The Pang Tong Yao

As previously noted, a hexagram’s “opposite” can be formed in two ways:  by physically inverting it, or by reversing the yang lines to yin and vice versa.  The former, known as the quian gua, is the method used to create most of the pairs in the traditional King Wen sequence.  But not every hexagram has a separate quian gua; if a hexagram is vertically symmetrical, the King Wen sequence pairs it with its reversed polarity opposite, the pang tong gua.

I was wondering what it would be like to ponder the judgment and line pairs formed by listing each hexagram beside its pang tong, rather than quian, gua.  Below is such a list; I call these line pairs the pang tong yao.  There are some interesting correspondences here and there.  A hexagram’s pang tong gua, and the result of changing its lines to form the anti-hexagram as described on the previous page, represent the “negative” of an I Ching reading:  what the current situation is not changing into, or what is being avoided by the indicated change.

On a side note, for those who see a relationship between the I Ching and the genetic code, this is the sort of relationship that DNA base pairs have, each line paired with its antisense opposite.

I have used a simple binary sequence for the hexagrams.  The decimal and octal (base 8) values of each hexagram are given beside the hexagram image; yin is 0, yang is 1, and the lines are read as a binary number from bottom to top.  Note that the octal values are simply the values of the trigrams, and make the hexagrams simple to look up.  Below is an index based on the traditional King Wen ordering, and a lookup table illustrating the octal values of the trigrams.

The Fu Xi sequence would be obtained by inverting each hexagram.  Note that the important thing about the pang tong yao is the pairings, not the sequence.

Index:

1Ch’ien / The Creative
2K’un / The Receptive
3Chun / Difficulty at the Beginning
4Mêng / Youthful Folly
5Hsü / Waiting (Nourishment)
6Sung / Conflict
7Shih / The Army
8Pi / Holding Together [Union]
9Hsiao Ch’u / The Taming Power of the Small
11T’ai / Peace
12P’i / Standstill [Stagnation]
13T’ung Jên / Fellowship with Men
14Ta Yu / Possession in Great Measure
15Ch’ien / Modesty
16Yü / Enthusiasm
17Sui / Following
18Ku / Work on What Has Been Spoiled [Decay]
19Lin / Approach
20Kuan / Contemplation (View)
21Shih Ho / Biting Through
22Pi / Grace
23Po / Splitting Apart
24Fu / Return (The Turning Point)
25Wu Wang / Innocence (The Unexpected)
26Ta Ch’u / The Taming Power of the Great
27I / The Corners of the Mouth (Providing Nourishment)
28Ta Kuo / Preponderance of the Great
29K’an / The Abysmal (Water)
30Li / The Clinging, Fire
31Hsien / Influence (Wooing)
32Hêng / Duration
33Tun / Retreat
34Ta Chuang / The Power of the Great
35Chin / Progress
36Ming I / Darkening of the Light
37Chia Jên / The Family [The Clan]
38K’uei / Opposition
39Chien / Obstruction
40Hsieh / Deliverance
41Sun / Decrease
42I / Increase
43Kuai / Break-through (Resoluteness)
44Kou / Coming to Meet
45Ts’ui / Gathering Together [Massing]
46Shêng / Pushing Upward
47K’un / Oppression (Exhaustion)
48Ching / The Well
49Ko / Revolution (Molting)
50Ting / The Caldron
51Chên / The Arousing (Shock, Thunder)
52Kên / Keeping Still, Mountain
54Kuei Mei / The Marrying Maiden
55Fêng / Abundance [Fullness]
56Lü / The Wanderer
57Sun / The Gentle (The Penetrating, Wind)
58Tui / The Joyous, Lake
59Huan / Dispersion [Dissolution]
60Chieh / Limitation
61Chung Fu / Inner Truth
62Hsiao Kuo / Preponderance of the Small
63Chi Chi / After Completion
64Wei Chi / Before Completion

 0 8 16 24 32 40 48 56 000 001 010 011 100 101 110 111 0 000 2 16 8 45 23 35 20 12 1 001 24 51 3 17 27 21 42 25 2 010 7 40 29 47 4 64 59 6 3 011 19 54 60 58 41 38 61 10 4 100 15 62 39 31 52 56 53 33 5 101 36 55 63 49 22 30 37 13 6 110 46 32 48 28 18 50 57 44 7 111 11 34 5 43 26 14 9 1

Columns are the upper trigrams, rows the lower.
The number at the intersection of a column and row is the King Wen number for the hexagram.
The sum of the column header and row header is the hexagram’s decimal value (24 + 1 = 25 for hexagram 17, for example).
The hexagram’s octal value is just the numbers of the two trigrams (31 for hexagram 17).

The circle-and-square hexagram arrangement, in modern binary numerical sequence (and clockwise).