8th August 2008 | Draft
Animation of Classical BaGua Arrangements
a dynamic representation of Neti Neti
- / -
Produced coincidentally on the occasion of the opening of the Olympic Games in China in 2008. Given the 5-ringed symbol of those games, the interlocking of the 5 moving rings that are the main focus of this exploration may be considered a form of symbolic celebration of the traditions of Chinese culture.
Hexagrams emerging from dynamic relationship between trigrams
Alternative representations and readings of the trigrams
Configuration of alternatives as a resonance hybrid
Mapping of I Ching hexagram coding onto Star of David
Misleading representation of fundamental symbols in two dimensions?
The representations below follow from arguments previously made with respect to the fundamental significance attached within Chinese culture to the BaGua configuration of 8 trigrams, especially given its significance for the I Ching -- the Book of Changes (Sustainability through Magically Dancing Patterns: 8x8, 9x9, 19x19, 2008). The implications of the dynamics of "moving symbols" were explored earlier (Moving Symbols: radical change in religious psycho-social energy policy? 2008). The alternation within such configurations is understood here as an indication of the challenge and potential of apophatic identity, notably in the light of the classic Sanskrit adage Neti Neti -- "not this, not that" (Being What You Want: problematic kataphatic identity vs. potential of apophatic identity? 2008).
The contemporary relevance of patterns resulting from combinations of trigrams to form the the I Ching hexagrams is the subject of an extensive experiment in interpretation (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). The commentary on this exercise notably explores the relevance of alternation in response to current challenges (Policy Alternation for Development, 1984; Development through Alternation, 1983, particularly its section on Development of Comprehension and Comprehension of Development, 1983). The exercise below is part of a general exploration into possibilities of a pattern language (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008).
The current relevance of exploring metaphors fundamental to other cultures, and notably those of Asia, has been extensively highlighted by Susantha Goonatilake (Toward a Global Science: mining civilizational knowledge, 1999).
As with the static configuration of I Ching hexagrams in the logo of this site, explained elsewhere (Challenges to Comprehension Implied by the Logo, 2007), the purpose here is to explore technical possibilities of representation that may elicit new insight -- engendered by greater cognitive resonance with such representations.
Given the extensive commentary on the two classical BaGua arrangements down the centuries, the focus here is primarily on the possibility of using web facilities to indicate how these might be represented dynamically rather than statically as is the practice.. The two classical arrangements are the "Earlier Heaven" (Hsien Tien) variant and the "Later Heaven" (King Wen or Lo Map) variant. Whilst these are normally represented statically, the transformations within them imply various kinds of dynamic. Only the most obvious are presented here in order to demonstrate the ease with which this can now be done with animations. These arrangements, in static form, have long been popularly used in "BaGua mirrors" in relation to the practice of feng shui. There are convex and concave versions of such mirrors.
It should be noted that the rotation of the arrangements presented below does not correspond to traditional representations.
Given that these representations were made for the web by a non-professional, the images in the animations contain unfortunate imperfections fromn a purely technical point of view. These can be reduced and eliminated. Of particular interest is the speed of the rotation used here. Ideally, with slightly different technology, the speed could be adjusted by the viewer according to the time preferred to contemplate individual images -- in contrast with the insights that may emerge from the patterns of more rapid movement. Similarly other conventions of transformation could be selected. (Note that a more extensive range of transformations is statically represented between the 64 hexagrams in the logo of this site).
The Later Heaven arrangement of trigrams is the basis for the "house organization" of the set of 64 hexagrams of the I Ching (see Organization of I Ching hexagrams in terms of traditional "houses", 1995). In the representation below, the Later Heaven arrangement in its classical static configuration is surround by a ring of trigrams (in the same sequence) which rotates clockwise. This rotation therefore ensures that each inner trigram is brought into relationship with each rotating outer trigram so that the complete set of hexagrams for that "house" emerges during the rotation.
Of particular interest in considering alternative representations are the assumptions made regarding how any arrangement is to be read. Should the top of the trigram (or the hexagram) be considered to be on the outside or on the inside -- namely is the viewer understood to be within the circle or outside it.
In the case of the arrangement of the hexagrams in the logo of this page, this resulted in two alternative interpretations of that configuration (see Alternating between Complementary Conditions -- for sustainable dialogue, vision, conference, policy, network, community and lifestyle, 1983).
