Complementary hexagrams in the sequence

[hilary]

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]

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]

(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?) http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

[hilary]

I like all that. http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif

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]

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

[simple_complexities]

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" http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif

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 http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif (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 http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif) Focusing on the beauty in the world around us is all the information we need in order to become wise.

Matt

[yly2pg1]

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:

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4708.gif
http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4709.gif

[yly2pg1]

Another way i can think of:

Shannon_entropy (http://www.pandasthumb.org/pt-archives/000232.html)

[yly2pg1]

After some calculations based on Shannon's entropy:

http://www.onlineclarity.co.uk/I_Ching_community/clipart/your_image.gif

[yly2pg1]

After some calculations based on Shannon's entropy:

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4722.gif

Feel free to input ideas ... http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

[freemanc]

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]

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]

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]

The idea:

An example:
http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4727.gif

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

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4728.gif
http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4729.gif

[yly2pg1]

The basic concept (of entropy) is helpful:

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4731.gif

[simple_complexities]

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]

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

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4734.gif

To S_C - http://www.onlineclarity.co.uk/I_Ching_community/clipart/zen2.gif

[yly2pg1]

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4736.gif

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 ... http://www.onlineclarity.co.uk/I_Ching_community/clipart/clown.gif

[yly2pg1]

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4738.gif

Any similarity?
Goodness!

[yly2pg1]

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

[freemanc]

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]

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?

[yly2pg1]

Hi Freemanc,

familiar pattern ...

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4742.jpg

[simple_complexities]

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]

S_C, your reminder about intuition comes on time. It could be 'telepathy' ... http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

[yly2pg1]

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'. http://www.onlineclarity.co.uk/I_Ching_community/clipart/zen2.gif

[freemanc]

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]

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

[simple_complexities]

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]

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.

[bradford_h]

tatami is the traditional woven floor mat in a Japanese house.
Because the size is fairly standard, room sizes are denoted by the number of mats in a rectangular layout, a fact which might relate your dream to one of the Yijing grids.
Why didn't you Google the word?

[bradford_h]

oops-
could also refer to more general processes like tesselation or the nesting of sets.

[yly2pg1]

tesselation?

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4763.gif

BTW, Why didn't I Google the word?
Coz I Ching is about connectedness. Aren't we are connected via 'negative-entropies' in one of a thread here? http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

[yly2pg1]

Hi Bradford,

I go through your document G-YiFigs.
It could be your call to solve a riddle here?

[bradford_h]

Si- tesselaton, with Yijing hypercubes no less!
Sixty four mat, big room.
Sorry - must ignore this call. You be puzzlemaster.
Am up to eyeballs researching next book.

[simple_complexities]

A pattern can be found if you use a 384 degree circle, rather than a 360 degree. Impossible you might say, its not. You just have to think a little differently, without rules. There are 384 aspects in the I Ching, and it puzzled me for so long, how this number could be significantly incorporated into a time cycle. A spiral galaxy was the image that inspired me, and it fitted perfectly with the data I had - strange that the shape of a galaxy or pine cone can be so similar in essence, but not strange at all.

What you call entropy, I call harmony.
What you call the disorder of a system, I call the natural order.
What you call a time cycle, I call the expression of mystery, it is not chaotic, neither is it unchaotic.
To try and divine events according to a model of time only gets you so far, then amazingly, one thing becomes overwhelmingly apparent - look within and without shall become clear.

Divination is the practice of triggering intuition using an outside model, coins, yarrow.
Intuition is the practice of letting go of the outside, knowing it is the reflection of the innner.
The I Ching/YiJing/Tao Ching, are all gently whispering the same message - look to the inner, not the outer. The whole system is like the web of a spider, but what makes the web of a spider useful? The space around it.

We cannot plan for future events, in doing so you exert a force on the space around you.
We can prepare for future events events, simply by letting go and living in the moment, then "time" has a dynamic that is beyond dynamics.

The oracle was not meant for acquiring knowledge through the use of "structures", it is meant as letting go of knowledge in favour of "non-structure". Then the true pattern will birth.

[yly2pg1]

384 degree?

The diagram is already in 384-scale, rather than 360-scale.

But it is not complete.
Any explicit ideas to input?

