Sequence of the Hexagrams

[fkegan]

Sequence Structure interpretation of Oracles

I take my daughter to her college class and the thread buzzes in my absence, I took a bit of time with Dobro's oracle, but I will do both just on the fly (having had gremlins abscond with my earlier work...

Dobro--week long silent retreat--
Oracle 60 2.3. 63.
60 Lining == This final hexagram of the set of Divine intervention in human life completes the final part of the double dichotomy with the expression of the establishment of infrastructure by the interaction of fluid elements with concrete situations.
Here Divine intervention comes to peaceful completion in simple situation

The entire set of 10 of which 60 is the completion begins with 51 as Monad...
51Swooping==The first hexagram of the 6th set of 10. Here is the pure energy of the Divine manifest in human life as the massive intervention from the Heavens. This is awe and majesty in its pure form and naked invocation.==Tetraktys Monad

From Monad to final, 10th hexagram in a decad the energy of the set is finally in its settled and quiescent state.
It moves from oracle hexagram to resultant, or the possible future with current momenta unaltered to hexagram 63...

63 Morning After == Only Yang places with Yang lines, 1,3,5 process of completion with everything in its place leaving only consideration of what has been completed exhausting its current energy==

There is no Monad to this final set, only 4 hexagrams based upon their overall line patterns.

The moving lines are 2 Yang >>> Yin --Structure (or legs one stands upon) expressing and exhausting themselves.
And 3 Yin to Yang--Passions moving from the background and becoming focus.

Reacting to your comments Dobro, I would suggest perhaps you will want to call your wife for your own issues of in re:"I should probably stay in touch with my wife by phone (cuz she doesn't like being left all on her onesie) with a successful week long silent retreat.

On to Martin,[Lindsay actually]--
“How can I achieve happiness and contentment in the year ahead?”

59.5.6 > 7.
Hexagram 59 Solution == This 9th hexagram of the set of Divine intervention in human life begins the final part of the double dichotomy with expression of the total fluid energy of both wind and running water. Here the emphasis is not on motion/stability, rather the forces taking apart stable infrastructure.
The Divine intervention that eliminates the structures humans develop and return situations to the Flux of events. ==

59 again is part of the decad with the Monad 51 (see above) but at the opposite polar axis from 60 (also above with Dobro's oracle). Rather than the quiescent final state when all 10 points from hexagram 51 are complete, this is the 9th--that is almost complete with that final completing dot being a driving vacuumn to fill(to put the cherry on top or the topmost ornament upon the Christmas tree, or finish that 10th dot to complete the Triangle of the Tetraktys). It is the intense energy to come to completion of one's experience of the Divine directly in one's life.

The moving lines are the 5th and 6th, the overall organization and the transition to the next. These are both Yang lines expressing and exhausting themselves. As they sink back into background, having their culmination achieved the oracle hexagram becomes hexagram 7 of the first set of 10--the concrete water cycle whose Monad is hexagram One, the Creative or Sunshine. Thus, like the Tarot card of the Tower, showing both a King and commoner falling from the high tower, they each and both become simply falling bodies, absolutely equal in their gravitational acceleration and final result when they reach the surface of the Earth.

For completeness' sake, here is the database listing for hexagram 7:

7Corps==First set, the water cycle. 7th place is the first of the initial pair of the Tetrad. Rain absorbed into the ground to form the mystery of energy and homeland. This is position without any movement though it is the preparation for all further development. The rain has fallen upon fertile land and been absorbed to make the fields the location where the mystery of life will take seeds and rain to produce the crop. None of this can be seen outside, it must be taken on faith, yet it is an objective reality and in due time it will move on to the next steps and all the rest of the cycle emerges from this inner mystery.

Overall, this is the situation where real action begins. All the preparation is over, the rain has fallen upon the fields and here begins the use of that rain to grow the crops and to feed the great rivers. Everything here is about organization and its results, although final accounting is still off in the future.==Tetraktys Tetrad

That seems at least moderately suitable as an oracle interpretation, and uses only the sequence numbers and hexagram line positions.