Closely associated with the interpretations of the BaGua in traditional Chinese philosophy, natural phenomena can be classified into the Wu Xing, or the five phases, usually translated as five elements, or more dynamically, as five movements or five steps.It will be interesting to determine the degree to which the five rings of the symbol of the Olympic Games is considered as related in some way to this framework. Strategically, such relationships are of course closely related to the classical Japanese martial arts text the The Book of Five Rings (Go Rin No Sho) by Miyamoto Musashi. This is divided into sections corresponding to those elements (The Ground Book, The Water Book, The Fire Book, The Wind Book and The Void Book). It continues to be highly valued in the study of strategy.
In an earlier exploration of the Comprehension of Appropriateness (1986), one section focused on Configuration of modes as a resonance hybrid (later presented as Patterns of alternation: Cycles of dissonance and resonance). The following paragraphs are an edited version of that argument -- demonstrating its relevance to understanding the relationship between the eight different modes configured as the BaGua.
Although the perspective of David
Bohm (Wholeness and the Implicate Order, 1980) on
the nature of implicate order clarifies the challenge further, it does not
say anything about the relationship between the different modes of perception
and organization which can emerge, other than in the sense that they can
be re-enfolded into an implicate order. Since the challenge is to deal with
co-existent, and very different, frames of reference another perspective
is also fruitful.
Such structures recall the context of Bohm's arguments concerning unfoldment of explicate forms. The wave function representing a stationary state of a resonance hybrid in quantum mechanics can be expressed as the sum of the wave functions that correspond to several hypothetical alternates. The proper combination is that sum which leads to a minimal energy for the system. Of significance in any social structure analogue is that the higher energy of each alternate is associated with some degree of "distortion" (different in kind in each case), which effectively renders the alternate meta-stable. (Also worth exploring is the contrasting concept of a "resonance particle". This is any exceedingly unstable high energy particle, which may be considered as a composite of several relatively stable low energy particles into which it may decay.)
Resonance hybrids could well provide a key to the conception, design and operation of coalitions of people or groups using forms of information or modes of information processing so different that the coalitions could not cohere for any length of time in one single form but could be stable if the coalition alternated between distinct forms. Underlying this possibility, hybrids are also of interest in integrating incompatible perspectives, paradigms and policies without eroding their distinctiveness in some simplistic compromise (see Figures 2 and 3). Whilst the value of using such resonance models may be contested, they do have the advantage of shifting the debate, currently somewhat sterile, to a level at which the merits of particular answers are no longer the sole issue. The need is for investigation of "resonable" structures, however "unreasonable" they may appear from any particular perspective. They open the way to more fruitful discussions both about how alternation between the contradictory information characteristic of a complex society can be improved and about the kinds of social structures that could be based upon such patterns of alternation.
Six lines are configured in a number of cultures to form a double triangular "hexagram". This is most commonly associated in the West with the Hebrew Star of David symbol. It is however also used by Christians (notably the Mormons) and in Islam. Six pointed stars are also to be found in the cosmological diagrams of Hinduism, Buddhism, and Jainism. The non-Jewish Kabbalah (also called Christian or Hermetic Kabbalah) interprets the hexagram to mean the divine union of male and female energy. In traditional alchemy, the two triangles represent the reconciliation of the opposites of fire and water.
In the earlier exploration noted above (Sustainability through Magically Dancing Patterns 8x8, 9x9, 19x19 -- I Ching, Tao Te Ching / T'ai Hsüan Ching, Wéiqí, 2008), using one particular triangular design convention, it is therefore also of interest to explore the configuration of the 6 lines of the I Ching hexagram into a double triangle consistent with such traditional symbolic use. The following table was presented in that document (as Table 6: Double triangular representation of hexagrams: Star of David)
The above set can now be presented as a dynamic pattern (as had been suggested in that earlier exercise) in what follows.
Whilst the 8 basic trigrams constitute a coherent system, major challenges to comprehension emerge when the insights are extended through use of a second such set. This may either take the form of a parallel set -- a second circular configuration -- or placing one trigram upon another to constitute a hexagram. This challenge is reflected in the case of the two triangles constituting the Star of David.
Common conventions are used in the orientations of the BaGua or the Star of David. As with other symbols, "upwards" is considered as the direction of the transcendent integrity of "heaven", and "down" as associated with mundanities and even "hell". Such uses of "up" and "down" metaphors have been well explored by George Lakoff and Mark Johnson (Metaphors We Live By, 1980).
