</a>Accommodation to constraints in symmetry comprehension: building your own qhomeq?

Dynamics of Symmetry Group Theorizing (Part #16)

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The constraints imposed by comprehension have been fruitfully analyzed from a mathematical perspective by Ron Atkin. Combinatorial Connectivities in Social Systems; an application of simplicial complex structures to the study of large organizations, 1977; Multidimensional Man: Can man live in three dimensional space?, 1981). Of particular interest, in the light of the reference to a triangle above, is Atkin's use of a triangle with vertices of 3 distinct colours in order to explain the challenge of comprehending their combinations -- and the experience of the "geometry" of what is not fully comprehended.

The discoveries of mathematicians with respect to symmetry are truly awesome. It is however curious that, just as the implications of other ways of knowing symmetry are considered irrelevant, so are the implications of not being able to comprehend such discoveries. Whether it is a question of deficiency in IQ (perhaps to be measured as in terms of a "Symmetry Quotient") or an inappropriate bias towards another mode of intelligence (cf Antonio de Nicolas, Habits of Mind, 2000), the challenge is how to design into one's psycho-social "home" the highest level of symmetry that one can comprehend.

The home construction metaphor is useful in that it highlights the reality of the cognitive space in which most are obliged to dwell. It clarifies the inappropriateness of appeals to higher orders of symmetry that one is unable effectively to comprehend, especially in the language in which they are communicated. Just as with the shacks in which the impoverished may be obliged to live in some socio-economic contexts, many may be obliged to dwell in psycho-social shacks constructed with elements of a relatively low order of symmetry -- for lack of materials or for lack of know-how. Extolling their inhabitants to more sophisticated construction may be as unhelpful and inappropriate in the second case as it is in the first.

More interesting from a symmetry perspective is the sense -- as with Alexander's pattern language (specifically focused on building design) -- that there may be many ways to design psycho-social symmetry elements into one's cognitive home, in a manner consistent with one's philosophy or belief system. The repertoire of patterns of symmetry that mathematicians have painstakingly classified could be understood as a resource to that end. This emphasizes the possibility of building one's house on the basis of the symmetry one "understands" -- of the configuration of design elements that one then "stands under".

Most depressing is the sense in which conventional understandings of a limited range of patterns leads to psycho-social dwellings conforming to a limited range of stereotypes -- as with the suburbia of the most developed countries. Constraints on innovative construction that are evident in such settings -- building codes, health and safety, fashion, etc -- have their equivalent in psycho-social construction for individuals, groups or communities.

Perhaps even more problematic is a potential implication that higher symmetry is better, even if it cannot be comprehended. This is where the mathematical capacity to handle spaces of thousands of dimensions -- within which such dwellings potentially emerge -- is a form of illusion. It may be possible to dream of dwelling in such celestial spaces -- encouraged by science fiction -- but there is a real need to render comprehensible higher orders of symmetry that are characterized by accessibility. Computer augmented intelligence may indeed facilitate the process through sophisticated management of communication protocols that stabilize such psycho-social constructs as viable environments. Experimentation in successive generations of virtual worlds (Active Worlds, Second Life, Emerging Virtual Institutions, Metaverse, etc) may be extremely helpful in that respect. There would appear to be many possibilities for organizing websites in terms of higher orders of symmetry (Transforming Static Websites into Mobile "Wizdomes": enabling change through intertwining dynamic and configurative metaphors, 2007).

Negative Symmetry Capability (adapted from the Negative Capability of poet John Keats, with apologies)

Capable of being in uncertainties, mysteries, doubts without any irritable reaching after fact, reason and higher orders of symmetry

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