[yly2pg1]

I notice that I have reversed the arrangement of 'entropy value' with respect to the Fu Hsi Circle Dynamic. It should look like this:

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4768.jpg

[yly2pg1]

Map the binary_tree (http://members.iimetro.com.au/~lofting/myweb/btree.png) into the Entropy_Chart to 'visualize' the link with the Recursion of a Dichotomy.

[yly2pg1]

http://www.onlineclarity.co.uk/I_Ching_community/clipart/new.gif
Map the binary_tree into the Chart to validate the entropy-value of the chart!

IOW, this chart is valid only for the Recursion of a Dichotomy due to the indeterminate value of '1-2' Pair in Shannon_Entropy. In the context of a Binary_Tree, this 'indeterminate' is 'filtered'.

Any comments? http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

[freemanc]

That's the most astonishing gosh-damn thing I ever saw. I think ya got you a capital-A Achievement on your hands, Yly.

Yly, Can you tell me about the ancient circle diagram? What's its name, source, etc? Can you help me find a really good big graphic file of it?

I'm like Bradford, I just don't feel up to geeking out very hard on this right at this point, but I'd like to get set up to do so when I feel like it.

On the other side of Yly's mystery, does anyone have anything semi-solid on the history of the tai chi symbol?

FC

[yly2pg1]

Symmetry (http://en.wikipedia.org/wiki/Symmetry)

[yly2pg1]

Freemanc,

Achievement on my hand?
If there is really any, it should belongs to this forum - 'Onlineclarity'. I learn a lot from this forum.

Ancient Circle (name, source)?
Honestly, i do not know much.
My sense of history is slightly 'distorted'. http://www.onlineclarity.co.uk/I_Ching_community/clipart/clown.gif

I would like to x'plore a new thread "Symmetricity and Order in I Ching" and some of the diagram of King Wen's Order (by Van Den Bergh) will be used as reference. http://www.onlineclarity.co.uk/I_Ching_community/clipart/zen2.gif

[freemanc]

Well, that's *apparently* two different inquiries, because they're two different sequences.

One, the matter of the ancient circle and the entropy formula and the alarmingly perfect tai chi symbol that the entropy formula+ancient circle yields.

My guess is that there's actually an underlying characteristic of order that's causing this, like my idea of "greyness", that can be described terms that a brilliant premodern shaman might have come up with.

Two, the King Wen order's neighborhoods and the operations linking pairs or webs of hexagrams.

I'm thinking about Steve Marshalls website's stuff about sequences. I think that there are "finding sequences" in all these.

I'm thinking of the simple and obvious case of the Mawangdui order. You memorize a certain order of the trigram, and then you look up the top trigram and then the bottom.

I hypothesize that there's a finding order rule in the King Wen order, but it's tricky and involves memorizing five or ten rules, like learning subtraction on an abacus. (Which I did when I was in college! Only subtraction; I could do my checkbook. http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif )

Harmen Mesker is a real Sinologist (as opposed to me; I'm a monoglot lit crit guy who likes puzzles) and has written a paper on the eight houses sequence. I'm going to read it really well sooner or later. It's on Marshall's web site. I hypothesize that Eight Houses is, *among other things* a finding order also. You learn a series of operations that involve turning one bar at a time.

Here is Steve Marshall's sequence page (http://www.biroco.com/yijing/sequence.htm) that discusses various sequences and has a link to Harmen's paper.

best,
FC

[lightofdarkness]

Deriving sequences:

(1) Recursion of yin/yang leads inevitably to the binary sequence. This sequence can represent (a) symmetric dichotomies (guassian distributions) and (b) asymmetric dichotomies (spectrums, power law stuff - and so such dichotomies as far-from-equilibrium/equilibrium - aka negentropy/entropy).

(2) ROTATE the hexagrams in the binary sequence and you get the 'changing line' sequence 'up' hexagrams 01/02 (depending on which end you start - this is in the form of a sequence of 64 hexagrams mapping to the set of 2^6 states in each hexagram's line patterns))

(3) given (2) we can work in reverse. For ANY hexagram derive its changing line sequence of 64 hexagrams and then rotate that sequence to give the derived 'natural' sequence for that or some other hexagram.

