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Cognitive osmosis through topological eversion and interlocking tori -- framing outside-inside otherwise
Cognitive Osmosis in a Knowledge-based Civilization (Part #8)
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Strange loops: This argument derives its inspiration from the improbable processes of sphere eversion, the eversion of the torus, and from the topological transformation between sphere and torus (as illustrated in an animation above). The challenge to the imagination and to cognitive significance can be variously envisaged (Transforming vehicles of identity between global and toroidal forms, 2016).
As prominent symbols of wholeness, it is this improbability which recalls the argument of Steven Rosen (Wholeness as the Body of Paradox. Journal of Mind and Behavior, 18, 1997). The point is made otherwise with respect to "strange loops", described by Wikipedia as a cyclic structure that goes through several levels in a hierarchical system: It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started. Strange loops typically involve self-reference and paradox, as proposed and extensively discussed by Douglas Hofstadter (Gödel, Escher, Bach: an eternal golden braid, 1979; I Am a Strange Loop, 2007).
With respect to such strangeness, the animation possibilities discussed suggest that consideration should also be given to the symbol as a whole -- with any serpents as being indicative of strange loops. One clue is offered by the pursuit of a pearl in the Chinese dragon dance. As a pearl of wisdom, this accords with the integrity implied by the ouroboros. However this can also be seen as implied by the hole which it frames and around which one or more serpents are entwined.
Potentially of great relevance to this argument are the international hopes associated with nuclear fusion, currently the focus of the International Thermonuclear Experimental Reactor (ITER). The toroidal form of the reactor is designed to contain plasma wih the potential to destroy it if not managed appropriately. The "snake" metaphor has long been used in the description of instabilities in the circulating plasma in the reactor -- including "runaway snakes". The project -- including the snake metaphor -- offers a remarkable range of metaphors of relevance to cognitive osmosis, as discussed separately (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006)
Holes: Such a symbolic hole merits the attention recently accorded to the mysterious nature of holes as explored by Roberto Casati and Achille C. Varzi (Holes and Other Superficialities, 1994) -- with respect to the borderlines of metaphysics, everyday geometry, and the theory of perception (reviewed by Steven A. Gross, What's in a Hole? The Harvard Review of Philosophy, 1994). Their unexpected implications are indicated in an extensive entry on holes in the Stanford Encyclopedia of Philosophy.
Such implications may be explored otherwise, as argued by Terrence Deacon as a cognitive anthropologist with respect to the role of what is missing (What's Missing from Theories of Information? 2010; Incomplete Nature: how mind emerged from matter, 2011; The importance of what is missing, New Scientist, 26 November 2011). He explores the paradoxical incompleteness of semiotic and teleological phenomena in terms of information to demonstrate how specific absences (or constraints) play the critical causal role in the organization of physical processes that generates these properties. For Deacon:
Basically, it means that our best science -- that collection of theories that presumably comes closest to explaining everything -- does not include this one most defining characteristic of being you and me. In effect, our current "Theory of Everything" implies that we don't exist, except as collections of atoms. So what's missing? Ironically and enigmatically, something missing is missing. (p. 1, emphasis added)
A sense of the missing can be specifically related to the ouroboros through the significance attached to a ring (Engaging with the missing -- however encircled or encycled, 2017). With the ring as symbolic of coherence, what is encircled by it? How is forming a circle or a ring understood as a container -- especially one with symbolic or magical implications? Formation of a circle of trust? What of defensively circling the wagons? The strategic implication has been extended to configuring problems in cyclic terms (Encycling, Enwholing and Wholth, 2014; Encycling Problematic Wickedness for Potential Humanity, 2014).
Directionality and wholeness: There is a curious but relatively obvious sense in which the serpents or dragons imply directionality and a quest. It is the manner in which their dynamic defines a (torioidal) ring which is intriguing -- given the relationship between torus and sphere, to the extent that the sphere is held to be more symbolic of wholeness. In conventional terms however, a sphere is essentially static rather than dynamic. What might be assumed to be the dynamics of sustainable globalization? Arguably the imagery of sphere eversion topology should inform reflection on the nature of such globalization (John M. Sullivan, Topological Stages in the Eversion; video of The Optiverse, 1998).
In their strange pursuit of wisdom, it is the serpents which embody that dynamic to a degree. Hence the potential significance of the helical, serpent-like nature of a triple, quadruple or quintuple models -- inspired by that of DNA, as noted above. As separately argued, these can be understood as engendering the symbolic stars which are so fundamental to representation of national identiy on flags and otherwise (Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension?, 2017).
| Triple helix representation in 3D compared with a visual rendering of colliding black holes | ||
 |  | Discussed with respect to Reconciling triskelion and triple helix: a topological transformation with psychosocial implications? (In: Psychosocial Learnings from the Spiral Form of Hurricanes Implications of the triple helix and the 3-fold triskelion as "cognitive cyclones"? 2017) |
Such an argument would seem to suggest a strange relationship between symbolic use of serpents, helices, stars and pillars. Are strategic stars and pillars to be usefully recognized as "frozen categories" -- "petrified" serpents, namely an "entombed" dynamic to which strategic helices are now conceived as providing a degree of remedy?
