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Nuclear / Mutual Hexagrams

breakmov

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Hi Surnevs

What attracted my attention in your graph was precisely the symmetrical distribution of all the nuclear hexagrams around the center and the fact that the two diagonals of the graph (1-28 and 43-44) also show the 16 nuclear hexagrams.
...I was curious if behind the distribution of trigrams that you left for the lower part (Ch'ien - K'an - Kén - Chén - K'un - Li - Tui - Sun) and the upper part there is some relation that is still to be discovered.


Thank You

breakmov
 

surnevs

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Hi breaknow,

Actually, the scheme on #11 had nothing to do with the "Core-of-the-core Mandala", but just to offer to you here a quick way to look up the nuclear hexagrams. Afterwards, when looking at it to check if it was right I did to my surprise see the symmetry of the core hexagrams between (as also shown in #11) and decided to play a little around with it.
In itself, I don't think there is much to be gained but by using the core-of-the-core hexagrams and the patterns they could possibly come up with maybe (sic.) insight can be achieved concerning the sequence of the king Wen hexagram arrangement...
 
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surnevs

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Core scheme arrangement 06a.jpg
Core scheme arrangement 03a.jpg

side 18.jpg
Bent Nielsen, A companion to YiJing Numerology and Cosmology, page 18

_______________________________________________________________________________________________________​

Core scheme arrangement 04a.jpg


side 37.jpg

Bent Nielsen, A companion to YiJing Numerology and Cosmology, page 37

___________________________________________________________________________________________________________

Core scheme arrangement 08a.jpg

side 34 II.jpg

Bent Nielsen, A companion to YiJing Numerology and Cosmology, page 34​



See also: A hidden Pattern (https://www.onlineclarity.co.uk/GritterHiddenPattern.pdf)
 
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surnevs

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I've attached picture C from posting #17 for print (1134 x 1134 pixels)
(I'm still a bit bewildered about whether the two sections in the lower triangle, among which is hex. 24 and 27 should be reversed and likewise in the upper triangle among which is hex. 28 and 44. )
 

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breakmov

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Hi Surnevs

By symmetry, at various levels, figure C shows much more symmetry than figure A.
I have in mind the symmetry of rotation around the center of the figure. This symmetry unites all hex pairs and their opposites in the 48 hexagrams.

For example, starting with hex15 and hex10, a link axis passes through the center of the figure and rotates clockwise.
In figure A this symmetry is also present, but what weighs in favor of fig C is the symmetry in energy (Xor) between the hexagrams. Here we also have symmetry patterns for all 48 hexagrams.

For example: hexagrams 27, 23 and 24 (nuclear hex2) represent the interaction energy for all 4 hex groups allocated to each nuclear hex.....even the nuclear hexes obey this energy.

-nuclear hexagrams(40,54,38),(43,28,44),(37,53,39),(23,27,24) all have this interaction energy.

-also all 48 hexagrams obey this energy within each group of 4 hexes corresponding to their nuclear hexagram.
This is just the "tip of the iceberg"...once you start to study patterns in more detail with the help of Xor, the C image appears to be much more symmetrical than the A image.

PS- hex 11 and hex17 have to switch places.
edit: hex12 and hex 17 have to switch places
- regarding #30: Do you know the pattern that appears when you relate the distribution of the upper trigrams with the distribution of the lower trigrams using Xor? ;)

breakmov
 
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surnevs

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Hi breakmov, Thank You for your reply. I have forgotten to name the sections. Due to the fact that the seasonal or vaxing/waning hexagrams - #17 B - are not equally divided over the sections, and the mandala, therefore, can't represent the seasons of the year (? that I'm not sure about yet, but -) I will despite that name them:

Lower triangle
Hex. 2 winter solstice
Hex. 23 New moon in November
Hex. 42-8 the four weeks in November
Hex. 27 New moon in December
Hex. 29-61 the four weeks in December

- and so on clockwise.

(The lower triangle Winter, the left Spring, the top Summer and the right Autumn)

You write: ".... PS- hex 11 and hex17 have to switch places. ....." about which I'm not sure: didn't You mean that hex. 12 and 17 should be reversed? The core hexagram of hex. 11 is hex. 54 and can't be removed to the third week of September (hex. 17)
______________
(And: I is no yang lines to VII, no yin lines.)
 

