Nuclear / Mutual Hexagrams

[surnevs]

"Second idea: So, when people derive meaning from examining nuclear hexagrams, it's more a way of jogging the mind rather than anything built into the Yi. Whatcha think?"
Seeing this puzzling around with the hexagrams as my hobby - it's exciting, and moreover now and then finding some of the ideas already written down hundreds or even thousands of years ago realising not to be that astray...
But so far also I haven't found "...anything regular and convincing. "
Here and there I've met the claim that Everything is encompassed in the I Ching, meaning that the 64 hexagrams are a final System: The system, no less nor more than exactly these 64 patterns. The right and undisputable sequence is broadly accepted to be that of king Wen.
When I "play around" with the sequence of the hexagrams mainly following Shao Yung's Idea that there is a connection between the Order and the Seasons and Time cycles I think - to be honest - it's like a hobby and I lay forth here all the possibilities that I stumble across... Maybe someone around here got insights that I miss, maybe? Explore, explore, could my attitude be called. Or rather: should our attitude be called...

 

[my_key]

My suspicions are that back in the early days and shamanic ways of I Ching there was a great deal of inspirational or intuitive influence. Even the great King Wen himself was more than likely graced with insightful experiences that brought about the current alignment of the hexagrams.

Now here we are thousands of years later and us mere mortals are doing what we do best which is striving to assign meaning to our experiences and the events of the world in and around us. I recently watched a You Tube video connecting Van Gogh's "Starry Night" painting to the mathematics of Turbulence theory which was being linked to the patterns of the strokes and the relative fluorescence of the paint pigments he used in different strokes. The presenter made a good case for proof of this piece of meaning, however I don't believe for a minute that Van Gogh had the slightest conscious awareness of any of this. He just looked out of the window of his asylum cell and followed his intuitive, creative urges to slap some paint on a piece of canvas to mimic the image of the starry night he saw.

There is much wonder to be had in taking in the beauty of a Starry Night just as there is marvelling at the beauty of the I Ching. Perhaps just seeing the beauty in the self perpetuating 1,2, 63, 64 pattern is enough for one life-time. Just as in the Mobius Strip and in any well intentioned Shamanic ritual there is always an unexpected twist to contend with. This is what gently leads us towards the next step, so perhaps there is not going to be any 'regular and convincing' connection at all in this dimensional reality.

All that being said, I too like to delve into the patterns. There is a great satisfaction, for me, in discovering a partial or unfinished / inconclusive pattern. Each dead end brings it's own sense of meaning and a new layer of beauty.

 

[dobro p]

My suspicions are that back in the early days and shamanic ways of I Ching there was a great deal of inspirational or intuitive influence.

^^ This.

A great deal of inspirational/intuitive influence = a gift from the unconscious (or the gods, depending on your worldview). Received more than crafted, in other words. To have aligned hexagram/line meanings consistently and according to nuclear hexagram groups would have been so left brain it would have been contrary to the spirit of the oracle. It's not supposed to be logical. It's supposed to be pigs and fishes.

But yes, I got out my pen and paper and spent a lot of time working out groups and families of hexagrams according to their nuclear hexagrams, and then searching for thematic connections in the text that corresponded. Sometimes I thought I spotted something, but it wasn't consistent. I concluded that if it's there, it's deeper than my understanding. That's why I wondered about it here. It's so useful to be able to compare notes with others.

 

[surnevs]

I think it's amazing, too. And significant - I think that the person(s) who put 63 and 64 at the end knew that. But when I looked at other hexagrams in terms of a relation between their meaning and their nuclear line structure, ........

If I'd understood this right actually Alfred Huang, in his book The numerology of the I Ching, works with the core/mutual hexagrams in relation to their meaning. (I've had it on my shelf for years and it can be recommended like his other books)

 

[dobro p]

In the introduction to his version of the I Ching (which I really like), Huang recommends examining the nuclear hexagram, but doesn't go into why. The book you mention goes into that, apparently. Good. Thanks.

