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Sequence of the Hexagrams

rosada

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In my recent efforts to memorize the IMAGES as translated by Wilhelm I have been becoming more aware of the sequence and the story it appears to tell. However, I understand the standard sequence we all use is not the only one considered valid. Can anyone give me a little background on why we use the sequence we do and any thoughts on alternative patterns?
 

sergio

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Hello Rosada;
there is a lot of excellentinformation about sequences in Steve Marshall's site and I'm pretty sure there was a very interesting blog by Hilary on that subject not so long ago.Also check Richard S.Cook on "Chinese Combinatorics" if you understand and speak fluid gibberish(the book is probably understood by Cook and his close friends only) and a series of very interesting thoughts on it by Frank Keegan.Also J Van de Berghe's site tackles the subject admirably.Nobody has arrived (yet)to a satisfactory answer to that question you posed.With all due respect from a junior member to a senior member I thought you already knew about all this.In any case ,check all this avenues and you will have some answers and many more questions.But I agree with Hilary on this one:the sequence is irrelevant.Historically there seems to be -or had been -three different sequences.The one we use now is the received sequence from the Imperial edition-Kang SHI -1715.Have fun!
Sergio
 

rosada

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Thank you Sergio. I was able to check out the Steve Marshall site but all I came up with was explanations of why the arrangement of the hexagrams made sence mathmatically. (I may not have explored his site sufficiently.)

What I am wanting to know is if there is an agreed upon plot line to the hexagram sequence. Wilhelm gives an explanation for why each hexagram follows the one before it in the second half of his translation but I don't find these explanations very satisfactory. They seem far fetched. For example, in discribing why 5.Waiting should follow 4.Youthful Folly we're told, "When things are still small, one must not leave them without nourishment. Hence there follows the hexagram Hsu. Hsu means the way to eating and drinking." This just doesn't satisfy me. I mean, I don't think the obvious next step when one is dealing with Folly is to say, "Well give the kid a sandwich." I can come up with my own reason for linking Youthful Folly to Waiting. I would say "When one is new to a situation asking questions wont always bring clarity. Sometimes when you are young or new you just have to be patient, you just have to Wait until you see a pattern that shows you what to do next." And perhaps you could add that when you are waiting you might as well enjoy yourself, hense the eating and drinking and good cheer...
And then look at the next explanation Wilhelm gives for why 5. Waiting leads to 6. Conflict, "Over meat and drink there is certain to be conflict." Come on, that's just plain not true. In my version, I would say Waiting leads to the resolution of Conflict. That is when things are not moving ahead and we find we're stalled, having to wait gives an opportunity to discuss our plans and intentions, to go back as Conflict's IMAGE advises and, "Carefully consider the beginning," that is review original intentions so we can figure out why our intentions are manefesting as they are, understand what is causing the delay, the conflict, and thus see what we need to do to disentangle the blockage. Thus:
4. the Young Fool who can't get his questions answered is guided to
5. Wait until things become a bit more clear by themselves and they will become more clear if he considers that
6.the world around him is the manefestation of his own original intention. Once he recognizes that, once the Fool realizes he created the delays and conflicts with his own half completed mixed signals, then he knows how to...
7. Get personally involved so as to sort out the confusion.

Is Wilhelm giving his own ideas when he talks about The Sequence, or is this a translation from a Chinese text?

So anyway, what I'm looking for here is not the mathmatical explanation of why the hexagrams were placed in this sequence, but the story line. I have come up with my own version of why one hexagram follows another, but I am wondering if there is an official one. In my own attempt to link the hexagrams together into a cohesive whole I am seeing a story of The Superior Man first attempting to impose order on the outer world and ultimately coming to recognize that he must discover and resolve the disorder within himself.
 