I hope at least this demonstrates the method to my madness in concrete terms.

When I first discovered the oracle casting techniques of asking someone "to tell me 2 natural numbers, 1 to 64, either the same number twice or two different numbers" and applied it at a family gathering of my friend in Belgium which included the current King's Counsel, I found that although stating two numbers was totally polite social inquiry, the structural analysis of the hexagram responses turned out to expose an intimacy which was not.

Any questions about how these interpretations could be applied to your actual questions or situations, I would be glad to try to answer too.

Frank

 

[Sparhawk]

When I first discovered the oracle casting techniques of asking someone "to tell me 2 natural numbers, 1 to 64, either the same number twice or two different numbers" and applied it at a family gathering of my friend in Belgium which included the current King's Counsel, I found that although stating two numbers was totally polite social inquiry, the structural analysis of the hexagram responses turned out to expose an intimacy which was not.

Any questions about how these interpretations could be applied to your actual questions or situations, I would be glad to try to answer too.

Frank

I imagine that technique works fine for people unfamiliar with the Yi, no? Have you found it to be useful among your Yi student peers? Honestly curious, by the way.

 

[fkegan]

Oh, no. Their knowledge of what are "good" and "ill" oracles interferes with the process. The requirement is that one has to allow one's mind to select numbers from its own inner workings. You could be expert in the line patterns and still use your mind to come forward with Arabic- Hindu numbers, but generally, even a mild familiarity with the hexagrams causes choppy waves in the process.

At its best, this technique invites folks to watch their mind process images. In workshops folks would describe what they experienced inside--e.g. first I chose these two numbers and then these other two pushed the first pair out of the way. So I interpreted both pairs, and she noted the first pair were who she would like to be and the second who she was. Or a chemistry prof, at that same party in Belgium who gave two small squares, saying that was all involved in his pick, but I noted that their were smaller squares in the set of natural numbers, and the pair he chose described his inner issues quite exactly.

One of the difficulties of the technique, with folks I didn't know but knew each other very well, was an image I chose simply in my ignorance of the people,from the oracle itself, struck my friend as so totally apt for one of the women in the group that he was unable to stop laughing about it, even though it was clearly impolite.

For those who can not "be random" about their number picks from 1-64 they have to use whatever method they generally use to cast the oracle, or in party situations, ask someone there not so hip to the hexagrams to tell them 2 numbers. In the latter case, the I Ching caster's oracle will include the other person's input as well--but that could be an interesting party game.
Frank

 

[martin]

I use numbers already for a long time, but I pick a big number, then divide it by 64 and the remainder is the hexagram number. I sometimes have used a digital watch too (the seconds, if it was possible to stop the watch) A few hexagrams missing (60-64) but you get a zero extra for 'no answer' or 'void'. When I was near the Himalayas in Nepal my watch very often said '52!'. Yeah, I would think, but what do you mean? That I should stop and sit still? Or that you like those mountains? Or both?

 

[fkegan]

objective numbers and subjective numbers

I use numbers already for a long time, but I pick a big number, then divide it by 64 and the remainder is the hexagram number. I sometimes have used a digital watch too (the seconds, if it was possible to stop the watch) A few hexagrams missing (60-64) but you get a zero extra for 'no answer' or 'void'. When I was near the Himalayas in Nepal my watch very often said '52!'. Yeah, I would think, but what do you mean? That I should stop and sit still? Or that you like those mountains? Or both?

Back in the day, when the Apple //e was state of the art, I used one of its functions to get a number from 0-254 or so determined by when exactly you pressed the next key, and then calculated a number function that delivered an answer 1-64. However, those are objective ways to determine a random number 1-64. They are just another way of calculating the 2's and 3's of the Oracle casting.

