Static description of cycles versus the dynamics of Cyclic experience

Cyclic Representation of Coherence as Knots and Otherwise (Part #11)

Relative orientation: Relatively frequent recognition is accorded to people, groups and initiatives of distinctive "orientation" -- clearly to be understood as a geometrical metaphor. Less evident is how an orientation is to be otherwise meaningfully understood and the range of orientations that can be fruitfully recognized. A compass rose is used in navigation of the globe to order and interrelate the diversity of orientations, suggesting the possibility of analogous understanding in cognitive space, as discussed separately (Ways of looking distinguished in terms of "compass" orientation, 2021).

It is somewhat tragic that in psychosocial terms there is a tendency to promite the one right way -- the right direction -- excluding definitively the possibility that other directions may have some relevance. Unity is then simplistically associated with the one direction, reinforcing the suppression of a diversity of perspectives. The compass rose usefully recognizes the variety of directions. Typucally missing is how relevance is accorded to alternative oritentations.

(Con)fusion: With the complexification of the images above, the twists may be twisted together at the centre of the form. This can be seen as a form of fusion -- potentially indicative of a melding of faiths, or disciplines, or other modalities. This could be understood in terms of viable integration of the modalities in each case. However, as is evident from the images, it could also be indicative of a form of confusion -- more typical of systemic relations in practice.

Disconnection: As noted above, the set of images excludes those forms in which there is no continuity -- a loop is then not continuous but has loose ends, suggesting a loss of systemic coherence. Such forms could well be explored as being indicative of many situations in practice and a fundamental challenge to viable sustainability -- exemplified by appeals for "joined-up thinking".

Interlocking: Potentially more intriguing is the situation in which loops are continuous, but are disconnected from one another, however they may interlock -- an unlink condition. The simplest much-studied case is that of Borromean rings, whether involving 3 rings or more. The helical models noted above could then be challenged in practice as to whether the loops are systemically unlinked although wound together. They too might be considered as exemplified by appeals for "joined-up thinking".

A set of 3 distinctive rings is a feature of Dante Alighieri's account of 3 wheels (tre giri) of the Holy Trinity in Paradiso 33 of the Divine Comedy (Arielle Saiber and Aba Mbirika, The Three Giri of Paradiso XXXIII, Dante Studies, 131, 2013, pp. 237-272). That remarkable interdisciplinary exploration combines insights from speculative theology, geometry and knot theory, as discussed separately (Borromean challenge to comprehension of any trinity? 2018).

Dynamics -- in 3D (or more)? There is a necessary constraint on the representation and engagement with the cyclic configurations above. Use of simple animation is a partial corrective. Efforts have been made separately to provide an interactive experience with 3D forms from previous exercises (Eliciting Insight from Mandala-style Logos in 3D, 2020).

Especially missing is engagement with any rotational dynamic -- given the static depiction of the 3D forms from a particular perspective. The significance of this is evident in the acknowledged role of rotation of functions -- as with the chairperson of a conference, an organization, or the UN Security Council. This extends to the rotation of venue in the case of a succession of international conferences. This is otherwise known as turn-taking and also applies to the contribution of participants to collective conversation (T. Stivers, et al, Universals and cultural variation in turn-taking in conversation,. Proceedings of the National Academy of Sciences. 106, 2009, 26)

Other than this specific application, arguably missing is the form of rotation deriving from the fundamental insight of Nicolas Tesla with respect to the potential implications of alternation and rotation in psychosocial fields, as discussed separately (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). Arguably there is no lack of "charged conditions" in society, with extremely limited insight into how these might be addressed and usefd creatively. Tesla succesfully derived electrical motors and dynamos by combining the charge associated with (necessarily polarized) magnetic fields and their rotation within a wiring pattern. .

