The I Ching is Chinese and specific to Taoism and the Chinese folk religion. The hexagrams are created by meditating on a problem while you cast coins or draw yarrow sticks. The former considered less accurate than the latter. The outcome of the coins or sticks dictates the appearance of the hexagram. You then read the explanation(usually poetic) from the book. Hexagrams can be dynamic and subject to changing lines(lines that change from broken to unbroken or vice versa) reflecting the changing nature of life. It is for this reason the I Ching is known as the Book of Change.

The hexagrams of the I Ching are numbered 1 through 64 and arranged in a particular order known as the King Wen Sequence. This sequence and the rules which determine its order is humanity's most ancient abstract formulation, its genesis dating from somewhere in prehistory. In fact, the precise rules governing the order of this sequence is still a mystery. Terence McKenna was the first modern to claim knowledge of this secret. In fact, by analysis and mathematical manipulation he derived a date for the end of the world: December 21, 2012. Strangely enough, this corresponds very closely with the end-date of the Mayan calendar. McKenna had no previous knowledge of the Mayan calendar when he derived his date. Interesting, eh? The details are given on his website and in his book, The Invisible Landscape

The I Ching supposedly represents the 64 archetypes around which all events in time are created. Thus by consulting it, it will reflect the conditions of the moment in which it is being consulted. In a nutshell: since the universe is a series of random probabilities, performing a random action (like flipping a coin) will result in a pattern (hexagram) that reflects reality enough to provide insight.

Chinese for "The Book of Changes". The I Ching (sometimes "I-Ching" or "IChing") is an ancient Chinese system of divination which became popular in the West in the 1960s. Legend has it that around 1042 B.C. Wên, king of the Chou, invented the sixty-four hexagrams and their names while languishing in prison at the hands of Chou Hsin, king of the Shang.

It works by dividing piles of yarrow stalks (traditional technique) or flipping three coins (modern technique) six times in a row while reflecting and meditating on your question. Depending on how the stalks/coins come up, you draw a yin line (broken), a yang line (unbroken), or a "moving" yin or yang line. If tossing coins, the head is yang and counts as three points, while tails is yin and counts as two points. Adding up all three coins yields a moving yin line (six points), a yang line (seven), a yin line (eight), or a moving yang line (nine).

The resulting six lines represent two trigrams which are combined into one of sixty-four hexagrams. Each trigram represents one of the following:

The resulting primary hexagram is an interpretation of the image of the first trigram (top) over the second (bottom). For instance, water over wood produces the image of the well ("Thus the superior man encourages the people at their work,/And exhorts them to help one another") while the sun over earth produces the image of progress ("Thus the superior man himself/Brightens his bright virtue.") Then the "moving" lines are reversed -- a moving yin becomes a yang and vice versa -- producing a secondary hexagram which is likewise interpreted.

Since the hexagrams can be quickly determined from random coin tosses, it's been popular for some time to use software to generate I Ching divinations. The Everything I-Ching is just one such example.

The I Ching (pronounced "Je Jeng", meaning "Book of Changes") is a 5000 year old Chinese book of divinations regarding future events. As the causal events leading up to the future develop, the I Ching is supposed to be able to "pick up" on the ebb and flow of the Tao as it expresses itself. By meditating on the question to be asked, calculating the lines and then following the advice of the result the I Ching gives the best route to take to get the best outcome (or avoid the worst).

These divinations are constructed using hexagrams which are each made up by combining two of a possible eight trigrams. These are calculated line by line either by flipping coins or the more traditional drawing yarrow sticks. There is an oracle on Everything2 if you want a computerised version.

The most basic component of a hexagram are the lines, either a full line (===) for Yang or a broken line(= =) for Yin. These are grouped into groups of three, and produce 8 possible trigrams.

 
       ------            --  -- 
Ch'ien ------ K'un -- --
------ -- --

-- -- ------
Chên -- -- Sun ------
------ -- --

-- -- ------
K'an ------ Li -- --
-- -- ------

------ -- --
Kên -- -- Tui ------
-- -- ------

These were given the following meanings:

The trigrams are then combined one on top of the other, and form a particular order, called the King Wen sequence. King Wen lived around 1150 B.C. The meaning of this sequence has been commented on by many, but non so "creatively" as Terrence McKenna and his Time Wave theory...

