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the baoti trigrams of the King Wen sequence

Is the King Wen hexagram sequence random?

  • yes

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  • no

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  • maybe

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  • Total voters
    5
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lienshan

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The baoti trigrams of a hexagram pair consist of:

line 3-4-5 of the first hexagram and line 2-3-4 of the second hexagram
line 2-3-4 of the first hexagram and line 3-4-5 of the second hexagram

the upper of the two baoti trigrams captures the baoti trigram below, if they are different!

X both baoti trigrams can capture each other
= the baoti trigrams can't capture each other
> the first upper baoti trigram can capture the second below baoti trigram
< the second upper baoti trigram can capture the first below baoti trigram

King Wen pairs ~~~~~ the baoti trigrams

01 !!! !!! 02 ::: ::: ~~~ !!! ::: X ::: !!! ~~~ (more)(less)
03 :!: ::! 04 !:: :!: ~~~ !:: ::! > ::: ::: ~~~ (less)
05 :!: !!! 06 !!! :!: ~~~ !!: :!! < !:! !:! ~~~ (more)
07 ::: :!: 08 :!: ::: ~~~ !:: ::! < ::: ::: ~~~ (less)
09 !!: !!! 10 !!! :!! ~~~ !!: :!! < !:! !:! ~~~ (more)
11 ::: !!! 12 !!! ::: ~~~ ::! !:: X !!: :!! ~~~ (less)
13 !!! !:! 14 !:! !!! ~~~ :!! !!: < !!! !!! ~~~ (more)
15 ::: !:: 16 ::! ::: ~~~ ::! !:: > :!: :!: ~~~ (less)
17 :!! ::! 18 !:: !!: ~~~ !!: :!! X ::! !:: ~~~ (more)
19 ::: :!! 20 !!: ::: ~~~ !:: ::! < ::: ::: ~~~ (less)
21 !:! ::! 22 !:: !:! ~~~ ::! !:: < :!: :!: ~~~ (more)
23 !:: ::: 24 ::: ::! ~~~ ::: ::: = ::: ::: ~~~ (less)
25 !!! ::! 26 !:: !!! ~~~ !!: :!! X ::! !:: ~~~ (more)
27 !:: ::! 28 :!! !!: ~~~ ::: !!! X !!! ::: ~~~ (less)(more)
29 :!: :!: 30 !:! !:! ~~~ !:: !!: X :!! ::! ~~~ (less)(more)

31 :!! !:: 32 ::! !!: ~~~ :!! !!: < !!! !!! ~~~ (less)
33 !!! !:: 34 ::! !!! ~~~ :!! !!: < !!! !!! ~~~ (more)
35 !:! ::: 36 ::: !:! ~~~ ::! !:: < :!: :!: ~~~ (less)
37 !!: !:! 38 !:! :!! ~~~ !:! !:! = :!: :!: ~~~ (more)
39 :!: !:: 40 ::! :!: ~~~ !:! !:! = :!: :!: ~~~ (less)
41 !:: :!! 42 !!: ::! ~~~ !:: ::! < ::: ::: ~~~ (more)
43 :!! !!! 44 !!! !!: ~~~ !!! !!! = !!! !!! ~~~ (more)
45 :!! ::: 46 ::: !!: ~~~ !!: :!! X ::! !:: ~~~ (less)
47 :!! :!: 48 :!: !!: ~~~ !!: :!! > !:! !:! ~~~ (less)
49 :!! !:! 50 !:! !!: ~~~ :!! !!: < !!! !!! ~~~ (more)
51 ::! ::! 52 !:: !:: ~~~ ::! !:: < :!: :!: ~~~ (less)
53 !!: !:: 54 ::! :!! ~~~ !:! !:! = :!: :!: ~~~ (more)
55 ::! !:! 56 !:! !:: ~~~ :!! !!: X :!! !!: ~~~ (less)
57 !!: !!: 58 :!! :!! ~~~ !!: :!! < !:! !:! ~~~ (more)
59 !!: :!: 60 :!: :!! ~~~ !:: ::! X !:: ::! ~~~ (less)
61 !!: :!! 62 ::! !:: ~~~ !:: !!: X :!! ::! ~~~ (more)(less)
63 :!: !:! 64 !:! :!: ~~~ !:! !:! = :!: :!: ~~~ (more)

