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The Sequence Problem as It Is?

peter

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Hello all,

I'd like to ask a simple question: where is the origin of the problem of the traditional sequence of hexagrams - so-called "King Wen's sequence"? I mean, who raised this problem as a problem? It seems to me that the sequence presents a problem only for "Occidental" minds, not "Oriental". I myself found it as an open problem in classical Russian translation by Shchutsky (and yes, this was the beginning of my interest in Yi Jing). Do Chinese really want to solve this sequence mathematically, or maybe some institutes of yijingistics (Yi-xue, "Yi studying") offer some money for discovering a formula?

Oh, hope I expressed myself clearly enough.
 
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hmesker

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Hi Peter,

I think the 'sequence problem' already originated very early, the Xu Gua chapter of the Ten Wings is one of the first attempts to explain the sequence in a rational manner. Maybe Mawangdui sequence is also the result of this problem, maybe they thought something better should be possible.

I have never heard that a Yi Xue institute offers money for breaking the code. Wouldn't be surprised, though.

Harmen.
 

dobro p

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"I have never heard that a Yi Xue institute offers money for breaking the code."

Which kinda assumes, Harmen, that there *is* a code. I think that whoever arranged the present sequence of hexagrams did so in a way that was pleasant to do and pleasing to his mind. Fun and esthetically pleasing, in other words; not cosmically significant.

I've read the notes that go along with the present sequence enough times to be convinced that you could arrange the hexagrams in almost any sequence you wanted, and you could come up with an equally convincing (equally *unconvincing*, actually) gloss for why the order was like that.

But the *pairs* of hexagrams are really significant, I think. I think the meaning of each of the pairs is intimately related to the other.
 
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hmesker

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dobro said:
Which kinda assumes, Harmen, that there *is* a code.
Erhm, yes, it does, although I personally doubt there is a 'code', just like you.

But the *pairs* of hexagrams are really significant, I think. I think the meaning of each of the pairs is intimately related to the other.
It indeed looks that way, there are a few interesting features in the text that support this view. It also means that you, if you want to find the rule behind the sequence, you could focus on the odd hexagrams 1, 3, 5 etc. But I doubt that you will find that rule. I received the book by Gennadij Fomyuk and Elena Kudina (http://gennadij-fomyuk.narod.ru/Book/book_engl.zip) who claim that they have cracked the code, but I find there material far too complex and totally incomprehensible. I'm not convinced.

Harmen.
 

lindsay

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I agree with you guys 100%. The King Wen sequence is not one of the great unsolved mathematical problems of our time. Nobody is willing to pay $1M for its solution, so why bother with it?

There is another kind of sequential explanation I find just as unconvincing as the mathematical ones: narrative sequences. Using the meaning of the hexagrams, some people have explained the order of the hexagrams as a kind of story. For example, Greg Whincup thought the King Wen sequence represented stages in the lifecycle of a typical junzi. In their aptly-named "Complete Idiot's Guide to I Ching," Elizabeth Moran and "Master" Joseph Yu developed the idea that each hexagram represented a chapter in the history of the great Zhou Conquest of Shang. Umm, that is, if there ever was a Great Zhou Conquest ... in fact, recent archeological work has much diminished both Shang and Zhou in size and importance from their legendary status. Only a "Complete Idiot" would believe some of the stories Moran and Yu serve up, but the authors apparently knew who they were writing for.

Years of intense study have convinced me the King Wen sequence is in reality a Bronze Age grocery list. Watch for my new book - "A Gourmet's Guide to the Zhouyi" - where I explore all the yummy recipes hidden in the text and gua.

Lindsay
 
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hmesker

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lindsay said:
Umm, that is, if there ever was a Great Zhou Conquest ... in fact, recent archeological work has much diminished both Shang and Zhou in size and importance from their legendary status.
Indeed, indeed. It the moment I am reading the fascinating book Landscape and Power in Early China - The Crisis and Fall of the Western Zhou 1045-771BC by Li Feng, an archaeologist who uses bronze inscriptions and locations of findings to reconstruct the fall of the Western Zhou dynasty. The picture he gives is this: soon after the fall of the Shang, the Western Zhou dynasty became weak, bad organized and had to deal with a lot of resistance from the regional states. Because the capitals were in the Wei River valley in the West, and the main regional states were located far in the East, the Zhou hardly had ways to control these regions, regions which became quickly independend. That in turn deminished the power of the Zhou dynasty, and it didn't take too long for the dynasty to collapse. That's not all of course, but that's how far I am in the book :) .

