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Framing the space for conscious creativity?
Framing Cognitive Space for Higher Order Coherence (Part #11)
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Polyhedral metaphor: The argument above explored the fundamental role of the cube (and more complex polyhedra) in framing a creative cognitive space -- inspired by the design constraints of supercomputer development. The question is how to enable a more conscious focus on the creative phases prior to integrative comprehension. Simple experiments with virtual reality applications are suggestive of this possibility. As illustrated below, the focus is on the cuboctahedron as a complexification of the cube. That polyhedron was a particular focus of the extensive work of Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975/1979), notably associated with his development of geodesic domes.
Arguably society has yet to develop approaches to computation to engender psychosocial analogues to geodesic domes, as discussed separately (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009; Interweaving Thematic Threads and Learning Pathways: noonautics, magic carpets and wizdomes, 2010). As illustrated by the following animations, the cognitive struggle is to enable disparate simpler configurations to cohere -- into the form of a cuboctahedron in this case (left-hand image).
The various animations offer cases in which the challenge is the configuration of the edges separately, the 6 square patterns, the 8 triangular patterns, or the 4 hexagonal circuits. The challenge is simplified by assuming that each colour rotates around one of three axes -- or is stationary in the case of a fourth. The challenge to coordination at the present time is obvious where the colours are indicative of political parties, the edges are indicative of their preferred projects, and the spheres are indicative of distinctive goals. The animations are helpful as indicating the strategic confusion (or "mess") of the times, whether for the individual or the collective.
| Proto-coherence represented by animation of modes of convergence on a cuboctahedral configuration | ||||
| Cuboctahedron | Animation of edge movement | Animation of squares of edges | Animation of triangles of edges | Animation of circuits of edges |
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Engaging with complexity: The limited number of elements in the cuboctahedron -- already greater than the simplicity of the cube -- offers a reminder that the complexity of the psychosocial system calls for a capacity to engage with a far greater number of elements and their dynamics. The complexification of the 8-fold cube of the original BaGua pattern of trigrams into the 64-fold pattern of the I Ching hexagrams is a reminder of the dynamics between the elements in each case.
As noted above, a polyhedron appropriate to mapping the 64 elements is the drilled truncated cube -- a complexification of the cube and the cuboctahedron. The following animations are indicative of the cognitive challenge in such a case.
| Alternative views of selected cycles of movement of parallels along edges of the drilled truncated cube Video version (.mp4); virtual reality (.x3d  This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License For further updates on this site, subscribe here |