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An organic arrangement of the 64 figures

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Philip_Aladdin

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Also see if anyone can spot the deliferate mistale I have cleverly hidden in the first image.
 
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charly

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Hi Phillip:

It seems to me that you have found one of the many solutions that the DeBruijn sequences allow.

An empirical method is to always start with six yang lines followed by six yin or vice versa. Go adding yin or yang lines randomly until a repeated hexagram occurs. Test then inverting the last line, if a repeated hexagram continues to appear, retreat inverting the previous line and moving forward again. Continue like this, advancing, retreating and advancing again, until it completes the sequence of 64 lines without duplication of hexagrams.

In Clarity you can read:

In Russell Cottrell's page,
a better mathematical approach:

Also can see here:

All the best,

Charly
 
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Philip_Aladdin

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Yes, I'm aware that it's a DeBruijn sequence, although I wasn't when I first arranged it. The most interesting part: if you apply to this to the 8 trigrams, only 2 arrangements are possible. A single shape can be thought of as moving upward through the lines, and that shape is the Taijitu in binary: 11101000 in one case and 00010111 in the other. This is an absolute inevitability when arranging the trigrams in this fashion. It seems some people have difficulty seeing the Taijitu in this shape: simply imagine 1 as white and 0 as black or vice versa (the S curve, of course, is not represented here). Taking all of the black bits as a whole, they encompass one offset white bit. Taking the white bits as a whole, they encompass one offset black bit. Each is offset "toward" its opposite. There is no symmetry, but perfect order - the centre in fact does represent an overlap between the two cases, and in this sense it has the same meaning as the S curve: superposition, or Taiji.
 
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Philip_Aladdin

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The 64-bit arrangement you linked looks similar to my overlapping extrapolation (like the Taijitu above) of my original 64 arrangement (see the gif in the original post; below is the shape which moves upwards in it). Notice that Heaven and Earth meet in the centre, the point of number 32 in my sequence:
Code: 
0101000110001011110000100100000011111101110101101001101100111001
Arranged in this way the final yang bit is the bottom line of the first figure, Already Complete.
 
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Philip_Aladdin

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I will emphasize this is about meaning and not simply structure. My ideas all came from inspiration or intuition and I'm no mathematician.
 
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Philip_Aladdin

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For my arrangement I think I did the opposite of what the guy in the other thread did. I started with 000000111111 then added 0s wherever possible, following the principle of the yielding, in order to allow the figures to arrange themselves. If you look at the 8x table, it becomes clear that the sequence has intelligibility.
 
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Freedda

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Philip Aladdin, a few points:

First, it seems to me that your arrangement is a little less 'organic' than you are describing: you made a conscious decision as to what hexagram to start with; and in a few places it looks like you interjected a choice or decision.

For example, for your hex 5, 'Beginning' (hex 03), it looks like you added a yang line to the bottom to make it your 6, 'Decreasing' (hex. 41), but to me the 'natural step would have been for it to be a yin line, make it 'Childhood' (hex. 04; your 11). Similarly with your 9 'Bringing Together' (hex. 45) the next 'organic' step to me would be to make your 10 'Watching' (hex. 20), but you choose to make it 'Increasing' (hex. 42).

I don't see a right or wrong here, only that you had a hand in which hexagrams follow which, making it not quite so natural or organic.

Next, and perhaps more importantly, why do this? Besides being an interesting game to pass the time, what purpose does it serve? I ask because I really don't see how it helps me with understanding and making use of the I Ching.

David.
 
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charly

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The first document where I saw a description of a «Wheel of Changes» as a combinatory wheel of 2^6 elements, by the catalan mathematician Prof. Jaume Aguadé:

«
La Roda de la Fortuna del Yijing
The Yijing Wheel of Fortune

If we visit the small local museum in Cape Bay, in the tormented northern coast of Terranova, we can admire a kind of ivory wheel (absurdly cataloged as an "old toy") that presents, along its entire perimeter, incisions in seemingly capricious disposition, formed by small segments, whole or divided in half.

Who knows minimally the story of Bagua, the secret sect of the eight trigrams, will recognize a "wheel of fortune" (or "wheel of changes", as it would be more appropriate to call it), whose use, as aid for divination through Yijing (I Ching in the Wade transcript), is well documented, at least since the time of the Xuan monarch.