Years of intense study have convinced me the King Wen sequence is in reality a Bronze Age grocery list. Watch for my new book - "A Gourmet's Guide to the Zhouyi" - where I explore all the yummy recipes hidden in the text and gua.
Of course! Why didn't I see it? The Soup of King Wen!

Harmen.
 

bradford

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Although I've seen many attempts and claims to have solved the puzzle, I still think the King Wen sequence (a.k.a. Hou Tian or Later Heaven) is a simple attempt at misdirection or a muddling of the waters, almost exactly half orderly and half randomized (a statement in itself). And I think there was some purpose in this misdirection. Of course the problem has consumed many thousands of scholar-years. This is where Tarot has an edge. Even though the cards can be put into several orders, they arent very useful until the sequence has been randomized again.
Besides, I think the "True" arrangement renders the other sequence irrelevant. It's pure binary mathematics and perfect in its geometry. It's The One, even though it wasn't discovered until the 11th century, wasn't comprehended by the authors, and is absolutely anachronistic. But of course, as Shchutskii sez, the mathematics and geometry of hexagons is absolutely unknown to the bees who build their hives with them.
 

lindsay

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Hi Brad!

I'm not sure I understand what you're saying. Do you think the King Wen sequence was a deliberate effort to mislead ("muddy the waters") people and maybe conceal something important? You said: "I think there was some purpose in this misdirection." Any ideas about what purpose?

Here's the part that baffles me. Before the invention of printing, at a time when maybe only 1 person in 10,000 could read or write, why would there be a need for "misdirection"? It's not like all kinds of people were looking over the diviner's shoulder, trying to second-guess him or steal his secrets. This isn't the Masons we're talking about, is it? The Illuminati?

And what's all this about the "True" sequence and the perfection of binary arithmetic? All that perfection is kind of inevitable when you're working on an intellectual platform of base 2, whether you call it yin and yang, good and evil, mind and body, etc. etc. Dualism is dualism. Not too many choices: 2, 4, 8, 16, 32, 64, 128, 256, 518, etc. Now 518 organizational categories might have made for a slightly unwieldy divination system, and 16 are definitely too few. How about 64? Sounds like a good round number - a humanly possible number - of concepts to work with.

Similar ideas occurred elsewhere for similar reasons. There are 78 cards in a modern tarot deck, 22 trump cards in the Major Arcana, and 56 cards in four suits in the Minor Arcana. Not identical to the Yi, but similar. Two main groupings (arcana, books) of 50-100 elements (cards, hexagrams) with complexity markers ranging from 4 to 6 (suits, lines). The same order of magnitude in both divination systems with the same level of complexity. Enough to be challenging, but also manageable by ordinary humans.

The really odd thing for me is why 6 lines? Why not 4 or 5 or 8? There's no binary magic in the number six. Leibniz wouldn't even put it on a T-shirt.

Is the magic really there even though no one knew about it (like you say)? Was Democritus really the father of atomic theory, or just an imaginative Greek windbag? Does a falling tree make a sound in the forest when no one is there to hear it? I guess, pace Shchutskii, it takes a human being to see mathematics in what the bees are doing. I guess it also takes a late twentieth-century mind - a mind enthralled by computer technology - to see binary arithmetic in what the Chinese were doing 3000 years ago with their heaps of yarrow.

You are wrong about one thing. Scholars have not spent thousands of scholar-years wringing their hands over the King Wen sequence. That kind of problem bores most professional intellectuals. It's the kind of thing only enthusiasts and cranks get excited about. Like flying saucers and the lost continent of Atlantis.

Lindsay
 

peter

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Harmen,

Thanks for the info on the institute :) Don't take Fomyuk's book seriously, he didn't prove anything (on my sight and on sight of another Russian explorer), but some ideas are not bad. And yes, I almost forgot about "Xu Gua Zhuan", but it's rather "narrative", "psychological" atempt of explanation, not strictly "logical", so to say.

