We can interpret the traditional I Ching as a product of small world network thinking, where LOCAL conditions will behaviour in an ad-hoc manner to take a ‘perfect form’ – the set of recursion-derived, and so highly ordered, highly structured, universals that make up the universal I Ching – and convert it to a small world network through the dynamics of actualising the potentials, describing them by analogy to local conditions, when interacting with the ‘randomness’ of reality – where by ‘random’ I mean that genetics cannot know the immediate interactions of individual and reality such that these interactions are considered as ‘random’.
As such, we are focusing on applying recursion to the regular/random dichotomy, out of middle of which develops the ‘small worlds’.
Thus the ‘universal’ I Ching, as a pool of potentials, is reflected in the below diagram (taken from D. Watts "Small Worlds" UPP ) as a network where all nodes, elements, hexagrams, are connected to each and so ‘regular’. Exposure of that universal to the randomness of reality will elicit adaptations to local dynamics and so give us, locally, a ‘small world network’ model – the middle network in the below diagram:
Thus individual/collective interpretations/translations of the I Ching will reflect small-world, or even random, configurations – the latter being in highly idiosyncratic interpretations that from the outside seem ‘random’, but inside, to the originator, all is ‘logical and fine’. If we convert the interpretations/translations to network-diagram representations, and make them transparent, stacking all of the different translations/interpretations will lead to the emergence of the regular network in that we are summing all of the local, ‘ad hoc’ links to bring out the full spectrum, the full set of actualised potentials of the regular.
Science does this in its piecemeal investigations of brain and behaviour, and in doing so shows each of us to have ‘small world network’ brains – each reflecting some unique element due to local adaptations in development, and yet ‘beneath’ the uniqueness, the difference, lies the sameness that makes us all members of the one species.
To see what the IC would look like as a regular network, just connect the hexagrams in the circle part of the below diagram to all others in the circle, and so reflect a ‘regular’ network of all connected to all else. In this network the ‘perfect’ integration means all is ‘static’ and so ‘potential’. If we remove all of the local terms associated with the ‘small world’ models, so we remove ‘colour’ to leave behind black and white forms expressed in very generic terms but linked together such that analysis of each part brings out aspects of all parts.
Note also in the above diagram (credited to Shao Yong) of the I Ching the use of the circle/square representations, where the inner square of hexagrams is the binary ordering of hexagrams reflecting ‘ideal’ structure and the realm of XOR, exclusive or-ness that allows us to derive universal categories. (more on squares and circles later)
As we review the dynamics of the I Ching, so we move from a focus on 64 ‘static’ hexagrams to 64 ‘changing’ hexagrams. This is in fact a movement from medium precision to high precision where we move to considering 2^12 (4096) distinctions as compared to the hexagram’s 2^6 (64) distinctions, and the trigram’s 2^3 (8) distinctions; with each distinction being made within the context set by the previous.
Thus, what are labelled as ‘changing line’ hexagrams are in fact static dodecagrams ‘compressed’ into six-line expressions. That compression ensures FOUR qualities per line (not changing x 2, changing x 2).
As such we can compare the trigram / hexagram / dodecagram perspectives to resolution power in star-gazing – trigrams are naked eye, hexagrams are binoculars, and dodecagrams are telescopes.
So, what do we get in the realm of the dodecagram / dodecahedron?
2 The Dodecahedron.
“Historically [the dodecahedron] has symbolized the concept of a fifth element, Ether (Aether) or Universe. It represents the perfect mediation of the infinite and the finite, the sphere and the cube, analogous to the circle and the square. It is reciprocal with the Icosahedron; whereas the Icosahedron has 20 faces and 12 vertices, the Dodecahedron has 12 faces and 20 vertices. Each shape can easily be transformed into the other by truncation or stellation.” Internet source.
In the I Ching the dodecahedron is manifest in the form of a dodecagram – 12 lines of yin/yang, compressed into 6 lines of changing yin/yang. Each line maps to a vertex of the dodecahedron. Note that through the further use of recursion and XOR-ing so all 4096 possible expressions are also mapped into each expression.
Note the comment above re ‘perfect mediation’ – mediation of a dichotomy is in the form of applying recursion to that dichotomy and so we move from 2^0 (1) to 2^12 (4096) distinctions, categories, where the realm of the dodecagram reflects high precision “XOR-ing” as we derive categories to represent reality, both dynamically and statically.
If we move to 2-D geometry we have:
“The Circle represents Unity and Totality. All points from the center radiate equally. It also symbolizes the void; the pre-manifest seed or germinal idea, expanding and asserting itself by will. It is the first, primordial, state of all things. The Beginning.” Internet source.