It was necessary to roll the wheel until it stopped and, then, read the six symbols to the right of the indicated point. Most remarkable is that, although the wheel only has 64 symbols on its perimeter, each of which is either a whole segment (yang) or a divided (yin), all the 64 hexagrams that make up the Yijing corpus are there represented.

When, at the Han time, multiple Yijing spurious versions began to appear, which unlikely multiplied the number of trigrams, possession or not of an appropriate wheel of fortune became the touchstone of each new modification. (With what precision Mei Sheng does not ridicule, the great poet, those deviners who appear with incomplete or excessive wheels!)

As might expect, the import of fortune wheels in the West vanished from their mystical content and turned them into kabbalistic or combinatorial magic toys. Tartaglia (which is known to have used, in esoteric circles, fortune wheels up to 2 elevated to 7 symbols on the perimeter) conjectured that only when n is prime, perfect square or perfect, there is a wheel with 2^n symbols .

As Borges reminds us very well, the solution to the enigma is always inferior to the enigma. It was an unknown employee of the post office of Königsberg who demonstrated the existence of wheels of fortune for all value of n and found how to build them.

The consequences, as expected, will be terrible: in 1813 the sect of the eight trigrams revolted against the emperor; Composed with the Bailian (the almighty sect of the "white lotus"), the country has a serious crisis that had to lead to the war of opium and, towards the end of the nineteenth century, to the revolt of the boxers.

The postal employee, needless to say, disappeared in very strange circumstances, which we can not imagine but as terrible.

What should be the theory of the post office employee?


Jaume Aguadé
»​

Source: http://mat.uab.cat/~aguade/articles/yijing.html (original in catalan)

May enjoy it!


Charly
 
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Philip_Aladdin

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David, read the post directly above yours. I did not start with a single figure, I started with the intersection of heaven and Earth: 000000111111 then when the arrangement was complete, my choice was to put Already Complete first, and Liberation last. This is because, in the spiritual journey, liberation is finding out where you already were.
 
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Philip_Aladdin

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Charly, thanks for posting that.
When, at the Han time, multiple Yijing spurious versions began to appear, which unlikely multiplied the number of trigrams
Click to expand...
I don't understand this (I may be missing something?), the number of trigrams can only be eight. I find the naming conventions very revealing of the workings of the Eastern and Western minds: we call them trigrams because we are focused on the details, which gives us the illusion that there could be infinite possibilities out there that we don't know about. The Chinese word Bagua emphasizes the whole instead, which is already complete from the get-go. Now I've found that the Taiji is necessarily hidden in those trigrams as binary (00010111), but who will hear me? Nobody who can't release themselves from the postmodern cultural background, which tells us that there are infinite possible unique-and-individual outcomes for any set of circumstances (and that's why you're so special). We think we are the multitude, not the union. What the I Ching should teach us is that each action has an appropriate reaction, not just some reaction. This is why I emphasize the "change pattern" or middle figure between Primary and Secondary: because it's determined, and so it can't be anything else, just like the Taijitu hidden in the Bagua. Any two figures can be put together, but any combination of two can only have a single change pattern. Our culture is terrified of determinism and desperately attached to free will and individuality, so this kind of thing makes us uneasy at best, but like it or not, this is the lesson of the I Ching. You are not as individual as you thought, you're the union not the multitude. Ultimately this tool will remove all obstacles to our coming together as a planet, because it is the superposition of yin and yang, east and west, right brain and left brain, free will and determinism, and ultimately: self and other. This is the tool which will enable us to realize we're the same. The world's first commercial quantum computer was just released, using a type of binary more similar to the I Ching than ever (it includes an analog for changing lines: superpositions) - what about when they realise that all they have to do to "create an intelligence" is to stop creating? Let the bits choose themselves; shut up and allow it to speak. But we can't trust that it will because we want intelligence for ourselves; who will submit themselves to foolishness and be bold enough to try listening? Most of us refuse to listen to the "monolith" of human creativity and only want to put words in its mouth or copyright it, because the voice it channels we can only conceive of through a paradigm of authority and judgement, because we feel WE are authors and WE are judges, and it mirrors our stories. "Uh oh, daddy's back - and he's angry!" If only we knew that all it is is a black mirror, we could use it to finally find ourselves. Whoever is reading this on a phone or tablet, lock the screen and you will see me.
 