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sergio

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Hi Rosada;
the question of the sequences is a difficult one indeed.What you are looking for is the crux of Gregory whincup's translation,'Rediscovering the I Ching".In it the tries first to present the YI in its "pure"or primitive form-the way it would have been in the Bronze Age before the Ten Wings and other commentaries were appended to it.Second he presents the whole sequence as the rise and fall of a certain character-warrior would be king-and explains the correlation of the hexagrams thus.The truth of the matter is that the King Wen sequence(the one we use or received)IS NOT MATHEMATHICALLY PERFECT.There seems to be no logic to it and so far noone has explain the rationale behind it.Whilhelm only explains the sequence taking in consideration the explanation from one of the wings-the second one if I am not mistaken.Other sequences may be based on a sound mathemathical approach as ,for example,Shao yung's famous square and circle arrangements but it is not -in my opinion-technically a sequence but an arrangement.The one discovered in the Mawandui silk copy is indeed different to the received one and it does have a logical organization.It is based on the interpretation of trigrams as family members(father,mother sons,daughters)and it follows a determined order or hierarchy as in a proper family thus derivating the hexagrams under a strict order.But that is as far as it gets.(so far)Please bear in mind that in the before mentioned second wing where the sequence of the hexagrams is discussed ,the implied order is (if follows as is written)different to the sequence in the text,namely the received text that Wilhelm translated.Thus the section is usually called 'mixed Hexagrams or Jumbled Hexagrams.there are other interpretations.For example Frank Keegan describes it very interestingly as a process of creation and development on Earth
A similar approach is taken by J.van DeBerghe in his Feng Shui site.H describes it as a landscape as seen by King Wen.Mine is a rudimentary description of his theory but I will try to provide a link to his site later.As you can see it is a very thorny issue to deal with ,with no clear answers in sight and nothing yet proven and accepted.There are said to be two other sequences that were lost in history maybe representative of different schols or interpretations of the text.Not so long ago Harmen Mesker provide a link to an excellent article dealing with analysis of these hipothetycal sequences.Again,as I am writing this from memory I will try to provide these links afterwards.Last but not least Bradford Hatcher provides a wealth of excellent material on the Yi so please also research his invaluable information.GOT TO GO!
Sergio
 

sergio

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Here is the link th D.van De Berghe sitehttp://www.fourpillars.net/articles.php
Sergio
 
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jesed

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Is Wilhelm giving his own ideas when he talks about The Sequence, or is this a translation from a Chinese text?
Hi rosada

What Wilhelm called "sequence" is his translation of one of the ten wings. Therefore, it is original Yijing. (Remember: Yiging is Zhouyi PLUS the Wings)

Best
 

sparhawk

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Jesed answered correctly. Furthermore, what's translated as "The Sequence" is the Ninth Wing or Xu Gua. So, it isn't something Wilhelm interpreted on his own.
 

rosada

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Thank you Jesed and Sparhawk!
One of these days I'm going to write out my own Sequence. Not to replace the ancients, but just as an exercise to set my own mind in order. In fact I just asked the I Ching for a comment on my intention and received

51.
The superior man sets his life in order
And examines himself.

So maybe this is not a bad idea.

Now to do it...
 

rosada

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Rather than posting my own ideas on the sequence, I thought it would be more helpful to post what Wilhelm has to say...

There is no text for the first two hexagram so we take up the story at hexagram 3...

After heaven and earth have come into existance, individual being develop. It is these individual beings that fill the space between heaven and earth. [It is like a difficult first birth] Hence there follows the hexagram of DIFFICULTY AT THE BEGINNING.

When, after difficulties at the beginning, things have just been born, they are always wrapped at birth in obtuseness. Hence there follows the hexagram of YOUTHFUL FOLLY. For youthful folly means youthful obtuseness. This is the state of things in their youth.
YOUTHFUL FOLLY means confusion and subsequent enlightenment.

When things are still small, one must not leave them without nourishment. Thus youthful folly leads to eating and drinking, WAITING.


Over meat and drink, there is certain to be conflict. Eating and drinking leads to CONFLICT.


When there is conflict, masses are sure to rise up. Hence Conflict leads to THE ARMY. Army means mass.

Among the masses there is surely a reason for uniting. Hence the army leads to HOLDING TOGETHER.

Through holding together, restraint is certain to come about. Holding together leads to restraint, THE TAMING POWER OF THE SMALL.

When beings are subjected to restraint the mores arise; hence there follows rules for good CONDUCT.

Good conduct, then contentment; thus calm prevails. Hence there follows the hexagram of PEACE. Peace means union, interrelation.

Things cannot remain forever united; hence there follows the hexagram of STANDSTILL.

Things cannot be at a standstill forever. Hence there follows FELLOWSHIP WITH MEN.

Through fellowship with men things are sure to fall to one's lot. Hence there follows POSSESSION IN GREAT MEASURE.

He who possesses something great must not make it too full; hence there follows the hexagram of MODESTY.

When one possesses something great and is modest, there is sure to be enthusiasm. Thus modesty leads to ENTHUSIASM.

Where there is enthsiasm, there is certain to be following. Hence there follows FOLLOWING.

When one follows others with pleasure, there are certain to be undertakings. Hence there follows WORK ON WHAT HAS BEEN SPOILED.

When there are things to do, one can become great. Hence there follows APPROACH. Approach means becoming great.

When things are great, one can contemplate them. Hence there follows CONTEMPLATION.

When there is something that can be contemplated, there is something that creates union. Hence there follows BITTING THROUGH. Biting through means union.

