Variety of "slippery" parameters in credible knowledge creation

Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks (Part #20)

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It is assumed here that "slipperiness" in relation to grasping, ordering or representing parameters about knowledge creation is -- self-reflexively -- inherent in the process of knowledge creation. An interesting metaphor is that of the plasma "snake" instability in a tokamak for nuclear fusion (cf Enactivating a Cognitive Fusion Reactor, 2006). Some of the relevant parameters, notably in the light of Table 3, are:

• configuration of polarities:
  • inner-outer (AQAL)
  • individual-collective (AQAL)
  • positive-negative
  • credibility-incredibility
  • weak conjecture-strong conjecture
  • low confidence (uncertainty, inadequacy)-high confidence (certainty, overconfidence)
  • closure-openness (Lawson)
  • comprehensibility-incomprehensibility
  • completeness (comprehensiveness, structural depth)-partiality (incompleteness, superficiality)
  • connectivity-isolation
  • (detached) explanation - (participative) engagement (even embodied knowing)
• cognitive styles or ways of knowing
• uncertainty principle
• cyclic transformation (Psychosocial Energy from Polarization -- within a Cyclic Pattern of Enantiodromia, 2007)
  • work cycle (Carnot)
  • coaction cycle (Haskell)
  • learning/action cycle (Young)
  • Golden Flower
• WH-questions (Conformality of 7 WH-questions to 7 Elementary Catastrophes, 2006)
• 4-fold:
  • conviction/logic/dreams/aesthetic
  • conviction/archetypes/logic/directives

Self-reflexively, the "conjecture" that there is a significant connectivity between these items, such as to constitute a higher degree of coherence, may be immediately rejected outright as "incredible", considered "weak" or potentially "strong". This exemplifies the challenge of knowledge creation with respect to any "pattern that connects" -- and the extent to which it is "moonshine" by any conventional standards.

Echoing the above dance metaphor, Ronan (2006) remarks:

The Monster...first arose as an enormous collection of operations: something to be studied, something to be constructed (did it really exist?), something to be understood. The fact that mathematicians can get a vague but but increasingly precise view of something that is 'out there' may come as a surprise to some people. We are not usually thought of as creative artists, yet in some mays what mathematicians do has a lot in common with what artists achieve....

A choreographer may know exactly what effect is needed, but fitting the steps to the music is what it is all about. In fact, let me compare an abstract group to a dance. The group can be represented in many ways, by many different dancers.... Another good analogy is music. A piece of music can be accompanied by words, movement, or dance, or can simply be appreciated on its own. It is the same with groups. (pp 50-51)

This implies that there may well be some form of "mapping" between the algebraic and symbolist theories of correspondences (or signatures) -- across the schizophrenic divide to which proponents of each subscribe. Is it possible that the algebraic theories are generic formalizations of the symbolist variants, hygienically occluding cognitive implications and their operational role in engendering those formalizations and rendering their connectivity comprehensible?

It is tragic that the subtlety of Ronan's comment has not been reflected in assessment of the claims of non-scientific cognitive styles, whether over past centuries or in the current "two culture", "two civilization", binary era. There are many repugnant, dysfunctional examples of the attitude of "mainstream" science to "fringe" science -- perhaps symbolically exemplified by a famous review by the editor of Nature questioning whether a book was "fit for burning".

An interesting issue is how to respond to preferences for sets of distinctions of different size -- namely how, in an orderly manner, to collapse them (conflating categories) or expand them. This relates to the consideration, noted above, of Lakoff and Núñez (2000) regarding called subitizing, namely the ability to count, add, and subtract up to about 4 or 5 -- and how much larger numbers are then handled through metaphorical constructions. Collapsing 4 conditions leads into the dynamics of 3 or 2 or the categorical absolutism of 1. Expanding to 5, as is characteristic of many alternative representations of the symbolic "elements" offers some interesting possibilities. With respect to the 4 Rg Vedic languages in Table 4, in relation to the 5 "modules" of the biocultural paradigm, Antonio de Nicolas (personal communication) remarks:

... the "languages" are descriptive of a psychosocial situation and the "bio-cultures" are embodied frames of invariant epistemologies. Each bioculture will produce for you a multiplicity of generic tables, but not in reciprocity since generic tables do not necessarily produce invariant/embodied epistemologies... Bio-cultures are the set of embodied epistemologies that give rise to the rest of the generic tables that appear in the market place. It is like a tree with multiple (5) trunks, each one in turn producing the multiple theoretical classification tables, and so on...

In this sense each quadrant then offers 5 possibilities of engaging in the knowledge creation process -- giving a total of 20 possibilities that is suggestive in the context discussed earlier.

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