text)”, derived from its original meaning of “regularity” or “persistency”, implying that the text describes the Ultimate Way 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:

  1. 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.
  2. 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.
  3. 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 (鄭玄 zhèng xúan) in his writings Critique of I Ching (易贊 yì zàn) and Commentary on I Ching (易論 yì lùn) of Eastern Han Dynasty.


Traditional view

Traditionally it was believed that the principles of the I Ching originated with the mythical Fu Xi (伏羲 Fú Xī). In this respect he is seen as an early culture hero, one of the earliest legendary rulers of China (traditional dates 2800 BCE-2737 BCE), reputed to have had the 8 trigrams (八卦 bā gùa) revealed to him supernaturally. By the time of the legendary Yu (禹 ) 2194 BCE–2149 BCE, the trigrams had supposedly been developed into 64 hexagrams (六十四卦 lìu shí­ sì gùa), which were recorded in the scripture Lian Shan (《連山》 Lián Shān; also called Lian Shan Yi). Lian Shan, meaning “continuous mountains” in Chinese, begins with the hexagram Bound (艮 gèn), 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 (《歸藏》 Gūi Cáng; also called Gui Cang Yi), and the hexagram Field (坤 kūn) 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 Force (乾 qián) revealed the rise of Zhou. He then gave each hexagram a description regarding its own nature, thus Gua Ci (卦辭 guà cí, “Explanation of Hexagrams”).

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 (爻辭 yáo cí, “Explanation of Horizontal Lines”) 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 (1122 BCE - 256 BCE).

Later, during the time of Spring and Autumn (722 BCE - 481 BCE), Confucius is traditionally said to have written the Shi Yi (十翼 shí yì, “Ten Wings”), a group of commentaries on the I Ching. By the time of Han Wu Di (漢武帝 Hàn Wǔ Dì) of the Western Han Dynasty (circa 200 BCE), Shi Yi was often called Yi Zhuan (易傳 yì zhùan, “Commentary on the I Ching”), and together with the I Ching they composed Zhou Yi (周易 zhōu yì, “Changes of Zhou”). 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 (see below). These reconstructions are dealt with in a growing number of books, such as The Mandate of Heaven: Hidden History in the I Ching, by S. J. Marshall, and Richard Rutt's Zhouyi: The Book of Changes, (see References, below).

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 complete 2nd century BC texts 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 (felt to be anachronistic by the Modernists), 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 BC.

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 (403/475 BC-256/221 BC), with some sections perhaps being as late as the Western Han period (206 BC-220 AD).


The text of the I Ching is a set of predictions represented by a set of 64 abstract line arrangements called hexagrams (卦 guà). Each hexagram is a figure composed of six stacked horizontal lines (爻 yáo), where each line is either Yang (an unbroken, or solid line), or Yin (broken, an open line with a gap in the centre). 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 (卦 guà). 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 (see, e.g., Shaugnessy 1993).

Each hexagram represents a description of a state or process. When a hexagram is cast using one of the traditional processes of divination with I Ching, each of the yin or yang lines will be indicated as either moving (that is, changing), or fixed (that is, unchanging). Moving (also sometimes called “old”, or “unstable”) 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. However, 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 anyway, regardless of the probabilities.

There have been several arrangements of the trigrams and hexagrams over the ages. The bā gùa 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 (e.g., using 0 and 1 to represent yin and yang, 000 + 111 = 111, 101 + 010 = 111, etc.).

The King Wen sequence is the traditional (i.e. “classical”) sequence of the hexagrams used in most contemporary editions of the book. The King Wen sequence was explained for the first time in STEDT Monograph #5, where it is shown to contain within it a demonstration of advanced mathematical knowledge.

The eight trigrams


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 (太極圖), but more commonly known in the west as the yin-yang (陰陽) 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 (八卦 bāguà):

Trigram Figure Binary Value Name Translation: Wilhelm, others Image in Nature Direction Family Relationship Body Part Attribute Stage/ State Animal
1 111
the Creative, Force heaven, aether
northwest father head strong creative horse
2 110
the Joyous, Open swamp, marsh
west third daughter mouth pleasure tranquil (complete devotion) sheep
3 101
the Clinging, Radiance fire
south second daughter eye light-giving, dependence clinging, clarity, adaptable pheasant
4 100
the Arousing, Shake thunder
east first son foot inciting movement initiative dragon
5 011
the Gentle, Ground wind

southeast first daughter thigh penetrating gentle entrance fowl
6 010
the Abysmal, Gorge water
north second son ear dangerous in-motion pig
7 001
Keeping Still, Bound mountain
northeast third son hand resting, stand-still completion wolf, dog
8 000
the Receptive, Field earth
southwest mother belly devoted, yielding receptive cow

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 (the last three lines of the hexagram), is the outer aspect. The change described is thus the dynamic of the inner (personal) aspect relating to the outer (external) situation. Thus, hexagram 04 ¦|¦¦¦| Enveloping, is composed of the inner trigram Gorge, relating to the outer trigram Bound.

