Middle East Peace Potential through Dynamics in Spherical Geometry (Part #12)
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"Voluminous thinking"? The emphasis here is on the contrast between the peace so desperately sought within a two-dimensional framework and that implied by a three-dimensional framework. The feasibility of peace in the former case were caricatured by comparison with the "forcing" the pieces into a jigsaw puzzle -- despite the fact that they do not interlock. Banging them in is not a viable solution -- irrespective of the quality of the "lateral thinking" applied to that process. The question explored here is with regard to a three-dimensional framework. Might the pieces fit together when understood in that way? The point was made above by reference to "voluminous thinking", illustrated by the example of housing shortage (From Lateral Thinking to Voluminous Thinking: unexplored options for subterranean habitats in dense urban areas, 2007).
A major concern is that two-dimensional peace is intuitively comprehensible and appealing, notably in the light of its implications regarding resolution of disputes over flat territory. However it is evident that this is perspective is inadequate -- as when the jigsaw puzzle pieces do not "fit" together. Three-dimensional peace indicates that it might imply counter-intuitive comprehension -- as suggested in some measure by the Biblical peace which "passeth all understanding". Hence the value of animations. The symmetry group mathematics and its visual renderings suggest that there may forms of peace which are an even greater challenge to comprehension (Dynamics of Symmetry Group Theorizing comprehension of psycho-social implication, 2008).
Ironically the three-dimensional approach lends itself more readily to comprehensible visualization as illustrated by the association football with which people interact worldwide. A "peace football" could be made simply by appropriately applying the symbols of the two conflicting Middle Eastern cultures to each of its 32 facets. This could well enable reflection on Transcending Simplistic Binary Contractual Relationships: what is hindering their exploration? (2012).
Peace as a meta-pattern: The nature of cognitive incommensurables, as reflected in geometrical patterns, may require the exploration of far more paradoxical forms. For example, the Stella Polyhedron Navigator facilitates visual exploration of patterns in four-dimensions to some degree. The epistemological implications were explored to a degree in the later work of Gregory Bateson (Angels Fear: towards an epistemology of the sacred, 1987). In this sense peace is best understood, not so much as a pattern in three dimensions, but as a meta-pattern to which Bateson refers (above). Such consideration of meta-pattern is evoked in Quaker reflection (Approaches to Peace and Non-Violence for Modern Quakers, 2005).
Emergent insight: Curiously the process of constructing a football from flat pieces results in a form of "emergence" of a new pattern when these are folded and stitched into spherical form. The step-by-step logic of this process can be readily followed, although it is only through the making process (understood as poieisis) that its significance is best realized -- as the emergence of a new form of order. It might be said to defy explanation and justification within a two-dimensional framework. Relevant arguments regarding recognition of the bigger picture implied by peace are offered by Silvia Hartmann (Meta Patterns and Genius: a simple game to increase a child's intelligence, 2005; The Problem With Peace: why peace is NOT the answer, 2009). Does the surprising recent recognition of a new form of carbon -- previously assumed to be one of the commonest and best known elements -- imply the possible emergence of a new form of peace?
Indications of counter-intuitive comprehension: It is useful to note the variety of metaphorical and other pointers to such a counter-intuitive form -- of which there is evidently a degree of intuitive comprehension:
With respect to the "weaving" metaphor of connectivity, it is appropriate to note the beading diagrams for the fullerenes as explored by Bih-Yaw Jin (C60 beading procedure. The Beaded Molecules: the wonderful world of beaded fullerenes, October 2011). It is also appropriate to note the importance of carpet design to the principles of order identified in the work of Christopher Alexander (A Foreshadowing of 21st Century Art: the color and geometry of very early Turkish carpets, 1993).
Design as its own metaphor: It is intriguing that the challenge of "peace", especially in the Middle East, could be framed metaphorically in terms of design and the tools which currently enable it. The production of the above animation, using one of the common design applications, enables a two-dimensional pattern to be manipulated into three dimensions. The key to this process is the common instruction to "select all", thereby grouping all the elements on the drawing board. With respect to "peace", the sense of how to "select all" remains elusive, usefully understood as the challenge of "seeing things whole" or the ability to distinguish the "wood from the trees". The tendency is simply to select a sub-set of elements, treating the remainder as externalities, as separately discussed (Reintegration of a Remaindered World: cognitive recycling of objects of systemic neglect, 2011).
Echoing the quest of physicists for a Theory of Everything in a universe characterized by subtle understanding of curvature, peace might then be understood in terms of enabling curvature into a "global configuration of everything". The challenge might be expressed metaphorically in terms of (en)activating the "great circle" pathways.
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