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breakmov

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didn't You mean that hex. 12 and 17 should be reversed?

Yes, exactly that. :)

..and sorry for my bad english...the way i want to express myself never comes out well in english.


One thing that caught my attention:
Lower triangle
Hex. 2 winter solstice
Hex. 23 New moon in November
Hex. 42-8 the four weeks in November
Hex. 27 New moon in December
Hex. 29-61 the four weeks in December

- and so on clockwise.

(The lower triangle Winter, the left Spring, the top Summer and the right Autumn)
if I'm not mistaken, you put spring under the influence of hex 63(second nuclear hexagram)....why?

I see spring as a transition between winter and summer, where the plant has to be born or "raised" itself again.
A time of uncertainty as to the final result:

"how many new branches will the tree have?... will it have a lot of light?..... how many fruits will it have? Will the fruits reach the mature stage?... will the plant be able to create new seeds?...e.t.c"

- So i see spring as a very uncertain phase, although full of new possibilities, and that's why I imagine the influence of hex 64. :)

breakmov
 
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surnevs

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I use the early heaven order or Fuxi's arrangement of the eight trigrams. In the east, You find the trigram Li and in the west the trigram K'an.
In the hexagrams, I see the lower trigram as coming and the upper as going.
In hexagram 63 Li is coming - thereby pointing to East/Spring - and K'an is going vice versa opposite with hex. 64 where K'an is coming - thereby pointing to West/Fall.
As Hex. 1 is summer and Hex. 2 winter there is hex. 63 and 64 left (still according to the Core of the core hexagram order.)
 

surnevs

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About hex. 12 and hex. 17 to be reversed I'm not sure. Look at the upper trigrams in respectively Spring-March and Autumn-September, how they "follow each other". And if they were reversed the symmetry I think would be broken... But yes: You could be right here, I have noticed it and will not reject the possibility. Thank You for pointing this out to me!

Add.: Just see that, concerning the upper trigrams in Spring-March, hex. 11 and hex. 18 maybe should be reversed... But then again: the symmetry would be broken ie. Hex. 11 (Spring-March) would not be in a horizontal line with hex. 12 (Autumn-September)

and one more thing: Hex. 63 being Vernal Equinox fits with Hex. 11 being situated in March as the Light- or the Yang lines grows up toward Hex. 1 (Summer Solstice) as well as Hex. 12 being situated in September shows the Dark- or Yin lines growing up toward Winter...
___________________________
% Attached, is justification for the symmetry in the order.
 

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surnevs

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Hi Surnevs


- regarding #30: Do you know the pattern that appears when you relate the distribution of the upper trigrams with the distribution of the lower trigrams using Xor? ;)

breakmov
Hi, I've made this jpg to print out (1: point in it, right-click and "Save as". 2: print out the saved image), or:

% attached a pdf to print out.

ADD.: the table for use, overview attached.


trigramtabel B.jpg
 

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  • Cover med kerneheksagrammerne.jpg
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surnevs

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Trigram table Draft.jpg

I think this could be close to a symmetry.

(1-2-3 etc. is the vertical axe)

EDIT ! The horizontal row shall of course be:

A-C-B-E-D-F-G-H (As the four center hexagrams D/E-E/D and 4/5-5/4 must stay in their places either way)
 
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surnevs

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Like with #33, for the seasonal hexagrams in red-, the double hexagrams in blue- and the big trigrams in green colour, it's (even more) symmetrical:

TrigramTable B1.jpg
 

surnevs

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breakmov, this is complicated; I've been playing around with the 64 hexagrams interrelation for years - like actually thousand of others have done through the millennials - and I will just say thank You for asking into this particular phenomenon ie. concerning the core- or nuclear hexagrams as seen in relation to the overall structure, so to speak. For my part, I don't expect any solution concerning their inter-relative Order. I think that Shao Yung was the one who came closest to a logical order (though not concerning the nuclear hexagram's role in it). Let the seeking continue

||::||
 

breakmov

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Hi Surnevs.