Especially intriguing in symbolic terms is the manner in which the dragon-serpents are intuitively understood to both intertwine and plunge into the hole which they thereby frame. This is strangely reminiscent of the process of intercourse and the fundamental significance attributed to it -- with a hole being the primordial attractor. It is therefore curious that the role of the double helix with respect to reproduction should now be "extended" to what is envisaged in relation to the triple, quadruple and quintuple helices -- if not more. Ironically this would seeem to anticipate the speculations of science fiction with regard to alien biologies requiring multiple sexual partners for viable fertilization. A quintuple helix model must indeed envisage 5-way cognitive osmosis. Globalization may indeed be more complex than conveniently assumed (Engendering Invagination and Gastrulation of Globalization: reconstructive insights from the sciences and the humanities, 2010).
Given the preoccupation of fundamental physics with the necessity for extra dimensions for any adequate theory of everything, any multiplication of helices could be explored in terms of intuitive recognition of the compactification of dimensions -- understood by physics to be "curled up" in some manner, as argued separately (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity, 2017). With serpents indicative of distinctive knowledge dynamics, the compactification of multiple modes of knowing beomes more comprehensible.
For cosmology, it is then understandable that a theory of everything would be associated with compactification into a singular serpent -- hence the ouoboros. However, should a triple helix model be understood as a "3-serpent model" -- or a quintuple helix model as a "5-dragon model", as Chinese culture might well find appropriate in the light of Wu Xing dynamics?
Given the insights from physics, the serpents and dragons might be better understood as features of visual renderings of the Calab-Yau manifold of string theory, as shown below -- or of Hopf fibration, namely a hypersphere in four-dimensional space. In their animated form, these featured as indications of Animations variously suggestive of "being a waveform" in an argument exploring the possibility that people could -- in the light of the understandings of physics -- experience themselves as waveforms (Being a Waveform of Potential as an Experiential Choice: emergent dynamic qualities of identity and integrity, 2013). Both featured in a discussion of Transforming vehicles of identity between global and toroidal forms (2016).
| Animations of visual renderings suggestive of higher-dimensional cognitive osmosis | ||
| Hypersphere (Hopf fibration) | Calabi-Yau manifold | |
 |
The image was previously used in a separate speculative discussion of Global Brane Comprehension Enabling a Higher Dimensional Big Tent? Strategic implication in encompassing nothing and coming to naught (2011). The animation of the original image made use of selected aesthetic possibilities of Photoshop -- of which many others might be employed to improve the suggestive quality of the animation. |  |
Interlocking tori: There is however also the possibility of inviting imaginative reflection on the toroidal ouroboros as a whole rather than solely on the zone of osmosis. The following animation suggests how a single head/mouth/anus might be depicted in a rendering of the more common symbol of a single serpent-dragon biting its tail. Whether the serpent is one torus or the other, the mouth/anus orifice is interlocked with it and of the same dimension -- the interlocked tori rotating with respect to one another. Such an animation offers usefully provocative and controversial connotations.
| Interlocking tori -- modelling a single-serpent ouroboros | ||
 |  | Discussed with respect to the Fearful attraction of a hole (In: Visualization in 3D of Dynamics of Toroidal Helical Coils: in quest of optimum designs for a Concordian Mandala, 2016) Red torus has a vortex (smoke ring) dynamic in the model; Blue torus has a wheel-like dynamic in the model VRML animation produced by Bob Burkhardt. X3D and VRML variants produced by Sergey Bederov of Cortona3D Consideration can be given to using the dynamics of the blue torus as the basis for the head/anus design in the schematic animation above |
| Mandelbrot set | ||
 | Discussed in: | |
| Fibonacci spiral | ||
 | Discussed in:
| |
Especially intriguing is how such imagery enables anyone to identify with the "dragon" -- riding around the torus with a view from the dragon's head, as the "questing beast". How is the consumption and injestion of "otherness" ("outsideness") to be imagined -- as well as its embodiment, following transformation, into "insideness"?
Transformation? Arguments enabled by animation are no guarantee of the integrative transformation purportedly implied by the ouroboros -- Jung's Mysterium Coniunctionis (1970). The distinction may be made in the light of the imagery of the pearl of wisdom pursued in the Chinese dragon dance, assuming the dragons in the ouroboros are engaged in a dance. The pearl is then mysteriously associated with the space they surround -- the hole in the centre.
This hole is not accessible by conventional means, however skillful the animation. Its nature could even be implied by "pointlessness" and "nescience" (¿ Embodying a Way Round Pointlessness ? 2012; Happiness and Unhappiness through Naysign and Nescience: comprehending the essence of sustainability? 2008). Missing is the sense of surprise associated with transformation -- and the cognitive risks associated with morphogenesis. Arguably the dynamics of the ouroboros could be explored as a cognitive black swan -- as with any revelation -- in the light of the arguments of Nassim Nicholas Taleb (The Black Swan: the impact of the highly improbable, 2010). Yet to be clarified is the distinction between such transformative experience and that offered by the psychoactive drugs so important to many, or those of being born again, so important to others (Varieties of Rebirth: distinguishing ways of being "born again", 2004).
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