 

[surnevs]

I have attached a scanning from the book where he partly explains the importance of nuclear hexagrams.

 

[dobro p]

Thanks for that. I've got a lot of respect for Huang, so I'll check it out. I see various possibilities regarding nuclear hexagrams, but the mains ones are:

* Despite what's said about Confucius and the ancient sages, they actually didn't consider the nuclear hexagram. This is likely, I think. Why? They provided commentaries on the hexagrams, lines and the Image. Why not on the nuclear hexagram?

* Confucius and the sages used nuclear hexagrams, but secretly, without passing on their knowledge. Unlikely, I think.

* Consideration of nuclear hexagrams wasn't formalised with Confucius and the sages, but it's useful and legitimate for us, and we can formalise it, ie generate the commentary. For instance, nuclear Hex 2 in the context of Hex 24 is different than nuclear Hex 2 in the context of Hex 27, so the meaning and the commentary for each would be different. I'm good with this, but the process would be messy, involving a lot of disagreement and competing versions.

* Consideration of nuclear hexagrams wasn't formalised with Confucius and the sages, but it's useful and legitimate for us, but we don't have to formalise it - you simply consider the nuclear hexagram in relation to and in the context of the main hexagram (and in relation to any relating hexagram, probably). I'm good with this, because I like the DIY approach half of the time.

 

[surnevs]

Concerning the question "When?", Richard Rutt mentions that : "The discovery and use of nuclear trigrams are variously attributed to Fei Zhi (50 BC - AD 10) and Jing Fang (77 - 37 BC). There is no suggestion that they were recognized earlier. " [Quote from Zhouyi, the book of changes, a new translation with commentary by Richard Rutt; Part I, The contents of Zhouyi, 'constituent trigrams' p. 97; the 2007 Ed.]
So here we are given two names in case we want to follow that track further ie. Fei Zhi and Jing Fang.
(My time at the moment isn't for following this part of it)

 

[surnevs]

The unfilledin Core-of-the-Core Diagram:

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Following the Guidelines mentioned in posting #55

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[dobro p]

I love your arrangement of hexagrams according to nuclear patterns - it's a mandala.

 

[surnevs]

Thank you. There are though still unlogic parts of it, for example, E 6 and 8, should they be interchanged? Same with L 8 and 6. Following the same Guidelines as above (#55 it's a good idea to right-click the mouse and choose 'Open in new Window' ...)
But as it looks here, without any numberings or letters it occurs rather like a Mandala than a Diagram, agreed.

 

[surnevs]

oooooOOO00000



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[my_key]

The reflections and the twists show up well in these images.

 

[surnevs]

Something, we can use even if this something doesn't fit anything, then it can be used to be excluded from the possible patterns / Logic that we are searching for. Nothing we can't use.
That the four main sectors, representing the 'core of the core' of the hexagrams can't be mingled together / Interchanged, is obvious as this Diagram represents this pattern.
I find it also logical to follow the waxing and waning of the balance between Yin and Yang lines ie from no yang lines over 1,2,3,4,5 to no yin lines (#55 from L clockwise to E and from E onward to L )
But whether it, inside this schedule, shall follow the sequence of the trigrams - The earlier or later Heaven arrangement - as lower trigram coming, upper trigram going (See hex. 11 and 12, the Judgement were king Wen almost implicit states this relation between lower and upper trigrams) I'm not sure. Just need to visualize the different possibilities for being able to see...

I must also lead the attention toward that I have made adjustments since the Diagram shown in post #53. Further adjustments may or may not show up if necessary but until now I've reached the one shown on #55. (To example the arrangement shown on #21 and 22 where Symmetry can be found, explained in these postings, could be closer to Logic; this arrangement doesn't follow a line regarding Lower/Upper trigrams. )

 

[surnevs]

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[surnevs]

I have attached the Core of the Core Diagram in four versions, 0: Without any numberings, A: With the king Wen numberings, B: With the Category I-VII added (I=0 yang lines to VII=0 yin lines) and C: With the twelve sequence letters added. Each of them is 36,13 x 36,13 centimeter or 14,22 x 14,22 Inch
I think I'm close to the arrangement of the hexagrams according to the system here...