Things should not unite abruptly and ruthlessly; hence there follows GRACE.

When one goes too far in adornment, success exhausts itself. Hence there follows SPLITTING APART.

Things cannot be destroyed once and for all, When what is above is completely split apart, it returns below. Hence follows RETURN.

By turning back one is freed of guilt. Hence there follows INNOCENCE.

When innocence is present, it is possible to tame. Hence there follows THE TAMING POWER OF THE GREAT.

When things are held fast, there is the provision of nourishment. Hence there follows THE CORNERS OF THE MOUTH.

Without provision of nourishment one cannot move; hence there follows PREPONDERANCE OF THE GREAT.

Things cannot be permanently in an overweighted state. Hence there follows THE ABYSMAL. The Abysmal means a pit.

In a pit there is certain to be something clinging within. Hence there follows THE CLINGING. The Clinging means resting on something.

After there are heaven and earth there are the individual things...After the individual things have come into being there are the two sexes...After there are male and female, there is the relationship between husband and wife...Then the relationship between father and son..and prince and servant..and superior and inferior. After the relationship between superior and inferior exists, the rules of propriety and of right can operate.

The way of husband and wife must not be other than long-lasting. Hence DURATION.

Things cannot abide forever in their place: hence RETREAT.

Things cannot retreat forever, hence THE POWER OF THE GREAT.

Things cannot stay forever in a state of power; hence PROGRESS. Progress means expansion.

Expansion will certainly encounter resistance and injury. Hence DARKENING OF THE LIGHT. Darkening of the light means damage, injury.

He who is injured without, of a certainty draws back into his family. Hence THE FAMILY.

When the way of the family comes to an end, misunderstandings come. Hence OPPOSITION. Opposition means misunderstandings.

Through opposition difficulties necessarily arise. Hence OBSTRUCTION.

Through release of tension something is sure to be lost, hence DECREASE.

If decrease goes on and on, it is certain to bring about increase. Hence INCREASE.

If increase goes on unceasingly there is certain to be a break-through. Hence there follows BREAK-THROUGH. Break-through means resoluteness.

Through resoluteness one is certain to encounter something. Hence there follows COMING TO MEET.

When creatures meet one another, they mass together. Hence there follows GATHERING TOGETHER.

Massing toward the top is called pushing upward. Hence, PUSHING UPWARD.

If one pushes upward without stopping, he is sure to meet with oppression. Hence, OPPRESSION.

He who is oppressed above is sure to turn downward. Hence THE WELL.

The setup of the well must necessarily be revolutionized in the course of time. Hence REVOLUTION.

Nothing transforms so much as the ting. Hence THE CALDRON.

Among the custodians of the sacred vessels, the eldest son comes first. Hence, THE AROUSING. (The Arousing means movement.)

Things cannot move continuously, one must make them stop. Hence KEEPING STILL.

Things cannot stop forever, hence DEVELOPEMENT. Developement means to progress.

Through progress one is sure to reach the place where one belongs. Hence THE MARRYING MAIDEN. The Marrying Maiden means the end of maidenhood.

That which attains a place in which it is at home is sure to become great. Hence ABUNDANCE. Abundance means greatness.

Whatever greatness may exhaust itself upon, this much is certain: it loses its home. Hence THE WANDERER.

The wanderer has nothing that might receive him; hence THE GENTLE, THE PENETRATING. The Gentle means going into.

When one has penetrated something, one rejoices. Hence THE JOYOUS.

After joy comes dispersal. Hence, DISPERSION.

Things cannot forever separate. hence, LIMITATION.

Through being limited, things are made dependable. Hence INNER TRUTH. Inner truth means dependability.

When one has the trust of creatures, one sets them in motion; hence there follows PREPONDERANCE OF THE SMALL. Preponderance of the small signifies transition.

He who stands above things brings them to completion. Hence there follows AFTER COMPLETION. After Completion means making firm.

things cannot exhaust themselves. Hence there follows, at the end, the hexagram of BEFORE COMPLETION.
 
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sergio

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So what's YOUR point?Are you going to copy the whole 9 th. wing?
Sergio
 

rosada

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Yeah, pretty dry isn't it? I hadn't realized how dry until I started writing it all out. I just thought it would be helpful if people could read the whole sequence in one place. My intention after I get this up is to then write up MY version and maybe other people will want to post theirs.
 

rosada

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Whew, okay that was interesting. Not sure I really get the whole picture any more clearly but reading it through did bring a few insights. Like I hadn't thought of Inner Truth as meaning Dependability particularly but when you see it as the out growth of Limitation it makes sence.
 