If you can get your mind to envision a pair of natural numbers, then you can watch the subjective process of casting an Oracle. Getting somewhere you can watch your mind work as it will is a major empirical experiment. The objective world isn't all that accessible until you have some clarity about your subjective perceptual apparatus in your mind that is filtering everything you perceive. If you were pondering an oracle question, noticing a number between 1-64 is another subjective number casting technique. Your mind is what is noticing that number at that time.

If it were my watch and I were in Nepal near the Himalayas, it would be telling me, "You are near the Himalayas, very special mountain range---do you see them? want to check them out? Let's do something cool with them!

Lindsay-- I called you Martin, and I didn't know it. I think by the time I got to your post, there was Martin's already up, and I thought the name at the bottom of my screen was the same as above...my apologies, but the structural analysis of the oracle remains the same.
Now, as I look more closely at the two posts, it seems they must be by very different folks. I was wondering why you were asking about your watch numbers.
Any comment on my structural analysis of your Yi Oracle? Does the concept make any more sense to you now? And you Dobro?

The sequence is not so much about the pairs or the next hexagrams
but an entire system of sets of 10, that arise from the One, the Two, and the Three, with the next step being the 10,000 things in China and the horoscope wheel upon perpendicular bisectors in Pythagorean metaphysics.

Frank

 

[dobro p]

Does the concept make any more sense to you now? And you Dobro?

The sequence is not so much about the pairs or the next hexagrams
but an entire system of sets of 10, that arise from the One, the Two, and the Three, with the next step being the 10,000 things in China and the horoscope wheel upon perpendicular bisectors in Pythagorean metaphysics.

Ah, you used YOUR sequence. (I thought you were going to shed some light on the King Wen sequence.) Okay, yeah - I see the idea behind your sequence more clearly now. But for me there are two parts to how I understand the Yi - the understanding of the meanings and mechanics of it, and the results I can get with it. So, I got one meaning from how I was reading it (I didn't bring any 'sequence' meanings into it), and you got a slightly different take - you brought my own motivations into the picture, and that was useful for me. (I'd been seeing the situation as me meeting my wife's needs, but of course that was incomplete, and less than the full truth, so your insight was useful.) [By the way, this morning, I'm reading the changing lines in my consultation a bit differently. I've decided that they represent a conflict of interests in me: one part of me wants to stay in touch with my wife during the retreat, both because that's what I want and also because she wants it ('Not emerging gate, courtyard: unfortunate') and another part of me wants to honor the rules of the retreat ('Not measure-like, consequently lamenting-like') because breaking silence will compromise the value of the exercise. However, because there's 'no fault' associated with this, it's perhaps okay to proceed with it (another reason for thinking it's okay is because 63 is the relating hex - everything falls into place, despite the inner conflict).]

So, to conclude, if you saw the bit that was useful to me (the bit about my own motivation in all of this) as a result of your own understanding of the decad of divine intervention applied to the last of the series with those particular changing lines, then yes, your approach is fruitful.

 

[dobro p]

Can anybody point me to a logical sequence of hexagrams based purely on line structure? For instance, let's say we subscribe to the idea that yang lines enter (and disappear) from the bottom. In that case, Hex 2 would be followed by Hex 24; Hex 24 would be followed by Hex 7; Hex 7 would be followed by either Hex 19 or Hex 46 - that sort of thing. I seem to remember a long time ago somebody here saying they'd seen a sequence like this, and that it made perfect logical sense. Anybody?

 

[Sparhawk]

The Fuxi binary sequence that Shao Yong re-discovered?? Again, Steve Marshall has a nice page about the sequences, here.

 

[dobro p]

Hey, thanks Luis. This is to satisfy my own curiosity about what different people have come up with. Cuz basically, I think the problem's insoluble. One of the biggest difficulties is that although the hexagram pairs make sense semantically, they don't make sense in terms of their line structure. Hex 1 and Hex 2 are opposites (every line changes into its opposite) but Hex 19 and Hex 20, for instance, are inverts (the hexagram is just turned upside down... duh).