Out of the next three Diagrams, it can be seen that there is a pattern when marking up the Inverse hexagrams. Nearly all of the hexagrams are in an inverse relationship diagonally, except for some:

Illustration A
Here the hexagrams without exceptions are following this pattern concerning the hexagrams in the middle Section.





Illustration B
The hexagrams in the outer section are likewise inverse diagonally except for those with blue and green arrows marked.





Illustration C.
The same question arise as with illustration B.
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But if those hexagrams marked in blue and green are going to be interchanged the principle with the sequence following the Early heaven trigram order (or Fu Hsi order), lower trigrams as coming, upper trigrams going (see #55 on ***) will have to be skipped.

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[surnevs]

Here is the arrangement that places all of the hexagrams in the outer circle diagonally opposite / inverse and the same for the middle circle. I will really appreciate reactions in case there are errors, hexagram numberings or hexagrams not following the core of the core scheme.

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[Add.: The red marked are those pairs that have been interchanged, and the blue marked diagonally are the pairs untouched.
Compare with the diagram on #76. Whether this adjustment is the right choice.... ? or not I hope either by myself or with a little help to clarify. ]
PDF with a further explanation attached.

LINK: JPEG

 

[my_key]

Hi surnev
You work looks quite beautiful and simply shows relationship. I am in awe of the hours you must have spent on this. However I have not been following closely your progress and so am not really able to offer you any productive feedback. Keep on keeping on though.

Good Luck

 

[surnevs]

Hi my_key,
Years ago my old friend Erik Thorell gave me a book that he had published, "Tai Divination Workbook", in which he mentions the Core of the Core phenomena, only mentioned briefly as this book holds more to Tarot divination, today past 80' of age I think he has retired but back then he practised Tarot divination in London where he lives. But my attention was caught. My next step will be to compare this Diagram with the Circular arrangement of the hexagrams made by Shao Yung, the Song-era philosopher (attached) and maybe find something interesting. Thank you for your encouragement! Hours fly by when puzzling with this thing and my job interrupts it momentarily - but in an inspiring way, like when in the middle of playing when a child's mum calls and the longing for going back to play grew the more.
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[surnevs]

The Cardinal hexagram positions in Shao Yung's arrangement seem to be:
Vertical hex. 1 & 2
Horizontal hex. 13 & 7
- and not hex. 63 & 64.
Green X's refer to the hexagram in KLM Quadrant, and Blue X's refer to the hexagram in the DEF Quadrant. (See below)

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The cardinal hexagram M61-D32-F62-K42 seems somehow to fit...

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[surnevs]

On #77 (Open in new window )in question:





Taking Shao Yung's Circular arrangement as an Answer list it seems to fit nicely, either way around, but one couldn't be satisfied with that, Or?

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As seen, these were the editing necessary to bring it in alignment with the Circular arrangement of Shao Yung:

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Attached is an edited PDF with this Core of the Core Arrangement brought in accordance with the Circular arrangement of the sixty-four hexagrams created by Shao Yung​

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But look at the lower / inner trigrams the outer circle around. Except for the hexagrams A36 and 52 plus G6 and 58, they are all following each other in pairs. To make this pattern be fulfilled these hexagrams (A36 and 52 plus G6 and 58) must be interchanged as well.

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[surnevs]

On #81: "But look at the lower / inner trigrams the outer circle around. Except for the hexagrams A36 and 52 plus G6 and 58, they are all following each other in pairs. To make this pattern be fulfilled these hexagrams (A36 and 52 plus G6 and 58) must be interchanged as well."

Here it is:

JPEG​

(I would have added this Diagram in #81 but my access to editing was closed.)

