Cyclic Representation of Coherence as Knots and Otherwise

Interestingness of curves of increasing complexity in relation to sustainability

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Introduction

Cyclic themes of interest at this time include the circular economy, environmental cycles, recycling, business cycles, and domestic cycles of violence -- as with the cycles of conflict. The following exercise is an exploration of the cyclic representation of coherence in the light of the increasing significance of such cycles separately, or however they may be combined with others.

With respect to "interest" and "coherence", the exercise follows from an earlier exploration of the somewhat obscure concept of interestingness, especially given its recognized importance to data mining  (Interestingness, suggestiveness, memorability and presentation, 2014). One concern is that, rather than being interesting, coherence and unity (for which many plead) may be boring to many for reasons that merit clarification. How might they be "re-cognized" as interesting?

The exercise was especially provoked by the switch of Facebook to a new logo for its new branding as Meta, and the latter's association with an emergent metaverse, as discussed separately (Future Psychosocial Implications of the Metaverse, 2022). The speculative investigation  of the latter highlighted the fundamental significance recently attached to the Mereon Trefoil as described by Louis Kauffman (Pattern, Sign and Space: Mereon Thoughts. 2003). Otherwise known and visualized as the Mereon Matrix, its potential significance is elaborated in a far more extensive work (Louis H Kauffman, et al, The Mereon Matrix: everything connected through (k)nothing, 2018; frontmatter).

More specifically the exercise here was inspired by the model developed by Sergey Bederov of Cortona3D to visualize that continuous curve in 3D, as presented in earlier studies -- notably of the familiar seam curve of the tennis ball and baseball (Seam Curve on Sports Balls, Wolfram Demonstration Project; Interactive display of generalized baseball and tennis-ball seam curves in 3D). The similarity of the seam curve and the Meta logo was noted. Of particular value was a variant of the modelling program used which enabled curve parameters to be modified to produce a variety of elegant knots. Like the Meta logo and the seam curves, these can be recognized as exemplifying cyclic representations of coherence, whether of symbolic, cognitive or of systemic relevance.

The exercise here is in many respects simplistic since it was unclear what configurations would emerge from exploratory modification of the program parameters. It was also unclear how best to present the many results to highlight the relationships between the confusing variety of configurations, whether understood as knots or otherwise. In that sense the results merit confrontation with the systematic studies of knot theory, although the emphasis here is on forms of visualization with which people can engage and readily comprehend (Cognitive embodiment of knots: knotting and knitting processes, 2021). As noted in the latter, knots have notably featured in the psychoanalytical work of Jacques Lacan and R. D. Laing. Global governance can itself be recognized as confronted with the archetypal Gordian knot (Mapping grossness: Gordian knot of governance as a Discordian mandala? 2016),

The results of the exercise do however lend themselves to presentation as screen shots in a set of tables, the primary mode used here. The variety of forms engendered by modifying the parameters is a limitation on efforts at web display whether in 2D or 3D. Some use is therefore made of gif animations as a means of giving a sense of the 3-dimensional nature of all the forms. Unfortunately current web technology constrains 3D representation of all the models in virtual reality.

The forms displayed are only those in which the curves are continuous. Many other curves can be generated in which those below are broken in some manner. These could be of significance to the visualization of the vulnerability of systemic coherence to various kinds and degrees of failure, as discussed separately (Variety of System Failures Engendered by Negligent Distinctions, 2016).

Of particular interest, in the commentaries which follow the curve presentations, is the degree to which  they offer a kind of dynamic three-dimensional pattern language through which degrees of coherence can be discussed and distinguished. Such comprehension may well relate to that offered by music. In that sense they may clarify degrees of interdisciplinarity, interfaith reconciliation, international integration, interethnic reconciliation, and the like. They may also clarify dynamic configurations which are suboptimal in contrast with any aspirations for more fundamental "unity" as these feature in the declarations of leaders.  This could prove especially valuable where "unity" and "harmony" are misleadingly assumed to be a simple matter, effectively denying the complexity with which many are confronted (Emergence of a Global Misleadership Council: misleading as vital to governance of the future? 2007).

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