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hilary

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It's dry... and I don't believe Wilhelm himself thought much of it, which of course doesn't help. 'The setup of the Well must necessarily be revolutionized in the course of time'?! Oh dear; sounds like an expensive plumbing project. ('The dao of the Well doesn't allow things not to be Radically Changed.')

But I believe this is a mnemonic recorded by someone with a strong understanding of the sequence. No need, of course, to write out all you know - just enough to serve as a reminder to the students. (Maybe that's why it so often just says this progression is 'necessary' or 'inevitable' and leaves you trying to see why!) You work out how the dao of the Well demands change, or why eating and drinking in a context of Waiting might lead to Argument. (If, for instance, you'd left behind your confidence that there would be enough for everyone...)

But who knows what the original author had in mind? Anyway, the text gives a starting point for thinking about the Sequence's 'story', which can only be good. It's a remarkable, beautiful thing, that received sequence, full of interweaving patterns that all hint (in tantalising ways) at something bigger. The most exciting single account of it I've seen would be Danny van den Berghe's (scroll down for 'The Explanation of King Wen's Order' and 'I Ching Landscape', both pdf files), but part of the excitement is seeing how many different possible accounts, or rather fragments-of-accounts, there are.
 

noxlux

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Howdy,

I always took the ninth wing to be a later ad hoc mnemonic device. More specifically I thought it's pseudologic connections between the hexagrams were in rhyme, simply in order to make it easier to remember by singing.

My knowledge of chinese howerver is to limited to confirm this. Do you know?

Best regards
Noxlux
 

dobro p

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The ramifications of pseudological connections in an ad hoc mnemonic device are apt to confound not only one's cognitive dexterity in its vain attempt to plumb the profounder depths of the truly multifaceted 'ecology' of the Yi, but also to defeat any attempted aesthetic appreciation of a more purely literary approach.

I rhyme
All the time
 

sparhawk

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The ramifications of pseudological connections in an ad hoc mnemonic device are apt to confound not only one's cognitive dexterity in its vain attempt to plumb the profounder depths of the truly multifaceted 'ecology' of the Yi, but also to defeat any attempted aesthetic appreciation of a more purely literary approach.

Even if English was my first language, I couldn't have said that better... :D
 

rosada

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I was just rereading this thread and realized I never acknowledged Sergio for his very detailed and helpful suggestions. Thank you for your post, Sergio, I followed up on some of your leads and got some useful insights.
Rosada
 

noxlux

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*furiously raging icons*
:) :) :)

Ok ok ok.

So here goes again.

I think it is part of chinese tradition to compose songs as an aid to the memory. Actually I thought the ninth wing was such a song. And that the connections proposed between the hexagrams were just whimsical ideas in order to create the songs lyrics in a way which can be rememebered.

Curiously I ask: is it possible to sing or rhytmically recite the ninth wing?

BREGER
N
 
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sergio

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Hi Noxlux,
I think you are right in saying it is a mnemonic device.I remember reading an article by Alfred Huang about songs and the I Ching.I'll try digging it but no guaranties because Huang's website is no longer functioning.I don't know Chinese so I wouldn't know if it rhymes or not but I wouldn't be surprised if it does.Sometimes we forget that the I Ching is not written in prose but in verse,a fact overlooked by translators too focus on conveying the meaning in spite of the form it was composed.
Do not get angry or frustrated,Dobro is the site's welcome commitee to junior members and will" bark at strangers"no matter what-even if agreeing with you.(LOL-LOL)
Sergio
 

sergio

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Hello Rosada;
thanks for acknowledging previous communication.Glad to be of help,anytime.
Sergio
 

lienshan

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The truth of the matter is that the King Wen sequence(the one we use or received)IS NOT MATHEMATHICALLY PERFECT.There seems to be no logic to it and so far noone has explain
the rationale behind it.
In 2002 this 3000 years old pottery pat with 4 six-number-sets + 1 arrow was found:

http://www.onlineclarity.co.uk/friends/attachment.php?attachmentid=399&d=1184489318

It's the hexagram sequence 7 - 8 - 9 - 10 in the king Wen order, if odd numbers symbolize
whole lines and even numbers symbolize broken lines? Studying this archaeological found
might explain the rationale behind the king Wen order, because the hidden secret might
be related to the original numbers instead of the later line-symbols? E.g. try this puzzle:

The even numbered hexagrams are vertical while the odd numbered are horisontal ...
and hexagram 7 is to be read from left to right (reversed) while hexagram 9 is to be
read from rigth to left (as usual) ...

