Hexagrams as path between trigrams

[heylise]

Chris,

I have several of your mails printed, and have been making notes.
There is one thing which is difficult for me: binary, especially the binary sequence, in regard to hexagrams. It implies, that one line has another value than another one. The top line is 1, the 5th line "10", or in binary 2. Line 4 "100", in binary 4, and so on.
If the values were according to the Fibonacci sequence, I would jump on it right away, because that is a sequence of life itself. Maybe I can figure out some day, if there is something like that . . .
On the other hand,with the binary sequence you combine 28 with 44, and that could very well explain the "bad" associations of 44. Da Guo (28) is great exceeding, but also big trespass, big faults, and it is used especially in an environment with many rules, like schools or the army, when these rules are transgressed. And wind "not trusting" fits very well with astrological air.

Somewhere else you mention dodecagrams, which are in between every two hexagrams. The Yilin has to do with them: 4096 verses, for every hexagram-pair one.
But going the other way, towards less lines, there are the trigrams, with 64 hexagrams between every two trigrams. Every trigram can change into 7 other trigrams and in itself (or be static).
Han Boering argued, that the Wings say :"the hexagrams . . by doubling the trigrams" and it is generally assumed that it means putting one trigram on top of another one. But what if it means doubling ONE trigram? After all, that is the literal text. A yang line can be doubled and becomes two whole lines when it is an old yang line, or an whole and a broken line when it is a young yang line. The trigram fire, consisting of only old lines, becomes water - through hexagram 61.

If wind changes to water, hex.25 is the "path".

Wind to wind (stays wind): hex.21 is the path.

For every two trigrams, it is easy to find the hexagram, and for every hexagram it is easy to find the two trigrams.

One difficulty is, that no one agrees about the right way to write young yang and yin. It is not a mistake of a translation, even in Chinese texts there is no agreement. But because it says, that in every yang there is some yin (inside, so below), I assumed young yang is a yang line above, and a yin line below/inside. In Wilhelm it is the other way, but it seems in the first German edition it was like I have it above, but in the next edition, the two bigrams have been swapped, and subsequently in all translations.

LiSe

 

[chrislofting]

Hi LiSe,

you wrote:
> Chris,
>
> I have several of your mails printed, and have been making
> notes.
> There is one thing which is difficult for me: binary,
> especially the binary sequence, in regard to hexagrams. It
> implies, that one line has another value than another one.
> The top line is 1, the 5th line "10", or in binary 2. Line 4
> "100", in binary 4, and so on.

Umm...No. Develop bottom-up through the full set of possible line pattern combinations - that gives you 0 to 63. Each of the six hexagram lines on its own reflects the value of 1, 2, 4, 8, 16, 32 bottom-up.

Thus if we step through hexagram 02 from bottom to top we have:

000000 (full hexagram, no change)
100000 (change line 1 - binary 1)
010000 (change line 2 = binary 2)
110000 (change lines 1 & 2 = binary 3)
...
...
000001 (change line 6 = binary 32)
100001 (change lines 1 & 6 = binary 33)
...
...
011111 (change all bar line 1 = binary 62)
111111 (change all lines = binary 63)

Call this the 'vertical' sequence. If you ROTATE each value in this sequence, and so get

000000 (hex 02)
000001 (23)
000010 (08)
000011 (20)
..
..
..

you get the 'traditional' binary sequence order of the I Ching with 32 yin hexagrams followed by 32 yang (or visa versa, depended where you start from, yin or yang ;-)) - this sequence is also derived through recursion of yin/yang building each symbol line-by-line bottom-up. (call it the 'horizontal' sequence).

There ARE issues here re trying to derive the hexagram binary NUMBER from this symbolism in that you have to work top-down OR rotate the sequence to the above line-change pattern and in doing so lose the sequence!