Hexagram Lookup Table

Upper →

Lower ↓

||| ()


|¦¦ ()


¦|¦ ()


¦¦| ()


¦¦¦ ()


¦|| ()


|¦| ()


||¦ ()


||| ()


1 34 5 26 11 9 14 43


25 51 3 27 24 42 21 17
¦|¦ ()


6 40 29 4 7 59 64 47
¦¦| ()


33 62 39 52 15 53 56 31
¦¦¦ ()


12 16 8 23 2 20 35 45

¦|| ()

44 32 48 18 46 57 50 28

|¦| ()

13 55 63 22 36 37 30 49

||¦ ()

10 54 60 41 19 61 38 58

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.

Hexagram R. Wilhelm Modern Interpretation
01. |||||| Force (乾 qián) The Creative Possessing Creative Power & Skill
02. ¦¦¦¦¦¦ Field (坤 kūn) The Receptive Needing Knowledge & Skill
03. |¦¦¦|¦ Sprouting (屯 chún) Difficulty at the Beginning Sprouting
04. ¦|¦¦¦| Enveloping (蒙 méng) Youthful Folly Detained, Enveloped
05. |||¦|¦ Attending (需 xū) Waiting Uninvolvement (Wait for now)
06. ¦|¦||| Arguing (訟 sòng) Conflict Engagement in Conflict
07. ¦|¦¦¦¦ Leading (師 shī) The Army Bringing Together
08. ¦¦¦¦|¦ Grouping (比 bǐ) Holding Together Union
09. |||¦|| Small Accumulating (小畜 xiǎo chù) Small Taming Temporary Restraint
10. ||¦||| Treading (履 lǚ) Treading (Conduct) Continuing with Alertness
11. |||¦¦¦ Prevading (泰 tài) Peace Pervading
12. ¦¦¦||| Obstruction (否 pǐ) Standstill Stagnation
13. |¦|||| Concording People (同人 tóng rén) Fellowship Fellowship, Partnership
14. ||||¦| Great Possessing (大有 dà yǒu) Great Possession Independence, Freedom
15. ¦¦|¦¦¦ Humbling (謙 qiān) Modesty Being Reserved, Refraining
16. ¦¦¦|¦¦ Providing-For (豫 yù) Enthusiasm Inducement, New Stimulus
17. |¦¦||¦ Following (隨 suí) Following Flourishing
18. ¦||¦¦| Corrupting (蠱 gǔ) Work on the Decayed Decaying
19. ||¦¦¦¦ Nearing (臨 lín) Approach Approaching Goal
20. ¦¦¦¦|| Viewing (觀 guān) Contemplation The Withholding
21. |¦¦|¦| Gnawing Bite (噬嗑 shì kè) Biting Through Compensation
22. |¦|¦¦| Adorning (賁 bì) Grace Entrapping, Deception, Lure
23. ¦¦¦¦¦| Stripping (剝 bō) Splitting Apart Stripping, Flaying
24. |¦¦¦¦¦ Returning (復 fù) Return Recovering
25. |¦¦||| Without Embroiling (無妄 wú wàng) Innocence Unanticipated Outcome
26. |||¦¦| Great Accumulating (大畜 dà chù) Great Taming Anticipated Outcome
27. |¦¦¦¦| Swallowing (頤 yí) Mouth Corners Fulfillment
28. ¦||||¦ Great Exceeding (大過 dà guò) Great Preponderance Nonfulfillment
29. ¦|¦¦|¦ Gorge (坎 kǎn) The Abysmal Water Darkness, Gorge
30. |¦||¦| Radiance (離 lí) The Clinging Brightness
31. ¦¦|||¦ Conjoining (咸 xián) Influence Attraction
32. ¦|||¦¦ Persevering (恆 héng) Duration Perseverance
Hexagram R. Wilhelm Modern Interpretation
33. ¦¦|||| Retiring (遯 dùn) Retreat Withdrawing
34. ||||¦¦ Great Invigorating (大壯 dà zhuàng) Great Power Resurrecting
35. ¦¦¦|¦| Prospering (晉 jìn) Progress Expansion, Promotion
36. |¦|¦¦¦ Brightness Hiding (明夷 míng yí) Darkening of the Light Injury, Persecution
37. |¦|¦|| Dwelling People (家人 jiā rén) The Family Community
38. ||¦|¦| Polarising (睽 kuí) Opposition Division, Divergence
39. ¦¦|¦|¦ Limping (蹇 jiǎn) Obstruction Halting, Hardship
40. ¦|¦|¦¦ Taking-Apart (解 xiè) Deliverance Liberation, Solution
41. ||¦¦¦| Diminishing (損 sǔn) Decrease Decrease
42. |¦¦¦|| Augmenting (益 yì) Increase Increase
43. |||||¦ Parting (夬 guài) Breakthrough Separation
44. ¦||||| Coupling (姤 gòu) Coming to Meet Copulation
45. ¦¦¦||¦ Clustering (萃 cuì) Gathering Together Association, Companionship
46. ¦||¦¦¦ Ascending (升 shēng) Pushing Upward Alienation, Rift
47. ¦|¦||¦ Confining (困 kùn) Oppression Restriction
48. ¦||¦|¦ Welling (井 jǐng) The Well Replenishing, Renewal
49. |¦|||¦ Skinning (革 gé) Revolution Abolishing the Old
50. ¦|||¦| Holding (鼎 dǐng) The Cauldron Establishing the New
51. |¦¦|¦¦ Shake (震 zhèn) Arousing Mobilizing
52. ¦¦|¦¦| Bound (艮 gèn) The Keeping Still Immobility
53. ¦¦|¦|| Infiltrating (漸 jiàn) Development Auspicious Outlook, Infiltration
54. ||¦|¦¦ Converting The Maiden (歸妹 guī mèi) The Marrying Maiden Inauspicious Outlook, Caution
55. |¦||¦¦ Abounding (豐 fēng) Abundance Goal Reached, Ambition Achieved
56. ¦¦||¦| Sojourning (旅 lǚ) The Wanderer Travel
57. ¦||¦|| Ground (巽 xùn) The Gentle Abandoning, Yielding
58. ||¦||¦ Open (兌 duì) The Joyous Accessing
59. ¦|¦¦|| Dispersing (渙 huàn) Dispersion Dispersal
60. ||¦¦|¦ Articulating (節 jié) Limitation Regulation
61. ||¦¦|| Centre Confirming (中孚 zhōng fú) Inner Truth Staying Focused, Avoid Misrepresentation
62. ¦¦||¦¦ Small Exceeding (小過 xiǎo guò) Small Preponderance Transition, Temporary Stage
63. |¦|¦|¦ Already Fording (既濟 jì jì) After Completion Completion
64. ¦|¦|¦| Not-Yet Fording (未濟 wèi jì) Before Completion Incompletion