Maybe this way is how at least chapter one (hexagram 1 to 30) was originally structured:

>-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T

( <=top left / >=top right / T=vertical between Tops / B=vertical between Bottoms)

That'll say, that one half of the even numbered hexagrams are between the bottom of
two odd hexagrams, while the other half are between the top of two odd hexagrams.

A problem is to show what's top and bottom of a hexagram ... all four hexagrams in the
sequence include at least one number 6 /\ showing a direction ... the only problematic
hexagram seen from this point of view is hexagram 1

lienshan
 
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lienshan

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Continued:

The structure with digits of four hexagrams like the above 7-8-9-10 found
could match the following text in The Ten Wings:

Shou Kua chapter two:

Heaven and Earth establish positions
Mountain and Lake circulate their material force
Thunder and Wind give rise to each other
Water and Fire refuse to destroy each other
In this manner the eight trigrams alternate with each other,
so that to enumerate what has passed, one follows their progress,
and to know what will come, one moves backward through them.

Sentence 1 means Hexagram 01 and 02
Sentence 2 means Hexagram 31 and 41
Sentence 3 means Hexagram 32 and 42
Sentence 4 means Hexagram 63 and 64

01-02-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T

31-32-<-B->-T-<-B->-T

41-42-<-B->-T-<-B->-T-<-B->-T-<-B->-T-<-B->-T

63-64

( <=top left / >=top right / T=vertical between Tops / B=vertical between Bottoms)

lienshan

an addition:

There is in fact one more found exavacated the same place, a gill fungus like a pottery pat too,
a complete one of 10.5 centimeters long with the facet of the pat facing upward. On the handle
were inscribed two lines of six numbers:

<I<I<I (hexagram 63)
I<I<I< (hexagram 64)

Maybe important: both too contain the direction showing number 6
 
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lienshan

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Can anyone give me a little background on why we use the sequence we do
The traditional sequence of hexagram pairs is in two chapters of 15 and 17 pairs.

4 of the pairs (1/2, 27/28, 29/30 and 61/62) are made of 8 hexagrams that look alike
seen from both top and bottom. The other 56 hexagrams look different when reversed,
so only 28 "two-way" hexagrams are needed to display these 56 hexagrams.

The first chapter is made of 1/2, 27/28, 29/30 + 12 "two-ways" = 18 hexagrams
The second chapter is made of 61/62 + 16 "two-ways" = 18 hexagrams

I'm at the moment studying the traditional sequence in details and use an online blog
to write down my thoughts in english ... you are welcome to follow the development:

http://www.mandala.dk/view-post-comments.php4?blogID=591&postID=5813
 

fkegan

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Explanation of the King Wen Sequence of the I Ching from Pythagorean Tetraktys

The commentary in Wilhelm referring to the sequence is said to have been developed as a memory aid for students trying to memorize the hexagram names in order. Their teachers found that narrative useful for their rote memorization (I vaguely remember it may rhyme in Mandarin).

From the few hints in the Wilhelm about the Yi being arranged in sets of 10, I twigged that those sets of ten relate to the Pythagorean Tetraktys which is a philosophical insight offering total analysis of any subject matter through ten detailed perspectives. Eventually I taught myself all about that Pythagorean system by its connection to explaining the King Wen sequence.

Explaining it to us modern folks requires making a connection in terms of shared tangible examples. The first 10 hexagrams of the Yi describe the Water cycle--the concrete reality of how the overall living process of our life on Planet Earth is controlled by the energy of sunshine interacting with the topography of surface of the Earth to develop everything else we experience.

Hexagram One is the Monad or complete explanation of the set of 10 in a single simple unit. That in itself is a major new insight. Six Yang lines together can't really say much. The traditional Chinese name is Ch'ien and its ideogram is a drawing of rays of sunshine burning off swampy mist to form clouds to water the fields. That water also runs off the local topography into streams and rivers flowing to the sea. That is the entire water cycle in a nutshell or single name.

You may have trouble finding my work on the King Wen sequence as my name is Frank R. Kegan :bows: (not "Keegan" :eek: that spelling a fine Anglo-Irish name, but not mine).:rolleyes:
The hyper link to my work on the King Wen Sequence exactly as an expression of the tetraktys is: www.stars-n-dice.com/tetraktys.html . The whole site is about related insights with the total overview being the Stars and Dice Perspective button from the Home Page.

Lots of folks have noticed that the sequence is divided into two halves after hexagram 30; and set up as 32 pairs with each even number the opposite line values of the preceding odd numbered hexagram. This is the basic structural pattern like the rhyme pattern in a sonnet. The genius of the King Wen Sequence is that it is able to also fit its highly sophisticated philosophy into that overall matrix.