The baoti trigrams are used to deside which hexagram to be first in the pairs of the King Wen sequence.
I've shown in another tread, how the King Wen sequence of pairs is made of "less" and "more" yanglines.
The "less" and "more" pattern has two exceptions: 1-2 and 43/44 - 45/46. The first is the hexagram of
only yang-lines (1) and the second are the baoti trigrams of only yang-lines, which King Wen placed first.

lienshan :bows:
 
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lienshan

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The baoti trigrams are extreme useful when exploring the King Wen sequence of the hexagram pairs.
16 of the pairs are complementary vertically read (13-07, 14-08, 31-41, 32-42, etc.), when the orders
of three hexagram pairs (03-04, 15-16, 47-48) are reversed:

:!! !!: < !!! !!! 13-14 31-32 33-34 49-50
!:: ::! < ::: ::: 07-08 41-42 19-20 04-03
!!: :!! < !:! !:! 05-06 57-58 48-47 09-10
::! !:: < :!: :!: 35-36 51-52 21-22 16-15

The next group of baoti trigrams looks uneven distributed:

::: ::: = ::: ::: 23-24
!!! !!! = !!! !!! 43-44
!:! !:! = :!: :!: 37-38 39-40 53-54 63-64

Either 37-38 or 39-40 and either 53-54 or 63-64 must be reversed to create complementary vertically read hexagram pairs; an example of the four possibilities:

::: ::: = ::: ::: 23-24
!!! !!! = !!! !!! 43-44
!:! !:! = :!: :!: 37-38 53-54
:!: :!: = !:! !:! 40-39 64-63

The last group of baoti trigrams too looks uneven distributed:

!!: :!! X ::! !:: 17-18 25-26 45-46 12-11
!:: !!: X :!! ::! 29-30 61-62
::: !!! X !!! ::: 27-28 02-01
:!! !!: X :!! !!: 55-56
!:: ::! X !:: ::! 59-60

My theory is, that King Wen made his sequence from an already existing sequence of hexagram pairs
that vertically read were complementary. If it's possible to identify the pairs, that he reversed, then
it's a great help, when translating his statesments. An example: Tuck is interpreting the hexagrams
11 Tay and 12 Pi ... and it looks like King Wen by purpose reversed the order of the two hexagrams!

lienshan :bows:
 

sergio

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The baoti trigrams of a hexagram pair consist of:

line 3-4-5 of the first hexagram and line 2-3-4 of the second hexagram
line 2-3-4 of the first hexagram and line 3-4-5 of the second hexagram
Hi Lienshan;
In page 14 of his book Nielsen says:"BAO TI:The contained or containing trigrams.The three outer lines(no.1,2 and 6 or nos.2,5 and 6)of a hexagram constitute a trigram which contains another trigram made up of the inner lines(nos.3,4,5 or nos.2,3,and4)..." This clearly defines them as been created from the outer lines of a hexagram thus containing another trigram.Had it been formed from the inner lines(2,3,4 and 5)as you wrongly suggest would obviously make them Hu Ti or, to us westerners nuclear hexagrams(interlocking hexagrams in Nielsen's translation).

Sergio
 

lienshan

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hi Sergio ... my source is this explanation and the beautiful hexagram-drawings by Mr. sparhawk:

http://www.onlineclarity.co.uk/friends/showthread.php?t=4122

The king Wen hexagram sequence pair hexagram 60 ( :I::II ) and hexagram 59 ( II::I: ). What I talk
about are the black trigrams, the contained trigrams. The complementary hexagram pair are the
hexagrams 55 ( ::II:I ) and 56 ( I:II:: ). It's obvious that one of the pairs has been reversed, because
the first hexagram of each pair aren't complementary, in this case the drawings by Mr. sparhawk.