To construct the lines, flip a coin 3 times. A heads is 2 (earth) and a tails is 3 (heaven). The total will be 6, 7, 8 or 9. The lines are constructed bottom to top. 6 and 8 are broken lines (= =), 7 and 9 full lines(===). 6 and 9 are "changing lines", so once you've made your first hexagram, make a second using the first, but any changing lines become their opposite. If there are changing lines, you'll need to read the corresponding latter part of divination result.

Use Everything I Ching if you want a quick way of doing it, although personally I like constructing the lines.

The following is a handy look-up table for the order of the 64 trigrams.

---->   C  C  K  K  K  S  L  T
Upper   h  h  a  e  u  u  i  u
        i  e  n  n  n  n     i
Lower   n  e  n
||      n
\/

Ch'ien  1  34 5  26 11 9  14 43
Chen    25 51 3  27 24 42 21 17
K'an    6  40 29 4  7  59 64 47
Ken     33 62 39 52 15 53 56 31
K'un    12 16 8  23 2  20 35 45
Sun     44 32 48 18 46 57 50 28
Li      13 55 63 22 36 37 30 49
Tui     10 54 60 41 19 61 38 58

The following is the in-order sequence of hexagrams that make up the King Wen Sequence of the I Ching.

  1. Ch'ien, The Creative
  2. K'un, The Receptive
  3. Chun, Difficulty at the Beginning
  4. Mo'eng, Youthful Folly
  5. Hsu, Waiting (Nourishment)
  6. Sung, Conflict
  7. Shih, The Army
  8. Pi, Holding Together (union)
  9. Hsiao Ch'u, The Taming Power of the Small
  10. Lu, treading (conduct)
  11. T'ai, Peace
  12. P'i, standstill (stagnation)
  13. T'ung Jo e'n, fellowship with men
  14. Ta Yu, possession in great measure
  15. Ch'ien, Modesty
  16. Yu, enthusiasm
  17. Sui, Following
  18. Ku, Work on What Has Been Spoiled (Decay)
  19. Lin, Approach
  20. Kuan, Contemplation (View)
  21. Shih Ho, Biting Through
  22. Pi, Grace
  23. Po, Splitting Apart
  24. Fu, return, the turning point
  25. Wu Wang, innocence (the unexpected)
  26. Ta Ch'u ,the taming power of the great
  27. I, the corners of the mouth (providing nourishment)
  28. Ta Ch'u ,the taming power of the great
  29. K'an, the abysmal (water)
  30. Li, the clinging (fire)
  31. Hsien, influence (wooing)
  32. Ho'ê'ng, duration
  33. Tun, Retreat
  34. Ta Chuang, the power of the great
  35. Chin, Progress
  36. Ming I, Darkening of the light
  37. Chai Jo'ê'n, the family (the clan)
  38. K'uei, opposition
  39. Chien, Obstruction
  40. Hsieh, Deliverance
  41. Sun, Decrease
  42. I, Increase
  43. Kuai, Break-through (Resoluteness)
  44. Kou, Coming to Meet
  45. Ts'ui, Gathering Together (Massing)
  46. Sho'ê'ng, pushing upward
  47. K'un, oppression (exhaustion)
  48. Ching, The Well
  49. Ko, Revolution (Molting)
  50. Ting, The Cauldron
  51. Cho'^e'n, the arousing (shock, thunder)
  52. Ko'ê'n, keeping still, mountain
  53. Chien, Development (Gradual Progress)
  54. Kuei Mei, The Marrying Maiden
  55. Fo'ê'ng, abundance (fullness)
  56. Lu, The Wanderer
  57. Sun, The Gentle (The Penetrating, Wind)
  58. Tui, The Joyous, Lake
  59. Huan, Dispersion (Dissolution)
  60. Chieh, Limitation
  61. Chung Fu, Inner Truth
  62. Hsiao Kuo, Preponderance of the Small
  63. Chi Chi, After Completion
  64. Wei Chi, Before Completion
Most of the informationis available in the Richard Wilhelm version of the I Ching, which is the most popular translation, available from Penguin Arkana. It also has a forwards by Carl Jung.
The Wilhelm/Baynes translation of the I Ching is indeed beautiful and thorough. The names of the hexagrams are romanized using the Wade-Giles system, which was the standard method during Mr. Wilhelm's time. The Wade-Giles system was officially replaced by the Chinese Government in 1979 with the Pinyin system, for reasons having mostly to do with pronunciation. It can be confusing when trying to compare more recent translations with those such as the Wilhelm/Baynes translation (and others), since the names are romanized by the two different systems.

