Abstract
(last update 7th August 2005)
The traditional I Ching (Book of Changes) is about change, about processes and sequences, but it is dependent upon structures to achieve its focus on events 'between' structures and/or within structures. Given this focus, so the emphasis here is on the "Book Of Structures" where the focus is not on change but the properties and methods of the structures, identifying their 'DNA'/Spectrum so to speak. Here we work from identifying the creation of these structures, their form as universals, and the details we can extract using various methods of analysis. As such there is little or nothing here about change or divination, more so the focus is on the non-changing, archetypal, universal, forms that get localised and turned into 'small world network' representations.
Octets of Hexagrams (binary sequences)
Details - XOR-ing (Getting a hexagram's spectrum)
Details - I Ching Wave Interpretations
Details - I Ching & Quantum Mechanics Interpretations
Details - Logic of Relationships
Details - Recursion, I Ching, and DNA
The I Ching, or Book of Changes, is a text dominated by a focus on process, on sequence. The methodology involved in creating the symbolisms of the I Ching is not just focused on process but on the processing around, within, between, archetypal, and so universal, structures. The following material is about those structures - how the method of derivation, the use of recursion of yin/yang (or more generically, the recursion of A/NOT-A), and so of self-referencing, extracts definite forms that serve as universals in describing processes. To describe a dynamic you need statics, objects, to make the point - even if these objects are products of relationships, they are universal products of universal relationships. In the context of the concept of "Small World Networks" so the universal form of the I Ching is a static, regular, form where all is linked together. When exposed to the 'randomness' of reality so that exposure sets up the nature/nurture dichotomy out of which emerges the 'middle' position of a "Small World Network" - derived from ad hoc links to 'fit' the dynamics of the local context:
The 'traditional' I Chings, all of the different interpretations/translations, come out of the middle position or right position in the above diagram. If we treat these as 'transparent', so stacking all of these local maps, one atop the other, will start to bring out the universal patterns, the potentials that are actualised in different contexts. As such, the "Book of Structure" covers the 'regular', the right element in the above diagram where all is linked together.
Our brains reflect this dynamic where the genetics is the nature and exposure to reality, nurture, skews development to fit the local context. This dynamic operates at all scales such that neural networks reflect 'small world networks' as do our social collectives.
In the formation of the genetic level, the 'complete' whole with all of its links, the method of deriving structures from yin/yang reflects the extracting of parts from a whole. In the brain this is done through recursion and the use of the XOR operator (exclusive OR). This operator allows us to extract objects out of complex patterns (and so allows us at time to 'err' in that process and end up with a sensory paradox). In the I Ching we move from the single dichotomy of yin/yang to complex forms of 2-line, 3-line, 6-line, and 12-line representations (digrams, trigrams, hexagrams, dodecagrams). The main focus here will be on the structures of hexagrams, with some reference to trigrams and dodecagrams.
The brain dynamics referenced above focuses on extracting from a complex pattern (an integrates 'whole', a focus on linking and so AND-ness) the parts that make up that pattern. In the I Ching this dynamic of XOR/AND will bring out 64 hexagrams of the I Ching - all ordered into a sequence of structures where the sequence is called the 'binary' sequence.
This sequence of 64 hexagrams is made-up of eight octets, where each octet is made up of eight hexagrams all with the same trigram as base. The WHOLE sequence of hexagrams has a STRUCTURAL focus that reflects TWO forms of interpretations regarding the nature of these structures and their relationship to all of the others.
The nature of the yin/yang dichotomy allows us to map to that dichotomy, and all of the structures derived from the recursion of that dichotomy, ANY dichotomies but in TWO forms - symmetric vs asymmetric.
A symmetric dichotomy is where the elements of the dichotomy are at the general nature, the same. For example, if we want to map the IQ or EQ of 'people' so the context is of 'all people' and we want to extract the spread of the expression of IQ or EQ. This process will give us a Gaussian, or 'normal', distribution curve. The generic qualities of the dichotomy are thus of like natures - differentiating/differentiating or integrating/integrating. The symmetry is in an aspect, e.g. positive/negative, and so the elements appear as 'opposites' where we are trying to categorise DIFFERENCES FROM SAMENESS.