===============

bradford,

Sorry for quibbling, but how do you understand "half-orderly and half-randomized"? What order do you see here, and which hexagrams do not fit in it?

===============

lindsay,

Yes, I don't like "narrative" explanations too, but we don't have anything else. The first such explanation was "Xu Gua Zhuan", mentioned by Harmen, and in the Internet I met Danny van der Berghe's explanation, and also some other modern views. I may confess that I also thought about this sequence as some historical records - after Marshall's "Mandate of Heaven" it seems not completely absurd. BTW, Shchutskiy gives about 30 versions of what Yi Jing is believed to be, and among them are "an alphabet", "history", "child verses" and many others, so your version of cooking-book fits well in this list. And that's cool. How many recipes did you find in Yi Jing? I agree, that the problem of the sequence is not of much importance - much less than the sequence of Later Heaven circle of trigrams, for example.

================

My own ideas were already posted in Russian, but I'll write them here too. As I see this sequence, there are 3 "parts", or "levels" in it:

1) pairing principle - asymmetrical hexagrams go with mirroring principle (fan), and symmetrical - with inversing principle (dui); this level is clear enough;

2) ordering in pairs - hexagrams divide on first and second in pairs, and why one hexagram is first, and another is second, is not evidental;

3) ordering of pairs - pairs of hexagrams go in some order, and this order is also unknown.

Another idea is that the sequence is not linear - it seems to be linear, but this illusion is caused simply by imperfection of ancient methods of writing and storing information. I also suspect that there are more than 2 parts of this sequence: say, one part is 3-10, another is 13-16, third - 19-26 etc.

But I don't think that my ideas are new. That's why I want to find a list with attempts of decipher this sequence.


P.S. for Chris Lofting personally: no, I don't want to see you here.
 

heylise

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Peter, take a look HERE
There are more than 64 hexagrams, when you look at them in the way of "pairs". It explains why they are divided at 30 instead of 32, and also how many pairs there really are, if you apply that rule (upside-down) in a strict way.

Nice stuff to play around with. I love it. But I stil think those old diviners simply had the complete Yi in their head, without any sequence apart from the pairs. When you write that down, you have to take one after the other, it is the only way to get them all. How do you make a grocery list? "O yes, apples, and what vegetable is in the shop now, and coffee, umm, what else.. o yes, I need new filters, and don't forget a big bag of onions, for that lindsaysoup"

LiSe
 

peter

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LiSe,

thanks, but I know about this presentation :) I even saw a diagram in "ZhouYi Da Cidian" (as it seems to me, Harmen, correct me if I'm wrong) where first 18 formed upper part of the table 6x6 and second 18 - lower part of that table. From that table I took the idea of my "crystal". Yes, 36 is a very interesting number, I forgot to mention it.
 

bradford

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peter said:
bradford,
Sorry for quibbling, but how do you understand "half-orderly and half-randomized"? What order do you see here, and which hexagrams do not fit in it?.

For the most part it's a randomized sequence of structurally meaningful pairs.
Every other sequitur has a structral explanation, in terms of inverse or opposite.
Then the whole sequence is made to begin and end with the most four most critical hexagrams, which by the way are the third points of the binary sequence (0, 21, 42, 63)
I think it's a tease. There never was an important connection between 2 & 3, 4 & 5, 6 & 7, etc. Just 1 & 2, 3 & 4, 5 & 6, etc.
 

denis_m

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.../

Hello Everyone,
Love lurking and following your posts. I have been entertained by reading the archives here.

