Recognition of correspondences, parallels and symmetries

Weather Metaphors as Whether Metaphors (Part #7)

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Parallelism: As noted with respect to the drilled truncated cube, perspectival parallelism was provisionally used to limit transformations to patterns of lines between which this obtained -- recognizing the manner in which the transformations then followed a distinctive cycle according to the type of transformation within the polyhedron. Whilst geometrical parallelism can be readily recognized in its more obvious forms, it is less evident how this can be determined systematically. Fortunately the Stella Polyhedron Navigator identifies parallels, as depicted above.

Detection of correspondences and parallelism is of importance in a number of information-related domains (Brian Walshe, et al, A Comparison of Complex Correspondence Detection Techniques, 2012; Dominique Ritze, et al, A Pattern-based Ontology Matching Approach for Detecting Complex Correspondences, 2009; Alberto Apostolico, et al, Parallel Detection of all Palindromes in a String, 1993; Zai-Sheng Wu, Parallel Detection of Protein and Nucleotide Sequences, 2011).

There is an extensive literature on parallelism and parallel detection in relation to computer applications, whether to increase efficiency or to avoid inefficiencies (Sungpack Hong, et al, Technical Report: On Fast Parallel Detection of Strongly Connected Components (SCC) in Small-World Graphs, 2013; Ken Kennedy, et al, Maximizing Loop Parallelism and Improving Data Locality via Loop Fusion and Distribution, 1993).

Cognitively parallelism can be explored in terms of correspondences, notably as in aesthetic associations, as well as resonance effects understood in musical terms (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007; Openness and Closure in Pattern Language Geometry versus Resonance, 2012; Complementarily of Qualitative Distinctions in Resonance, 2013).

Of relevance to this argument is the question of how parallels between qualitative information derived from multiple senses reinforce each other to enable some form of cognitive fusion. Whilst this is relevant to individual cognition, it has implications for group decision-making -- and ultimately for the coherence of operations of a global brain however that is envisaged.

Of interest is the argument of Wilson Harris (Adversarial Contexts and Creativity, New Left Review):

The detection of parallels woven into the evolving weave and cycle of fiction can be exciting in its illumination of profoundest unity of the human spirit.

Animation commonality: cubes and 12-foldness: Of particular interest is the commonality between the four disparate animations, and the significance variously associated with them. This is evident with respect to the cube central to all of them and the pattern of 12-foldness characterized by it and otherwise. As discussed separately, it is profoundly curious that society attributes particular significance to 12-foldness (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011). **** K insert polyhedra

This is especially evident in the organization of round tables and juries. This proclivity can be explored with respect to global governance (Eliciting a 12-fold Pattern of Generic Operational Insights: Recognition of memory constraints on collective strategic comprehension, 2011; Imagining Attractive Global Governance: questioning possibilities and constraints of well-boundedness, 2013; Enabling a 12-fold Pattern of Systemic Dialogue for Governance, 2011).

The pattern of course has its highly valued symbolic echoes (12 Apostles, 12 Imams, 12 Tribes of Israel, the Gods of Olympus, transformed into those of imperial Rome). Missing from such widespread appreciation is any sense (beyond indicative myth) of the distinctive dynamics between those so assembled, as discussed separately (Implication of the 12 Knights in any Strategic Round Table, 2014; Generic Reframing of the 12 Tribes of "Israel", 2009).

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