Experimental 3-phase animation of classic Sri Yantra (core "wiring" configuration passing through a succession of phases)
Animation through 3 phases)	Animation through 8 phases	Animation through 16 phases

As suggested by the earlier discussion of the implications of rotation suggested by technomimicry, there are clues to this possibility in quite disparate domains:

Helicopter development: The argument for technomimicry is inspired by the insights of Arthur M. Young, designer of the Bell helicopter, as separately discussed (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011). Young envisaged the possibilities of applying the principles of helicopter control -- notably involving challenges of rotation -- to the development of a "psychopter" or "winged self" (Geometry of Meaning, 1976; The Bell Notes: A Journey from Physics to Metaphysics, 1979). Possible understandings are discussed separately (Characteristics of phases in 12-phase learning-action cycle, 1998; Typology of 12 complementary strategies essential to sustainable development, 1998).
Nuclear fusion: The design principles required to render plasma control feasible in a toroidal reactor (as in the ITER project) also suggest insights of psychosocial relevance, especially when plasma is understood as the flow of attention (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006)
Fluid flow: Considerable insight into the functioning of vortices in nature emerged from the work and applications of Viktor Schauberger, as separately discussed (Enabling Governance through the Dynamics of Nature: exemplified by cognitive implication of vortices and helicoidal flow, 2010). His principal argument was that humanity could benefit considerably by learning from nature -- specifically the dynamics of water -- rather than trying to correct it (Douglas Hofstadter, Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995). Schauberger's concern was to liberate people from dependence on inefficient and polluting centralized energy generation. A subsequent development of this turbine is now known as the "vortex generator" (although many others now exist with that name).
Circulation of the light: This can be considered as a form of "technology" potentially to be related to Tesla's preoccupation with light (Circulation of the Light: essential metaphor of global sustainability? 2010). It has been significant in other cultures, notably with respect to the discipline of Neidan. The nature of the metaphorically-enhanced use of word-play in Neidan is admirably clarified in essays by Isabelle Robinet (The World Upside Down: essays on Taoist internal alchemy, 2011), remarkably translated from the French by Fabrizio Pregadio:

Internal alchemy, or Neidan, is a technique of enlightenment whose earliest extant written records date from the eighth century. It appeals both to rationality, which gives order to the world, and to what transcends rationality: the unspeakable, the Totality. Its main tools are the trigrams of the Yijing (Book of Changes) and a number of key metaphors, some of which are alchemical in nature, whence the name, "internal alchemy"....

The toroidal form of the "wiring" (in some of the configurations above) emphasizes the value of exploring the psychosocial dynamics which might be associated with them (Visualization in 3D of Dynamics of Toroidal Helical Coils -- in quest of optimum designs for a Concordian Mandala, 2016). This then frames the question of living on a torus in contrast to assumptions regarding life on a flat Earth or one that is spherical (Imagining Toroidal Life as a Sustainable Alternative From Globalization to Toroidization or back to Flatland? 2019; Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011; Distribution of significance "within" a torus: using a third dimension for "Engagement with reality", 2006).

The limited recognition accorded to the toroidal form can be usefully challenged through the animations below showing how the Mereon Trefoil (discussed above) is generated from a torus by rotating a circle of 3 spheres moving around the torus, then rendering visible the winding path they trace in the course of the combined movements. For clarity the animation is also reversed. Bederov's technique can also be applied using 2 spheres moving around a torus oriented vertically (below centre). In this case it generates a more classical trefoil. With the same method, using 1 sphere, another form can be generated in 3D (below left). The animations are unfortunately jerky due to constraints on video recording and web display. (Smoother interactive 3D variants can be explored using the X3D variants as indicated, and potentially via an X3DOM context) [NB: These animations offer insight into the meaning of "sphere" in the animations above]

Animations indicating the generation of relatively complex forms around s torus Reproduced from (Contrasting orientations indicative of complementary cognitive modalities, 2022)
One-sphere	Two-sphere	Three-sphere
Classic twisted form (screen shot)	Classic trefoil generated around a torus	Mereon trefoil generated around a torus

	Interactive x3D	Interactive x3d
Adapted from models developed by Sergey Bederov of Cortona3D