Below is a table showing the Pinyin and Wade-Giles versions of the names of each hexagram of the I Ching.
I Ching Hexagram Name Translations
     Pinyin   Wade-Giles (Wilhelm/Baynes)
--------------------------------------------------------
 1.  Qian     Ch'ien, The Creative
 2.  Kun      K'un, The Receptive
 3.  Zhun     Chun, Difficulty at the Beginning
 4.  Meng     Mêng, Youthful Folly
 5.  Xu       Hsü, Waiting
 6.  Song     Sung, Conflict
 7.  Shi      Shih, The Army
 8.  Bi       Pi, Holding Together
 9.  Xiaoxu   Hsiao Ch'u, The Taming Power of the Small
10.  Lü       Lü, Treading
11.  Tai      T'ai, Peace
12.  Pi       P'i, Standstill
13.  Tongren  T'ung Jên, Fellowship with Men
14.  Dayou    Ta Yu, Possession in Great Measure
15.  Qian     Ch'ien, Modesty
16.  Yu       Yü, Enthusiasm
17.  Sui      Sui, Following
18.  Gu       Ku, Work on What Has Been Spoiled
19.  Lin      Lin, Approach
20.  Guan     Kuan, Contemplation
21.  Shike    Shih Ho, Biting Through
22.  Bi       Pi, Grace
23.  Bo       Po, Splitting Apart
24.  Fu       Fu, Return
25.  Wuwang   Wu Wang, Innocence
26.  Daxu     Ta Ch'u, The Taming Power of the Great
27.  Yi       I, The Corners of the Mouth
28.  Daguo    Ta Kuo, Preponderance of the Great
29.  Kan      K'an, The Abysmal
30.  Li       Li, The Clinging
31.  Xian     Hsien, Influence
32.  Heng     Hêng, Duration
33.  Dun      Tun, Retreat
34.  Dazhuang Ta Chuang, The Power of the Great
35.  Jin      Chin, Progress
36.  Mingyi   Ming I, Darkening of the Light
37.  Jiaren   Chia Jên, The Family
38.  Kui      K'uei, Opposition
39.  Jian     Chien, Obstruction
40.  Xie      Hsieh, Deliverance
41.  Sun      Sun, Decrease
42.  Yi       I, Increase
43.  Guai     Kuai, Break-through
44.  Gou      Kou, Coming to Meet
45.  Cui      Ts'ui, Gathering Together
46.  Sheng    Shêng, Pushing Upward
47.  Kun      K'un, Oppression
48.  Jing     Ching, The Well
49.  Ge       Ko, Revolution
50.  Ding     Ting, The Caldron
51.  Zhen     Chên, The Arousing
52.  Gen      Kên, Keeping Still
53.  Jian     Chien, Development
54.  Guimei   Kuei Mei, The Marrying Maiden
55.  Feng     Fêng, Abundance
56.  Lü       Lü, The Wanderer
57.  Xun      Sun, The Gentle
58.  Dui      Tui, The Joyous
59.  Huan     Huan, Dispersion
60.  Jie      Chieh, Limitation
61.  Zhongfu  Chung Fu, Inner Truth
62.  Xiaoguo  Hsiao Kuo, Preponderance of the Small
63.  Jiji     Chi Chi, After Completion
64.  Weiji    Wei Chi, Before Completion
The names of the trigrams in the two systems are less confusing, but are listed here for completeness.
I Ching Trigram Name Translations
     Pinyin   Wade-Giles (Wilhelm/Baynes)
--------------------------------------------------------
 1.  Qian     Ch'ien
 2.  Kun      K'un
 3.  Zhen     Chên
 4.  Kan      K'an
 5.  Gen      Kên
 6.  Xun      Sun
 7.  Li       Li
 8.  Dui      Tui

The Pinyin versions of the trigram and hexagram names are taken from "The Zhou Book of Change" (Chinese-English Bilingual Edition), translated into English by Fu Huisheng, Shangdong Friendship Press, 2000.

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