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Patterns of complementary hexagrams

Every hexagram of the I Ching has its complement: the hexagram created by changing every line to its opposite. The complement of hexagram 1 is hexagram 2 –

hexagram 1 |||||| hexagram 2 ::::::

and the complement of hexagram 63 is hexagram 64 –

Other complementary pairs appear through the Sequence, particularly to mark the end of each Canon. But are there larger-scale patterns to be found? The next pair of complements aren’t adjacent in the Sequence; they span most of length of the book. Hexagram 3, Sprouting, complements Hexagram 50, the Vessel:

I find what follows fascinating. 51/52 complement 57/58; 55/56 complement 59/60; 53/54, 61/62 and 63/64 are all self-contained complementary pairs. So the space between 51 and 60 contains all its own complements – and so does the much bigger space between 3 and 50, like a giant Vessel in its own right. It’s as if the pace of discovery, of opening and closing loops of complete transformation, accelerated greatly over the final few hexagrams.

Encouraged by this, I’ve gone looking for other patterns of complements. It’s an experience of equal parts fascination and frustration: the hints of a pattern are constantly emerging, but evaporate away when you look for a recurrence.

Oddly enough, the most regularities emerge when you group the hexagrams by decades, not (as might seem more intuitively obvious) in eights. Try writing hexagrams in rows of five pairs, and try beginning this regiment with hexagram 7 (ie begin the second row with 17, and so on). As you mark in the complements, some distinct, way-beyond-coincidence patterns show up, particularly in the way your rows begin and end.

Beginning the rows, 17/18 are a complementary pair, and so are 27/28 and 29/30. 37/38 find their complements in 39/40. And ending them, 5/6 complement 35/36; 25/26 complement 45/46, creating an interlocking ‘fence’ down the right-hand side.

And there are a couple of other decade-related connections: 23/24 completed by 43/44, 31/32 by 41/42. But it doesn’t do to get too carried away – what about 19 through 22?

There are also some regularities in which decades are linked to others: 21 through 26 all link to the 40s, and then 27 through 30 are two self-contained pairs. The 30s and 40s stretch further afield.

I looked for larger self-contained, closed loops inside the bigger ‘Vessel’ between 3 and 50. Apart from 37-40, there is one other, between hexagrams 7 and 16. 7/8 with 13/14; 9/10 with 15/16; 11/12 at the centre, their own circle, and the whole neatly ‘tied off’ with another complementary pair, 17/18. (There’s a very similar pattern from 51 to 60: five hexagram pairs with the same relationships, though the symmetry’s broken, and again punctuated by following it with a complementary pair.)

Perhaps there might be a series of discrete loops, or a concentric pattern, or maybe an interlocking chain? No – nothing so simple. Patterns are created and broken (deliberately? I think so), and every chart I draw ends up as an almighty tangle. But I’m still left with the strong impression that I’m looking at the work of a master weaver and just don’t have the eyes to see.

What am I missing?

5 responses to Patterns of complementary hexagrams

  1. Could be. There are complementary patterns and trigram patterns and types-of-pair patterns and now I learn there are patterns in changing lines from one hexagram to the next, too. But it rapidly gets far too complicated for me to describe any ‘rules’.

    (There’s at least one person who’s described the whole thing with very advanced maths – but I’d be prepared to bet they haven’t accounted for all the layers of patterning.)

  2. Talking about patterns, I don’t know if you have discussed this earlier but will mention anyway just in case.

    Have you noticed, that with the exception of the 8 Hexagrams, 1 and 2, 27 and 28, 29 and 30, and 61 and 62, if you take the hexagram of 3 and turn it upside down, it becomes Hexagram 4? Same with all the others except for the 8 I mentioned. Hexagram 7 turned upside down becomes Hexagram 8 and so on. With the other 8 if they are turned upside down they remain the same. But those 8, with all moving lines become the one following it – the complement.

  3. Yes – there’s been lots of intriguing work done lately with pairs of hexagrams. Here’s an article by Stephen Karcher on the subject, and then there’s Yijing Wondering and Wandering by Jane Schorre and Carrin Dunne. They call the symmetrical hexagram pairs you mentioned Dragon Gates – and the four you didn’t mention (that are inverted pairs as well as complementary ones) ‘River Crossings’. The first half of their book is almost completely online now; I strongly recommend buying a copy to read part 2, Wandering.

  4. Thanks Hilary,

    I went to the links and went wandering around and have to go back. On one of the links I found a site that I had been looking for and couldn’t find because I had the wrong name. The wonders of the Internet! Yea!

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