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Complementary hexagrams in the sequence

hilary

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There are doubtless many people here who've spent a whole lot longer than I have looking at complementary hexagrams. (*Waving to Mattt*) So probably you already noticed that...

1 and 2 are complements
3 and 50 are complements
All the hexagrams between 3 and 50 have their own complement within that span.
Then it's 51-57, 52-58, 53-54, 55-59, 56-60, 61-62, 63-64.

This span encompassed by 3 to 50, with 51 to 64 as a kind of 'epilogue', has to be intentional. But what does it mean?
 

yly2pg1

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This span encompassed by 3 to 50, with 51 to 64 as a kind of 'epilogue'...

My opinions:
(1) 1-2 is a kind 'first chapter'.
(2) 61-62, 63-64 is a kind of 'synopsis'.
 

yly2pg1

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(1)A whole "1-2" encompasses the yin-yang concept, the relationship between the Sun and the Moon, Man and Woman etc etc.

(2) A whole "63-64" is about the complementary everchanging yin-yang cycle.

(3) A whole "61-62"?
The form the TRUTH manifests itself.
IOW there is no truth without the transistory nature of things in reality.
It is just a reflection (or illusion?)
 

hilary

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I like all that.


What still eludes me is why the arc from 3 to 50, as if something conclusive happens at 50. What's special/ different about the last 14 hexagrams as a group?

Maybe if you think of the decades of hexagrams as decades of life, this would be a time for completion and closing loops rather than opening them? (Being only at Yi's half-way mark myself, I really wouldn't know.)
 

freemanc

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I love this line of thought, Hil, and I don't have much good to add to it.

But I am absolutely convinced that the King Wen order is painstakingly constructed. There are too many of these medium-sized symmetries, and neighborhoods of rigorous symmetry.

I think a good way to think about this is not like math, but like the formal structures that make a poem hang together. But that kind of summary tends to stop us from playing with it, and I don't like that so much.

I just keep feeling that someone could find a nice layout pairing off symmetries that would make the King Wen order unfold into a big spiral.

But then, damaged or broken symmetries that fall into partial patterns this way or that: why, that's "Aesthetics 101". It's the crack that makes the glazed dish beautiful.


very fondly,
FC
 
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simple_complexities

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Imagine a universe completely different from ours...in this reality exists a form of energy that is pure, complete, perfect. Its a universe where everything is connected, everything vibrates at a level of equality, a harmony. Many would call this heaven, some would call it "the higher plane", some refer to it as "the higher astral realm". There are many words, but one meaning - This is a place where all energies exist in complete one-ness.

Now imagine our universe with its polarised qualities, the yin and the yang, the cold and the hot, the light and the dark. In our universe, energy is separated into distinct classes which help us define their relation to one another. The I Ching is a tool to help us understand how this energy changes and responds, but its so much more than that. Its a guide to helping us understand and ACHIEVE the unified energy, also known as enlightenment in many circles. I prefer to call it "the adventurous journey home"


The complementary hexagrams as you mentioned are formed as you all know by opposites of lines. So yang fits with yin, and yin fits with yang, and suddenly there is no more polarisation, there is harmony, a unification. Each energy (yin and yang) is now balanced, in a complete way. Thats why they are very important in the I Ching. They represent the balance of all opposites, the field and force combined in partnership.

This is the slightly tricky bit, so I'll try to be as clear as possible. We are all familiar with nuclear hexagrams or "the hidden possibility" in each of the texts. The only two hexagrams that do not have a nuclear hexagram are 1 Force and 2 Field, this is because they represent each energy type at its most extreme level.

However, all of the other hexagrams do have nuclears. If you take all the nuclears in the I Ching, you will have 16 different hexagrams (or 8 sets of 2 complementary hexagrams) that each occur 4 times, these are; 1-2, 23-43, 24-44, 27-28, 37-40, 38-39, 53-54 and 63-64. These are very significant beceuase they are a glimpse of the mechanics behind the system, a look at how the engine revs.