That's my pointe. The pre King Wen hexagram sequence looked almost like this Mr Mair lay out:

http://www.appositive.net/oysterbay/iching/kingwen.pdf

but with these hexagrams reversed: 1-2, 3-4, 11-12, 15-16, 25-26, 39-40, 47-48, 63-64
and with the pair 43-44 placed ahead of the pair 45-46 ... explained here on my blog:

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

Should we name the two line trigrams 5-4-3/4-3-2 and 4-3-2/5-4-3 ... Hu Ti (nuclear trigrams)?
I think that it might be confusing, because Hu Ti (nuclear trigrams) use to describe two trigrams
in one hexagram ... while the trigrams we are discussing are one trigram from two hexagrams.

lienshan
 

solun

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There are many available manipulations of the hexagram patterns. One is by Shao Yong - the square diagram - though i am not sure what the relevance of this diagram is. I suppose it's some poetic mathematical representation of how nature would distribute the grams. If this type of work brings you benefit in your understanding, then good. It does bring some pleasure and reassurance to playful minds, or doubtful ones looking for further proof, etc. But I see these as you refer to lienshan as nuclear hexagrams. Maybe King Wen is the source of this notion.
 

sergio

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Hi Lienshan;
Yes i understand what you are doing but my contention was as to the denomination of this procedure as Bao Ti.In Mr.Sparhaw's diagram the red lines are the Bao Ti,i.e the containing trigram and the other,inner lines are the contained trigram-the first one is exercising the action over the other trigram.
As for your speculations I agree with you-what do we call them?Of course not Hu Ti as that would be referring to the inner trigrams but that is your baby so you name it...These are interesting structural issues you are raising-not so sure where they lead to,though but I'll keep reading your following posts.
I truly advise and humbly suggest you buy Bent Nielsen's book-you will find tons of ideas to explore.Although is a little bit pricey it's well worth its value.
Sergio
 

boyler

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Hi there,

Speaking of baoti, and Nielsen's book, p. 15. table 1. Isn't there some mistakes in the table, or I did not got it quite right?

It says, zhen contains gen in Bi (#08) and in Zhen (#51) (column 4) ... shouldn't it be Tun (#3) instead of Bi (#08)?

It says, zhen contains li in Ji Ji (#63) and in Wei Ji (#64) (column 5) ... shouldn't it be Gui Mei (#54) instead of Wei Ji (#64)?

also, in the lower part of the table

It says qian contains zhen in Xiao Xu (#09) and in Zhong Fu (#61) (column 2) ... shouldn't it be Da Chu (#26) instead of Xiao Xu (#09)?

and

It says xun contains zhen in Lin (#19) and in Huan (#59) (column 7) ... shouldn't it be Gu (#18) instead of Lin (#19)?

Thank you

--
robert matusan - boyler
 

sparhawk

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Hi Robert,

Yes, I agree. I noticed that too when I first read it. It is an editing oversight by the editor or Bent. There some others in the book. The concept is easy to grasp though and a good table can be constructed easily. As I said in the other thread, I think it could be used in interpretation. I also like Harmen's comments in this regard.
 

sparhawk

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BTW, I like all this formality and "Mr. Sparhawk," etc. From now on though, I'll accept nothing short of "Sparhawk Zi," the sage from the wilderness of South Jersey. :D
 

sergio

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No problem Mr.Spockhawk-glad you like it Mr.Spockhawk Tze.
Tzer Chi O
 

boyler

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Yes, I agree. I noticed that too when I first read it. It is an editing oversight by the editor or Bent. There some others in the book. The concept is easy to grasp though and a good table can be constructed easily.
Good. I am relieved. It seems I got it right. Thank you.

As I said in the other thread, I think it could be used in interpretation.
Yes, it probably could.

I also like Harmen's comments in this regard.
I appreciate his work, but there are few things I respectfully disagree with him, and as it happens to be, his interpretation of the baoti is one of this things.

He said in another thread,
The captured trigram cannot express his qualities because of the oppressive/protective nature of the capturing trigram.
Although, in my studies, I did not meet with a text that uses the interpretation of the baoti yet, nevertheless, I learned that trigram which "cannot express his qualities", is usually overturned or hidden, and this is not a case of baoti.