As such you need to differentiate symbol from position OR change the association of 1=yang, 0= yin to 1=yin, 0=yang! The binary sequencing as such establishes a very tight link of one hexagram to that that comes before and after and allows us to work with pairs where the pair of hexagrams have emerged from a pentagram and two pentagrams have emerged from a tetragram and two of those from a trigram and two of those from a digram and two of those from yin or yang.

> If the values were according to the Fibonacci sequence, I
> would jump on it right away, because that is a sequence of
> life itself. Maybe I can figure out some day, if there is
> something like that . . .

The values *are* derived from the fibonacci sequence in that both are derived from the Zierpinski gasket from which is derived Pascal's Triangle. The SUM of the coefficients of each row in the triangle reflects powers of 2 and so the recursion element. The fibonacci sequence sums at an angle across rows of Pacal's triangle.

The fibonacci sequence reflects a less rigid 'either/or' perspective and as such is also less 'precise' in expression. In my IDM material I use the concept of the "Dimension of Precision" which has the realm of the UNARY at one end and the BINARY at the other. If we convert each point on this dimension to number sequences we can get:

0,1,1,1,1,1,1.... UNARY
0,1,2,3,4,5,6.... first level 'memory' where the previous context frame feeds into the current (n = 1 + n-1) Here is the first steps in developing a history, a memory, a sense of 'development'. Next we consider the past TWO context frames to give us..

0,1,1,2,3,5,8,13... the fibonacci sequence (use the previous TWO context frames (n = n-1 + n-2))

Keep doing this (next is the tribonacci sequence - last THREE context frames as feedback to determine the current and so on) and out pops...

0,1,2,4,8,16,32... binary sequence (use the sum of ALL previous context frames to mark the current frame)

(see old diagram at the bottom of http://pages.prodigy.net/lofting/dicho2.html )

Geometrically these sequences ALL map to patterns of spirals from the fibonacci sequence onwards but the 'round' nature of the spiral from the fibonacci sequence gives way to a square spiral of the binary, we move increasingly to EITHER/OR perspectives and so angles are all 90 degrees, the 'circle' has become a 'square' ;-)

To go BEYOND the binary means we move from the stable to the unstable, we move into the realm of complexity/chaos and so the realm of emergence where we put in more energy than is there in the first place and so allow for 'transcendence' concepts etc. As such there is a dimension of stability reflecting ratios from 1.618 to 2.00. Each position on this dimension is a possible perspective upon reality moving from the general but qualitative of the fibonacci to the particular but more quantitative of the binary.

The fibonacci sequence reflects conservation of energy but also allows for a small, slower, degree of development. LESS than that there is little/no development, all is balanced, integrated, still (and so 'dead', no differentiations). As you put in more energy so the dynamics shift from a slow, approximations biased, path of development to something high energy, fast, VERY A/NOT-A and so very energy expending.

The benefits of the binary are in its precision BUT it can also be too precise in that it deals with PARTS more than WHOLES but our consciousness, a seeming product of increased energy expenditure and development, works out of a more binary perspective and considered itself to be originating and so can confuse parts with wholes.

Our species-nature works mindlessly off instincts and as such is at the unary end of the dimension. Our consciousness-nature is ever increasingly mindful and so increasingly binary oriented - the more precise you want to be the more distinctions you need to make, the more 'cuts' of the whole into parts. As you keep cutting so you can go too far and things become unstable.

As such, ALL of this *is* rooted in the fibonacci patterns where before that pattern there is no sense of 'memory'. In ancient Spiritual Geometry the Golden Ratio we find in the fib. sequence was considered the closest one could get to 'god', reflecting the use of the term 'god' as a metaphor for the Universe where the Universe was anthropomorphised, we projected ourselves, our 'lifeforce' into the Universe. This interpretation of reality reflects *integration*, to blend-IN. As we move to the more binary perspectives so transcendence, differentiation, is more attractive and we get a sense of 'god' through moving 'upwards', forwards rather than backwards - this gets us into issues of 'fundamentalism' etc - lots and lots of 'gurus' etc! ;-)