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Freedda

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Philip_Aladdin said:
David, read the post directly above yours. I did not start with a single figure, I started with the intersection of heaven and Earth: 000000111111 then when the arrangement was complete, my choice was to put Already Complete first, and Liberation last.
Click to expand...
Okay, as I said - and perhaps I needed to make it clear that this is my main point - I don't see the 'why?' in all this. I don't see that it helps me understand the I Ching. And you don't really make any connection to using it that I can see. Or did you present it and I missed the meaning?

As to '00000011111,' I might have a clue what you mean, but still may main point stands. And again, my other point was you made some decisions and choices about the order of your sequence (as you describe above) which means you had a hand in its 'organic' or 'natural' order. Nothing bad or good here, just restating what you said above.

Philip_Aladdin said:
This is because, in the spiritual journey, liberation is finding out where you already were.
Click to expand...
That is your opinion. Mine is the order of the I Ching starts with the primal forces of Heaven and Earth, and then goes on to show 64 ways that these manifest (as the hexagrams and trigrams) and many more ways (the changing lines) that these interact with each other - and that's all I need to know really; that's as 'spiritual' as I need the I Ching to be for my purposes. I am not looking to find order or rearrange the Yi to find that order. You can of course do that.

And again: what is the point of your new sequence and how does it help me in using the I Ching.


David.
 
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Trojina

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Philip_Aladdin said:
Charly, thanks for posting that. I don't understand this (I may be missing something?), the number of trigrams can only be eight. I find the naming conventions very revealing of the workings of the Eastern and Western minds: we call them trigrams because we are focused on the details, which gives us the illusion that there could be infinite possibilities out there that we don't know about. The Chinese word Bagua emphasizes the whole instead, which is already complete from the get-go. Now I've found that the Taiji is necessarily hidden in those trigrams as binary (00010111), but who will hear me? Nobody who can't release themselves from the postmodern cultural background, which tells us that there are infinite possible unique-and-individual outcomes for any set of circumstances (and that's why you're so special). We think we are the multitude, not the union. What the I Ching should teach us is that each action has an appropriate reaction, not just some reaction. This is why I emphasize the "change pattern" or middle figure between Primary and Secondary: because it's determined, and so it can't be anything else, just like the Taijitu hidden in the Bagua. Any two figures can be put together, but any combination of two can only have a single change pattern. Our culture is terrified of determinism and desperately attached to free will and individuality, so this kind of thing makes us uneasy at best, but like it or not, this is the lesson of the I Ching. You are not as individual as you thought, you're the union not the multitude. Ultimately this tool will remove all obstacles to our coming together as a planet, because it is the superposition of yin and yang, east and west, right brain and left brain, free will and determinism, and ultimately: self and other. This is the tool which will enable us to realize we're the same. The world's first commercial quantum computer was just released, using a type of binary more similar to the I Ching than ever (it includes an analog for changing lines: superpositions) - what about when they realise that all they have to do to "create an intelligence" is to stop creating? Let the bits choose themselves; shut up and allow it to speak. But we can't trust that it will because we want intelligence for ourselves; who will submit themselves to foolishness and be bold enough to try listening? Most of us refuse to listen to the "monolith" of human creativity and only want to put words in its mouth or copyright it, because the voice it channels we can only conceive of through a paradigm of authority and judgement, because we feel WE are authors and WE are judges, and it mirrors our stories. "Uh oh, daddy's back - and he's angry!" If only we knew that all it is is a black mirror, we could use it to finally find ourselves. Whoever is reading this on a phone or tablet, lock the screen and you will see me.
Click to expand...


It's really hard to read one big chunk of text with no paragraphs. Unfortunately a forum bug affecting newbies does this it isn't your fault but if you wish to correct there is advice from Hilary here as to how to get paragraphs and format and so on link doesn't work but you go to 'forum setting's then' general settings' and switch editor
 
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Philip_Aladdin

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That is your opinion. Mine is the order of the I Ching starts with the primal forces of Heaven and Earth, and then goes on to show 64 ways that these manifest (as the hexagrams and trigrams) and many more ways (the changing lines) that these interact with each other - and that's all I need to know really; that's as 'spiritual' as I need the I Ching to be for my purposes. I am not looking to find order or rearrange the Yi to find that order. You can of course do that.
Click to expand...
I'm sorry Dave, I'm afraid I can't do that.
 
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Freedda

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Philip_Aladdin said:
I'm sorry Dave, I'm afraid I can't do that.
Click to expand...
That's fine. To each his own. We all have our own way of being spiritual and of being with the Yi.

But I'm still curious about my main point, which I've raised a few times now: how does this help me understand and better interpret the Yi?


d.
 
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