(4) from (3) comes a world focused on a logic of relationships (A is to B as X is to Y etc)

See summary on logic of relationships in:

http://www.iimetro.com.au/~lofting/myweb/icstruct.html

see lots of sequences in:

http://www.iimetro.com.au/~lofting/myweb/icmatrix.html

Then note that each of these hexagrams in the binary sequence express all of the others. And so we move into the XOR dynamic of extracting the '27-ness' etc of each hexagram. (also covered in the icstruct.html pages)

Working with the binary sequence is a rich source of discovery re meaning generation and how it is all linked together and the IC metaphor is a reflection of what is in between our ears ;-)

Chris.

[jte]

Yly -

Can you give some commentary to explain your diagram above. It's been a *long* time since I've tried analyzing anything geometrical such as a sine wave or algebraic expression.

I understand that you've put 384 degrees to the circle instead of the standard 360, what else did you do to map the lines and why is this of significance?

Thanks much!

- Jeff

[yly2pg1]

Freemanc,
Thanks for the link.
There are 'orders' in the sequence but need to match with the right theorems. Same applies to the Eight House. Good luck! http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

Jte,

What else to map?
Anything that could be categorized/grouped under the Recursion of Dichotomy (or Recursion of ying/yang) - the binary sequence/order.

Significance?
I am still looking into it, the 'tatami' puzzle etc. Off hand, the chart may be a good indicator of 'time arrow'. Exactly how to use it, is still under investigation. You got any ideas?

[jte]

Yly -

Actually, I was hoping you would explain what your diagram is showing - I don't quite understand what it shows/how you constructed it.

If I understood what the diagram is showing better, I might have some ideas how to use it (although I don't want to make any promises :-) ).

- Jeff

[yly2pg1]

Jeff,

How to construct?

(1) Use Excel spreadsheet
(2) Key in the data (1~64) using the method i posted above i.e 2^0, 2^1 ... 2^5, and calculate the n value.
(3) Then use Shannon's Entropy. You will notice that you need to convert n to p and q of simplified Shannon's Entropy formula.
(4) In Excel, you will get a table of entropy value for 1~64. (For Hex 1 and 2, equate them to zero)
(5) Construct using Chart type - 'Radar'

(6) You can rearrange the entropy value in ascending sequence. That gives you a graph "Hexagram Pairs vs Entropy Value" in spiral form

(7) From this graph, you can further expand the graph (in 64-scale) using the method of 'binary-tree mapping' as explained above (also confirmed by Chris -(2)). Notice that it is like a 'mirror effect'.

(8) With that you get a graph of 'Tai Chi Profile'.

[jte]

Um. You lost me at step 2. What is step 2 "doing" - IOW, what is the data? What is the signficance of the method (what is the method showing us by taking 2 and squaring, cubing, etc up to the 5th power? How does that relate in anyway to a Hexagram?)? What does the n value mean?

Similar questions for 3 and 4 above, too.

If someone who's good at explaining math verbally (not the easiest thing in the world to do, I know) would like to step in, that is fine...

Thanks,

- Jeff

[yly2pg1]

The basic idea is to convert the binary number to decimal number.

e.g. 100001<font size="-2">2</font>=2⁵+2⁰=33<font size="-2">10</font>

[yly2pg1]

In simpler way:
If a system can be 'mapped/grouped' according to the binary order, and you are able to identify the binary level for each and every component of the system to the binary system (e.g. brain dynamics in IDM), then we are at a good position to 'see' its implication, with respect to this Entropy Graph/Profile.

[yly2pg1]

My opinion about 384-scale:

The space-sharing property (http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4227.html) in the binary Tree is the reason why the 384-scale is not explicitly shown in the Chart.

[yly2pg1]

http://www.onlineclarity.co.uk/I_Ching_community/messages/48/4962.gif

[yly2pg1]

Probably, the ancient people do know something about logarithmic calculation and the Shannon's Entropy? http://www.onlineclarity.co.uk/I_Ching_community/clipart/blush.gif

[freemanc]

Information Entropy, no.

Logarithms, yes, or anyway the idea of weighting the different yao "numbers" differently and adding 'em up, yes absolutely.

OOOOhhhhhhh... gosh damn! Cursory web search shows that place value number system came from guess where and co-occured wih the origin of guess what.

http://aleph0.clarku.edu/~djoyce/mathhist/china.html

So get rid of my inverted commas around "numbers."

Good stuff, Yly!

Hypothesis: Divination = Origin of place value numbers.

