Nested sequence of polyhedra

Evoking Authenticity: through polyhedral global configuration of local paradoxes (Part #7)

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The geometry of the set of spherically symmetrical polyhedra is such that there are pathways of transformation from one to another [more]. The simplest are embedded implicitly in the more complex in which features of the simple are elaborated in more and more complex ways.

If polyhedra can be used to hold "paradoxes" (as suggested above), can these be used to distinguish patterns of dynamic constraints on different systems, as follows:

• simplest polyhedra: plants and animals are constrained and guided in their behaviour by a set of "tropisms": heat/cold, food/satiety, security/vulnerability, etc. In the case of humans, these -- or their analogues -- may also apply (as explored by Maslow's need hierarchy) [more];
• more complex polyhedra: the features of simpler polyhedra (encoding the simpler tropisms) become implicit or virtual, with the emergence of more complex sets of paradoxes that exemplify or frame the virtual tropisms;
• maturation: a final stage might be distinguished in which all paradoxes become explicit to awareness, although the more fundamental are now implicit as patterns of symmetry in the geometry rather than explicit on the surface of the polyhedra.

The "maturation" process, through the sequence of polyhedra, then provides progressively greater sensitivity to the contextual challenge of embodying complexity. In a sense any given polyhedron in the sequence could be understood as functioning like an antenna -- a polyhedral array -- sensing the potential of the next complexification. The emergence and nature of higher forms of organization might also be explored in the light of two seemingly contrasting evolutionary forces:

• the necessity to switch from the simple, and essentially passive, spiracle-based respiratory system of insects to that of the active circulatory system of vertebrates permitting bodies of larger volume
• the necessity to switch from the complex, non-focusing faceted eyes of insects to the non-faceted eyes of vertebrates in order to provide a more integrated perspective.

This progression points to the manner in which authenticity offers the requisite degree of complexity (in terms of Ashby's Law of Requisite Variety) to provide coherence to the ecosystem of paradoxes. But the set of paradoxes active to consciousness in the struggle for coherence may be only of tertiary significance, leaving more fundamental paradoxes unaddressed, except by analogy and correspondence.

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