It's interesting to pair them in terms of opposites, rather than the present arrangment. (I know, I know - you can add 'pairing libertine' to my description...See, I'd be willing to pair opposites if I saw an ontological or semantic relationship between them.) So, we keep Hex 1 paired with Hex 2, and Hex 11 paired with Hex 12, and Hex 27 paired with Hex 28.

But Hex 24 is now paired with Hex 44 - interesting, yes? 24 talks about contacting friends and everything being relaxed and gracious, whereas 44 talks about contact that's problematic and to be kept at a discrete distance. In opposite pairing, 19 pairs with 33, and you can see how the meanings are opposite/complementary. In opposite pairing, 35 pairs with 5 (both are gracious, light-filled situations, but 35 moves ahead while 5 waits). 20 pairs with 34, and their opposite/complementary natures are immediately apparent. Other opposite pairings that seem to work along these lines: 15 and 10, 16 and 9, and there are more.

These new, opposite pairs often have 'opposite' meanings, but the system doesn't always work so neatly. For example, 25 and 46. Do you see a connection there? 25 and 46 don't seem opposite to me, they seem to be moving in similar directions. And what about 41 and 31? (foregoing the girl; taking the girl?) And what about 42 and 32? (Adding more; continuing as before, more of the same? That seems to be a similar direction, not opposite.) And 38 and 39 would be paired, and it seems they're resonating more than being opposite.

Sigh. And so, in the end, the only thing I can conclude is that trying to systematize the Yi is a waste of time. I'd like to know if the people who put it together arranged it that way intentionally in order to keep it alive, knowing that a systematic approach always sucks the life out of any system. What's strange in all this is that I see the universe as orderly, as unfolding out of Principle at the source, and Archetypal Principles arising out of source. Why shouldn't an oracle that reflected that order work really well? I think it's an important question.

 

[crystal_blue]

For instance, let's say we subscribe to the idea that yang lines enter (and disappear) from the bottom. In that case, Hex 2 would be followed by Hex 24; Hex 24 would be followed by Hex 7; Hex 7 would be followed by either Hex 19 or Hex 46 - that sort of thing.

I don't follow; why would Hex #46 follow Hex #7?

 

[Sparhawk]

I don't follow; why would Hex #46 follow Hex #7?

Actually, 19 is the right answer for a binary sequence...

 

[dobro p]

I don't follow; why would Hex #46 follow Hex #7?

Well, if yang lines enter and disappear from the bottom up, then which hexagram follows 7? You can either add a yang to position one, which produces 19, or you can add it to position three, which gives you 46. I'm playing with this, trying to understand if there *is* a logical sequence in terms of hexagram structure.

 

[crystal_blue]

Actually, 19 is the right answer for a binary sequence...

Or #4, if the placement system corresponds from top-to-bottom, as it were; any Hex with two Yang lines could technically follow #19 and still preserve a binary sequence (it would just be highly non-intuitive).

 

[crystal_blue]

Well, if yang lines enter and disappear from the bottom up, then which hexagram follows 7? You can either add a yang to position one, which produces 19, or you can add it to position three, which gives you 46.

Why can one add a Yang to position 3 - you mean Yang builds upwards from any existing Yang (and there is an implicit Yang beneath the Hexagram)?

 

[dobro p]

Why can one add a Yang to position 3 - you mean Yang builds upwards from any existing Yang (and there is an implicit Yang beneath the Hexagram)?

Well, that's the bit I don't understand. Okay, back to square one.

Let's start with Hex 2. It seems natural that this would be followed with 24, right? What comes after 24? Well, you add another yang at position two, and that gives us 19. But what comes after 19? Do you add another yang at position three, which gives us 11? Or does the Hex 19 position one yang disappear, giving us Hex 7? I think it's 7, because I think you should deal with all the lower possibilities before moving on to higher positions. So what comes after 7? You tell me. We can't go back to 19. So it seems natural to move on to the next position - position three - and add a yang. Hex 46. No?