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The "Ideal-line" for the Blue square is the black line from hex. 1 to hex. 2 and likewise the "Ideal-line" for the Red Square is the dotted black line from hex. 5 to hex. 35. In Shao Yung's Circular arrangement, the "Ideal-line" would be one who goes from hex. 13 to hex. 7. Here, the lines for hex. 1 to 2 and the lines for hex. 63 and hex. 64 shows themselves asymmetric as seen in the Circular system:

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[surnevs]

I'll like to share a visualisation of the way the Categories I to VII ie no Yanglines to no Yinlines look at both the Circular Diagram made by Shao Yung and the Core of the Core Diagram (% a PDF has been attached with the same two diagrams to make a better overview. )

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The unmarked hexagrams are all those of Category III

In both Diagrams, it will be noticed that:
Category I is opposite to Category VII
Category II is Diagonally opposite to Category VI
Category III is Diagonally opposite to Category V
Category IV is Diagonally opposite to its own Category.
[A similar phenomenon can be observed at the Dice: 1 eye is opposite to 6 eyes, 2 eyes are opposite to 5 eyes and 3 eyes is opposite to 4 eyes, each opposite pair added giving the sum 7. Concerning the inter-relation between the Category's in the Diagrams the sum of each opposite Category is 8. ]
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In this comparison of the Circular arr. of Shao Yung and the Core of the Core Diagram above it's obvious that there is a connection:

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- better to be able to see this connection look at the green and the red separately + the black and the blue separately.

Like here (the same Diagram as the above):

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[surnevs]

% Attached is the Diagram / Mandala referred to. (Also posted HERE)

Here are the Diagonal arranged hexagrams in accordance with the King Wen sequence of the 64 hexagrams. Red numberings mark reverse numerical. Underlined are those following each other.

1-2 (Inner section)
2-1
3-50 (Outer section)
4-49
5-35
6-36
7-13
8-14
9-16
10-15
11-12
12-11
13-7
14-8
15-10
16-9
17-18
18-17
19-33
20-34
21-48
22-47
23-43 (Middle Section)
24-44
25-46 (Outer Section)
26-45
27-28 (Middle Section)
28-27
29-30 (Outer Section)
30-29
31-41
32-42
33-19
34-20
35-5
36-6
37-40 (Middle Section)
38-39
39-38
40-37
41-31 (Outer Section)
42-32
43-23 (Middle Section)
44-24
45-26 (Outer Section)
46-25
47-22
48-21
49-4
50-3
51-57
52-58
53-54 (Middle Section)
54-53
55-59 (Outer Section)
56-60
57-51
58-52
59-55
60-56
61-62
62-61
63-64 (Inner Section)
64-63

% attached overview

 

[my_key]

Hi surnevs
Your core of the core diagram shows clearly the nuclear family lineage from each of the 4 core hexagrams (1,2,63, 64). It's clear that you have put alot of work into these displays. I do like the colour coding that makes the patterns a bit easier to follow. That has been helpful for me.

I have a couple of observations, which I hope you can explain. Both in post #83.

(i) You speak of looking at blue and black separately to green and red which makes the patterns clear. However I am unable to see why in the coloured core of core diagram both 63 and 64 are green and black seems to miss out on a central core place of origin. What is the reason for this in your thinking?

(ii) In the hexagram pairs diagram you have aligned the square with the 1/2 vertical axis if the outer circle of hexagrams. This makes sense. What this produces is the 'twist' or misalignment that occurs in the position of the 63/64 axis. 90 degrees in your square from the 1/2 axis but somewhere around 55 degrees when the dotted line is drawn between 63 and 64.

From a shamanic perspective there is always a 'twist' in any pattern of change otherwise there is just a same old, same old repeat of what was before. Even change has to change! The twist, like lemon in a glass of sparkling water, provides the element of subtle refreshment as we take each next step forward in life. The 'twist' of offsets and asymmetry, shown clearly in your colour coordinated 3rd diagram, are representative of how this change pattern pans out within and through the world of change.