The first set of 10 is the complete explanation of the water cycle from the 4 philosophical perspectives of the Monad or one hexagram, the Dyad or polar opposites in two hexagrams, the Triad or narrative process of three hexagrams, and finally the Tetrad of the double dichotomy or perpendicular axes.

You can see this expressed just in the traditional nature images of the trigrams. There is no use of the trigram li or Fire since there is no fire in the Water Cycle.

It starts with all sunshine. This is the Monad.

The Dyad is hexagram 2 and 3, First the negative polar extreme or the Planet Earth topography, how the surface of the earth is carved to different depths to create mountains, plains, rivers and oceans which determine the workings of the water cycle.
Hexagram 3 is water over thunder or the positive pole, the energy of thunder is the active agent to cause spring rains to fall upon the fields and streams to start the active process of the water cycle.

The rest are:
The Triad 4,5,6--water seeping out of the base of the mountain, water over sunshine as water vapor not yet rain to fall upon the topography, water under sunshine--rain falling through the sunshine or below the sunshine so it lands on earth and not turned into virga and re-absorbed by the atmosphere.

And the Tetrad of 7,8,9.10 or water absorbed into the earth--to--water flowing along the topography of the earth and winds over sunshine yielding the weather systems that control the movement and intensity of clouds and rain---to the lake under sunshine or the final resting state of the water cycle which has flowed down to sea level and now sits under the suns rays waiting to evaporate and start the water cycle all over again.

The only other major sequence of the hexagrams is the ancient predecessor to the King Wen sequence which uses the hexagram line patterns as a binary counter from 0 to 64 or in a circle to mark out with those numbers a sine wave pattern--which is also the T'ai Chi or yin-yang pattern. That was the ancient Yi that used the simple binary math and sine wave trigonometry still used in Western computers and modern physics with the sad results of our current global crises.

There are also teaching sequences, such as the trigram houses where the task of memorizing 64 line patterns is broken down into 8 sets of trigram combinations--taking one trigram as fixed in each set and combining it to the eight other trigrams. Also the set of developmental patterns, the four hexagrams with the various possible lines in the 3rd and 4th place, then the 16 nuclears with each of those four having their four possible pairs in the 2nd and 5th place and then the full 64 organized in sets by those nuclear hexagrams.

You can establish your own sequence based upon whatever overall pattern feels most interesting or important to you. It is not the sequence that is so hard to imagine, it is coming up with an overall philosophical or personal matrix worthy of the task.

Good Luck,

Dr. Frank R. Kegan
 

sergio

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The traditional sequence of hexagram pairs is in two chapters of 15 and 17 pairs.

4 of the pairs (1/2, 27/28, 29/30 and 61/62) are made of 8 hexagrams that look alike
seen from both top and bottom. The other 56 hexagrams look different when reversed,
so only 28 "two-way" hexagrams are needed to display these 56 hexagrams.

HI Lienshan
maybe this link would interest and/or help you.Ithink is in your line of work:
http://iching.egoplex.com/king-wen-new-symmetry.html
SERGIO
 

fkegan

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Academic poetry and the King Wen Sequence

I remember my big sister years ago commenting upon the new use of computer analysis in the English lit field. Clearly doggerel poetry ( to those who read entire poems and compared them with other entire poems) were found by the computer to have amazingly sophisticated patterns of inconsistency in their meter and rhyme. That was back in the prior century, early in the process of computer use in academia. My sister's comment was that perhaps it made more sense to use such analysis on poetry by authors who were known to have consciously and intentionally have made their special tweaks to their poetry.

The traditional authors of prior millennia, including the one just passed had a fascination with complex rhyme schemes or other matrix rules such as the sets of pairs in the Ken Wen, not from any belief that alone was sufficient for anything; but rather as the blank page or sonnet pattern within which they were composing their magnum opus.

The philosophical question is what is the meaning of any particular hexagram which then is carried though in the rationale for the sequence of the hexagrams used to organize and display the set of those meanings. The rationale for a sequence comes from the meaning expected from the entire set--then individual hexagrams are aligned to follow that rubric.

If a hexagram is seen as a 6-place binary counter then the sequence is determined by the binary number line--or put into a circle the sequence counts out the T'ai Chi or sine wave pattern of the mathematical contemplation of natural events.

The question then becomes, are the King Wen hexagrams in pairs by line pattern from the meaning of the Sequence or just as flourish of poetic simplicity to show the ultimate mastery of the design? Most of the analysis based upon the trigram composition or number value of the sequence assume the Yi is organized still as a mathematical counter where the line values and not the hexagram meaning is most important.

However, consider the change from the binary counter view of the earlier sequence to be a development of philosophical meaning, not just a new mathematical number line. The overall rationale for the entire Sequence should be clearly demonstrated in the set of hexagrams in order, not requiring advanced computational analysis to reveal it.