And the Tai Chi symbol literally a logarithmic spiral.

FC

[lightofdarkness]

you need to go deeper - all this here is expression not what is trying to be expressed - LOCAL expressions will be selective and so hide the full spectrum of what is being delt with - the universals.

In the TWO forms of dichotomy coming out of the neurology we have:

symmetric - from where guassian distributions and the sense of 'opposites' comes from. These types of dichotomies show DIFFERENCE from SAMENESS (e.g. individual IQ/EQ from all members of the species)

asymmetric - from where spectrums and so power laws and log scales etc come from. These sorts of dichotomies show SAMENESS ACROSS DIFFERENCES (core common patterns despite different energy expressions)

You can rotate one to get the other if you like. (and so the traditional binary sequence is derived from XOR and so recursion. Rotate it and you get the 'changing' line sequence 'up/down' 01/02 etc etc etc - see patterns in the icmatrix pages)

For background re the IC and Mathematics etc see

http://members.iimetro.com.au/~lofting/myweb/icmaths.html

- IC and Maths are BOTH metaphors for the underlying patterns of meaning derived from the neurology (blend, bond, bound, bind)

the integers were formally derived by Peano from recursion of the empty set (Dedekind brough that to attention of mathematics)

The IC hexagrams reflect derivation from the binomial theorem (A + B)^n and IT is manifest in Pascal's Triangle and IT is a particularisation of the Sierpinski gasket.

The Sierpinski gasket is what emerges in sensory systems where a bounded space lets in 'noise' that will 'bounce' around and in that bouncing a pattern forms in 'meaning space'.

The derivation of integers etc etc from the sierpinski gasket, and the derivation of hexagrams etc from the same form shows isomorphism.

There is a 'translation' table for basic qualities from differentiate/integrate through emotions and into the IC and on into socioeconomic categories at:

http://members.iimetro.com.au/~lofting/myweb/translation.html

if you dig deep enough through the specialist perspectives you will start to hit the underlying universals but that does not mean that the specialists perspectives were precisely aware of those universals, their properties and methods. Specialist work is ad hoc, piecemeal, 'small world network' etc. that aims to reveal universals but only in THEIR language and in that revelation the local context customises perspectives and so 'the whole truth' is not shown.

Chris.

[martin]

There is no end to going deeper.
Neurology is again only an expression. It reveals something and hides something else.
Our reality is bottomless.

[lightofdarkness]

there is an end to going deeper - the method used to derive meaning determines all meaning.

Communication of meaning thus has a 'bottom' for us. Anything outside of that will be interpreted from inside and so appear as if paradox - see my page on paradox where the focus is on it coming out of the XOR realm.

http://members.iimetro.com.au/~lofting/myweb/paradox.html

This XOR realm aims to maximise bandwidth to identify something "NOW". If it cannot do that it will present through oscillation all of the aspects it is trying to deal with - IOW it will recruit TIME (past/future) to aid in resolving the 'paradox'. (and so my comments on this dynamic being the 'root' of our drive for argument)

The bandwidth/time dichotomy is a specialist dichotomy reflecting differentiating/integrating and as such an asymmetric dichotomy - a focus on a spectrum, power laws etc... all meanings derivable from differentiating/integrating dynamics are meanings derived from the METHOD where in our species the core method is in the neurology and it then gets relabelled as we specialise, ground universals in local contexts.

Since, using this method we can map the seed of consciousness back to the beginnings of the universe, as well as clearly differentiate basic particle physics dynamics (fermions/bosons) or basic molecular biology dynamics (mRNA/DNA) so the method covers a lot. ANYTHING outside will not be detectable other than as paradox and paradox is derived from a couple of issues (See the above page).

Now, if you need to IMAGINE there is more, if you NEED your reality to be bottomless, that is another matter and not necessarily representing 'what is'.

As a neuron-dependent species, in the communication meaning, it is objects/relationships, differentiating/integrating, yang/yin, all of the way. The richness is in the seemingly infinite ways those patterns can be expressed.

Chris.

[yly2pg1]

(A) Quote:
<font size="-2">Neurology is again only an expression. It reveals something and hides something else.</font>

I find this statement interesting which may shed some light on the meaning and implication of why the "Tai Chi" curve is right in the "middle" of the "Feng Shui Compass".

