King Wen sequence

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. Each transition within a pair appears to be the correlating opposite of the other transition within the pair.

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.{{cite journal |last1=Hacker |first1=Edward A. |last2=Moore |first2=Steve |date= 6 May 2003 |title=A brief note on the two–part division of the received order of the hexagrams in the Zhouyi |journal=Journal of Chinese Philosophy |volume=30 |issue=2 |pages=219–221 |doi=10.1111/1540-6253.00115 |url=http://www.biroco.com/yijing/Hacker_Moore_Note_on_two_part_division.pdf |accessdate=31 May 2010 }}{{cite book|author=Bent Nielsen|title=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)|url=https://books.google.com/books?id=mQ4im_ICmbYC&pg=PA83|accessdate=31 May 2010|year=2003|publisher=Routledge|isbn=978-0-7007-1608-1|page=83}} 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.{{cite web|url=http://www.biroco.com/yijing/scan.htm |title=Yijing Dao - Archive of Yijing-related scans from Chinese and other sources |date=20 February 2010 |accessdate=19 May 2010}}

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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.

There have been recent attempts to apply mathematical combinatorics in explaining the logic behind the King Wen sequence, for example Richard S. Cook's proposal.{{cite web|url=http://www.biroco.com/yijing/images/kwscook.jpg |author=Cook, Richard S. |title=《周易》卦序詮解 (Zhou yi guaxu quanjie)|format=JPEG Image, 1024x793 |year=2006 |accessdate=22 May 2010 }} STEDT Monograph 5: [http://stedt.berkeley.edu/html/publications.html#mng5 Classical Chinese Combinatorics]: Derivation of the Book of Changes Hexagram Sequence. 660 pages. {{ISBN|0-944613-44-6}}. OCLC 77009740.

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

• Terrence McKenna
• Wenwanggua

• {{OEIS el|sequencenumber=A102241|name=Hexagrams of the Yi Jing interpreted in base 10|formalname=Hexagrams of the Yi Jing [or I Ching] interpreted in base 10, with the top line = 2^5 (most significant bit) and the bottom line as 2^0 (least significant bit)}}
• [https://web.archive.org/web/20080125095543/http://www.levity.com/eschaton/waveexplain.html 'Derivation of the Timewave from the King Wen Sequence of Hexagrams'] -([https://web.archive.org/web/20080125095543/http://www.levity.com/eschaton/waveexplain.html Archive link])
• [https://www.saxofoon-studio.nl/yijing-modes/wp-content/uploads/2022/06/The-King-Wen-Sequence.pdf 'A numerological interpretation of the King Wen sequence ']

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Category:Chinese philosophy

Category:I Ching

Category:Taoist cosmology