King Wen sequence

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The King Wen sequence (Chinese: 文王卦序) is an arrangement of the sixty-four divination figures in 易經 Yì Jīng, the I Ching or Book of Changes. They are called hexagrams in English because each figure is composed of six 爻 yáo—broken or unbroken lines, that represent 陰 yin or 陽 yang respectively.

The King Wen sequence is also known as the received or classical sequence because it is the oldest surviving arrangement of the hexagrams. Its true age and authorship are unknown. Traditionally, it is said that 周文王 Zhōu Wén Wáng (King Wen) arranged the hexagrams in this sequence while imprisoned by 商紂王 Shāng Zhòu Wáng in the 12th century BC. A different arrangement, the binary sequence named in honor of the mythic culture hero 伏羲 Fú Xī, originated in the Song Dynasty. It is believed to be the work of scholar 邵雍 Shào Yōng (1011–1077 AD). As mirrored by the 先天 Earlier Heaven and 後天 Later Heaven arrangements of the eight trigrams, or 八卦 bā guà, it was customary to attribute authorship to these legendary figures. Of the two hexagram arrangements, the King Wen sequence is, however, of much greater antiquity than the Fu Xi sequence.[1]

Structure of the sequence[edit]

The 64 hexagrams are grouped into 32 pairs. For 28 of the pairs, the second hexagram is created by turning the first upside down (i.e. 180° rotation). The exception to this rule is for the 8 symmetrical hexagrams that are the same after rotation (1 & 2, 27 & 28, 29 & 30, 61 & 62). Partners for these are given by inverting each line: solid becomes broken and broken becomes solid. These are indicated with icons in the table below.

Given the mathematical constraints of these simple rules, the number of lines that change within pair partners will always be even (either 2, 4, or 6). Whereas the number of lines that change between pairs depends on how the pairs are arranged, and the King Wen Sequence has notable characteristics in this regard. Of the 64 transitions, exactly 48 of them are even changes (32 within-pairs plus 16 between-pairs) and 16 are odd changes (all between-pairs). This is a precise 3 to 1 ratio of even to odd transitions. Of the odd transitions, 14 are changes of three lines and 2 are changes of one line. Changes of five are absent.


Iching-hexagram-01.svg Iching-hexagram-02.svg Iching-hexagram-03.svg Iching-hexagram-04.svg Iching-hexagram-05.svg Iching-hexagram-06.svg Iching-hexagram-07.svg Iching-hexagram-08.svg Iching-hexagram-09.svg Iching-hexagram-10.svg Iching-hexagram-11.svg Iching-hexagram-12.svg Iching-hexagram-13.svg Iching-hexagram-14.svg Iching-hexagram-15.svg Iching-hexagram-16.svg
1  ↕  2 3  ~  4 5  ~  6 7  ~  8 9  ~ 10 11 ~ 12 13 ~ 14 15 ~ 16
Iching-hexagram-17.svg Iching-hexagram-18.svg Iching-hexagram-19.svg Iching-hexagram-20.svg Iching-hexagram-21.svg Iching-hexagram-22.svg Iching-hexagram-23.svg Iching-hexagram-24.svg Iching-hexagram-25.svg Iching-hexagram-26.svg Iching-hexagram-27.svg Iching-hexagram-28.svg Iching-hexagram-29.svg Iching-hexagram-30.svg Iching-hexagram-31.svg Iching-hexagram-32.svg
17 ~ 18 19 ~ 20 21 ~ 22 23 ~ 24 25 ~ 26 27 ↕ 28 29 ↕ 30 31 ~ 32
Iching-hexagram-33.svg Iching-hexagram-34.svg Iching-hexagram-35.svg Iching-hexagram-36.svg Iching-hexagram-37.svg Iching-hexagram-38.svg Iching-hexagram-39.svg Iching-hexagram-40.svg Iching-hexagram-41.svg Iching-hexagram-42.svg Iching-hexagram-43.svg Iching-hexagram-44.svg Iching-hexagram-45.svg Iching-hexagram-46.svg Iching-hexagram-47.svg Iching-hexagram-48.svg
33 ~ 34 35 ~ 36 37 ~ 38 39 ~ 40 41 ~ 42 43 ~ 44 45 ~ 46 47 ~ 48
Iching-hexagram-49.svg Iching-hexagram-50.svg Iching-hexagram-51.svg Iching-hexagram-52.svg Iching-hexagram-53.svg Iching-hexagram-54.svg Iching-hexagram-55.svg Iching-hexagram-56.svg Iching-hexagram-57.svg Iching-hexagram-58.svg Iching-hexagram-59.svg Iching-hexagram-60.svg Iching-hexagram-61.svg Iching-hexagram-62.svg Iching-hexagram-63.svg Iching-hexagram-64.svg
49 ~ 50 51 ~ 52 53 ~ 54 55 ~ 56 57 ~ 58 59 ~ 60 61 ↕ 62 63 ~ 64

