King Wen sequence: Difference between revisions

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Revision as of 07:13, 14 January 2009 editMakeSense64 (talk \| contribs)4,127 edits added some info under Other Sequences← Previous edit		Revision as of 07:29, 14 January 2009 edit undoMakeSense64 (talk \| contribs)4,127 edits →Chessboard presentation: added numbersNext edit →
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	== Explanation ==		== Explanation ==

Revision as of 07:29, 14 January 2009

The King Wen sequence (文王卦序) of the Yi Jing (易經) is a series of sixty-four binary figures (hexagrams), each composed of 6 lines, either solid (yang 陽) or broken (yin 陰).

The King Wen sequence, also known as the classical hexagram sequence, is sometimes considered the second–oldest formal arrangement of the hexagrams, preceded only by the Fu Hsi (伏羲) arrangement, though the Fu Hsi arrangement is most often associated with the Song Dynasty scholar Shao Yong (邵雍). The historical legend is that King Wen of Zhou (周文王) designed this sequence in the 12th century BC while imprisoned by the tyrant King Zhou of Shang; King Wen is said to have died in 1050 BC, by one interpretation of the evidence (Shaughnessy).

Notable characteristics

The 64 hexagrams are grouped into 32 pairs. The second partner in each pair is created by inverting the first. In four of these pairs inversion (i.e. 180° rotation) of either hexagram effects no change (in which case all six lines will change). The number of lines that change between pair partners is always even (either 2, 4, or 6).

The number of possible different arrangements of the 32 partner pairs is 32! = 2.63 * 10^35.

In moving from one hexagram to the next a minimum of one line must change. There are no instances in which exactly five lines change.

The ratio of even to odd numbers of line changes between the hexagrams is exactly 3:1.

64 hexagrams × the 6 lines of a single hexagram = 384, the same number of days as found in ancient annual lunar calendars (that were based on 13 'months' of lunations).

Chessboard presentation



1	2	3	4	5	6	7	8

9	10	11	12	13	14	15	16

17	18	19	20	21	22	23	24

25	26	27	28	29	30	31	32

33	34	35	36	37	38	39	40

41	42	43	44	45	46	47	48

49	50	51	52	53	54	55	56

57	58	59	60	61	62	63	64

Explanation

Over the centuries there were many attempts to explain this sequence.

Its true combinatorial mathematical basis was reportedly explained for the first time in 2006.

There is evidence for a mathematical structure in the sequence.
Several clusters of hexagrams point to a careful arrangement rather than a random distribution. .

Other Hexagram Sequences

Binary Sequence, also known as Fu Xi sequence or Shao Yong sequence.
Mawangdui Sequence.
Eight Palaces sequence (attributed to Jing Fang).

Notes

《周易》卦序詮解 Classical Chinese Combinatorics, Cook
The explanation of King Wen's order, by D.H. Van den Berghe
Yijing hexagram sequences Animations of all the main Yijing sequences, by Steve Marshall

External links

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