Moving axes of comprehension and communication

Periodic Pattern of Human Knowing (Part #3)

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The challenge of the previous paragraph was the theme of earlier explorations (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007; Conditions of Objective, Subjective and Embodied Cognition: mnemonic systems for memetic coding of complexity, 2007; Comprehension of Appropriateness, 1986). The first notably endeavoured to map the associated dynamics onto a single diagram (Imagining the Real Challenge and Realizing the Imaginal Pathway of Sustainable Transformation, 2007). The assumption is that there is a need for a degree of self-consciousness and self-reflexivity in advancing and endeavouring to comprehend formulations that claim to be of a more integrative order.

A further exercise, in anticipation of the challenge of the formlations highlighted below, is to consider the following "psychosocial" processes which typically are irrelevant to the composition of such formulations from a mathematical perspective (in contrast with judgements on the quality of the mathematics) -- and deprecated in any mathematical lexicon. Terms commencing with "co-" are used to offer a provocative mnemonic set.:

In earlier explorations the following figures were used to present the interrelationships between conventional categories and processes and those which were notably characteristic of lived reality. (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008)

Fig. 1: Interrelating problematique, resolutique, "imaginatique" and "irresolutique" [click for larger version in source]	Fig. 2: Indication of relationship between dimensions relating to engagement with symmetry [click for larger version in source]

Rather than use the real and imaginary axes of the complex plane as in the figures above, in the figure below they are treated as extremes on the same axis, with a second axis based on temporary/invariant. This allows any approach (of an individual or a group) to challenging formulations to be positioned within the arena -- as illustrated by the dashed smaller diagrams ("crosshairs" of identity) -- each structured to reflect its position in the arena. Learning, as collectively recognized, then involves movement into the top right quadrant. Much daily subjective experience is in the bottom left quadrant. More interesting is that the dashed constructs are not static but may move around the arena, alternating between various positions -- with the representative construct adjusting accordingly. The challenge with any definitive formulation (of the type identified below) is that it is a characteristic outcome of processes in the top right quadrant. The "co-" processes (above) are characteristic of the other quadrants, notably in imagining (intuiting) their possibility or recognizing one's ignorance when faced with learning about them.

Fig. 3: Mapping the comprehension/communication challenge

Formulations characteristic of the top right quadrant are effectively set in "cognitive stone". In navigating towards them through a learning process, delicate associations of connectivity are imagined between phenomena. These may be understood as "pathways" but possibly best described as "elven pathways" negotiable only by the light and swift of cognitive foot, as discussed elsewhere (Walking Elven Pathways: enactivating the pattern that connects, 2006; Climbing Elven Stairways: DNA as a macroscopic metaphor of polarized psychodynamics, 2007).

The most remarkable tale regarding such unconventional connectivity is that relating to the discovery of the Monster Group of symmetry, a feature of the discussion below (Mark Ronan, Symmetry and the Monster: one of the greatest quests of mathematics, 2006). Curiously there are many mathematical papers explaining the associated theory of "monstrous moonshine", as discussed separately (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

The issue is what degree of connectivity is necessary to move into the top right quadrant, and are other degrees of connectivity appropriate for other purposes -- justifying any reluctance to aspire to move there. Part of the response is to be found in the nature of meaningful "correspondences" -- an issue at the heart of the controversial "moonshine", as discussed separately (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007). One interesting formulation of the challenge of appropriate connectivity is the famed 10 ox-herding images of Zen Buddhism, as discussed elsewhere (Progressive integration of the shadow of non-self-reflexivity, 2007). In such terms, at its simplest perhaps, should formulations (as with those discussed below) be progressively interrelated, namely:

• be variously framed and separately positioned (like icons) on the walls of one's cognitive domain?
• should there be some design to their placement, with some suggestion of complementarity or sequence?
• should their placement configure (or imply) some larger cognitive whole, together functioning as a form of cognitive antenna?
• is there some sense in which progressive engagement with them is personally transformative (as attributed to mandalas)?
• etc

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