Dual hexagrams[edit]

The I Ching book was traditionally split up in two parts with the first part covering the first 30 hexagrams of the King Wen sequence and the second part with the remaining 34.[2][3] The reason for this was not mentioned in the classic commentaries but was explained in later Yuan dynasty commentaries: 8 hexagrams are the same when turned upside down and the other 56 present a different hexagram if inverted. This allows the hexagrams to be displayed succinctly in two equal columns or rows of 18 unique hexagrams each; half of the 56 invertible hexagrams plus the 8 non-invertible.[4][5]

䷀  乾 qián
The Creative, Heaven
 1 →  ||||||
䷁  坤 kūn
The Receptive, Earth
 2 →  ¦¦¦¦¦¦
䷂   屯 chún
Difficulty At The Beginning
 3 →  |¦¦¦|¦   ← 4  ䷃  蒙 méng
Youthful Folly
䷄  需
Waiting
 5 →  |||¦|¦   ← 6  ䷅  訟 sòng
Conflict
䷆  師 shī
The Army
 7 →  ¦|¦¦¦¦   ← 8  ䷇  比
Holding Together
䷈  小畜 xiǎo chù
The Taming Power of the Small
 9 →  |||¦||  ← 10  ䷉  履
Treading (Conduct)
䷊  泰 tài
Peace
11 →  |||¦¦¦  ← 12  ䷋  否
Standstill (Stagnation)
䷌  同人 tóng rén
Fellowship with Men
13 →  |¦||||  ← 14  ䷍  大有 dà yǒu
Possession in Great Measure
䷎  謙 qiān
Modesty
15 →  ¦¦|¦¦¦  ← 16  ䷏  豫
Enthusiasm
䷐  隨 suí
Following
17 →  |¦¦||¦  ← 18  ䷑  蠱
Work On What Has Been Spoiled (Decay)
䷒  臨 lín
Approach
19 →  ||¦¦¦¦  ← 20  ䷓  觀 guān
Contemplation (View)
䷔  噬嗑 shì kè
Biting Through
21 →  |¦¦|¦|  ← 22  ䷕  賁
Grace
䷖  剝
Splitting Apart
23 →  ¦¦¦¦¦|  ← 24  ䷗  復
Return (The Turning Point)
䷘  無妄 wú wàng
Innocence (The Unexpected)
25 →  |¦¦|||  ← 26  ䷙  大畜 dà chù
The Taming Power of the Great
䷚  頤
The Corners of the Mouth (Providing Nourishment)
27 →  |¦¦¦¦|
䷛  大過 dà guò
Preponderance Of The Great
28 →  ¦||||¦
䷜  坎 kǎn
The Abysmal (Water)
29 →  ¦|¦¦|¦
䷝  離
The Clinging, Fire
30 →  |¦||¦|
䷞  咸 xián
Influence (Wooing)
31 → ¦¦|||¦ ← 32 ䷟  恆 héng
Duration
䷠  遯 dùn
Retreat
33 →  ¦¦||||  ← 34  ䷡  大壯 dà zhuàng
The Power of the Great
䷢  晉 jìn
Progress
35 →  ¦¦¦|¦|  ← 36  ䷣  明夷 míng yí
Brilliance Injured
䷤  家人 jiā rén
The Family (The Clan)
37 →  |¦|¦||  ← 38  ䷥  睽 kuí
Opposition
䷦  蹇 jiǎn
Obstruction
39 →  ¦¦|¦|¦  ← 40  ䷧  解 xiè
Deliverance
䷨  損 sǔn
Decrease
41 →  ||¦¦¦|  ← 42  ䷩  益
Increase
䷪  夬 guài
Break-Through (Resoluteness)
43 →  |||||¦  ← 44  ䷫  姤 gòu
Coming To Meet
䷬  萃 cuì
Gathering Together (Massing)
45 →  ¦¦¦||¦  ← 46  ䷭  升 shēng
Pushing Upward
䷮  困 kùn
Oppression (Exhaustion)
47 →  ¦|¦||¦  ← 48  ䷯  井 jǐng
The Well
䷰  革
Revolution (Molting)
49 →  |¦|||¦  ← 50  ䷱  鼎 dǐng
The Cauldron
䷲  震 zhèn
The Arousing (Shock, Thunder)
51 →  |¦¦|¦¦  ← 52  ䷳  艮 gèn
Keeping Still, Mountain
䷴  漸 jiàn
Development (Gradual Progress)
53 →  ¦¦|¦||  ← 54  ䷵  歸妹 guī mèi
The Marrying Maiden
䷶  豐 fēng
Abundance
55 →  |¦||¦¦  ← 56  ䷷  旅
The Wanderer
䷸  巽 xùn
The Gentle (The Penetrating, Wind)
57 →  ¦||¦||  ← 58  ䷹  兌 duì
The Joyous, Lake
䷺  渙 huàn
Dispersion (Dissolution)
59 →  ¦|¦¦||  ← 60  ䷻  節 jié
Limitation
䷼  中孚 zhōng fú
Inner Truth
61 →  ||¦¦||
䷽  小過 xiǎo guò
Preponderance of the Small
62 →  ¦¦||¦¦
䷾  既濟 jì jì
After Completion
63 →  |¦|¦|¦  ← 64  ䷿  未濟 wèi jì
Before Completion