“The first step in manifestation is differentiation. So, the circle will split and divide by two at the center, bilaterally. The Cosmic idea is preparing to self-replicate. This is Logos.” Internet source.
In George Kelly's Personal Construct Psychology Kelly writes:
"Our psychological geometry is a geometry of dichotomies rather than the geometry of areas envisioned by the classical logic of concepts, or the geometry of lines envisioned by classical mathematical geometries. Each of our dichotomies has both a differentiating and an integrating function. That is to say it is the generalized form of the differentiating and integrating act by which man intervenes in his world. By such an act he interposes a difference between incidents -- incidents that would otherwise be imperceptible to him because they are infinitely homogeneous. But also, by such an intervening act, he ascribes integrity to incidents that are otherwise imperceptible because they are infinitesimally fragmented. In this kind of geometrically structured world there are no distances. Each axis of reference represents not a line or continuum, as in analytic geometry, but one, and only one, distinction. However, there are angles. These are represented by contingencies or overlapping frequencies of incidents. Moreover, these angles of relationship between personal constructs change with the context of incidents to which the constructs are applied. Thus our psychological space is a space without distance, and, as in the case of non-Euclidian geometries, the relationships between directions change with the context." (Kelly, 1969)
Continuing with the geometry:
“As the splitting has begun, new radiating points are formed, and new tangents created. The area of the two inner circles equals one-half of the outer one, yet the circumference of them both is identical to the latter; thus the paradox where the two and one are united. There cannot be two without first, the One. This synthesis and interplay of opposites-as-unity is also revealed in the Chinese Yin-Yang symbol” Internet Source.
In IDM (http://www.iimetro.com.au/~lofting/myweb/idm001.html ) we have the concept of the ‘dimension of precision’, derived from analysis of how our brains deal with precision, that shows increasing degrees of precision as we move from the ‘circle’ to the ‘square’, general to particular, vague to crisp, ‘right brain’ to ‘left brain’ – the latter being binary precision, XOR, EITHER_OR mapping. In other words, we can detect from this basic mapping of precision issues in our brains the roots of our sense of ‘squaring the circle’, and such concepts as the dodecahedron being the ‘perfect mediation of the infinite [sphere] and the finite [cube], “analogous to the circle and the square”. In other words, these metaphors rooted in the geometric are expressing the development of our neurology and its focus on information processing.
Thus the mediation involved in ‘squaring the circle’ is manifest as a dodecahedron – as is the oscillations of the brain across differentiating and integrating gives us the IMPLICIT whole. (There is a pattern of development in how we process information where we take the whole and apply it to itself. Thus given 8 qualities I jump to 64, given 64 to 4096, given 4096 to 16+ million. This process is called ‘hyperbolic development’ – N^2 rather than 2^N – in the long term this is energy conserving in that for each development step we get a really big house to move into and so develop without having to ‘move again’ too soon!)
Given the focus on ‘rigid’ networks, in the ‘small world network’ models, the focus is on difference from sameness – this reflects the actions of a symmetric form of dichotomy. Reality in fact shows that we have developed a bias to processing asymmetric dichotomies – sameness from difference, where we get a spectrum ordering different energy levels from low to high. As such, our seemingly ‘mechanistic’ structures are in fact ‘organic’ when we introduce the asymmetry that comes with the differentiating/integrating type of dichotomy (symmetric is more differentiating/differentiating or integrating/integrating).
Note that these ‘forms’ idealisations are just that, idealisations, where the development of ‘ideal forms’ stems from basic, mindless, growth dynamics. Thus, the tetrahedron (a closed system by the way, as are all ‘ideal’ forms) is a manifestation of our sense of taste developing by maximising the distance of each of the four tastes from each other, and so ensure ‘clarity’ in perception (plant leaves do the same ‘optimising of distance’ and in so doing show Fibonacci spirals in their growth).
For taste, LOCAL distinctions/distortions means that the tetrahedron representing taste has rough surfaces with ‘spikes’ sticking out, reflecting some local adaptation ‘at odds’ with the norm.
These forms stem from the dynamics of differentiating/integrating. In that dynamic so states emerge that can survive, develop robust configurations that make them stable and so hard to remove. Then we come along, see these ‘stable’ forms, ignore the BILLIONS of years of heuristics in development of the universe, and ‘insist’ there is a ‘helping hand’ at work – there is no need for such a hypothesis.
The discussion in this text reflects properties of a deeper nature, the properties of our senses that ‘determine’ our reality. The dynamics of our senses, feeding into, and being ordered in, our brains leads to the method we use to derive meaning, and that method is the recursion of differentiating/integrating (See IDM) – all else follows.