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Re-cognition of N-fold sets of modes, ways, moves and ploys


Encoding Coherent Topic Transformation in Global Dialogue (Part #7)

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The question underlying this exploration of dialogue is: why is there a tendency to distinguish sets of particular size in organizing concepts, strategies and ways of doing anything?. Puzzling in this connection is how rare it is to see any explanation as to why information is clustered in a particular way -- rather than another. In the examples cited above with respect to pedagogical dialogue, one approach took the form of an 8-fold cluster, whilst another offered a 12-fold cluster. An earlier discussion of the phenomenon included many examples from a wide range of domains (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980; Examples of Integrated, Multi-set Concept Schemes, 1984)

It is in this sense that it is interesting to explore the contrasting implications of:

Examples of unexplained preferences for other patterns include:

With respect to dialogue, this unexplained tendency is evident in assertions regarding dialogue, for example:

The implied question could be enriched by interpretation in terms of arity -- understood as the number of arguments or operands taken by a function or operation in logic, mathematics, and computer science. Examples distinguished include: nullary, unary, binary, ternary, quaternary, quniary, senary, septenary, octonary, novenary, and denary. These suggest a degree of relationship to the lemmas of increasing rarity by which discourse and governance may be challenged: dilemma, trilemma, tetralemma (or quadrilemma), pentalemma (or quintilemma), hexalemma, heptalemma, and octalemma (Cognitive glass ceilings impeding integrative comprehension, 2019).

Especially intriguing is any sense that any set of modalities is complete (and exhaustive) -- rather than incomplete. There is obviously little enthusiasm for extending a 10-fold set to 11, or a 12-fold set to 13 -- or reducing it to 10. It is in this sense that any 8-fold clustering of dialogic modalities merits a degree of challenge, especially when it clusters some 33 categories (rather than 32 or 30).

Of interest is then what might constrain the extension of a set and how the extension might reveal unsuspected constraints. Examples include:

  • use of an 8x8 board game, as with chess, within which experts recognize how they are constrained to 20 opening moves. How many "opening moves" can be recognized within what kind of understanding of engaging in dialogue?
  • much has been made of discovering the minimum number of moves required to solve a 3x3x3 Rubik Cube. However it is only recently that it has been determined that the minimum number of moves in which it can be solved is 20. The process has been described in the following terms by those involved: God's Number is 20; Twenty as "God's number"? (2018).
  • constraints on jury size and the possibility of changing any commitment to a jury of 12 (Fundamental operational concepts, jury size, financial ratios and "the Greeks", 2018).

With respect to dialogue, there is considerable familiarity with the lore of viable collective dialogue, namely that it should be limited to 7, as tends to be commonly accepted in terms of the need for requisite variety:

The question can be explored more generally in terms of the constraints on the articulation of any viable set of strategies (Eliciting a 12-fold Pattern of Generic Operational Insights: recognition of memory constraints on collective strategic comprehension, 2011).

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