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 (19904 – 19967).

Tai Xuan Jing( 太玄) 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 (earth), U+268A (yang), U+268B (yin).


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 (see the divination paragraph below) 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 Confucianist 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 (1703) 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 (a neo-Confucian and Taoist) 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 (reproduced in Hu Wei's I Thu Ming Pien ch.7, pp 2b,3a and elsewhere).

This Segregation Table of yin/yang symbolism was derived from a 12th century document. It sets forth the formulation of the sixty-four hexagrams in a diagrammatic manner. Here the inherent yin/yang symbolism associated with each hexagram is represented by black and white squares, where each row of spaces represents an individual line of the sixty-four hexagrams.

The top row represents Line 6, and consists of 32 yin and yang spaces.

The 2nd row from the top, Line 5 consists of 16 yin and yang spaces.

The 3rd row from the top, Line 4 consists of 8 yin and yang spaces.

The 4th row from the top, Line 3 consists of 4 yin and yang spaces.

The 5th row from the top, Line 2 consists of 2 yin and yang spaces.

The 6th row from the top, Line 1 consist of 1 yin and yang space.

If one considers each hexagram as a column of yin and yang spaces, the individual lines of each hexagram can be easily determined from the diagram.

Recent research The I Ching Project by John Compton has indicated that this segregation table by Shou Yung has been derived from the much earlier Fu Hsi's Diagram of the derivation of the sixty-four hexagrams. This is probably the earliest example of yin/yang symbolism. His in-depth mathematical analysis suggests that the Ma-Wang-Tui(2nd century BC) arrangement of hexagrams identification numbers is the original I Ching hexagram arrangement.