The "expressed" part and the "hidden" part are both happens in parallel, giving a kind of "equilibrium".

(B) Quote:
<font size="-2">you need to go deeper - all this here is expression not what is trying to be expressed - LOCAL expressions will be selective and so hide the full spectrum of what is being delt with - the universals.</font>

That explains why the Tai Chi curve is a dynamic mechanism that flesh out the LOCALs (at a level) when the "small world network" at that particular level is achieved!

[yly2pg1]

(C) Quote:
<font size="-2">In the TWO forms of dichotomy coming out of the neurology we have:

symmetric - from where guassian distributions and the sense of 'opposites' comes from. These types of dichotomies show DIFFERENCE from SAMENESS (e.g. individual IQ/EQ from all members of the species)

asymmetric - from where spectrums and so power laws and log scales etc come from. These sorts of dichotomies show SAMENESS ACROSS DIFFERENCES (core common patterns despite different energy expressions)</font>

The complete mapping of the "small world network" at a level and/or across the whole spectrum of all levels, will involve both symmetric and asymmetric processes.

Nuerology is an example.

[yly2pg1]

This symmetric/asymmetic forms of dichotomy is an important "milestone" to unlock the secret behind the title of this thread- Complementary hexagrams in the sequence.

[freemanc]

Hi Chris...

I'm sorry, I'm exceedingly pleased with Yly helping me kinda dimly understand how a bronze age genius might have invented place value, mapped it onto quantities, and somehow ended up drawing a logarithmic spiral.

I think this is an absolutely fabulous result, and someone who's a student of archaeomathematics (surely there is such a thing?) ought to see it.

Anyway, evidently Yly understands your four or five dimensional patterning or whatever from all over foundation of mathematics and number theory and fractals and recursive function theory and all that, so y'all carry on; I however will retire to my cave and finger-paint on the walls.

best,
FC

[lightofdarkness]

It gets into issues of grammars. Chomsky's hierarchy covers reflective forms, repetitive forms etc and they map to the sequences of hexagrams derived from recursion.

Thus the template is bit patterns over which we can place some local dichotomy and then interpret invarious ways since they all elicit 'meaning'.

Given a sequence, a row, of qualities derived from recursion so I find (a) a focus on reflection and so opposition/complements (01 to 02 etc as in 01 VS 02) and (b) a focus on repetition where we increase energy levels - thus 01 is interpreted as the actualisation of the potentials in 02.

We also find 'variations on a theme' where the yin-based half slide over the yang-based half.

(a) is a symmetric focus. (+1/-1)

(b) is an asymmetric focus. (0/infinity, potential/actual, worthless/priceless)

(a) works in a particular level, (b) spans all levels - and yet zoom-in to either and out will pop the other - reflecting the 'entanglement' of perceptions.

This gets into the WHOLE being a gerund and IMPLICIT (Wu Chi) out of which is extracted 'something', T'ai Chi, that, if kept in focus long enough breaks down into its parts - yin/yang.

Thus from the gerund, the -ING state comes (a) the OBJECT state, the noun, of A <something>, and (b) the RELATIONSHIP state, the verb, of TO <something>.

We can in fact treat this as a dichotomy and recurse it to give us all of the possible combinations of verb/noun dynamics.

As such the IC is a book of gerunds and local context then takes the universals as grounds them - BUT there is still a subtle bias to yin/yang. Thus yin-ness is more relational but can be interpreted as an object but not with the same intensity of 'thingness' as yang. So here we have the energy-level interpretations etc.

This we find competitive interpreations (opposites, dark vs light) and cooperative interpretations (complements, male + female).

All of these properties reflect properties of a language and as such the IC reflects a language based on qualities, on feelings, rather than on precise strings of letters etc.

The clue to recursion is in the PAIRING and this is reflected in both the 'natural' binary sequence as well as the 'traditional' sequence; both show us 32 PAIRS of hexagrams. Thus the grammars applicable to the binary are also applicable to the traditional.

