Volume 27, Issue 3, 2017
Values and Ideals. Theory and Practice: Part IV
Mikhail A. Pronin
Dialogue as a Knot
The First Ideas of Dialogue Ontology
The paper proposes an idea of explicating the invariant universal structure of dialogue through the mathematics of knots and braids, which is relevant, both for the development of particular models of communication and/or dialogue, and for constructing a general theory of dialogue, or the theory of utterances. The possibility of modeling dialogue with the help of the mathematics of braids and knots—categories, entities and their attributes—is shown by use of some well-known examples such as parts of the sentence in grammar. Entities and their attributes can be considered as knots, either right or false. The idea is to visualize the chains of these entities: to formalize them not to keep in mind, neither in the text, but to work with them graphically.
Nodes, as final structures, and braids that generate them, allow to reveal paradigmatic anomies, conflicts, logical and ethical disagreements, etc., and vice versa: “synonimies,” mutual understanding, unanimity, in a fundamentally new format of perception and understanding of the context of genesis (braids) and results (knots) of dialogue.
The visualization of verbal utterance on the basis of the knot and braid mathematics is a significant step towards formalizing the theories of dialogue, both in general theoretical and purely practical plans. The latter is analyzed by the example of the person’s inner dialogue with herself/himself in making decisions: rational and/or irrational (emotional), which allows conducting a specific work with clients of psychotherapy, coaching, management consulting, mediation, etc.