An old Yijing mystery solved

JULY 25 03

I saw Steve Moore and William Fancourt for a drink yesterday lunchtime at our old haunt, the Museum Tavern. Steve tells me his paper with Edward Hacker – 'A brief note on the two-part division of the received order of the hexagrams in the Zhouyi' – has at last been published in the June issue of the Journal of Chinese Philosophy (30:2, pp 219–221). He showed me this excellent discovery quite some time ago and I have been waiting until the work was published before mentioning the finding.

In short, people have long wondered why the 64 hexagrams in the received order have been divided into two unequal parts, the first part containing 30 hexagrams and the second 34. A number of theories have been put forward, but I believe the Hacker & Moore solution is the correct one, which is backed up by a diagram in the 'Zhouyi Tushi Dadian' they have cited from page 601 (the original comes from the 'Zhouyi Qimeng Yizhuan' by Hu Yigui, born 1274). I have found a further diagram on page 762 showing the same idea.

Essentially, the principle rests on this: some hexagrams are the same upside down whereas other hexagrams are a different hexagram when inverted. 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.