Insights from dialogue, multi-part singing and periodicity

Transcending Simplistic Binary Contractual Relationships (Part #7)

Dialogue: Interpersonal relationships, and those between collective bodies, are informed by the nature and quality of dialogue. There is then a case for deriving insights from proposals for new forms of dialogue which in some way transcend the binary processes only too evident in dialogue. These binary processes of course take the form of a preoccupation with distinguishing right/wrong, agree/disagree, informed/misguided, and the like, as notably challenged by Edward de Bono (I Am Right -- You Are Wrong, 1990). He has offered alternatives (Six Thinking Hats: an essential approach to business management, 1985; Six Action Shoes. 1991).

Curiously, whilst there are numerous references to dialogue in relation to mathematics education, ironically the single passing reference to "mathematics of dialogue" was in relation to Kashmir (J. R. Aryan, Kashmir and India's soft stand, Early Times, 18 November 2011).

A more complex system of dialogue might then be seen as exemplifying the non-binary approach seemingly necessary in order to address more complex psychosocial situations, as variously argued separately (Sustainable Dialogue as a Necessary Template for Sustainable Global Community, 1995; Transdisciplinarity through Structured Dialogue: Beyond sterile dualities in meetings to the challenge of participant impotence, 1994; Typology of 12 complementary dialogue modes essential to sustainable dialogue, 1998; Resolving the Challenge of Faith-based Terrorism: Eliciting the dynamic of two-body, three-body and n-body variants, 2005).

The papers cited point to possibilities of a more formal description of non-binary dialogue, as does, most notably, the work of Anthony Blake (The Supreme Art of Dialogue: structures of meaning, 2008). A possibiliy extensively informed by insight from cybernetics has been articulated by Stafford Beer (Beyond Dispute: The Invention of Team Syntegrity, 1994) and implemented in the "syntegration" process. .

The possibilities of structured dialogue are also central to the collaborative work of Thomas R. Flanagan, Kenneth C. Bausch and A. N. Christakis (A Democratic Approach to Sustainable Futures: a workbook for addressing the global problematic, 2011; The Talking Point: creating an environment for exploring complex meaning, 2010).

Curiously it can be argued that such initiatives do not come to mathematical terms with what is so widely recognized through metaphor in dialogue itself, namely the reference to "making points", "point of view", "line of argument", and the like, as discussed separately (Experience of Cognitive Implication in Fundamental Geometry: Unexamined metaphoric framing of strategic discourse, 2012). This suggests that a more formal mathematical exploration follows from the implications of the work of R. Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975-1979), as discussed in Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics (2009) and elsewhere (Metaphorical Geometry in Quest of Globality, 2009; Engaging with Globality: through cognitive lines, circlets, crowns or holes, 2009; Geometry of Organizations, Policies and Programmes, 1992).

Geometry, as with topology, would seem to offer a template through which to approach the non-binary possibilities of social organization informed by dialogue. In the light of the work of Fuller, these have been partially explored through the use of polyhedra (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008; Coherent Value Frameworks: Pillar-ization, Polarization and Polyhedral frames of reference, 2008; Topology of Valuing: dynamics of collective engagement with polyhedral value configurations, 2008).

Such investigations suggest the possibility of eliciting the non-binary characteristics of dialogue from patterns of dialogue -- as exemplified by the archetypal "round table", and the inspiration that continues to offer, as separately discussed (Enabling a 12-fold Pattern of Systemic Dialogue for Governance, 2012). The argument was developed there through the following sections:

Of some relevance to this argument, internet fora may well explicitly clarify the nature of interventions considered unacceptable -- effectively requiring participants to agree to a code of conduct, namely a form of contract.

Multi-part singing: Of particular interest in terms of comprehending non-binary possibilities, and as a basis for engaging mathematical insight, are the Clues to patterns of dialogue from song, most notably in the form of multi-part singing -- a well-recognized form of "dialogue" between distinct "voices". More generally it is of course the case that mathematics has been extensively engaged in articulating the theory of musical harmony -- itself an aesthetic exemplification of non-binary possibilities and their relationship to the binary world.

Of specific interest is the recognition of the many different voice types used by vocal pedagogists and variously clustered in voice classification systems. The challenge in dialogue and in psychosocial organization would seem to be admirably clarified by recognition of the different "voices" which seek expression -- as only too evident in political discourse.

It is from this perspective that the separate discussion (noted above) highlighted the widespread recognition of polyphony and multi-part singing as being indicative of widespread understanding, across cultures, of non-binary possibilities through which the relationship between contrasting "voices" could be explored. There is the particular possibility of the relevance of this understanding in cultures otherwise challenged by the dominant mindset (Knowledge Gardening through Music: patterns of coherence for future African management as an alternative to Project Logic , 2000).

Although interpreted otherwise -- from a semiotic perspective -- it is appropriate to note that "polyphony" was a main theme of the 2009 Conference of the International Association for Dialogue Analysis. The 2010 Conference had as its theme Political Dialogue Analysis. Very limited use is made of mathematical techniques -- despite the innovative mathematical appropach to semiotics initiated by Rene Thom (Per Aage Brandt and Wolfgang Wildgen (Eds.), Semiosis and Catastrophes: Rene Thom's semiotic heritage, 2010).

Periodicity: Widespread understanding of music scales, tuning systems and musical rounds is consistent with recognition of periodicity as providing a richer context for binary preoccupations. This has been partially illustrated by the fictional exploration of relationships in terms of a chemical metaphor by Johann Wolfgang von Goethe (Elective Affinities, 1809). The novel is based on the metaphor of human passions being governed or regulated by the laws of chemical affinity, and examines whether or not the science and laws of chemistry undermine or uphold the institution of marriage, as well as other human social relations. The novel pre-dates the development in 1869 of the periodic table of chemical elements credited to Dmitri Mendeleev, which illustrated the periodic trends in the properties of the then-known elements. That has in turn been used as a metaphor for an ordering of his interpersonal relationships by the chemist Primo Levi (The Periodic Table, 1975). The relevance of the chemical metaphor has notably been explored by Johan Galtung (Chemical Structure and Social Structure: an essay on structuralism, 1977).

The struggle to detect order in an elusive pattern is well-highlighted by the history of that periodic table and its representational imagery (J. W. von Spronsen, The Periodic System of Chemical Elements: a history of the first hundred years, 1969). With respect to the latter, this struggle continues regarding understanding and representation of that pattern of qualitative properties in the light of more sophisticated understandings of relationships from mathematics (Denis H. Rouvray, et al, The Periodic Table: Into the 21st Century, 2005; The Mathematics of the Periodic Table, 2005). The synthesis represented by that table continues to be upheld as one of the most fundamental achievements of science.

In a separate discussion of the binary challenge of social relationships (Us and Them: Relating to Challenging Others: patterns in the shadow dance between "good" and "evil", 2009), reference was made to the possibility of a Periodic table of relationships between "us" and "them" (2009). This might be understood as consistent with efforts to classify "plots" characteristic of the dynamics of human relations (Georges Polti, The Thirty-Six Dramatic Situations, 1916). The historical (and continuing) debates regarding the numbers of chemical elements in groups, or their attribution to such groups, provides an admirable indication of the nature of such a process of distinction in pursuit of some form of closure. Ironically the challenge is one shared by both the "two cultures".

Following this possibility, in a related exploration (Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order, 2009), the cognitive challenge of comprehending distinctions in a complex pattern was addressed in the light of the structure of the Periodic Table.

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