Dynamics of psychosocial systems suggested by force-directed layout

Oppositional Logic as Comprehensible Key to Sustainable Democracy (Part #5)

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]

It is appropriate to note that the extensive range of available images on oppositional geometry are typically static variants of polyhedra (perhaps necessarily) -- typically transformations of the octahedron. "Necessarily" because the images are primarily designed for papers scheduled for academic journals. These are not designed to handle whatever may be implied by animations in 3D -- even when papers are made available online.

Missing from any representation of oppositional logic/geometry is therefore any sense that particular polyhedral edges in a configuration might be over-emphasized or under-emphasized in a context in which a particular otherness might be stressed. This takes the use of any polyhedral configuration beyond the logical abstractions for which the geometrical metaphor has been borrowed. The question is then whether it is possible visually to associate such contrasting degrees of emphasis with distortions of the original "ideal" configuration. Two possibilities are explored below.

That on the left is derived from a more systematic exercise using force-directed graph drawing -- offering access to a range of other polyhedra (Use of force directed layout to elicit memorable polyhedra, 2015). Unfortunately, due to subsequent browser upgrades, incompatibilities notably restrict the interactive variant to Internet Explorer.

The animation in the centre is made from a suggestive distortion of the truncated octahedral graph, namely the graph of vertices and edges of the truncated octahedron. The distortions do not however affect the topological properties fundamental to its use for logical analysis. The animation on the right is a feature of the use of icosahedral tensegrity by management cybernetician Stafford Beer (Beyond Dispute: The Invention of Team Syntegrity, 1994). This explores the emergent balancing dynamics between non-compressible ("non-negotiable") and flexible elements in group discourse, as suggested with respect to a UN Earth Summit (Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues, 1992)

Screen-shot of force-directed layout of truncated octahedron dynamic variants (mp4 video; interactive, possibly only operative in Internet Explorer)	Animation of truncated octahedral graph suggestive of dynamics of group discourse with shifting emphases	Rotation of spherical tensegrity (indicative of "problem jostling")

In considering oppositional logic of any kind, it is appropriate to give consideration to the encoding of 64 contrasting conditions by the traditional Chinese classic -- the I Ching, as the Book of Changes -- and the 384 transformations between them. The 64 conditions (effectively of otherness) are the subject of distinctive metaphorical commentary which can be adapted into policy language, recognizing that the pattern as a whole has been much valued in Chinese governance over millennia (Transformation Metaphors -- derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). This goes far beyond the constraints of any simple binary encoding but is well-recognized as building upon it.

The 64 conditions can be uniquely mapped onto be 64 edges of the drilled truncated cube (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015), This lends itself to a force-directed layout presentation (below left). The central image (and animation) shows a traditional circular pattern of the 64 hexagrams with transformations between them. With each of the 64 conditions potentially transforming into an other through 6 distinctive pathways, consideration can also be given to the 64x6 transformations (namely 384). Since the transformations are in both directions, however, these can o be considered as only 192 bidirectional pathways.

Transformations between 64 condition encoded by the hexagrams of I Ching
Drilled truncated cube - 64 edges	Adaptation of traditional configuration	64 vertices each with 6 transformations
Screen shot of interactive force-directed version (with node labelling)	Screen shot of animation (mp4) of inner circle of trigrams relative to outer circle	Screen shot of 192 2-way pathways force-directed layout animation

The above possibilities are discussed and further developed separately:

• Visualization Enabling Integrative Conference Comprehension: global articulation of future-oriented 3D technology (2018)
• Enhancing Strategic Discourse Systematically using Climate Metaphors: widespread comprehension of system dynamics in weather patterns as a resource, (2015)
• Path-ology: eliciting dynamic patterns of empowering and disempowering conditions (2015)
• Interplay of cognitive patterns in discourse on systemic change (2015)

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]