Whats the purpose of this you may ask? Good question! The purpose is finding which hexagrams can be broken down into their basic energy groups, either Yin (2 Field) or Yang (1 Force). So now, lets look at the nuclears for these remaining 16 hexagrams and see if any of them revert back to their orginal state, again hexagrams 1 and 2 need not apply as they are already in their purest form. It goes like this:-

23 Stripping - nuclear is 2 Field
43 Parting - nuclear is 1 Force

24 Returning - nuclear is 2 Field
44 Coupling - nuclear is 1 Force

27 Nourishing - nuclear is 2 Field
28 Great Exceeding - nuclear is 1 Force

But the things change! As we can see each of these complementary energies have reverted back to their original state. Thats 8 more gone... 8 to go...but when we reach the last 4, we see a somewhat different picture:-

37 Dwelling - nuclear is 64 Not Yet Fording
40 Taking Apart - nuclear is 63 Already Fording

38 Polarising - nuclear is 63 Already Fording
39 Limping - nuclear is 64 Not yet Fording

53 Infiltrating - nuclear is 64 Not yet Fording
54 Converting Maidenhood - is 63 Already Fordg

and 63-64 are the same, always re-occurring.

So we have found all but 8 hexagrams can be reverted back to their original state of Yin or Yang. Why do these final 8 not revert? Why does everything lead back to 63-64 as the only surviving energies? Its quite simple, they are the catalysts for change!! One accumulates the energy (64) and the other releases it (63), all other hexagrams are inherently born from their partnership of igniting the spark.

It would take too long to explain the work I have done in this area, and the cycles I have managed to form, but over time, I'll leak them out, Im sure most of you will be happy without the technical/math side!! Im certainly happier myself in the intuitive side
(but I do a little math too)

Hilary (or was it Val?) mentioned in another thread, that Yang is strongest on the lines 1 3 and 5, yin on 2, 4 and 6. And if this was so, why is 63 Already Fording the best hexagram in the oracle? It has this structure purely so it can not be broken down, so all lines can remain independent of their father and mother (1 and 2).4 Not yet fording accumulates energy, and 63 releases energy, a perfect partnership for infinite transformation. And as I mentioned in an earlier post, this process is exactly the same as Einsteins famous E=mc2 equation. The process of mass being converted to energy and energy back to mass etc.

Summarising, using the nuclears, we have reverted all hexagrams back to their purest state, either yin or yang, except 8 hexagrams who survive to tell the tale. And 63 Already Fording and 64 Not yet fording are the pivots for change.

Now I know many of you use the oracle for reasons to build intuition, open the heart, find the key questions in life and hope synchronicity and experience will bring you greater awareness of your world. Thats the way I see it also, no different at all. So what Im trying to say, is getting technical over the structure of the I Ching is not at all necessary, intuition is the greatest unmapped gift. Its just been my personal interest to work with intuition and intellect simultaneously, I like to know how things work. So please dont feel confused if you do not grasp the concepts here (probably my fault for explaining them bad
) Focusing on the beauty in the world around us is all the information we need in order to become wise.

Matt
 

yly2pg1

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What still eludes me is why the arc from 3 to 50, as if something conclusive happens at 50. What's special/ different about the last 14 hexagrams as a group?

Interesting work by D.H.Van den Berghe:


 

yly2pg1

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After some calculations based on Shannon's entropy:



Feel free to input ideas ...
 

freemanc

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Wow. That looks like it took an epic piece of data entry. How'd you render the chart??

I'm trying to think of a way to think about what "information entropy" means for the *form* of an octet of bits.

I think it's a measure of "Greyness" or "busy-ness".

So, 1&2 are not "grey" at all, 11&12 are not very grey and ones with just a "mishmash" of bits have more information.

Here's a thought experiment. If you took off your glasses, or were in a dim room, and you had a conveyor belt with hexagrams painted on it going by, you'd recognize 1 & 2 & 11 & 12 easily, but others would be more uncertain. They would take more information to transmit with certainty over a fuzzy or analog channel. (I *think* this is a pretty good story about what information entropy is measuring.)