An asymmetric dichotomy is where the elements of the dichotomy are at the general nature, different - where this difference is in exaggerations of one element from the other - e.g. the dichotomy of ACTUAL/POTENTIAL. Recursion applied to this type of dichotomy will create a SPECTRUM (and so a focus on power laws) of categories and as such span levels of a hierarchy, from general-to-particular, potential-to-actual, crisp-from-vague, precise-from-approximate, hot-from-cold (as such we are not at a single level of analysis - hot/cold reflects a hierarchy of temperature differences and so spanning energy levels). With these sorts of dichotomies the focus is on identifying, categorising, SAMENESS ACROSS DIFFERENCES. The core focus is on the elements that generically reflect association of differentiating/integrating elements in the dichotomy.
Symmetric dichotomies focus on analysis WITHIN a level, a single context. Asymmetric dichotomies focus on analysis BETWEEN levels and so cover multiple contexts. The abstract nature of yin/yang, also representable in 'bit' (BInary Digit) form as 0/1, allows for the I Ching to reflect both forms of dichotomies and the nature of recursion ensures that these different types of dichotomies are linked together as fundamental to the structure of the I Ching.
Due to the nature of these two forms of dichotomies, when applied recursively, the binary sequence is interpretable as a 'mirrored' system of STRUCTURAL opposites as well as STRUCTURAL complements. Due to the self-referencing, so each octet reflects the properties and methods of the WHOLE sequence - this is called 'fractal' behaviour where we see the same patterns reflected at different scales.
To cover the basic nature of the octets that make up the binary sequence, below is that sequence presented with brief comments on each octet. Later material will then flesh out more details on hexagram structures etc., and so explain some terms mentioned below such is 'skeletal forms' and '27-ness'.
Here are links to pages describing the basic qualities of each octet - a set of eight hexagrams all with a particular trigram as their base - together with links to pages covering each hexagram in detail.
In the octet material there is occasional reference to such terms as 'skeletal form' and '27-ness' of a hexagram. These references are to the application of the XOR-operator to EACH hexagram to derive more details of its PARTS nature - and so more details on STRUCTURE.
Due to the manner in which the I Ching is represented, as fixed or broken lines or as 'bit' sequences of 0s and 1s, so we are able to extract finer details of a hexagram, what contributes to its overall meaning.
Due to the manner in which the structures of the I Ching are formed, so each hexagram is in fact made-up of its own nature plus the input of all of the other hexagrams. As such, we can consider each hexagram and coming with a 'genetic code' sequence, or its 'spectrum', made up of the expressions of other hexagrams THROUGH the particular hexagram under consideration.
What is reflected here is the influence of CONTEXT on the expression of some ARCHETYPE through that context.
Since the I Ching is a form of language, in that it describes 'all there is', so we realise that it cannot not map its 64 hexagrams (or 4096 dodecagrams) to 'all there is' in a 1:1 format - it must predominately use analogy and metaphor to describe 'all there is'.
The finite nature of the I Ching means that as a language so all parts are 'entangled' with all other parts to make-up the whole. In this entanglement, each hexagram will contribute to expressiveness of any other hexagram, and this expressiveness is only describable by analogy to the characteristics of some other hexagram.
For example, we find that the nature of hexagram 27 is on the skeletal form of 'something' and the focus on being discerning about how we add 'meat and muscle' to that skeleton. Thus, through using the XOR operator to apply 27 to any other hexagram we will bring out the skeletal form of that hexagram. Thus, of we apply 27 XOR 01 we will get, by analogy to another hexagram, the description of 01s skeletal form, and we find it is in hexagram 28; hexagram 28 covers the focus on 'excess' such that the focus here is on 01s skeletal form being described as 'too much yang'.