I'm not trying to convince you, by the way. I have no idea where this is going lol.

 

[Sparhawk]

Or #4, if the placement system corresponds from top-to-bottom, as it were; any Hex with two Yang lines could technically follow #19 and still preserve a binary sequence (it would just be highly non-intuitive).

Nope, binary sequences are very precise (bottom line is rightmost number):

000000 (2 in the KWS)
000001 (24 in the KWS)
000010 (7 in the KWS)
000011 (19 in the KWS)
000100 (etc...)
000101
000110
000111
etc...

 

[crystal_blue]

Let's start with Hex 2. It seems natural that this would be followed with 24, right?

By any Hex with one Yang line, to me. But I digress...
-

What comes after 24? Well, you add another yang at position two, and that gives us 19. But what comes after 19? Do you add another yang at position three, which gives us 11? Or does the Hex 19 position one yang disappear, giving us Hex 7? I think it's 7, because I think you should deal with all the lower possibilities before moving on to higher positions. So if the sequence goes 19>7, what comes after 7? 19 or 46? Do you add the new yang to the first position or the third? What's the criterion for adding/subtracting lines? If you follow the principle of dealing with lower positions first, then the answer to this one is 19 (cuz position one is lower than position three, so you change that one first).

Okay, so what happens after 19?

Do you mean to go to #19 twice (#19 -> #07 -> #19)? I'd say it goes #07 -> #46, because once you've reached #07 you've exhausted all combinations of the two first positions (#02 -> #24 -> #19 -> #07), therefore attention moves to the third position.

 

[crystal_blue]

Nope, binary sequences are very precise (bottom line is rightmost number)...

The point is the bottom line is the rightmost member only by convention - a sequence is still technically binary if the bottom line is the leftmost member, or the second from rightmost member, and so forth.

 

[dobro p]

But so that we're all on the same page with this, let's say that the bottom position is on the right.

If that's the case, then the sequence Luis posted works. It's logical.

 

[martin]

Can anybody point me to a logical sequence of hexagrams based purely on line structure? For instance, let's say we subscribe to the idea that yang lines enter (and disappear) from the bottom. In that case, Hex 2 would be followed by Hex 24; Hex 24 would be followed by Hex 7; Hex 7 would be followed by either Hex 19 or Hex 46 - that sort of thing. I seem to remember a long time ago somebody here saying they'd seen a sequence like this, and that it made perfect logical sense. Anybody?

I came up with a similar idea a few years ago and posted it on this forum. To get a 'next' hexagram delete line 1 and add a whole or broken line on top. So every hexagram has two successors. The successors of hex 7, for instance, are hex 24 and hex 27 (what you are doing is the reverse, that may make sense too btw).
Hexagram 1 and 2 are special, because 1 is a successor of 1 and 2 a successor of 2. These hexagrams can chose not to change, so to speak. Somehow that seems to reflect their transcendent or (potentially) absolute nature.

The idea is based on what happens to trigrams (including the inner trigrams, line 2,3,4 and line 3,4,5) in hexagrams if you assume that there is an upward flow or transformation in hexagrams. To get the next trigram (upward) you delete the bottom line and add a whole or broken line on top.
I discussed this with Chris Lofting back then and somewhat to my surprise (because the idea is not so easy to reconcile with his approach) he liked it.

I don't know if anyone in the (distant) past did something similar, but it's not improbable. Whatever you think, somebody, somewhere, probably already thought it.

 

[crystal_blue]

But so that we're all on the same page with this, let's say that the bottom position is on the right.

If that's the case, then the sequence Luis posted works. It's logical.

Fair enough.
-

 

[Sparhawk]

The point is the bottom line is the rightmost member only by convention - a sequence is still technically binary if the bottom line is the leftmost member, or the second from rightmost member, and so forth.