I also love, as you do, to discover patterns in the sequence of 64 I ching hexagrams. When I see symmetries like the one you showed in #30, I wonder what factors contributed to that symmetry.

The sequence arranged in the upper trigram row and the other in the lower trigram row are the direct contributors to that symmetrical arrangement of the core hexagrams and (to my great surprise) the 16 hexagrams of the diagonals that also represent the core hexagrams.

That's why I wonder what's "special" about those two trigram arrangements:

The trigrams above bring to mind, as everyone knows, the historical sequence attributed to the "birth of the trigrams" that stems from the interaction between heaven and earth.
The sequence of lower trigrams made me curious if there was something there that would help to advance a little more in the "explanation" for that symmetry.

On the other hand, the table of 64 hexagrams is the result of the interaction between these two trigrams sequences, so why not try to understand the energy of interaction between them, through Xor?

I leave an image using the two trigrams sequences you left at #30 and the Xor result.

simetria xor.png
breakmov
 

surnevs

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alf ?( of the later...)

Xor?

- I don't quite know what these abbreviations mean...
If they refer to parts of a system You have developed ? - can You hint me to it?
 

breakmov

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... :LOL::)

Half of the Later Heaven Sequence.

Xor: Just search the history of this wonderful forum.


breakmov
 

Liselle

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I managed to miss all of this until Hilary linked to it in Friends' Notes.

Thank you for doing all of this, Surnevs. Haven't read all of it quite yet, but I like your diagrams. And your post #11 is very interesting indeed.
 

surnevs

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Thank You, Liselle! Actually, it's a study with offspring in the strange phenomena that the four hexagrams, 1,2,63 and 64, placed at each end of the king Wen sequence of the sixty-four hexagrams are the core-of-the-core hexagrams of the rest. And my curiosity got awakened in the possibility that the 60 hexagrams beyond could maybe be seen in the light of the year cycle. Until now nothing points toward this. But it's worth not rejecting this possibility - where I think one should be "caught in it" to avoid.
______________________
Add.: (Maybe out of context) I sometimes imagine this king sitting enjailed puzzling with the hexagrams.
Were it to bring an Order into it, easier to remember each hexagram's place (like in libraries books arranged A to Z, easy to locate?)
Did he know that the four hexagrams, 1,2,63 and 64 were the Core of the Core hexagrams of the 60 hexagrams between, or did he place the two last hexagrams there because they were equally divided in broken and unbroken lines? And to the former, I simply can't get rid of the thought: What a coincidence! Well, we probably will never know - or?
 
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surnevs

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This posting could deserve its own thread but as it's about the king Wen sequence and its relation to some patterns shown in respectively the Early- as the Later Heaven arrangement of the eight trigrams I'll post it here.

Trigrammer Fu Hsi Orden B.jpg
The Early heaven, or Fu Hsi arrangement


Trigrammer king Wen Orden A.jpg
The Later Heaven, or the king Wen arrangement

In my eyes, it speaks for itself that the symmetrical pattern of the hexagram numberings according to the king Wen sequence of the sixty-four hexagrams can be seen in the Early Heaven- but not in the Later Heaven arrangement.
What these two arrangement shares, interestingly, are that the Cardinal hexagrams 29, 30, 63 and 64 are those that end the Upper- as well as the Lower Canon of the sixty-four hexagrams respectively Hex. 1-30 and Hex. 31-64.
I'm sure that there are more to be concluded out of it, but these where the thing I found worth sharing here....
 

surnevs

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Shao Yung scheme 3.jpg
Scheme according to Shao Yung (or Fuxi) Early Heaven arrangement.