We can in fact do this sort of 'extraction' to ALL hexagrams where we can obtain for each hexagram as sequence of 64 hexagrams describing the expression of all of the archetypes THROUGH each hexagram serving as a description of context. (for more on this, see the page on line meanings)
The XOR operator works where, given x and y as line values (0 = yin, 1 = yang) we create a third representation based on rules derived from this 'truth' table:
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Y |
X XOR Y |
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0 |
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0 |
1 |
1 |
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1 |
0 |
1 |
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1 |
1 |
0 |
Thus, XOR-ing hexagram 27 with hexagram 01 gives us hexagram 28:
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Hexagram 27 |
Hexagram 01 |
27 XOR 01 = Result - Hexagram 28 |
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(line 6) 1 |
1 |
0 |
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(line 5) 0 |
1 |
1 |
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(line 4) 0 |
1 |
1 |
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(line 3) 0 |
1 |
1 |
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(line 2) 0 |
1 |
1 |
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(line 1) 1 |
1 |
0 |
Put ANY hexagram in the first column and the XOR process will describe, by reference to some other hexagram, the expression of that first hexagram 'through' the middle hexagram - and so an expression of a part. - and so the 27-ness of 01 is described by analogy to the generic qualities of hexagram 28. This information is given in the seperate pages for each hexagram linked off the below table (under the heading "line meanings"):
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A point to note here - if we can get this sort of detail from recursion of any dichotomy then this raises some
points of interest in the recursion of purines/pyramidines in that it is that recursion that gives us the codons
used in DNA/RNA processing. Note that if we take the naturally-derived binary sequence of
the I Ching, where we develop hexagrams bottom up adding yin/yang at each level, we get, using the traditional
numbers, the following order - note I have taken the sequence of 64 and packed it into a matrix of 8 octets - each
octet made up of 8 hexagrams all with the same base trigram:
02 23 08 20 16 35 45 12 (earth base)
15 52 39 53 62 56 31 33 (mountain base)
07 04 29 59 40 64 47 06 (water base)
46 18 48 57 32 50 28 44 (wind base)
24 27 03 42 51 21 17 25 (thunder base)
36 22 63 37 55 30 49 13 (fire base)
19 41 60 61 54 38 58 10 (lake base)
11 26 95 09 34 14 43 01 (heaven base)
If we then REPLACE each number above with the number derived from XOR-ing the associated hexagram with hex 27 (and
so derive the 27-ness) we get this sequence:
27 24 42 03 21 51 25 17
22 36 37 63 30 55 13 49
41 19 61 60 38 54 10 58
26 11 09 05 14 34 01 43
23 02 20 08 35 16 12 45
52 15 53 39 56 62 33 31
04 07 59 29 64 40 06 47
18 46 57 48 50 32 44 28
We have seen this before - it is the root horizontal sequence of 27/28 pair, covered in the ICMatrix
pages How is it derived? By applying line changes 'up' a hexagram and then rotating the hexagrams in the resulting
sequence (see the vertical sequence for 27/28 above) Thus the material covered in the icmatrix link is associated
with the XOR-ing process where a seemingly 'different' method elicits the same results.
The focus here is on association of XOR with recursion and rotations - properties present in the IC and a property
of recursion in general - and so showing the strong association of XOR and recursion as roots of meaning derivation
in our brains - and so the basic qualities of the IC are hard-coded into our brains in a universal form of a regular
network where all is connected together.
In the process of building hexagrams we move from the general to the particular, bottom to top, vague to crisp, approximate to precise. What is indicated in this process is a change in qualitative meanings, a change not reflected in the yin/yang line structures where their only apparent difference is in their order, their magnitude remains 'constant' (0 XOR 1, yin XOR yang).
Analysis of this movement from general to particular shows us a method of interpretation through the summing of wave patterns.
In a time where particle/wave duality is a well-discussed concept, we can see this 'duality' emerge as a property of combining dichotomous thinking with indeterminacy. This is done through taking the 64 hexagrams of the I Ching and introducing indeterminism by only working with PAIRS of LINES. In so doing we reduce the 64 hexagrams to 27 symbols. Using 1s and 0s we can show two columns, the left being the explicit 64 hexagrams, the right showing their 'compression' into 27 symbols. If we then graph those 27 symbols we find they form a wave-interference pattern (see diagram following the columns in the folllowing link)
To continue the theme on structure, so the categories derived from recursion of yin/yang form a sequence of hexagrams called the 'natural binary sequence' - where the term 'natural' reflects the fact that the sequence is derived from simple recursion of the yin/yang dichotomy - no more. What we find in this process is a primitive 'logic of relationships' where, given the core focus on yin/yang as 'opposites' so the relationship of yin to yang is reflected in all PAIRS of structures derived. For example, if we recurse to the level of trigrams, and using 0 for yin and 1 for yang we have:
000, 001, 010, 011, 100, 101, 110, 111
The relationship of 000 to 111 is of 'opposites', of pure yin vs pure yang. This relationship is repeated in the other trigrams as:
001 to 110 (read as "001 is to 110 as 000 is to 111")
010 to 101
011 to 100
BUT, due to recursion so it is also reflected in such pairings as:
000, 001 (read as "000 is to 001 as 000 is to 111")
010, 011 (read as "010 is to 011 as 000 is to 111")
100, 101
110, 111
This 'little' pattern is in fact extendable to cover ALL relationships where, for example we can map out the general relationship of 010 to 101 to particular trigrams (or extend to hexagrams), but how?