Explanation[edit]

Over the centuries there were many attempts to explain this sequence. Some basic elements are obvious: each symbol is paired with an "upside-down" neighbor, except for 1, 27, 29, and 61 which are "vertically" symmetrical and paired with "inversed" neighbors.

Its combinatorial mathematical basis was explained for the first time in 2006.[4]

Other hexagram sequences[edit]

See also[edit]

References[edit]

  1. ^ a b Marshall, Steve Yijing hexagram sequences
  2. ^ Hacker, Edward A.; Moore, Steve (6 May 2003). "A brief note on the two–part division of the received order of the hexagrams in the Zhouyi". Journal of Chinese Philosophy 30 (2): 219–221. doi:10.1111/1540-6253.00115. Retrieved 31 May 2010. 
  3. ^ Bent Nielsen (2003). A companion to Yi jing numerology and cosmology: Chinese studies of images and numbers from Han (202 BCE-220 CE) to Song (960-1279 CE). Routledge. p. 83. ISBN 978-0-7007-1608-1. Retrieved 31 May 2010. 
  4. ^ a b Cook, Richard S. (2006). "《周易》卦序詮解 (Zhou yi guaxu quanjie)" (JPEG Image, 1024x793). Retrieved 22 May 2010.  STEDT Monograph 5: Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram Sequence. 660 pages. ISBN 0-944613-44-6. OCLC 77009740.
  5. ^ "Yijing Dao - Archive of Yijing-related scans from Chinese and other sources". 20 February 2010. Retrieved 19 May 2010. If you look at the scan of ztd601 you will see two rows of 18 hexagrams, and notice that the hexagrams that are different when inverted have the hexagram name written upside down above them (the table reads from right to left, with hexagram 1, Qian, upper right). This is the secret of it, a single hexagram is made to represent two hexagrams when its inverse differs. There are eight hexagrams the same both ways up, occurring in the following pairs: 1/2, 27/28, 29/30, and 61/62. If you look now at the diagram you can see that six of these hexagrams occur in the top row of 18 hexagrams while only two appear in the bottom row of 18. This means that the top row represents 30 individual hexagrams while the bottom row accounts for 34 hexagrams. This very clever and yet simple arrangement appears to be the reasoning behind the unequal division, which is actually an equal division when 'dual hexagrams' are used in this way. The same principle is also shown in ztd762. 

External links[edit]