</a>Polyhedral relationship networks?

Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance (Part #14)

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Whilst emphasis may be appropriately placed on the larger challenge of global governance and the new approaches seemingly required, it is useful to be aware of the many challenges faced by family and interpersonal relationships at this time. The incidence of family violence and divorce are but indicators of this. It could however be argued that the inadequacies of personal relationships are reflected in the inadequacies in governance relationships. As remarked by Gregory Bateson: We are our own metaphor.

As noted above, there is a blossoming of awareness of social network relationships -- especially beyond the family. Extended family networks, and kinship networks, remain of significance to many. Beyond the partners often desperately sought, individuals tend to be very focused on supportive networks of friends.

The question might be asked as to whether, other than the somewhat arbitrary structure of such "networks", are there other ways of understanding those relationships that might enhance a sense of well-being and identity to a greater degree. Is the coherence and quality of a set of relationships enhanced by what is effectively its configuration as a polyhedron of some form -- which may evolve or transform in response to circumstances, as with any sense of team?

Given the complexities of the relationships within which many are embedded, would such configuration enhance the kind of desirable outcome to which family therapists may aspire? Alternatively, what is it that gives significance and a sense of well-being to an ordered pattern of relationships -- beyond the hierarchical, patriarchal or matriachal models?

Viable projects and businesses make much of the elaboration of an appropriate "business model". Is it possible that the set of polyhedra might highlight unforeseen patterns of relationship -- as "psycho-social models" -- that would enhance the meaning of those so engaged and empowered? One concrete approach is that explored by Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994) based on the icosahedron -- and subsequently subject to restrictive licensing. Inspired by Fuller, the concept of a self-organizing geodesic democracy has, for example, been developed in a series of documents by Roan Carratu (The Geodesic Direct Democratic Network; Structure; Process; Modes; Finances; General Archives; Projects; Growth; Details of Specific Procedures, 2005) and on an associated website on geodemocracy. Like syntegrity, it focuses on small group processes icosahedrally organized -- but set here in a larger context (see explanation of Geonet, 2000). Is there a much larger range of possibilities to be explored from which many might benefit -- if only in the learnings to be derived from their explorations of them? The explosion of social networking offers an ideal context for such exploration -- with an early proposal providing an interesting example (Group Questing or Twelving: proposal for a large-scale small-group development process, 1976).

Given that understandings of transparency and its desirability in configurations of relationships, there is a case for exploring this metaphorically through new understandings of glass -- especially given the widespread strategic use of optical metaphors (perspectiove, focus, vision, etc). Glass may be understood as an inorganic product of fusion, cooled to a rigid condition without crystallizing. Whereas the solid state of all known metals and metallic alloys consists of regular, periodic arrangements of the atoms, a metallic glass consists of metallic atoms arranged in a random manner with no obvious long-range correlation in the atomic positions. These new have proved to be of considerable technological importance for their unique magnetic, mechanical and corrosion-resistance properties. It might be asked whether this suggests a way of thinking about potentially valuable new configurations of psycho-social relationships.

The work of Subir Sachdev (Icosahedral Ordering in Supercooled Liquids and Metallic Glasses, 1992) focuses on the structural properties of dense and supercooled systems of atoms interacting with each other through spherically symmetric forces. He finds that there are significant short-range orientational correlations between the atomic arrangements applicable to any dense, supercooled liquid of spheres interacting with a pair-potential which has a repulsive hardcore and a weak long-range attraction -- readily modelled in computer. Perhaps ironically a key property of the systems considered is that they are "frustrated". Sachdev remarks:

By 'frustration' we mean that particles in the ground state cannot simultaneously sit in the minima presented to them by pairwise interactions with their neighbors. This leads to a large degeneracy in the ground state. In phase space, the system has large numbers of nearly equal free energy minima separated by substantial free energy barriers. If the system gets locked into one of these minima upon cooling from the liquid, a glassy or amorphous state can result. Our main objective shall be to determine the atomic correlations at a 'typical' local minimum of the free energy.

Sachdev's discussion of how the the "frustration" of flat three dimensional space is relieved, by appropriate minimum-energy icosahedral packing of polyhedra, points to possibilities of ordering relationships in new ways.

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