--
robert matusan - boyler
 

sparhawk

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I appreciate his work, but there are few things I respectfully disagree with him, and as it happens to be, his interpretation of the baoti is one of this things.
I would say that the keywords there were "his interpretation."

Although, in my studies, I did not meet with a text that uses the interpretation of the baoti yet, nevertheless, I learned that trigram which "cannot express his qualities", is usually overturned or hidden, and this is not a case of baoti.
If you are referring to Western works, me neither. OTOH, it is a fairly obscure concept and a fairly new one at that (12th century). Not enough exegesis exist about it or its practical use.

Please, elaborate further about your understanding of "overturned or hidden" trigrams.
 

lienshan

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As for your speculations I agree with you-what do we call them?Of course not Hu Ti as that would be referring to the inner trigrams but that is your baby so you name it...
Luis Ti ... :D
 

boyler

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Hi Luis,

I would say that the keywords there were "his interpretation."
Of course.

If you are referring to Western works, me neither. OTOH, it is a fairly obscure concept and a fairly new one at that (12th century). Not enough exegesis exist about it or its practical use.
If it's really all about containing and contained trigrams, I think it would be relatively easy to evaluate it, and prove it or disapprove its usefulness in the interpretation, from the standpoint of the school of images and numbers. Unfortunately, at the moment I have no much time to play with it.

Please, elaborate further about your understanding of "overturned or hidden" trigrams.
It's not my understanding, but understanding of Shang Binghe 尚秉和 (1870-1950). Namely, I am trying to translate his Jiao Shi Yi Lin Zhu 焦氏易林主, (see Harmen's Yi Lin translation project forum) and there, among the other things, he uses overturned (fangua 反卦 or fugua 覆卦) and hidden trigrams (fugua 伏卦) to explain the wording of the poems from Yi Lin 易林. No doubt the same concepts could be used for explanation of the wording of the Yi Jing proper, but as I said above, at the moment I have no much time to try to do that on my own.

As for examples of overturned and hidden trigrams used as trigrams which "cannot express his qualities", below are translations of the two poems from Yi Lin, together with commentaries by Master Shang 尚氏 which demonstrate how he uses them.


Example #1:

01-06

Dragon-horse is up in the mountain,
Which is without any spring of water.
Its throat is dry, its lips are cracked,
And its tongue is unable to speak.

[Qian symbolize dragon-horse, as well as mountain, and it is situated above, kan is situated below and center symbolize fire and sun, hence, “spring of water is exhausted”. Dui symbolize throat and tongue, as well as lips, but dui is overturned and next to fire, hence, “dry”, “thirsty”, and “unable to speak”.]

(Boyler's note: Above is an example of overturned dui (lines 3, 4, and 5), which "cannot express its qualities" because it is overturned. See gua Song (#06). Besides above mentioned images of dui, it also symbolize marsh, that is, water, but because it is here overturned there is no water so it causes thirst, etc.)


Example #2:

01-11

There is no wind and there is no rain,
Just clear and bright white sun.
It is suitable to go out and hurry up,
As all have benefit from the Great Dao.

[Xun is hidden, hence, “no wind”, and there is only a half of trigram kan, hence, “no rain”. Zhen symbolize white color, qian symbolize sun, and zhen also symbolize exiting, hurry, great way, and benefit for all.]

(Boyler's note: Above is an example of hidden xun, which "cannot express its qualities" because it is hidden, and an example of a half of trigram or semi-trigram (banti 半體) kan, which "cannot express its qualities" because there is only half of it, that is, it is incomplete. See gua Tai (#11). Xun symbolize wind, but here xun is hidden (lines 3,4, and 5), therefore, "no wind". BTW, there is also overturned xun (lines 2, 3, and 4). Kan symbolize rain, but there is only a half of kan (lines 3 and 4), therefore, "no rain".)