Let me try again... Lets separate the set of "binary" numbers from hexagrams. In a binary representation of numbers, you read them as any other number, i.e. the rightmost digit is the smallest quantity (as in the decimal system, in the number 234, 4 is the units, 3 is the tens and 2 is the hundreds). In the binary system you read them likewise but, the rightmost digit is read as the indicator of "odd" and "even" numbers.

 

[crystal_blue]

I came up with a similar idea a few years ago and posted it on this forum. To get a 'next' hexagram delete line 1 and add a whole or broken line on top. So every hexagram has two successors.

I had a similar idea, but the other way around (delete line 6, add Yang/Yin to the bottom) - the idea being, line 6 is the 'oldest', line 1 'newest'. It also matches descriptions that in #24/#44 that Yang/Yin has 'entered from below' and that in #23 the 'strong Yang line is about to be overwhelmed'.

 

[crystal_blue]

Let me try again... Lets separate the set of "binary" numbers from hexagrams. In a binary representation of numbers, you read them as any other number, i.e. the rightmost digit is the smallest quantity...

Not all numbers (and hence, not 'any other number') denote the smallest quantity as the rightmost digit. However, as above, I'm willing to agree with you for the purpose of this discussion.
-

 

[dobro p]

I discussed this with Chris Lofting back then and somewhat to my surprise (because the idea is not so easy to reconcile with his approach) he liked it.

Well, that makes it immediately suspect.

I suppose somebody's already thought of that.

I understand your idea of sequence. It's a way to generate a sequence, for sure. But it doesn't seem entirely organic to me (I like organic ) because it doesn't work with existing line positions, but instead destroys and creates line positions. I prefer the idea of keep the existing positions intact, but changing the yangs and yins in those positions. Just my bias, I guess.

But I'm going to start a new thread to pursue the idea that's even more important to me than this vexatious one of sequence.

 

[Sparhawk]

Not all numbers (and hence, not 'any other number') denote the smallest quantity as the rightmost digit. However, as above, I'm willing to agree with you for the purpose of this discussion.
-

Should I have been more specific and say "natural numbers", which is what I had in mind?? Are we splitting hairs here?? You want to have the last word? Are you my wife in disguise, saying you live in the UK when you are only a couple of miles from my office??

 

[dobro p]

Crystal Blue is your wife in disguise, Luis. Live with it. You have my sympathies.

 

[lienshan]

I had a similar idea, but the other way around (delete line 6, add Yang/Yin to the bottom)

The sequence below is inspired by the Shuo Kua quote: "The number three was assigned to Heaven,
the number two to Earth, and from these came the other numbers." Read the sceme the chinese way.
I've used ancient chinese numbers < (6) to symbolize broken lines and + (7) to symbolize whole lines.

<<<<<+ <<<+<+ <<<<++ <<<+++
+++++< +++<+< ++++<< +++<<<
+<<<<+ +<<+<+ +<<<++ +<<+++
<++++< <++<+< <+++<< <++<<<
<+<<<+ <+<+<+ <+<<++ <+<+++
+<+++< +<+<+< +<++<< +<+<<<
++<<<+ ++<+<+ ++<<++ ++<+++
<<+++< <<+<+< <<++<< <<+<<<
<<+<<+ <<++<+ <<+<++ <<++++
++<++< ++<<+< ++<+<< ++<<<< etc.
+<+<<+ +<++<+ +<+<++ +<++++ (7)
<+<++< <+<<+< <+<+<< <+<<<< (6)
<++<<+ <+++<+ <++<++ <+++++ (5)
+<<++< +<<<+< +<<+<< +<<<<< (4)
+++<<+ ++++<+ +++<++ ++++++ (3)
<<<++< <<<<+< <<<+<< <<<<<< (2)

(50-65) (34-49) (18-33) (2-17)