Now the "macro" picture of the King Wen order we get from this is that first of all, this ain't a nice flat scatter. If you made several such roses with just noise, a random permutation of 0-63, they wouldn't look like this. One thing we see is that something really is different with the region from 46 to 62 or so. They're more busy, greyer. Also, they're not so "spiky". That's pretty interesting.

SO, hm. Do odd-even neighbors have similar or opposite entropy? Sometimes one, sometimes the other. Does this correspond to whether it's an inversion (flip figure upside down) or a complement (flip bits)?

Some other figures that would be interesting if you can produce them *easily* would be this figure with the even-odd connectors removed. Another with the inversions highlighted. And yet others would have only 32 entries and be just the even or odd hexes.

Kinda cool, Yly.

FC

Here's some refs:

http://en.wikipedia.org/wiki/Information_theory

http://en.wikipedia.org/wiki/Information_entropy
 

freemanc

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I'm really uneasy about bringing up my own book, but H. and Yly are just right there stirring up exactly the bees in my bonnet.

It sounds vain or whatever, but I really think someone could find all kinds of interesting patterns correlating the King Wen order to the Zhou Conquest narrative, in my book or otherwise.

I pretty resolutely ignored the formal patterns of the King Wen order when I wrote the Chameleon Book. I looked at neighboring Odd-Even texts, but otherwise almost completely ignored the King Wen order.

But I really, really think there's a lot there to be persued. I'm a true believer in the King Wen order, though I can't articulate why very well. Countless little hints that I haven't pulled together into anything.

In particular, I wonder if the spiral thing points to a hidden chronology.

A messy chronology. Perhaps to a deliberately constructed analogy between the times of Wen, and Wu, and Dan.

To the Chameleon Book, the chronology of the Zhou Conquest is cut to pieces, except for some runs, and the stories of Wu and Dan are shot through each other, with echoes and analogies. Ambiguities that I am convinced are engineered rather than murk or damage to the text.

The $64 question is: Do the pieces form something simple and lucid? Does the vase go back together?

This might be for Zhouyistas a hundred years from now when more basic things are settled.(Such as, if TCB's reading of specific hexes in terms of the Zhou Conquest is totally full of beans or not!)

I just don't know.

warmly,
FC
 

heylise

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The complementary pairs of the Wen order have some which are not 'visible'. If you take them all as upside-down, then 1 is complementary with 1, and 2 with 2. Same for 27, 28 and several others. In total there are 40 pairs instead of 32...
I really wonder how Yly's figure would look if they were entered as such?

And thanks Freemanc for explaining entropy, first time it made some sense to me. Always tried to get it with glasses on...

LiSe
 

yly2pg1

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The idea:

An example:


Get the n value to derive the p and 1-p for Shannon's entropy 'simplified' formula for ease of calculation.


 
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simple_complexities

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I have to say Im not a great admirer of entropy. Don't get me wrong it is a vital component for measuring the disorder of a system(s) we know little about, so we may know more about at a later time. But there is always going to be a certain ammount of entropy when we do not know the pattern or true theory behind how something works. It is just the human obsession that we try and balance and measure even things we do not understand, we try and make order from chaos by assigning probability values to its disorder, it seems a little crazy to me!

I remember when I was reading Stephen Hawking's "A Brief History of Time", I came across the term entropy in the chapter discussing black holes. I was familiar with the term, having been interested in chaos theory many years ago. Without going into too much depth about Stephens dilemma, he had formulated a new theory on black holes, though to test his theory was almost impossible because we dont know how the inside of a black hole is structured, so another scientist stated that they could measure the entropy at a point of the black hole we did know about and postulate as to the entropy inside the black hole, the area they didnt know about! Hawking hated the idea of entropy, he felt it took away the beauty of his original idea.