Some of the challenges to advanced theories of communication focus on the relationship between form and medium, as featured in the work of Niklas Luhmann (Die Gesellschaft der Gesellschaft, 1997) and discussed by Michael Schiltz (Form and Medium: a mathematical reconstruction, Image [&] Narrative, 6, 2003) in relation to the calculus of indications. Schiltz argues with respect to conventional indication in writing, for example:
These arguments were considered with respect to the conceptual constraints associated with articulation of concepts in tables -- the standard two-dimensional matrix used by many "conceptual models" (including explanations of the Earlier and Later Heaven BaGua arrangements in Wikipedia). The possibility explored, notably in the light of Schiltz's insight, was the greater appropriateness of representation on a torus -- in fact on two intertwined tori (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006).
Mathematically, and especially geometrically, it is appropriate to investigate more complex representations that can be "reduced" to the classic elegant simplicity of the trigram/hexagram mapping in two dimensions. An illustrative metaphor of the possible advantages and disadvantages is the distinction between black/white TV and colour TV. The former may indeed be more appropriate in that colour is implied and must be imagined -- eliciting a degree of active engagement absent in the case of experience of the latter.
The relevance to the above use of two configurations of 8 trigrams is that in three dimensions these two sets may be related in other ways. Such possiblities may then hold mnemonically more complex insights -- more appropriate to the degree of complexity of the challenges they endeavour to encompass and indicate. The representation in two dimensions is not thereby challenged, rather it is seen as a projection of a three-dimensional representation into a two-dimesional symbolic form.
The possibility to be considered is then:
In both examples, the separate symbols (interlocked in this way) can then be understood as moving in relation to one another. In the case of the BagGua, in three dimensions each flat circular configuration becomes a tube -- with the two tubes intertwined as shown below. Their movement with respect to one another is then best shown in virtual reality.
A curious feature of allowing such fundamental symbols to be represented in three dimensions, rather than two, is that it echoes other symbolic representations such as people linking arms or the Mobius strip (as echoed in 2 dimensions by the infinity symbol and the number 8). Interlocking triangles are, for example, of significance both to Celtic symbolism, to Renaissance art and to family therapy.
Further implications of moving out of planar representation of fundamental symbols are explored in Psychosocial Work Cycle Beyond the plane of Möbius (2007) within the dynamics of polarization and enantiodromia (Psychosocial Energy from Polarization within a Cyclic Pattern of Enantiodromia (2007).
As a mnemonic indicator the rotation into the third dimension suggests a dissociation of the reality associated with the lower trigram from the framework associated with the upper trigram. It implies a different orientation or a different modality. The interlocking through their respective centres implies, however, a degree of intimate association that is a more explicit challenge to the comprehension than when the trigrams are positioned one above the other in a hexagram. In the latter case the necessary creative "magical twist" in understanding is implicit rather than explicit. At the same time, the intertwining is indicative of the fundamental challenge of "transmission" between the two domains -- bridging polarizing implications such as up-down,
The traditional symbolic associations of the two triangles of the Star of David -- as male and female -- are more evident in the interlaced twin tori, especially in their movement with respect to each other, effectively entraining each other. The dynamic representation suggests the processes of consumption and birthing and, in a further indication of the "transmission" challenge, offers pointers to the nature of cognitive embodiment (as argued by George Lakoff and Mark Johnson, Philosophy In The Flesh: the embodied mind and its challenge to western thought, 1999; Francisco Varela, et al., The Embodied Mind, 1991). The relevance of the latter focus is discussed elsewhere (Psychology of Sustainability: embodying cyclic environmental processes, 2002).
Also relevant is the manner in which clockwise and anti-clockwise movements are necessary to this entrainment. Also discussed in the earlier paper (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006) is the complex nature of the common centre, bounded by the tubular forms of the two tori -- in movement -- reminiscent of the symbol of the Tao characteristically positioned at the centre of the BaGua mirror.
There is a certain charm to the fact that the original BaGua arrangement is held to have been revealed to Fu Hsi by the "supernatural" -- with the irony that the structure of the benzene model as a resonance hybrid is famously held to have come to Kekule in a day-dream of a snake seizing its own tail (a common symbol in many ancient cultures known as the Ouroboros).
David Bohm. Wholeness and the Implicate Order. Routledge, 1980
Johan Galtung. Methodology and Ideology. Christian Ejlers, 1977
Susantha Goonatilake. Toward a Global Science: mining civilizational knowledge. Indiana University Press, 1999
George Lakoff and Mark Johnson:
Michael Schiltz. Form and Medium: a mathematical reconstruction. Image [&] Narrative, 6, 2003) [text]
Francisco Varela, Evan Thompson and Eleanor Rosch. The Embodied Mind. MIT Press, 1991
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