Structure of The 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.
| 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 |
Read more about this topic: King Wen Sequence
Famous quotes containing the words structure of and/or structure:
“... the structure of a page of good prose is, analyzed logically, not something frozen but the vibrating of a bridge, which changes with every step one takes on it.”
—Robert Musil (1880–1942)
“There is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed. There is therefore no such thing to be learned, mastered, or born with. We must give up the idea of a clearly defined shared structure which language-users acquire and then apply to cases.”
—Donald Davidson (b. 1917)