Legge early in British I Ching interest, understood the ordering of the hexagrams was occult, which satisfied his curiosity on the subject. :brickwall:

Those for whom that conclusion is a beginning not an emphatic end point, then must look at the rules of occult meaning. The fundamental Law is that of the macrocosm/microcosm: As Above, So Below. Therefore, the symbol system must reflect the relationships and timing as established in natural systems such as the rising and setting of the Sun, stars, and planets (astrology), and the water cycle (tied to seasons determined by the Planet Earth orbit and inclination of the Globe from the vertical).

Traditional symbolic mapping is carried out through geometry and number theory generally integrated into cyclic patterns with sequence points. When the King Wen Sequence is arranged in a circle, with the core 60 hexagrams making up 360 lines (first and last pair put outside on perpendicular axes as Heaven and Earth and Rising and Setting) a functional correspondence is established with the astrological Zodiac and demonstrated in the correlation of individual line judgments with Sabian Symbols.

This shows the rationale of the Sequence is to be found, in terms intelligible to Westerners, in the philosophical symbolism of Pythagoras rather than the mathematics developed from algebra and computer analysis.

That Pythagorean symbolism is based in the Tetraktys, which defines total analysis in terms of 4 perspectives, the Monad or total unity or everything seen within one symbolic circle; the Dyad or a perspective of a single pair of polar opposites; the Triad or narrative of process with a beginning situation, a middle state, and a final result; and the Tetrad or the perspective of double dichotomy or analysis in terms of perpendicular axes.

I found that the I Ching hexagrams in the King Wen Sequence is the best detailed example of a complete Tetraktys analysis that remains available in general publication. Therefore looking at the sequence in terms of the Tetraktys is the best if not the only way to get beyond the surviving text fragments about it that refer to it only by the equation 1+2+3+4 =10 or conclusions that the Pythagoreans swore by it and thought it was the greatest thing until sliced bread.

This Tetraktys rationale of the ordering of the hexagrams does require accepting that the Chinese development is something none of us have learned anything about in our academic training and requires looking at the question with fresh eyes.

As the continuing climate crisis slowly forces it to dawn upon us we need new insights. Even in the cloisters of Academia, in the system set up in the 13th century to mimic their beliefs and their acceptance of the authority of Plato's Academy in their "academic " curriculum the light begins to dawn if only in the realization that the anomalies as you try to keep using those 700 year old dogmas are really proving those paradigms are not useful or interesting any more.

So, Sergio--Good News, the King Wen Sequence is mathematically perfect (Pythagorean math) and its rationale is clear, it just is terra incognito for those of us born in the prior millennium though it will be well learned by whoever survives these opening decades of this one. :)

Frank
 

lienshan

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Hi Sergio

Thanks for the link, but the King Wen order isn't a matter of mathemetics. As a diviner I think practically:

Only 18 flat sticks/slips with a hexagram written on both sides were needed to show all the 64 hexagrams:

The hexagram order of side one: 1-2-4-6-7-10-12-13-16-18-20-22-23-26-27-28-29-30

1-2 establish the position of Heaven and Earth
4-6-7 (3-5-8) connect Water with Mountain (Thunder), Heaven and Earth
10-12-13 (9-11-12) connect Heaven with Lake (Wind), Earth and Fire
16-20-23 (15-19-22) connect Earth with Thunder, Wind (Lake) and Mountain
18-22-26 (17-21-25) connect Mountain (Thunder) with Wind (Lake), Fire and Heaven
27-28 above show Mountain and Lake circulating their material force
27-28 below show Thunder and Wind arousing each other
29-30 show Water and Fire refusing to destroy each other

01 !!! !!! Heaven
02 ::: ::: Earth
03 :!: ::! 04 !:: :!: */Water
05 :!: !!! 06 !!! :!: */Water
08 :!: ::: 07 ::: :!: */Water (upside down)
09 !!: !!! 10 !!! :!! Heaven/*
11 ::: !!! 12 !!! ::: Heaven/*
14 !:! !!! 13 !!! !:! Heaven/* (upside down)
15 ::: !:: 16 ::! ::: */Earth
17 :!! ::! 18 !:: !!: Mountain/*
19 ::: :!! 20 !!: ::: */Earth
21 !:! ::! 22 !:: !:! Mountain/*
24 ::: ::! 23 !:: ::: */Earth (upside down)
25 !!! ::! 26 !:: !!! Mountain/*
27 !:: ::! Mountain/Thunder
28 :!! !!: Lake/Wind
29 :!: :!: Water
30 !:! !:! Fire