Hope that above two examples of use of overturned, hidden, and half trigrams, by Master Shang, show how they are used in the interpretation of the words of the text (in this two cases, the text of the poems from the Yi Lin) which belong to a hexagram. Contained trigrams are not overturned, hidden, or halved, so IMHO they should retain their attributes, which are to be expressed inside the containing trigram.

(NOTE: Any emendation and criticism of the translation, as well as any comment about the translation are most welcome. Thank you.)

--
robert matusan - boyler
 

frank_r

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The baoti trigrams of a hexagram pair consist of:

line 3-4-5 of the first hexagram and line 2-3-4 of the second hexagram
line 2-3-4 of the first hexagram and line 3-4-5 of the second hexagram

the upper of the two baoti trigrams captures the baoti trigram below, if they are different!

X both baoti trigrams can capture each other
= the baoti trigrams can't capture each other
> the first upper baoti trigram can capture the second below baoti trigram
< the second upper baoti trigram can capture the first below baoti trigram
You are writing that the baoti trigrams can't capture each other. Why not? Is somebody writing that this is not possible? I liked the examples that Harmen mentioned. Found the ones that were captured by themselves the most interesting ones. Harder to understand but that was the more challenging I thought.
 

sparhawk

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Hi Robert,

It's not my understanding, but understanding of Shang Binghe 尚秉和 (1870-1950). Namely, I am trying to translate his Jiao Shi Yi Lin Zhu 焦氏易林主, (see Harmen's Yi Lin translation project forum) and there, among the other things, he uses overturned (fangua 反卦 or fugua 覆卦) and hidden trigrams (fugua 伏卦) to explain the wording of the poems from Yi Lin 易林. No doubt the same concepts could be used for explanation of the wording of the Yi Jing proper, but as I said above, at the moment I have no much time to try to do that on my own.

As for examples of overturned and hidden trigrams used as trigrams which "cannot express his qualities", below are translations of the two poems from Yi Lin, together with commentaries by Master Shang 尚氏 which demonstrate how he uses them.
Ah, yes, the Jiao Shi Yi Lin, the 800 pound gorilla in the room. Thanks for sharing Master Shang's ideas on the overturned and hidden trigrams (was him part of the Nanking Group together with Gao Heng?). It occurs to me though that the use of those are more for the interpretation of the JSYL verses, from a philological POV, than for the received text of the Yijing, no? In any case, they bring a very interesting way to picture and disecting the hexagrams.

Sigh, I wish I had the time to sink my teeth into the JSYL translation... Well done, Robert.
 

lienshan

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I've corrected my blog to include both containing and contained trigrams of the King Wen sequence:

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

Put in short: The seven pairs 1-2, 3-4, 15-16, 25-26, 39-40, 47-48, 53-54 has been reversed.

The pairs 1-2, 3-4, 25-26, 39-40, 53-54 are unsymmetric viewed both containing and contained.
The pairs 15-16, 47-48 are only unsymmetric viewed contained.

That the pair 1-2 has been reversed is legendary. The pattern of containing and contained trigrams
confirms, that the first hexagram of the pre-Zhouyi oracle was the second hexagram Earth. Another
indication is the pattern of less and more yanglines. Earth before Heaven leaves only one exception,
that the pair 43-44 is placed before the pair 45-46. Why? They are part of the Lake-sequence, that
was created by reversing the pair 47-48 ... maybe the purpose was to underline the trigram order:

pair 43-44: Lake - HEAVEN (HEAVEN - Wind)
pair 45-46: Lake - EARTH (EARTH - Wind)
pair 47-48: Lake - WATER (WATER - Wind)
pair 49-50: Lake - FIRE (FIRE - Wind)

lienshan :stir:
 
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boyler

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Ah, yes, the Jiao Shi Yi Lin, the 800 pound gorilla in the room.
:)

Thanks for sharing Master Shang's ideas on the overturned and hidden trigrams (was him part of the Nanking Group together with Gao Heng?).
No.

It occurs to me though that the use of those are more for the interpretation of the JSYL verses, from a philological POV, than for the received text of the Yijing, no?
No. As you know the received YJ also uses texts of the Great and Small images for the explanation of its hexagrams, trigrams, and lines, which are based on their attributes from the Shuo Gua (or rather vice versa). It's just that some different images are "chosen", and more attention is paid on individual lines and their position in a hexagram, because one of most important part of YJ are line texts.

