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Blog post: Additive hexagrams?

hilary

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OK, here’s the off-the-wall idea for the day.

What if you could add two hexagrams together? Not changing lines to move from one hexagram to another, but ‘adding’ them, on the basis that yin + yin = yin, but yang + yin = yang, because you imagine the yang line ‘filling’ the empty yin space.

This idea first hit me years ago, reading what LiSe had discovered about hexagram 15 and the ‘uniting bird’. A quick summary, since I want to share the whole odd idea with you in one post: the name of hexagram 15 is made up of two components, ‘words’ and ‘uniting’. The idea is that ‘words’ is a more recent addition, and the original might just have been ‘uniting’. That could then have various implied meanings, which were only subsequently differentiated and made explicit by adding different radicals: ‘words’ for ‘Modesty’, ‘rodent’ for Rutt’s Rat… and then LiSe says that

Substituting ‘words’ (part 1 of the character) for ‘bird’ gives Jian1, a mythical bird with one wing and one eye. Two of them could fly: the perfect cooperation.

Well… I look at this, and at 15 combined with 16, its paired hexagram and the one that joins imagination to 15’s realism, and get this…

15.gif
+
16.gif

=
62.gif


- hexagram 62, whose Oracle reads,
‘Small exceeding, creating success,
Constancy bears fruit.
Allows small works, does not allow great works.
A bird in flight leaves its call,
Going higher is not fitting, coming down is fitting.
Great good fortune.’

And that is a rather lovely coincidence.

Then just now I was reading this article:
Why you must learn to love the goo.
To begin with, this makes me think of Hexagram 27, Nourishment. I often compare what goes on in the inner lines of 27, where the regular channels of nourishment are rejected, to what happens to a caterpillar inside a pupa. Something like a full internal replumbing or rewiring *is happening… our way of perceiving and receiving nourishment changes completely.

So here is this brilliant article talking about the ‘goo’ phase between being caterpillar and butterfly (and also sounding quite a bit like hexagram 29, incidentally, which has 27 as its nuclear hexagram), and suddenly it says,

You know you’re in deeply into the goo when the old form has completely dissolved – but the new form has not yet emerged.

Well… spot the hexagrams…

23.gif
+
24.gif

=
27.gif


…do you suppose?

Let’s look at the other two hexagrams we can build symmetrically in this way: 28 and 61.

45.gif
+
46.gif

=
28.gif


…maybe? There’s a gathering of people, forces, waters, resources, investment, intensity… and there is purpose and direction and the need to move and make progress.

‘Great Exceeding, the ridgepole warps.
Fruitful to have a direction to go.
Creating success.’
Not completely implausible, is it?

And

19.gif
+
20.gif

=
61.gif


Nearing and Seeing are about presence and awareness, and together are also about mutual help. Also, they describe the approach of a spirit and how it is seen in the space opened up by not acting. All of this seems to me to fit very beautifully with Inner Truth.

So anyway, here are some ideas to play with. (Do you know if anyone else has already described this?) I wonder if it’d feel right applied beyond these few symmetrical hexagrams. (Does 24 + 16 = 51? or 24 + 8 = 3?)
 

rodaki

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(Do you know if anyone else has already described this?)

hi Hilary,

what you describe sounds a lot like Chris Lofting's XOR-ing method
15 (+ catalyst 16) > 62 (or, in Chris' words, 15 XORed with 16 gives 62)

I know that's also half of an Operators system (Karcher's?) Not sure who came up with it first but it was Chris's posts that taught me the method so I prefer to refer it back to him.
 

Sparhawk

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So anyway, here are some ideas to play with. (Do you know if anyone else has already described this?) I wonder if it’d feel right applied beyond these few symmetrical hexagrams. (Does 24 + 16 = 51? or 24 + 8 = 3?)

What Dora said. This was explored, extensively, by Chris Lofting. It is Exclusive Or or XORing. The only thing you forgot was that a Yang+Yang=Yin. Remember all those conversations about the XX-ness of a hexagram, as in the "27-ness of XX"? Well, that was XORing a given hexagram by H27. I even made a Yitoon about the idea to tease Chris... :D

20070110-My63-nessisbetter-thumb.gif
 

hilary

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Along with Dora, I also thought that Chris's XOR-ing was the same as a change pattern/operator, ie the yang lines in your pattern for the change mark which lines will change. 15 with the change pattern of 16 would indeed give 62, but only because it so happens that 16 marks line 4 as the one to change. 16 with a change pattern of 16 would be 2, because any line with a yang line 'acting' on it changes to its opposite, either way.

That's not what I had in mind. I was just adding hexagrams, not using one as an 'operator'. The yang lines are filling up spaces left by yin lines, not requiring that they change. '15+16' isn't the same idea as having 16 be the active principle at work to change 15. Not my fault if it actually looks completely identical, since it still gives you a yang line where you had a yin one before, and so this all looks pretty silly.

Anyway, however silly I look... the way I'm thinking of it, you couldn't do '16+16' or '24+19' or whatever, because you can't 'fit' another yang line into the space one already occupies. It's like jigsaw pieces, or Lego - slots and holes. Heh, where is Charly when we need him? Anyway, you could only 'add' hexagrams where the yang lines didn't clash - pieces that were designed to slot together like the parts of a jigsaw, so you could see the picture they made together.
 

Sparhawk

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Anyway, however silly I look... the way I'm thinking of it, you couldn't do '16+16' or '24+19' or whatever, because you can't 'fit' another yang line into the space one already occupies. It's like jigsaw pieces, or Lego - slots and holes. Heh, where is Charly when we need him? Anyway, you could only 'add' hexagrams where the yang lines didn't clash - pieces that were designed to slot together like the parts of a jigsaw, so you could see the picture they made together.

Just what Charly needs, encouragement... :D

Thanks for explaining. The nuance upon the XORing idea, only because you called it "adding," is interesting. So, it is only a matter of superposing an hexagram with yang lines upon another where there are no yang lines in the same place as the first one, right?
 

hilary

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Right. I don't really do maths, but I can at a pinch do simple jigsaws. Should've called the post 'jigsaw hexagrams'.
 

rodaki

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uh-huh . . sometimes things look identical but are different. This is divination after all, meaning is in the eye of the beholder
 

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