The shown above inner structure of the King Wen order of the first 30 hexagrams looks logic to me
and explains the use of an upside down hexagram in the earliest known example of the King Wen order:

I Ching hexagram sequence 7-8-9-10 with no 7 upside down has been found on an
3000 years old pottery-pat exavacated in 2002 (on another pat is inscribed 63-64)
Upside down hexagrams are known from the late-Shang-dynasty Sipanmo scapula with
the three hexagrams 12-34-64 of which the no 34 in the middle is inscribed upside down.
Another upside down example is hexagram no 60 on an early Chou bronzeware now in
the Ku-kung collection in Taiwan described by the I Ching expert Chang Cheng-lang.

lienshan (working on the side two of the 18 sticks/slips)

PS. The broken "yin" lines were originally symbolized by both the number six /\ and eight )( signs
and that's a problem to the theory of Dr. Frank R. Kegan, because there is no emty space in a /\
 
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fkegan

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the King Wen order isn't a matter of mathematics.

PS. The broken "yin" lines were originally symbolized by both the number six /\ and eight )( signs
and that's a problem to the theory of Dr. Frank R. Kegan, because there is no emty space in a /\
It isn't that Yin symbolized by even numbers like 6 or 8 have an open space in their numeral in any language--it is that the hexagram matrix is an open framework, in which an oracle forms in the open space between the broken lines in the overall symbolic matrix. It is an alternative perspective which rejects the notion of independent Yin lines at all. Or the notion that ancient tombs or Chinese ideograms hold the final word on anything in the I Ching. [ cf. www.stars-n-dice.com/fluxtome.html ]

I would suggest that any and every perspective can find its place in the King Wen Sequence--that is a standard feature of all such systems. The problems finding mathematical or computer analysis answers in the Sequence is an expression of the lack of real world basis to those mathematical and computer techniques.

However, it is not the numerals in ancient Chinese that are essential, as you say the order is not a matter of mathematics. I would suggest it is a matter of philosophy in general and the Tetraktys in particular which transcend all these details.


Frank
 

dobro p

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The King Wen sequence? Somebody just made it up. Maybe his name was Wen. There's no logic to it. If there was a pattern, a million people would have seen it by now. But it's not like that. Somebody just played mind association football with it and standardized the order, which we now foolishly call a 'sequence'. Of course, this is just opinion.

Carry on.
 
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lienshan

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However, it is not the numerals in ancient Chinese that are essential, as you say the order is not a matter of mathematics. I would suggest it is a matter of philosophy in general ...
I agreed with Dobro until a year ago, when Sparhawk and Harmen posted new information and pictures of hexagrams with lines of numerals on this forum. Now I'm sure, that the structure of the King Wen order is logic ... and as you explain "a matter of philosophy in general".

E.G. The second 4-6-7 (3-5-8) part of the sequence, where trigram Water is connected with Mountain/Thunder, Heaven and Earth. Water, Mountain and Thunder have in common, that they only have one whole line. The third 10-12-13 (9-11-14) part of the sequence connect trigram Heaven with Lake/Wind, Earth and Fire. Lake, Wind and Fire have in common, that they have two whole lines.

This look logic to me as an visual explanation of how the trigrams alternate with each other, but in another way than the two wellknown trigram orders! This third and oldest trigram order is shown in the 43-45-47-49 (44-46-48-50) part of the sequence, where trigram Lake/Wind is connected with Heaven, Earth, Water, Fire ... while Water and Fire shift places in the 33-35-37-39 (34-36-38-40) part of the sequence ... and in front of both sequences is a combination of either Mountain/Lake or Thunder/Wind

31 :!! !:: Lake/Mountain
33 !!! !:: Heaven/*
35 !:! ::: */Earth
37 !!: !:! */Fire
39 :!: !:: Water/*
41 !:: :!! Mountain/Lake
43 :!! !!! Lake/Heaven
45 :!! ::: Lake/Earth
47 :!! :!: Lake/Water
49 :!! !:! Lake/Fire

32 ::! !!: Thunder/Wind
34 ::! !!! */Heaven
36 ::: !:! Earth/*
38 !:! :!! Fire/*
40 ::! :!: */Water
42 !!: ::! Wind/Thunder
44 !!! !!: Heaven/Wind
46 ::: !!: Earth/Wind
48 :!: !!: Water/Wind
50 !:! !!: Fire/Wind

The second part of the King Wen order is otherwise structured than the first; like Shuo Kua:

Heaven and Earth establish positions
Mountain and Lake circulate their material force
Thunder and Wind give rise to each other
Water and Fire refuse to destroy each other

lienshan
 

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