> On the other hand,with the binary sequence you combine 28
> with 44, and that could very well explain the "bad"
> associations of 44. Da Guo (28) is great exceeding, but also
> big trespass, big faults, and it is used especially in an
> environment with many rules, like schools or the army, when
> these rules are transgressed. And wind "not trusting" fits
> very well with astrological air.
>

The differences in meaning are in the differences of the top line. 28 (011110) reflects the integrating bias of the pentragram of 01111 whereas 44 (011111) reflects the differentiating bias of the same pentagram. At the really generic level of meaning there is no distinction of 'good' or 'bad' and so just as 28 reflects 'great exceeding' in a negative context, it also reflects 'going beyond what is required', to 'go the extra distance' for someone/something as a positive concept (reflects the lack of trust in others meaning we have to do things ourselves and so do extra work and that is interpretable as 'going beyond what is [usually] required' - the behaviour can be interpreted as being 'kind and generous' but it can reflect a hidden lack of trust in anyone else doing the task 'properly')

With this binary sequence ordering we get patterns repeated at all levels such that zoom-in to the octet of wind:

46, 18, 48, 57, 32, 50, 28, 44

and the yin(integrating,balancing)/yang(differentiating, exaggerating) roots of the original dichotomy of yin/yang get repeated such that 44 is the exaggeration of 46, 28 the exaggeration of 18, 50 the exaggeration of 48, and 32 the exaggeration of 57.

Thus, for example, the integrating, balance-oriented focus on entanglement in 46 is exaggerated to become the hard-core, intense, competitive, persuasion/seduction entanglement issues of 44. The 'correcting corruption' of 18, going about and 'balancing' things, restoring values, qualities etc, is exaggerated in the excess of 28, we can go too far etc. and so on.

For the octet as a whole (46,18,48,57) are the 'yin' and (32,50,28,44) the 'yang'. Zoom-in to each of these sequences and we have (46,18) is the yin, (48,57) the yang of (48,18,48,57) whereas (32,50) is the yin and (28,44) the yang of (32,50,28,44). Zoom-in on the pairs and 46 is yin, 18 is yang of (46,18) and so on.

These relationships apply to all octets of the binary sequence, as they do to the whole of the sequence (32 yin-based hexagrams vs 32-yang based hexagrams etc) in that the method of recursion will encode in all parts, as PAIRS, the root whole, that is the root distinction of yin/yang.

> Somewhere else you mention dodecagrams, which are in between
> every two hexagrams. The Yilin has to do with them: 4096
> verses, for every hexagram-pair one.

? should not this be 64 dodecagram verses for each hexagram? There are 64 dodecagrams that are manifest through the changing line patterns in a particular hexagram.

> But going the other way, towards less lines, there are the
> trigrams, with 64 hexagrams between every two trigrams.

? 8 hexagrams map to each trigram where the expression of the hexagrams is in changing-line patterns in trigrams.

> Every trigram can change into 7 other trigrams and in itself
> (or be static).

yup. see the comments on changing line trigrams above (as well as the link).

> Han Boering argued, that the Wings say :"the hexagrams . .
> by doubling the trigrams" and it is generally assumed that
> it means putting one trigram on top of another one. But what
> if it means doubling ONE trigram? After all, that is the
> literal text.

Sure, but consider this applied to lines. This is reflected in my changing trigram line 'quick I Ching'

see http://pages.prodigy.net/lofting/lofting/proact3.html

where given three questions (and so a trigram format) I have the rules of:

yin line becomes two yin lines
yang line becomes two yang lines
yin-into-yang change becomes yin line followed by yang line
yang-into-yin change becomes a yang line followed by a yin line

Thus:

001 trigram becomes
000011 hexagram

if the first line of the above trigram is changing then I have:

x01 (here x = yin into yang)

and it becomes the hexagram of

010011

Thus, for example, the trigram of fire (101) extends into the hexagram of 110011 - 61. SEMANTICALLY there is still the link of a yang boundary, pushing outwards, reflecting outwards, within which is the core yin. (this is also covered in my webpages on generation of dodecagrams - http://pages.prodigy.net/lofitng/64dodecagrams.html)

