Challenges of cognitive integration -- square dancing?

Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks (Part #19)

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The following exploration is based on the assumption that a preferred degree of correspondence within one cognitive style may necessarily be perceived as inappropriate from another, but the challenge is to recognize the conditions under which each form of correspondence may be appropriate. The various flavours of "correspondences" explored in the annex might therefore be tentatively juxtaposed in a framework such as Table 4.

The question however is how best to embody in any such tabular representations a range of dimensions relating to knowledge creation in pursuit of connectivity such as best to ensure its wider credibility.

The challenge of reducing high degrees of complexity to a simple four-fold table is that any such reduction is best described as being cognitively "slippery". The nature of such slipperiness is partly to be understood by comparison with the choice of a musical tuning system. Each tuning system offers advantages and disadvantages and in opting for one the challenge of the choice may be forgotten -- even though alternatives may be favoured in other cultures. What meaningful process might then be associated with "category tuning systems"? Given the challenge in the musical case, how is "goodness of fit" to be determined in any such attunement?

In this respect, a particular challenge is the possibility of equivalents to issues of discernment that might be metaphorically described as: tone deafness (no "ear" for music), lack of visual taste, an uneducated palette, or a lack of aesthetic "feel".

One insightful approach to understanding knowledge creation is that of Marcus Berliant and Masahisa Fujita (Knowledge creation as a square dance on the Hilbert cube, 2006). Their model incorporates two key aspects of the cooperative process of knowledge creation by "myopic" agents:

(i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while
(ii) the very process of cooperative knowledge creation affects the heterogeneity of people through the accumulation of knowledge in common.

It is interesting to consider their method (which relies on symmetry, even mirroring) as also being potentially applicable to distinct cognitive styles or processes (as implied by Table 3), whether or not they are associated with single individuals (the focus of the model), groups, movements, cultures or "civilizations". The authors note :

The model with only two people is very limited. Either two people are meeting or they are each working in isolation. With more people, the dancers can be partitioned into many pairs of dance partners. Within each pair, the two dancers are working together, but pairs of partners are working simultaneously. This creates more possibilities in our model, as the knowledge created within a dance pair is not known to other pairs. Thus, knowledge differentiation can evolve between different pairs of dance partners. Furthermore, the option of switching partners is now available. We limit ourselves to the case where N is divisible by 4. This is a square dance on the vertices of the Hilbert cube. When the population is not divisible by 4, our most useful tool, symmetry, cannot be used to examine dynamics.

Their analysis identifies points of relatively unproductive equilibria and conditions for sustainable productivity:

We have seen that once the agents reach the bliss point (where the growth rate is highest), achieved from large initial homogeneity by cycling through all partners as rapidly as possible, they break into groups of 4.... This dance pattern allows them to remain at the highest productivity forever.

They offer explanations for why 4 is the "magic number" by placing the model in a more general context. There is a strong case for integrating their work with the management cybernetics of Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994; Gunter Nittbaur, Stafford Beer's Syntegration as a Renascence of the Ancient Greek Agora in Present-day Organizations, Journal of Universal Knowledge Management, vol 0, 1, 2005), as well as with the work of Edward Haskell (Generalization of the structure of Mendeleev's periodic table, 1972) with respect to engendering entropy and negentropy in a coaction cycle as discussed elsewhere (Psychosocial Energy from Polarization within a Cyclic Pattern of Enantiodromia, 2007). Also of relevance is the focus of Lakoff and Núñez (2000) on an innate human ability, called subitizing, namely to count, add, and subtract up to about 4 or 5 -- and how much larger numbers are then handled through metaphorical constructions.

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