Given the method of deriving the above sequence of trigrams from 'natural' recursion, we find that if we rotate that particular sequence it gives us a sequence that reflects changing lines 'up' a trigram - in particular the two trigrams of 000 and 111. This rotation in fact reflects applying recursion to a trigram. Given this fact, if we (a) apply recursion to 010 we will get the 'changing line' sequence 'up' that trigram and related to the opposite of 010, 101.
(b) ROTATING the sequence derived in (a) will give us the same pattern of a 'logic of relationships' as we have in the 000-111 pairing described previously. The particular patterns we get for 010-101 are:
(1) 010, 110, 000, 100, 011, 111, 001, 101 - rotate to give:
(2) 010, 011, 000, 001, 110, 111, 100, 101
This now reads as:
010 is to 011 as 010 is to 101
000 is to 001 as 010 is to 101
110 is to 111 as 010 is to 101
100 is to 101 as 010 is to 101
This method applies to all of the trigrams as well as all of the hexagrams where we deal with 64-hexagram sequences. (for a number of sequences see the matrix page)
An observation of trigram and hexagram dynamics introduces a perspective where a hexagram 'encodes' the preferred response to its stimulus in the form of swapping the trigrams of a hexagram. Thus hexagram 36, earth over fire, 'prefers' a response to its stimulus in the form of hexagram 35, fire over earth; hexagram 16, thunder over earth, prefers as response to its stimulus earth over thunder, hexagram 24. These are reciprocal relationships where those hexagrams with the same trigrams reflect the self-referencing of 'pure' forms - and so 01 begats 01 as a response (competitivness elicits competitiveness etc)
What is indicated in this perspective is that the dynamics of HEAVEN/EARTH are encoded in these stimulus/response dynamics such that the presence of MAN moves in-between HEAVEN and EARTH and in doing so the context, 'demanding' the preferred reply, will elicit change in the hexagram associated with MAN. This focus is on the intrusion into a context, where we know that context PUSHES our instincts, will elicit a change to conform to the context. For example, given a context of hexagram 34, and so a preferred response of hexagram 25, if any hexagram other than 25 is representing MAN, it will have changing lines to make it become 25. (e.g. hex 05 would be expressed as 05 with changing lines 2,3,4, and 6). The emphasis here is on that moving into a context will force a change over time into the 'preferred' response to that context. Given that information so the individual can be proactive and develop the appropriate response, or simply 'move on', or, being a conscious individual, try to assert their own context to replace the existing. The latter is the most energy-expending.
Thus there is the perspective that when an individual derives a hexagram, that hexagram covers the local situation from the perspective of the individual. Changing lines reflects the influence of the context on that individual - the 'push' to conform to what the context wants as the 'preferred' response to it as stimulus.
if there are no changing lines then the derived hexagram 'fits' the context, is the preferred response to that context and so all is 'correct' structurally.
In the binary ordering of the I Ching we have listed that order in PAIRS where pairing indicates the use of recursion to derive the pairs. This method appears in the traditional sequence. (in the hexagram links in the pair page, when the page comes up you can click on the hexagram symbol to get another page of information).
These are initial, and highly speculative, notes on genetic coding. The full map is not included here since it requires all 6 levels of the template to manifest itself fully. The template is discussed in the text on dichotomy. The relationship to the I Ching is simply the METHOD used to categorise - recursion.
Gladwell, M., (2000)"The Tipping Point" Little Brown
Buchanan, M., (2002)"Small World" Phoenix
Popper, K., (2002)"The Povery of Historicism" Routledge
Barabasi, A-L (2002)"Linked : The New Science of Networks" Perseus
Strogatz, S., (2003)"Sync" Allen Lane
Watts, J.D., (2003)"Six Degrees" Heinemann
Ball, P., (2004)"Critical Mass : How one thing leads to another"Heinemann
In this context consider the page on historic development patterns etc