The red, blue and yellow marked areas refer to the cyphers in parentheses or the Nuclear hexagrams.
The Circle beneath the drawing simply shows the direction in which the Trigrams are ordered, starting from "A" being Li and clockwise on.
It's obvious that the red markings point toward groups of hexagrams while respectively blue and yellow marked areas (maybe) seem to be parts of squares. If so a rearrangement (maybe) is needed to make the Symmetry Complete?
(I've made the same scheme with the king Wen or Later Heaven arrangement and found no such groupings/or symmetric patterns)
 

surnevs

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Concerning Early / Later heaven arrangement, though not in exact alignment with the above posting:
https://svenrus.dk/thesixlinesa.pdf

In the pdf, there's a link to Gregory C. Richter's translation of the Zhouyi which is no more existing. (LINK)
 
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surnevs

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I've skipped the consideration of the Symmetry (mentioned in posting #17) and here focused on the inner/lower trigrams deciding the order of the hexagrams. From category II to VI you'll find these trigrams in accordance with the Early Heaven Order. Instead of the yearly references, call February for A and so on.

000 Core of the Core Seasonal Order EDITED 27 Okt. 2022 JPG.jpg
 
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surnevs

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I should have added that this is not the definitive order... (Nearly every day I look at it searching for possible lacks in the Logic)
 

surnevs

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This image is just to be able to discuss the arrangement of the hexagrams.

Core of the Core Basic I C.jpg


* The overall principle is that all of the hexagrams nuclear hexagrams can be followed from the outer ring to the middle ring and finally can be found in the four initiating and ending hexagrams ie 1, 2, 3 and 4.
** The order in which the hexagrams are arranged follows the principle:
I: no yang lines to VII: no yin lines. (1)
*** The principle in which they follow this order:
from L 8 and 9 clockwise to E 5 and 6 the lower trigrams arrive and from E 8 and 9 to L 5 and 6 the upper trigrams leaves, in reference to the "Early Heaven trigram arrangement" (2).
_________________________________________________

I'll show the above Diagram compared to the Sequence ascribed to king Wen (and hopefully get the time to do so too with it compared to the sequence found in the Mawangdui manuscript, the Circular Order of Shao Yung and the Binary system... )

wen seq. 2.jpg





____________________________

1) See page 4 (Here)

2) |:: |:| ||: ||| :|| :|: ::| :::


3) ......





 

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surnevs

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PDF so far attached
 

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surnevs

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Core of the Core Binary Sequence.jpg
In this Equivalent Diagram, nearly everything seems remarkable! Compare with #55 and in the PDF attached below.

_________________________

The Diagram or Mandala with numberings according to the Shao Yung sequence:

Core of the Core Binary numberings 1.jpg
__________________

% Attached: schemes for fill out, PDF
 

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dobro p

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Question: What do you think the chances were that the people who came up with the I Ching were into hexagram structure at this level of analysis?
 

surnevs

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I guess that, if they (who came up with the I Ching) were those referred to in the commentaries ie the Ten wings (Ta Chuan, The Great Treatise, Part I, ch. XI, ), namely the sages about whom, in this commentary, it is said that they were divine, my answer would be yes but not a yes to that they were into it the way I study it. My mandalas or Diagrams are not final, far from... It is also said in this chapter that they, the Sages, redraw in secret and this leaves us whit questions and nothing more than questions.
But if they, who came up with the I Ching, were like those shamans mentioned now and then throughout this forum, who consulted the oracle only following tradition, I guess I would answer no ie then they were not into such speculations at all but rather occupied with the answers given in and with this or that hexagram and not speculating at all in what system this or that hexagram were situated.
All in all, when asking who created the I Ching I guess we are left to hold on to the tradition ie king Wen until excavations come up with further information. That's about how little I know about it.
I still do think thou that it's remarkable that king Wen placed the four hexagrams, 1,2,63 and 64, that all of the hexagram's cores end up at on respectively the beginning and the end of his system.
 

dobro p

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I still do think thou that it's remarkable that king Wen placed the four hexagrams, 1,2,63 and 64, that all of the hexagram's cores end up at on respectively the beginning and the end of his system.

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, I couldn't see anything regular and convincing. Occasionally, yes, but not regularly. So my conclusion was that meanings were assigned to hexagrams and lines mostly according to pairs (two by two the animals boarded the arc) but not according to how their line structure related to the line structure of other hexagrams. So, for example, in terms of meaning, there's no commonality between the hexagrams that reduce to Hex 1. Whatcha think?

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?

I'm not lobbying for these ideas - but they're how I'm seeing things at what people sometimes like to call 'this point in time'.
 
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