Now I know entropy is valuable for situations like in the one above, but it is a system based on effect rather than cause. But I feel the I ching has a beautiful pattern throughout, an order to the chaos, which has not yet been discovered. And before anyone argues this (which is a deffinate "probability" though entirely expected in advance by me)let me remind you that humanity has still not found a Grand Unified Theory for matching Quantum physics with Classical physics! Even our sciences are in dispute! We have Einsteins "pattern" for the larger universe, and then we have particle physics for the tiny universe, neither agree with each other, but both seem to work well independently. This says to me, that there is an order we have not yet found, a wonderfully complex pattern of union between chaos and order that we have not yet seen! Or maybe we are trying to be TOO LOGICAL, humans are good at this.

And again I come back to intuition, a force we know little about in sciences, but put in the same category as "psychic" or "paranormal" phenomena. It only sits in this group because it cannot be explained scientifcally, and intuition is the guiding tool of the I Ching and synchronicty...there lies the key to understanding the order to the disorder.
 

yly2pg1

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Before going further, the value in H(p) chart is discrete. I fill with 'color' to see if there is any pattern.



To S_C -
 

yly2pg1

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The value for '1-2' is indeterminate (wu2 ji2?).
Anyway, it is just for fun and curiosity, until my intuition tells me if there is any significance ...
 

yly2pg1

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Hmm, the arrangement of 'circle dynamic' seems to map well with the increase/decrease profile of the 'entropy value' of 64 hexagrams.
 

freemanc

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I just heard about the bombings in London. I hope you're all safe. I'm sad and angry and offended.

Anyway. Yeah, the smooth spiral would have something to do with the Fuxi order, H is a smooth function, p is a linear function of n, and n is the position in the Fuxi order. I think. I don't feel much like geeking out with it now.
 

antonioacuna

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This is very fascinating, but I have a fundamental problem with the order, Wen's or anyone's. Who said that the current numbering or sequence is right? the I Ying on silk follows a different numbering that the received text, so is it wrong?.

I think the key to the hexagrams is the fact that they stand on their own first as a message. We assume there is an order to them, but they could just point to fundamental moments in time, mathematical points of change or transformation with no necessary sequencing or dependance on anything before or after. Maybe I am totally off here, it is just somthing I have been thinking about lately, think about it, why are 3 and 50 complments? why exactly?
 
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simple_complexities

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Thats a great picture Yly2pg1!!

Its similar to the design I have! uncanny! Maybe it reminds you of the yin-yang symbol? Or a spiral galaxy? Or a pinecone? (looaking at it from the bottom) These were all things that inspired me.
 

yly2pg1

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S_C, your reminder about intuition comes on time. It could be 'telepathy' ...
 

yly2pg1

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Maybe it reminds you of the yin-yang symbol? Or a spiral galaxy? Or a pinecone?

If we can 'extrude' the graph in 3D with time-axis (normal to this polar chart), it is a 'spiral'.
 

freemanc

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Yly, what a neat diagram!

We're pretty far from King Wen, though. This is sort of Fuxi order, at least piecewise.

I haven't totally parsed it out, and I have to go to a conference. Will post again in a couple of days.

fondly,
FC
 

freemanc

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Oh! It is EXACTLY the same as the ancient circle diagram omigosh!
 
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simple_complexities

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hehe its great isnt it! The system I have been working on is much like that last diagram, inspired originally by the way the sun hit the water when I was walking on the beach. Then a series of events (studying galaxy formations and tripping over pine cones!) advanced the idea slightly. The only problem Im having is making the model, which looks 5 dimensional at the moment.
 

yly2pg1

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Hi Freemanc and S_C,

(1) Having been away for few days, my intuition reminds me that the diagram is not complete. There is still lots of work on. If the missing link is found, we may be able to complete the diagram.
And Freemanc, your work may be a good tool and "look-up table" in that process.

(2) We can put to test this 'diagram' first. My intuition tells me the 'entropy value' can be used to predict the time vector in I Ching consultation and divination. And for S_C models, that could be helpful. If anyone is interested here, we could devise a test plan to proceed.

(3) In fact, i have a dream yesterday about this diagram. When i wake up, a word keep coming to my mind ... 'tatami'. What is that? I don't know. Will find out later. Feel free to advise.
 

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