There is something about the KW Sequence that reminds me of hexagram names. Many of the names seem to be arbitrarily assigned, yet they have lead to fertile associations. For instance, thunder over earth could have been called Sui [Follow], and marsh over thunder could have been called Yu [Rousing]. But since we were given the assigned names, we have gone ahead and built associations on them. The paired names (as we find them) provide intriguing contrasts, and they fit more or less with the composition of the hexagram figures.[Ex. #23 and #24]
In the same way, the sequence was assigned by the authors. The pairs could have been in a different order. But the order given yields fertile associations. For instance, think of the little segment---#23, #24, #25, #26. A contrast between decay and vital beginnings is followed by a contrast between innocent impulse and accumulted wisdom. Looking back on these contrasts adds something to the XZ of #26, in which the superior man "learns about words and deeds of men in the past, to cultivate his virtue."
I think the sequence was connected with the writing and placement of line statements. A few items of evidence: All the occurrences of hui3-wu2 ("regret disappears") occur in the lower canon. All occurrences of the words gui1 and qu3 (words for marriage) occur at the ends of six figure segments. (One figure yields two hexagrams, unless it is symmetrical.) I mention symbolically relevant patterning and placement of lines in my article "The Dance of Qian and Kun."

It's certainly reasonable to take the KW Sequence with a grain of salt. I wish I could take time to look more closely at the binary sequence, especially those amazing correspondences with DNA coding. The only reason I've taken time with the KW Sequence is because associations have built up in my thinking as I've read along in the text.

In reference to what Peter says, maybe 6 is a special number because 6 to the 2nd power is 36, and 2 to the 6th power is 64.
Six seems to be the only number whereby the binary patterns [6 to the 2nd power] when read both ways yield the number of hexagrams [2 to the 6th power]. Note that this does not work for 4. Four to the 2nd power is 16, and 2 to the 4th power is 16, but the number of binary figures yielding 16 tetragrams is 10.
To me this validates the elegance of what Larry Schulz calls the collapsed KW Sequence, where 36 figures are used to show the 64 hexagrams.

Regards,

Denis Mair
 

bradford

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Warren S. McCulloch, an early neurophysiologist and one of the founders of cybernetics, points out in "Embodiments of Mind" that neurologically Six is the highest perceptible number, or that the nerves themselves can identify six things. Anything higher has to be counted by the brain.
 

peter

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bradford,

Yes, surely, order in pairs and chaos outside.

And to another post: I remember some numbers "7 plus-minus 2": it is proved by scientists that a man can hold only so many objects in attention at one time. At least 5, but no more than 9. I suppose it was found later than McCulloch's number 6.

=================

denis_m,

Well, I didn't want to discuss hexagrams' names at all. If you'll find Mawangdui version, you can also play with other names of hexagrams (but not in this topic).

Yes, "collapsed", or "folded", Wen-wang sequence is an interesting thing. Look also at this picture: http://yijing.narod.ru/Images/c11_64h_ww36.gif (it is what I was telling about to LiSe).

Peter
 

lindsay

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Brad -

That's fantastic! I love it! Warren S. McCulloch has the obvious answer. We can keep track of a maximum of six things before our brain kicks in. That explains why I like the Yi so much. I always knew there was a simple explanation for having six lines in a hexagram. Case closed! Thank you!

Lindsay
 

martin

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peter said:
I remember some numbers "7 plus-minus 2": it is proved by scientists that a man can hold only so many objects in attention at one time. At least 5, but no more than 9. I suppose it was found later than McCulloch's number 6.

You are probably referring to an article by Miller, "The magical number seven, plus or minus two".
I read it about 35 years ago and I still remember that funny title. :)
But it appears - I just looked it up on the web - that 5-9 popped up more or less accidentally.

Wikipedia:
"However, this limit was eventually found to be a result of using subjects who were speakers of English to remember sequences of single digits. It turns out that one component of human working memory, the phonological loop, is capable of holding around 2 seconds of sound. Two seconds is the duration of the English spoken form of 7±2 digits (in Chinese it is around 9 and in Welsh around 6) .."

Sorry Lindsay, or are you Welsh? :D
 

toganm

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lindsay said:
The really odd thing for me is why 6 lines? Why not 4 or 5 or 8? There's no binary magic in the number six. Leibniz wouldn't even put it on a T-shirt.