IOW reflection in the traditional is in the form of:

01 - 64
02 - 63
03 - 62
04 - 61
etc etc

in the binary in the form of:

01 - 02
43 - 23
14 - 08
34 - 20
etc etc

Repetition is in the mapping of octets where columns show repeats, same pattern in DIFFERENT contexts:

02 23 08 20 16 35 45 12
15 52 39 53 62 56 31 33
07 04 29 40 64 .. 47 06
etc etc

02 = trust in another in devotion
15 = trust in another in self-restraint
07 = trust in another in containment
etc etc

and note that EACH of these octets can be treated as if the whole and so reflective relations of 02 to 12, 23 to 45, 08 to 35, 20 to 16, etc etc

We also have where the octet reflects variations on a theme - we slide one half over the other e.g.:

01 02 03 04 05 06 07 08
33 34 35 36 37 38 39 40
etc etc

in the binary e.g.:

02 23 08 20 16 35 45 12
24 27 03 40 51 21 17 25
etc etc

There are a LOT of these (and then we move into the XORing etc!)

The derivation of bit representations, where we recurse 0/1, gives us a template that allows us to use logic operators etc to bring out relationships that come from the methodology of recursion (and so XORing etc)

By recursing differentiate/integrate we get representations isomorphic to recursion of emotions, IC, social categories etc etc and all applicable to interpreting the template as either asymmetric or symmetric.

Since the differentiate/integrate and anger/fear dichotomy are HARD CODED into us, so we have a representation system for all of the other categories derived by abstraction (and so consciousness).

For example, if I recurse the basic categories of the MBTI (way past the levels of the current form, we move from 8-16 types to 64-4096) we can apply the 'bit' representations and so the XOR-ing. In that process we discover, for example, that the XNTP 'type' has a skeletal format (its 27-ness) described by analogy to The I Ching listing of hexagram 35 (XNTP maps to hex 51).

51 as you know covers such concepts as the 'new', some new idea, birth etc etc. 35 covers the generic focus on 'bringing something into the light' - which IS the basic skeletal form of what XNTPs/Hex 51 does.

IOW given the generic qualities of the MBTI categories and the generic qualities of the IC, with their isomorphism due to recursion so we can use one perspective (the IC) to flesh out details in another (MBTI) - and so move beyond the current limitations of the 'traditional' MBTI etc. as we can move beyond the current limitations of the 'traditional' IC - and start to see the invarient, the universals hard-coded into all of us as neuron-dependent life forms.

Given that revelation, so we can REFINE local conditions etc by better understanding the universals.

Chris.

[lightofdarkness]

Hi FC,

dont understand why you are apologising! my point is that there is more at the level of the neurology and so the one area we have in common with those of 10th century BC. There are universals present, and so invarient forms free of local 'colourings' and so usable to flesh out the universal IC ;-)

As for log spirals, they do stem from a more 'primitive' time - these days the spiral is not circular, it is more square, showing the XOR precision level we work off.

(mysticism in the past was attracted to the log spiral and phi etc - the geometric representations were considered as close and you could get to 'god' etc. These days the focus is more 'precise' - we move from the geometric to the algebraic, the field to the point and focus on transcendence - IOW a focus on being god rather than having a relationship with, getting close to, god! - this path can lead to psychosis or to some 'higher plane' ;-))

As such, log spiral development is focused on conserving of energy over time and so 'gentle' in development and looks 'back' only a few contexts to aid in developing the current; the vibe is more qualitative than quantitative.

OTOH square spirals are energy expending and look back to 'the beginning' to aid in development of the current. (and so a push to discover beginnings and so aid in being more precise!)

From a brain perspective, the right is more 'circular' spiral, the left more 'square' spiral and in between a range of states moving from circle to square (and so the notion of squaring the circle!? it is intuitively attracting! ;-))

SO - in 10th century BC and before, with the same brain structure the same universals were present - but the interpretations of what they were was at times 'unique' ;-) - take into consideration a few thousand years of work in understanding brain/mind and we are now in a position to get a better understanding of those universals and so from there a better understanding of what we are dealing with re the I Ching etc.

So if it your eyes start ache, your vision starts to fade in that cave due to fatigue just give us a yell and we will come with the technology to make that cave 'light up'! ;-)

Chris.

[martin]

There are many references to the bottomlessness (is that a word? http://www.onlineclarity.co.uk/I_Ching_community/clipart/howmuch.gif) of reality in the Tao Te Ching.
"Meet it, you cannot see its face; Follow it, you cannot see its back."