To derive the *hexagram* of fire requires closer consideration of the three questions to get 101101 = X1X (yang into yin (10), pure yang (11), yin into yang(01)) IOW the changing lines of the trigram give us more precision in the context of working with trigrams as reflections of WHOLE situations. As such the general nature of what we call the fire trigram does NOT extend to become the hexagram of fire, there is finer detail at work when we introduce changing-line trigrams.

For each trigram there are 8 possible hexagrams expressing the full range of change etc, just as when we zoom-in to working with hexagrams there are 64 dodecagrams applicable to the one hexagram. Thus at the trigram level where we treat the trigrams as WHOLES and the hexagrams as PARTS there are 64 parts. Change scale to the hexagram level where we treat the hexagrams as if WHOLES and the dodecagrams as PARTS there are 4096 parts. Thus the same area of 'parts' is cut into finer and finer distinctions and this will be reflected in the different levels such that at the trigram level the trigram of 101, as reflecting a WHOLE, does NOT, cannot, contain the PART that is 101101. (the only invarients here are 111 and 000)

The trigram model is 'general' and the move to hexagrams, dodecagrams etc gives us increasing details. It is like working with numbers, at the level of WHOLE numbers there is just 1,2,3,4... zoom-in and we move to rational numbers, PARTS (the harmonic series etc) and so finer detail. Zoom-in again and we move to include irrational numbers and so move to REAL numbers. From here we have to include dynamics and so introduce imaginary numbers that allow us to create COMPLEX numbers.

Zoom-in again and we need to use Quaternions and from there we move to Octonions. We cannot go really any further (although some have tried) in that the laws of Algebra break down too much. Note the powers of 2 here where we represent values in real number forms:

REAL = a [1]
COMPLEX = a + b [2]
QUATERNION = (a + b), (a + b) [4]
OCTONION = ((a + b), (a + b)),((a + b), (a + b)) [8]


> A yang line can be doubled and becomes two
> whole lines when it is an old yang line, or an whole and a
> broken line when it is a young yang line.

yup ... the process of change is sequential such that a changing yin line is representable at the next scale by a yin line *followed by* a yang line etc.

> The trigram fire,
> consisting of only old lines, becomes water - through
> hexagram 61.
> [ Fire ] [ hex. 61 ] [ Water ]
>

!! see above where I use the same fire->61 example.


>
> One difficulty is, that no one agrees about the right way to
> write young yang and yin. It is not a mistake of a
> translation, even in Chinese texts there is no agreement.
> But because it says, that in every yang there is some yin
> (inside, so below), I assumed young yang is a yang line
> above, and a yin line below/inside. In Wilhelm it is the
> other way, but it seems in the first German edition it was
> like I have it above, but in the next edition, the two
> bigrams have been swapped, and subsequently in all
> translations.
>

I dont bother with these terms. The issue is resolved in the consideration of DIRECTION, as in moving 'UP' a hexagram. Thus changing yin line becomes a pair of lines of yin followed by yang, as changing yang becomes yang followed by yin - and so reflecting the change as a sequence of events. You could interpret this sequence where yin gives birth to yang and so 'young yang' as yang can give birth to yin and so 'young yin'.

Due to the differences in yin/yang so young yang reflects transformation (an exaggeration out of the yin), whereas young yin reflects transcendence (from high energy emerges a 'new' level that is initially 'reactive' in expression and in need of differentiation as we develop into this 'new' realm - note the link to the thunder trigram etc).

Chris.

 

[heylise]

Ufff

Well, thanks for your answer.
Guys, i will be on holiday for quite some time, with a long mail, off to an inhabited island.

Ah no, won't do, no dictionaries and Google there. I will have to do it all right here at home . . .