The I Ching and the Binary Code relationship may be deduced from the "Lines" section, incorporated within the Commentaries of the I Ching, where the interpretation and meaning of each hexagram oracle is usually given. Each particular line of the hexagram has a significant meaning. The explanation commences with a sentence, which describes the respective yin or yang component of the hexagram line together with its position within the hexagram symbol, i.e. "Six in the Beginning......." or "Nine at the Top....." etc.(Yin lines are represented by the number 6, and yang lines by the number 9).

In this manner, a unique numerical yin/yang code has been assigned to each individual hexagram symbol.

For Example, consider the "Lines" of hexagram No.1 - Ch'ien / The Creative - this is represented by the following sentences:

Nine in the beginning:

Nine in the second place:

Nine in the third place:

Nine in the fourth place:

Nine in the fifth place:

Nine at the top.

Clearly, these sentences refer to yang(unbroken)line components represented by the number 9.

Similarly, we can consider the "Lines" of hexagram No.2 - K'un - The Receptive - represented by the following sentences:

Six in the beginning:

Six in the second place:

Six in the third place:

Six in the fourth place:

Six in the fifth place:

Six at the top.

These sentences refer to yin(broken)line components represented by the number 6.

This yin/yang code has mystified scholars and researchers for many centuries. However, Gottfried Leibniz realized that this numerical symbolic code represented a binary coded system based on the multiplication "powers" of the number 2. Where number 9 and 6, respectively represent the binary values of 1, and 0 (Zero).

In essence, the modern day binary code consists of a pattern of numbers formed from numbers 1 and 0.

Thus, the I Ching's yin/yang code can therefore be converted into the modern day binary code by assigning the binary value of 0 (Zero) to the YIN hexagram component(represented by the line value of 6), and assigning the binary value of 1 to the YANG hexagram component (represented by the line value of 9).

The binary code devised by Leibniz is based on the "powers" of the number 2.


     20 = 1
     21 = 2 x 1 = 2
     22 = 2 x 2 = 4
     23 = 2 x 2 x 2 = 8
     24 = 2 x 2 x 2 x 2 = 16
     25 = 2 x 2 x 2 x 2 x 2 = 32

These binary values are assigned in this particular order:

     25 : 24 : 23 : 22 : 21 : 20

The highest value is assigned to the bottom hexagram line, whilst the lowest value is assigned to the top hexagram line.

In this manner the I Ching's symbolic code can be converted into the binary code. Thus, the numerical denary value for each hexagram may be determined by adding the respective binary numerical values for each YANG hexagram line.

It should be noted, that there is sufficient evidence to show that the ancient Chinese mathematicians knew the mathematical methodology of the binary code, as it is graphically portrayed in the Mt.Meru "Holy Mountain" diagram c.200BC.

Reference - The I Ching Project - The I Ching Key - Volume 1 - The Secret Computer of the Ancient Gods ISBN 978-0-9554482-0-1.

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 (change) or non-transformation (non-change) can be represented numerically, as follows:

A POSITIVE(unbroken line) transforming into a NEGATIVE (broken line) = 9; A POSITIVE (unbroken line) transforming into a POSITIVE (unbroken line) = 7; A NEGATIVE (broken line) transforming into a POSITIVE (unbroken line) = 6; A NEGATIVE (broken line) transforming into a NEGATIVE (broken line) = 8;

This changes the ancient symbolic linear language of the I Ching into a simple numerical language that enables the practitioner to created 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 Middle Kingdom, vol. 1, p. 632)


The flag of South Korea, with Taegeuk in the centre with four trigrams representing Heaven, Water, Earth, and Fire (beginning top left and proceeding clockwise).
Flag of the Empire of Vietnam used Trigram Li - Fire

The Flag of South Korea contains the Taijitu symbol, or tàijítú, (yin and yang in dynamic balance, called taegeuk in Korean), 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 (Fire) trigram and was known as cờ quẻ Ly (Li trigram flag) because the trigram represents South. Its successor the Republic of Vietnam connected the middle lines, turning it into the Qián (Heaven) trigram. (see Flag of the Republic of Vietnam).

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 Roman 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 (p. 311) stated: "Yet really they [Han dynasty scholars] would have been wiser to tie a millstone about the neck of the I Ching and cast it into the sea."

Abraham (1999) 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" (p. 12).


  • 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 (1998) Yî King: A Beastly Book of Changes. Red Flame: A Thelemic Research Journal (5) 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. (2nd edition). 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.
  • Wilhelm, R. & Baynes, C., 1967. The I Ching or Book of Changes, With foreword by Carl Jung. 3rd. ed., Bollingen Series XIX. Princeton NJ: Princeton University Press (1st ed. 1950).
  • 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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