 

[surnevs]

Hi my_key,

The point of my "playing around" with these arrangements is merely to compare the Core of the Core Diagram with Shao Yungs circular arrangement of the 64 hexagrams, or: to see if any similarities occur.
I don't think, though I really can't know if, Shao Yung made his arrangement in comparison with any Core-of-the-Core patterns. It's known that he worked with the hexagrams in a chronological sense ie the hexagrams in relation to time epochs *, and I try to search out here if there could be a possibility that this Core-of-the-Core Diagram in it could have a hint to the arrangement of the hexagrams in relation to Time. In #53 I've pointed out a temporary Idea showing the Diagram in relation to the months of the year, but I don't think it really can be set up this way or: I have doubt about it.
So, I will ask you to simply look at my diagrams in light of this - me placing and replacing the hexagrams in an attempt to find a reasonable Logic that may be visible where Symmetry occurs or where it fits with the work of Shao Yung maybe helping to gain insight to his point of view. Besides this, there is no deeper philosophy involved. And I know that there is a risk that this whole thing gets a bit too comprehensive and messy - which it may be already is?
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Add.: but also to share my passion with this aspect of the I Ching, maybe for someone to be useful (?)

* for more on this: Anne D. Birdwhistell's "Transition to Neo-Confucianism. Shao Yung and Symbols of Reality", Stanford University Press, California 1989
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% The attached Diagram I think, is the closest logical arrangement (for now) attainable...

 

[my_key]

Hi surnevs
Climbing into the mind of Shao Yung after all this time is not a task for the faint hearted. Your efforts at 'playing around' in amongst all the patterns is highly commendable. There is structure and form to your patterns. Whether they are those that skipped through Shao Yung's mind is impossible to say.

I have no worries that you are not able to commit to some sort of conclusion around why black does not take a position of either 63 or 64 in your core of core diagram. From the other things I read it just struck me that it ought to reside there. But that's my 'playing around' and not yours. A temporary idea would have been enough to hear at this time, however if there are none then that will have to suffice.

There is a simple clarity in your diagrams, and my observation of the potential shamanic linkage is not intended to muddy any waters, or make things philosophical, more rather to support the simplicity that you have reached as being valid. Many people view symmetry as having to be perfectly symmetrical. Your diagrams do not display a perfect symmetry but become 'perfect' when considering that the very nature of all things contains a twist.

Whether or not anyone else finds your 'playing around' useful doesn't matter. Following a passion ads vitality and purpose to the 'playing around' for you. Not that it matters, but I for one have found exploring your diagrams useful, So, thank you, surnevs!

Take care

 

[surnevs]

And thanks to you too. My posting #83 is more or less to share a visualisation of the way the Categories I to VII ie no Yanglines to no Yinlines look at both the Circular Diagram made by Shao Yung and the Core of the Core Diagram, meaning that I lay weight on this categorisation explained there. From section L clockwise waxing to section E where it culminates and further back to L where it is waining: like pointed out there is Category I with no Yang lines / unbroken lines over Category II with one Yang line etc. etc. and the colours are solely used to underline this process.
I will always like to be criticised in case of mistakes, mistakes that my experience tells me easily sneaks in if one isn't fully focused and constantly check out if anything has been done properly.

 

[surnevs]

Another observation of some remarkable symmetry: the symmetry of the connected hexagrams in the inner section compared to the hexagrams in the middle section of the "Core of the Core mandala" (attached) as seen when these are projected into the Circular arrangement by Shao Yung.

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[surnevs]

- and that the 48 hexagrams in the Outer Section are equally divided into six parts, eight in each, between their Core- and Core of Hexagrams (the mittel and inner section) could show that Shao Yungs Circular arrangement has a reference to this, ie. the Core and Core-of-the-Core system. And I'm not saying that Shao Yung made this Circular arrangement with this aspect in mind... Just that it's clearly observable.