To my understanding there are two reasons in terms of chinese philosophy

  • Qi is one of the core concepts of chinese philospohy. So 6 is how qi is differentiated in man/nature. That is what will be qi be like in tai yang, shao yang, yang ming, tai yin, jue yin and shao yin. In a way those six are linked to the unity of the qi in a being. So very line describes the state of qi is
  • The six lines are from bottom to up earth, man and heaven. Yet there has to be yin and yang so for each of them there has to be two options; yin yang. So not individual lines yet a pair of lines are needed for each ( earth,man,heaven)

Togan
 

lindsay

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Thank you, Martin, I'm feeling very Welsh, although I've had a few shots of Mom's favorite therapist (Jack Daniels). And thank you, Togan, but I'm going to have to do some homework before I understand what you said.

Consider this:

"According to ancient and Neoplatonic systems, 6 is the most perfect number as it is both the sum and the product of its parts: it is formed either by adding 1 + 2 + 3 or by multiplying 1 x 2 x 3. Furthermore it is the product of the first male (2) and first female (3) numbers. From the psychologist's viewpoint, it represents a combination of analysis and synthesis in its simplest form: 2 x 3. It summarizes all the plane figures of geometry (point, line, and triangle), and since the cube is composed of 6 squares, it is the ideal form for any closed construction."
-- Annemarie Schimmel, "The Mystery of Numbers"

The clincher: How many days did it take God to create the world?

From all this, I think it should be crystal clear why the ancient Chinese chose the number 6.

Lindsay
 

bradford

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The nearest best guess is 4.86 trillion days and still only half done
 

bradford

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Good Lord-
I just realized something about 4.86 trillion
That's about exactly how much Bush and 2000-2008 Republican Congress will have overspent
to bankrupt American grandkids - literally a dollar a day since the beginning of time.
 

peter

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Hey, hey, guys, don't fall offtopic. 6 is a good number, and 36 too, of course, but return to the view on the Wen-wang sequence.

It is interesting to me, who was the first who raised this problem in "our times", so to say. Chinese wrote "Order of Hexagrams" ("Xu Gua Zhuan") and relaxed. But who with "Occidental" mind wasn't satisfied with it? For example, I didn't find any notion of it in Richard WIlhelm's texts, but I read not all of them, so maybe WIlhelm somehow tried to shed some light on this problem? Or maybe Hellmut Wilhelm?..

Oh, and one more thought I have: maybe simply meditate on this sequence and wait when my mind will discover some laws? Did anybody try to open to the sequence?
 
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frank_r

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In qabalistic symbolism 6 is the number of self-concious, capable of experience.

when you look to the Lo shu everything counts up to 15. also 6 together.

That's why I found the the book by Gennadij Fomyuk and Elena Kudina (http://gennadij-fomyuk.narod.ru/Book/book_engl.zip) quit interesting.
I tried to understand it but I didn't finish it it was quit complicated, but some points were really intersting.

Like the idea that it were 9 perfect Lo Shu figures. There were 9 squares, 81 together. So by using the code of the King Wen sequence you can go beyond self conciousness and go to the 9, the number of the essence of being itself.

"It explains the assumption of imperfection on the part of perfection. The Absolute would be Nothing, would remain in the condition of Nothingness: therefore in order to be concious of its possiblities and to enjoy them, it must explore the possibilities. " Aleister Crowley

Maybe there was no concious code before but there is always a perfect balance somewhere in a system also in the KW sequence. There was also first the KW sequence and later there found the Fu Shi sequence. And there always have been a DNA code but only after finding the perfect way to describe it started to exist in the concious minds of us people.

Frank R
 

peter

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Entering the 9th element bases on suppose that the original 8 trigrams are imperfect. But 8 is not less independent number than 9, they're simply different, but equally applicable. And if you'd want to fit 8 trigrams into He Tu with its 10 elements - how would you expand 8 to 10? Yes, Fomyuk entered that 9th element in attempt to explain the order, but he failed. (That's my main claim upon him - he pretends on an explanation, but gives nothing.)
 

frank_r

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Ha Peter,

Another interesting part about the book of Fomyuk for me was that the magic square of the 9 gave always 369. a perfect triade.

6 is also as old yin. double yin, and 9 is old yang, double yang. In the diagram of the seasons then 6 is winter and 9 is summer.

Looking to the He Tu 6 is at the place of water the lowest most yin point and 9 is at the place of lake, the most reflective point. So 6 the place of conciousness(more yin than this it will never get) and 9 the place of transition.

Frank R
 

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