The trigrams below (to the right) show horisontal from left to right the Fu Shi trigram order:
<<+ Thunder +<+ Fire <++ Lake +++ Heaven ++< Wind <+< Water +<< Mountain <<< Earth

The order shows vertical upwards from right to left the hexagrams in binumerical order from 2 to 65
<<<<<< Earth (2) ++++++ Heaven (3) etc. to <<<<<+ (65)

Each hexagram of six numbers (either </6/even or +/7/odd) is counted this way:

6th = 0 or 2 / 5th = 0 or 4 / 4th = 0 or 8 / 3th = 0 or 16 / 2th = 0 or 32 / 1th: < even = 2 and + odd = 3

The last five numbers have value 0 if equal (even or odd) to the 1th number. Some examples:
<<<<<< (0-0-0-0-0-2=2) ++++++ (0-0-0-0-0-3=3) <+<+<+ (2-0-8-0-32-3=45) +<+<+< (2-0-8-0-32-2=44)
<<++<< (0-0-8-16-0-2=26) <<++<+ (2-4-0-0-32-3=41) +++++< (2-4-8-16-32-2=64) <<<<<+ (2-4-8-16-32-3=65)

lienshan :bows:

 

[crystal_blue]

Thank you, lienshan.
-

 

[fkegan]

Moving sequence or simply sequential ordering?

Dobro,
You raise an interesting question whether the King Wen Sequence is about one hexagram moving to or becoming the next, or just being ordered or numbered one after the other.
In terms of actively moving from one hexagram to the next, the ordering you speak of is either the pre-King Wen binary counter or the calendar month correspondence where not just one yang line moves along, but the entire column of Yang lines moves up and out from 1 to 44 to 33 until the Yang all disappear into 2 and then start again with 24, 19, 11. 34.

The ordering you speak of by yang-to-yin transformation would be equivalent to a set of oracles with all 6 lines moving. That would highlight the implications in a hexagrams meaning when it totally expressed and exhausted itself in the process of focusing upon what had been background in the original hexagram. Certainly an advanced exercise in the oracle meaning of the individual hexagrams.

As to the difference between King Wen's sequence and "mine" they have the same ordering by number, they don't however move from one to another in pairs. I relate the pairs to the rhyme scheme in poetry such as the sonnet and the King Wen Sequence as following the rhyme scheme while not having it control its meaning. Rather the meaning is conveyed by the philosophical concepts of the Monad--everything in a single image; the Dyad-- the topic described as the interaction of polar opposites, the Triad or the perspective of a process or narrative, and the Tetrad or the perspective that views the process in terms of a double dichotomy, like the horoscope in astrology or the Cartesian axes of analytical geometry and of course, the T'ai Chi in Chinese philosophy.

All of which relates to your musing question--

"What's strange in all this is that I see the universe as orderly, as unfolding out of Principle at the source, and Archetypal Principles arising out of source. Why shouldn't an oracle that reflected that order work really well? I think it's an important question."

I find the King Wen Sequence I Ching Oracle arising from that ordering at source, working very well and its archetypal principle being the perspective represented by the T'ai Chi symbol or the Pythagorean Tetraktys though not springing concretely from those symbols.
The unity of one symbolic circle then the one radius is bisected to form the two eyes at the midpoint of that radius which allow the dual swirls to form for the TWO which together with the original outer circumference make the Three of the narrative or process view for the whole symbol. Taken all together, the two swirls and the two eyes (double dichotomy) form the whole image of the T'ai Chi from the same philosophical process that can be applied to analyze any and all of the 10,000 things.

It is a symbolical geometrical perspective not based in the specific graphics or number theory of the lines.

BTW, do any of you into the historical artifacts of ancient China know what the Chinese used for the geometrical construction of the T'ai Chi symbol? The Greeks were very insistent upon compass and straight-edge which based their constructions upon perpendicular bisectors. Clearly, there is not a perpendicular explicit in the T'ai Chi, though compass and straight-edge construction would have involved many as intermediate steps.

Frank