Symmetry as a strange attractor

Dynamics of Symmetry Group Theorizing (Part #11)

A key to understanding what might be the possible "moves" associated with "psycho-social symmetry" might be the manner in which symmetry attracts -- and functions as an attractor. Marcus du Sautoy helpfully points to some of the attractiveness of symmetry, and the dependence on it in nature:

as a very basic form of communication, as in the relationship between flower and bee
as a feature of superior motor skills resulting from superior capacity to balance ("The food goes to the animal with the most symmetry")
as a characteristic of economy, efficiency and stability
in organizing words in song and poetry
in design, notably architecture

He makes the point that: "Huge swathes of mathematics, physics and chemistry can be explained in terms of the underlying symmetry of the structures under investigation" (p. 21). Of continuing concern is in what way the satisfactory nature of the explanation derives from the satisfaction with the symmetry "somehow present in the inner structure of our intellect".

As he indicates:

The human mind is constantly drawn to anything that embodies some aspect of symmetry. Our brain seems programmed to notice and search for order and structure....Symmetry is about connections between different parts of the same object. It sets up a natural internal dialogue in the shape.

But, as he asks: "symmetry is a slippery concept. What exactly is it?". This is the question that has motivated the work of many mathematicians in seeking to classify its forms and to discover its basis. However, before venturing down that trail, it is appropriate to reinforce the relevance of symmetry as an attractor in psycho-social organization in response to contemporary challenges. For example:

values: The (widely acclaimed) dependence on "values", and their (universal) attractiveness as drivers ("peace", "liberty", etc), suggests that the "moves" in question might indeed be fruitfully understood in terms of the dynamics of "strange attractors" (Human Values as Strange Attractors, 1993). How might sets of such values (in declarations and charters) become more attractive by ensuring that their relationships are patterned in terms of higher orders of symmetry, whether as implied by music or by the geometry of polyhedra? (cf A Singable Earth Charter, EU Constitution or Global Ethic? 2006; Topology of Valuing: psychodynamics of collective engagement with polyhedral value configurations, 2008)
networks: There are strong indications that the emergent -- and increasingly preferred -- mode of organization through networks might benefit from unforeseen degrees of symmetry to achieve the robustness that was acclaimed for the hierarchies for which they often now fruitfully substitute (Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008). How are higher orders of symmetry to be embodied into this mode of organization?
strategic governance: It is increasingly clear that governance, especially at the global level, is much challenged by the inadequacies of its fragmented modes of conventional organization in a period when higher degrees of coherence are desperately required. What do subtler forms of symmetry have to offer in that respect, notably as reflected in polyhedral and multi-dimensional forms rather than in patterns of polarization (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008)?
meetings: Given the central role played by meetings in enabling essential dialogue, whether face-to-face or virtual, a critical question is whether the coherence of dialogue processes can be enhanced through greater input from a symmetry perspective (Spherical Configuration of Interlocking Roundtables: internet enhancement of global self-organization through patterns of dialogue, 1998; Polyhedral Conference Representation as a Catalyst for Innovation: polyhedral animation of IPRA 2008)

In each case there is the challenge of understanding the abstraction through which higher symmetry may need to be appreciated.

The exploration of such possibilities should clearly be informed by subtler insights from symmetry group theory and how they are communicated. This is especially the case where they might be enhanced by the development of an appropriate pattern language (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008). Of significance in this respect is the relevance of rendering evident the aesthetics of subtler forms of symmetry to increase the comprehensibility of such possibilities. The advent of the web, and the potential of the semantic web, suggests that symmetry might play a vital role in the design of new communication algorithms and protocols to enhance the possibility of emergence of psycho-social structures of greater subtlety and attractiveness. These might be said to have been curiously prefigured by the global role of music -- with presumably little recognition of the forms of symmetry that music promotes in psycho-social structures (cf Jacques Attali, Noise; the political economy of music, 1985).

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Symmetry as a strange attractor