I like that. It rings true, intuitively. And my inner experience confirms it.
Seeking for solid inner ground to stand on I only find no-ground. Endless falling .. Surprisingly, it turns out that there is nothing more grounding than that!
But one must allow oneself to fall. It requires trust, I guess. http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif

[lightofdarkness]

Martin, what you are touching on is the focus on contractive blending, to dissapear into the context. In so doing you lose the bounds of your ego and in so doing move into the realm of the species-nature that is unconscious but still constrained by the bounds of differentiating/integrating.

The realm of T'ai Chi, of a particular whole, is alread one step removed from 'the void' - Wu Chi. Wu Chi covers 'without extension' and T'ai Chi is 'great extension'.

Even though the characters are different, the above can be interpreted as 'breathless' (Wu chi) and 'great breath' - the inhalation that gives something 'life'.

Hold onto T'ai chi in your mind and it will break down into its parts - yin/yang.

Interestingly, there are two main 'preferences' for ecstatic/orgasmic experiences, one is the integration of all to become 'one', the expression of ego etc in the form of a sense of all-powerful, self-devotional, hubris. The other is the experience of losing the boundary, to sink back into the 'universe' and so dissolve.

This sinking back is into the 'equilibrium' state of species immersed in the environment, living off instincts, operating 'smoothly' and without thought since all thought is an exaggeration from the equilibrium state.

Our consciousness being mediating focuses more on the 'ego' realm - the differentiated; the Tao Te Ching tries to describe the undifferentiated, the uncut block (see verse 28) where the focus is on KNOWING how to be 'ego' (yang) but living the everyday in 'yin' etc.... which is what we do re consciousness/autopilot.

The way of the superior is to work through in detail all of the aspects of the IC, habituate them, and then forget them as your species-nature takes over through context pushing your newly-developed buttons.

It is this 'falling' that is emphasised in many texts in that the fall is to fall back onto your instincts AFTER you have used consciousness etc to refine them. As such the 'trust the force luke' perspective is to recognise that with good training you do not need to think and so can 'dissolve' into being integrated with 'reality'.

Our consciousness is but a PART of our full being, but with its development thinks it IS our full being - it isnt but nore is there a bottomless pit - there is a ground that is not detectable immediately, consciously, other than as an intuition that gets stronger the more you develop instincts and so trust intuition.

If we apply recursion to yin/yang 'forever' so we will head towards a continuum, BUT for us it is still bounded by the extremes of differentiating/integrating from when we get qualities to describe things. At the same time, the asymmetric element shows the differentiating emerging from the integrated - as we see in particle physics where fermions emerge in PAIRS from the Bose-Einstein Condensate as things 'warm up'.

Thus the path from bosons to fermions is a path of an asymmetric dichotomy that forms two categories that form a symmetric dichotomy orthogonal to the original asymmetric dichotomy. - IOW from bosons forms the fermion pair of electron/positron that 'splits' since they are opposites - and if they then meet they destroy each other by turning into bosons - the flash of light.

This dynamic is a mapping of properties of differentiating/integrating, yang/yin, and as such the words are metaphors for the underlying universals linked to some specialist context.

(SAME patterns go for mRNA/DNA dynamics such that the realm of DNA is 'diffuse', 'vague', 'general', where cut'n'paste is required to extract a particular from the general. That particular is formed into the contiguous code for a gene now in the form of mRNA, 'crisp', 'particular', 'concentrated', that is then 'read' by the ribosome and tRNA picks up amino acids coded into the gene to link and for th protein chain to develop.

The realm of being, of experiencing, 'bottomless' is the DNA realm in that in the realm of the vague so explicit identity is not present; it is all implied and so MANY possible relationships (and so a sense of being 'bottomless' when consciousness tries to reflect on this area)

Chris.

[martin]

I don't know what this 'bottomlessness' is. Animals seem to recognize it when merging or "falling" happens. I often have the impression (especially with horses) that they like it.
So it's probably a 'species' thing, a potential state that we all have in common. But the merging or falling is not necessarily a fall into unconsciousness, darkness. Sometimes it's more like falling "into the light", so to speak. Awareness becomes more crisp, more clear and there is a sense of awakening.

One problem with states of extreme merging (such as samadhi states) is that it may look from the outside as if the merging individuals have fallen asleep. They don't speak or move, eyes are closed, etcetera. And they may afterwards have no memory of what happened. Blank. So it seems that they were unconscious. But is that true?

