Psycho-social operationalization of polyhedra through tensegrity representation

Polyhedral Pattern Language: Software facilitation of emergence, representation and transformation of psycho-social organization (Part #11)

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A major difficulty with abstract forms such as polyehdra is how they engage with psycho-social organization -- irrespective of their inherent aesthetic properties and appreciation of them as "sacred geometry". And, irrespective of recognition of their role in the architecture of biological cells (and radiolaria), this difficulty is evident in efforts to use such forms in the architecture of buildings -- especially those polyhedra of greater complexity.

It is in this respect that learnings from their application through tensegrity -- tensional integrity -- to unusual constructions (such as geodesic domes) are of significance (see Documents relating to Networking, Tensegrity, Virtual Organization). Tensegrity is the means through which polyhedral forms are "operationalized" in building and therefore, with some probability, in psycho-social organization. This raises the question of whether an as yet undiscovered "geodesic" form of psycho-social organization might notably be of great relevance to global governance.

As an additional feature therefore, the capacity in Stella to generate tensegrity representations of polyhedra would be an advantage -- where this is possible and appropriate . A principal reason is that there is a range of arguments suggesting that the viable structure of the more complex polyhedra -- if constructed -- is dependent on the kinds of distribution of forces associated with the tensegrity variant. This is notably true at the level of the biological cell (Donald E. Ingber, Tensegrity and Systems Biology, Journal of Cell Science, 2003).

As defined by R Buckminster Fuller (Synergetics: explorations in the geometry of thinking. 1975):

A tensegrity system is established when a set of discontinuous compressive components interacts with a set of continuous tensile components to define a stable volume in space.

As models, the tensile elements (tendons) can be cables or strings, functioning like a network. The compressive elements can be beams or rods (struts) and function as spacers to prevent the network from collapsing. Despite the generality attributed to tensegrity principles (and explicit in the subtitle of Fuller's study), it should be stressed that most of the literature recognizes only their application to material structures. Of interest to any exploration of tensegrity are the following:

• Within the architectural context, the application of studies of management cybernetician Stafford Beer on "syntegrity" (synergistic tensegrity) in team building are ignored -- perhaps necessarily so. This is equally true of those of cybernetician Gordon Pask on the Fuller-Snelson prismatic tensegrity as a Borromean link model of the interactions in a minimal stable concept; it has been extended to modelling entailment meshes of concepts as spin networks. He noted that "a tensegrity, or tensionally integral structure, is an organizationally closed system, informationally open, viable system and an organism" (Interactions of Actors (IA), Theory and Some Applications, 1993). This work, a generalization of Pask's conversation theory and his work on self-organization and coherence, has subsequently been variously developed, notably by Nick Green (Axioms from Interactions of Actors Theory, Kybernetes, 2004); he has considered the isotopy of the orthogonal Borromean link and the icosahedral tensegrity. Such work is presumably highly relevant to the challenges of psycho-social organization.
  
  
• Curiously, whilst the concept of "network" has proven valuable in both material, psycho-social and abstract contexts, the interplay of forces fundamental to tensegrity has not as yet -- even though "network" is inherently related to that dynamic in practice. The same might be said of "virtual organization" in cyberspace. A noted weakness of psycho-social networks in practice may however be their tendency to design out "tension" -- which features in the "hierarchical" forms to which they are a reaction -- thereby inhibiting their capacity (Tensing Associative Networks to contain the Fragmentation and Erosion of Collective Memory, 1980; Tensed Networks: balancing and focusing network dynamics in response to networking diseases, 1978)
  
  
• Both in the architectural context, and in the non-architectural application of tensegrity developed by Stafford Beer, issues of priority and intellectual copyright have proven to be extremely important -- even disagreeable -- possibly even to the point of inhibiting further development. It is therefore interesting to speculate, in the light of "syntegrity", on the possible intellectual copyright with respect to the application of tensegrity to psycho-social organization. Of related interest is any patent constraint on the application of tensegrity construction methods to dome-like "buildings" constructed virtually in cyberspace or to any tensegrity art in that context. Given the fundamental role that Pask's focus gave to tensegrity in relation to interaction between actors, the emergence of a concept, and self-organization, one might ask how the important sense of "territory" is held in that context, and -- provocatively -- whether this is itself implicated in such considerations in unsuspected ways (cf Einstein's Implicit Theory of Relativity -- of Cognitive Property? Unexamined influence of patenting procedures, 2007)

One of the advantages of such structures is as a representation of a configuration of polarizing factors in social organization -- forces which may be essential to its viability, as discussed elsewhere (From Networking to Tensegrity Organization, 1984; Groupware Configurations of Challenge and Harmony: an alternative approach to alternative organization, 1979; Implementing Principles by Balancing Configurations of Functions: a tensegrity organization approach, 1979).

Just as tensegrity principles are fundamental to the architecture of the biological cell, they may also be fundamental to the coherence of psycho-social organization and community -- to community "architecture". Such tensegrity structures may be especially significant in determining the patterns of (electronic) communication essential within cyberspace to the viability of an organization, a community or some other collective initiative.

One of the challenges in deriving tensegrity structures for architectural purposes is what is termed "form-finding" (cf Milenko Masic, et al, Algebraic tensegrity form-finding, 2005). There is a case for understanding the challenge of matching or fitting psycho-social organization to polyhedra (discussed above) as an analogous process of "form-finding". In both cases a polyhedron provides a template for the solution, but the challenge is to find it. Hugh Kenner (Geodesic Maths and How to Use it, 1976) offers guidance on "choosing a polyhedron" (ch. 11) which usefully frames the challenge.

The challenge is to "massage" chaotic network representations into a "global" configuration as primitively envisaged as a challenge to mathematics (Preliminary Clarification of Some Problems of Processing Networks of Entities -- in order meaningfully to map psycho-social relationships, 1973). This may now be more readily feasible with the aid of "polyhedral" network analysis (cf P. Doreian, Polyhedral Dynamics and Conflict Mobilization in Social Networks, 1981).

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