Master Shang, in his JSYLZ tried to prove that YL also used the same trigram and hexagram attributes as the YJ, and from the same source, but since it has only one text for each of 4096 hexagram changes, which incorporates in itself situations from when no line changes, single line changing, multiple line changing, up to the all line changing, it pays less attention on the individual lines, and their positions, and rather focus on the hexagram as whole, with all its mutations, but it's totally in accordance with xiangshu tradition, and although it is an independent work, it could be considered an extension of, or addition to YJ itself, just from another historical period.

Personally, I find it very useful, especially in multiple changing lines situations, which sometimes could be confusing, especially for beginners.

The variety and richness of images of the trigrams and hexagrams, and their various combinations and interactions enable us to construct and/or reconstruct almost infinite(?) number of situations under the Heaven.

In any case, they bring a very interesting way to picture and disecting the hexagrams.
Yes, one can learn much this way.

Sigh, I wish I had the time to sink my teeth into the JSYL translation...
Well, I will need some good proofreaders for my translation :eek:

--
robert matusan - boyler
 

erime

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I have proposed a rational method for obtaining the Early Heaven and Later Heaven Sequence of trigrams based upon the ancient Chinese art of astronomy using a 9 sector circular diagram (8 'portions' and a central sector). I posted a thread going in to the detail surrounding such a mechanism on this forum HERE. See what you think. There is a detailed discussion about it's cultural context after the method is explained.
 

sparhawk

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Hi Erime,

Please tell us more about you and your journey with the Yijing. I'd like to know more about the person. I saw you thread with your theories before but preferred not to participate on it. Trigram and hexagram sequences tend to be a touchy subject for some here...

Have you seen the work of Richard S. Cook on the KWS? How about the work of Schuyler Cammann on trigram sequences?

Cheers,
 

erime

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Hi Sparhawk, maybe a better introduction is in needed. I don't do I-Ching divination, and I have no beliefs which one could call 'superstitious'. I am more of a Zen Buddhist than a Taoist, and yet the Tao comes in to Zen very much it seems. My deepest interest in the I-Ching comes from internal martial arts, Bagua Zhang (or Pakua Chang), where in some disciplines one is taught to move through the 64 hexagrams in sequence. This physical manifestation of the hexagrams - a channelling if one likes - I see as an everyday biological expression more than a mystical power. I do not practice the art, but am a dynamic qigong enthusiast. The trigrams and the I-Ching have been incorporated in to many Chinese martial arts systems, but the only definitively Taoist art - Bagua Zhang (famous for it's circle-walking meditative methods) is the one which seems to delve in to the I-Ching the most.

My thread on the King Wen Sequence construction is a bit lengthy and requires a bit of study from the person reading it, so I wasn't expecting much of a response actually. Yes, it does seem that the I-ching has a very personal relevance in people's lives, judging from some of the responses on the forum. For me it is something that links everyone together via a common 'nature'.

I have investigated Richard Cook's work, although I do not have his book, and it seems a bit 'specialist', while Schuyler Cammann I am less familiar with as I can not access his articles online, and no one appears to be able to put his ideas across properly. I came to the forum prompted by Michael Erlewine's thread on origin of Early and Later trigram arrangements. I will go back there and post a more accessible and hopefully tempting summary of what I have discovered.

I see no reason to 'publish' my theory, as I seek no academic acclaim or reward, other than being treated with an open mind and the reader summoning enough enthusiasm to go through the steps necessary. Frank_r has begun, but it seems he is too busy to go the whole way. My theory has no complicated maths or strange sequences of steps (as far as I am aware), it appears to be a logical interaction between the way ancient Chinese astrologers viewed and mapped the heavens, calibrated to the yin/yang properties of the numbers in the Lo Shu 3x Magic Square. As I said, anyone can discuss the simple side to my theory on Michael Erlewine's orginal thread here.
 
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