There is no way to be sure about it but I suspect that animals like cats, dogs and horses are as awake and aware as I am and perhaps even more aware.

"It is this 'falling' that is emphasized in many texts in that the fall is to fall back onto your instincts AFTER you have used consciousness etc to refine them"

There might a relationship between the ability to stay awake (or become more awake) during merging and "refined" conceptual abilities.
I'm originally a mathematician (later my interest changed and I returned to the university to study psychology) and in merging states I recognize the same "crispness" and lucidness that I know from math. It's on another level, more perceptual instead of conceptual, but the quality is the same. And I think that my training in math is helpful somehow. Without it I would probably fall asleep more often. http://www.onlineclarity.co.uk/I_Ching_community/clipart/zzz.gif http://www.onlineclarity.co.uk/I_Ching_community/clipart/lol.gif

[hester]

ummm. : )

[martin]

Hmm? http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif

[lightofdarkness]

The other end of the scale is in expansive blending - this is a focus on a total, crisp, sense of self, very yang, differentiating. In the realm of drug use this state can be brought about using amphetamines/cocaine/aminergic_pathway.

With the sense of personal integration can come a sense of power, of positiveness, that can change quickly if difference is introduced into the immediate context - the positive gives way to paranoia and the negative.

The opposite focus is on a focus with others - sharing etc - gets into use of ecstasy, psychedelics etc and a sense of 'connection' with others etc. The issue is the 'down' that comes in the form of depression once the up is over.

With amphetamines the issue is in possible psychosis due to lack of sleep etc and taking risks due to the overwhelming sense of clarity and power, self-confidence to the level of hubris.

Thus clarity comes with high precision, it is explicit, discrete, differentiating. Move down the scale a bit and clarity becomes increasingly implicit - we identify by what we DONT know rather than DO know. Keep going and the realm of the implicit takes over to the point of losing boundaries etc.

In the context of Mathematics, a major focus has been on its discretisation, the move from the geometric to the algebraic, the field to the point, the dimensional to the dimensionless that THEN allows us to re-build dimensional perspectives with high precision.

The 'point' as such is more the concentration of a whole into that point - but that leads us into the realm of syntax, the label that reflects the concentration of semantics in a hierarchy where all that matters, where all that is 'important' is one's position.

This also gets into the specialist dichotomy of bandwidth/time where differentiation is the increase in bandwidth to identify something/someone NOW. If that cannot be done then we shift to past/future to aid in identification.

IOW there is a link of identity issues to the dichotomy of explicit/implicit, bandwidth(now)/time(past/future), differentiating/integrating, expansive blending/contractive blending, yang/yin.

Chris.

[martin]

I don't recognize this very yang sense of self and power, but I have seen it in others.
I'm probably more an "I am nothing" than an "I am everything" type. One the other hand it doesn't feel contractive. More expansive, really, but in a mellow way, like melting. These things are difficult to describe ..

[lightofdarkness]

;-) the problem in descriptions comes from the recursion. Thus the extreme yang sense of power is yang in yang (digram) but it also presents in the realm of yang in yin. This gets us into the two 'threads' of experience covered in the binary ordering of the IC.

As we zoom-in to make finer distinctions so we come up against the WHOLE binary sequence expressed in EACH element of the sequence! - IOW we start to 'see' 01 in 02, 02 in 01 etc but this is often due to the pairings - as you focus on one element of the pair you can exhaust it properties to suddenly find youself dealing with properties in fact of the other element in the pair!

In the realm of yin, the extreme yang state is expressed through such hexagrams as 28,44 with their focus on extremes BUT in service to the context shared with others/another rather than self (IOW despite the intensity of yangness in 44 the base yin line focuses that yangness on another/others through the energy used in persuation/seduction of another/others).

In the yang realm the associated hexagram pair is 43,01 with the 'spreading of the word' being one's own word etc. and the competitive, singlemindedness, devotion-to-self of 01 etc.

The split in the binary sequence to yin/yang shows the 'variations on a theme' perspective where we take the yin-based 32 hexagrams and put them next to the yang-based 32 hexagrams; the only difference for each hexagram in the pairs being in the bottom line. (as compared to the differences being only in the top line when we focus on the binary sequence as derived - e.g. 02,23 08,20 .... 34,14 43,01)

Chris.