Toroidal configurations as fruitful loopery

Changing Patterns using Transformation Pathways (Part #10)

Paradoxical cognitive twist: The nature of such a "twist" in reconciling "camp-us" and "alien" perspectives -- namely the transformation associated with "rabbit hole" and "looking glass" are the surfaces of the Möbius strip and of the Klein bottle, as shown below. Especially noteworthy is the manner in which both are associated with a curious form of "hole". Each frames that hole in ways which raise the question as to the meaning which might be associated with such nothingness.

Suggestive paradoxical cognitive relationship between "Us" and "Them" (images adapted from Wikipedia)
Möbius strip	2D representation of the 4D Klein bottle immersed in 3D space

These paradoxical forms suggest a means of representing the relationship (or transition) between the objectivity of "mechano-linearity" and the subjectivity of "fruitloopery", as separately discussed otherwise (¡¿ Defining the objective ∞ Refining the subjective ?!: Explaining reality ∞ Embodying realization, 2011). Use of these forms is consistent with arguments of Steven M. Rosen (The Moebius Seed: a visionary novel of planetary transformation, 1985; Bridging the "Two Cultures": Merleau-Ponty and the crisis in modern physics, 2009).

The cognitive issue is how to engage with the associated experiences as can be variously discussed (World Introversion through Paracycling: global potential for living sustainably "outside-inside", 2013; Living as an Imaginal Bridge between Worlds: global implications of "betwixt and between" and liminality, 2011). These help to frame the question as to the insight one requires to be able to see the world whole when challenged by the paradox of "us" and "them" -- and potentially to enable that globality (Intercourse with Globality through Enacting a Klein bottle: cognitive implication in a polysensorial "lens", 2009).

Toroidal configuration: In a society whose organization is widely represented as "global", it is remarkable that the intimate relationship of the geometry of that form with the torus is systematically neglected -- despite its consideration by astrophysicists with respect to the shape of the universe (notably the three-torus model of the universe).

Animation of toroidal comprehension of globality
(reproduced from Wikipedia description of torus)

Could the challenge of "global civilization" be more fruitfully explored through a torus, notably as exemplifying various forms of cyclic looping otherwise framed as of cognitive or strategic significance (feedback loops, recycling, business cycles, adaptive cycle, life cycles, and the like)? More intriguing is the possibility that the noosphere, rather than as a "sphere", could be better understood through the form of a Klein bottle -- a topological variant of the torus.

The value of the a torus in the development of this argument has been explored separately:

The proposed relevance of the toroidal drilled truncated cube can be considered in this light.

Aside from its potential value in configuring seemingly disparate elements, of particular interest (as argued above) is the locus it suggests for living awareness -- a focus for the dynamics of life in the moment. This may be variously considered through a set of complementary metaphors, each necessarily with limitations:

a furnace, in the sense of providing a central, dynamically enclosed, container within which unusual processes can occur. This would be consistent with the inspiration of alchemy with respect to an athanor to provide heat for alchemical digestion. This metaphor can be explored through the recent work of Steven Rosen (Dreams, Death, Rebirth: a multimedia topological odyssey into alchemy's hidden dimensions, 2014)
a fusion reactor of toroidal form, as with that under development through ITER (the International Thermonuclear Experimental Reactor), discussed below with respect to "cognitive fusion". Aside from the latter implications, the effort to combine mechano-lateral design principles with the challenges of fruitful loopery is particularly significant. This is especially the case through the recognized need to sustain a fundamentally alien environment of 150-300 million degrees Celsius -- ten times Hotter than the Sun (ITER Mag) -- in order to enable a sustainable source of energy (Bringing the Power of the Sun to Earth, Fusion for Energy). This highlights the manner in which life itself may be sustained by the dynamics of the 64 elements, however they may be imagined to be configured. This reinforces the sense in which, from the perspective of mechano-linearity, life is itself truly alien -- calling for extraordinary conditions analogous to "millions of degrees Celsius". Does the "pot" required for Science 2.0 call for enaction of a toroidal reactor for cognitive fusion?
a digestive tube through which reality is attentively consumed, namely a form of "attention scoop", digesting present experience, engaging with the future, and moving on from the past (Investing Attention Essential to Viable Growth: radical self-reflexive reappropriation of financial skills and insights, 2014).
dynamically intertwined loops, as depicted in the form of intertwined tori -- one with the "digestive function", and a second ensuring its stability (as with the fusion reactor).
wiring diagram, as suggested by the connected edges of the structure, especially when understood as conductors for patterns of control information in a cybernetic sense (feedback loops, etc). This perspective is notably relevant in terms of the control of the system of magnets of a toroidal fusion reactor, with the implications for control of the flow of attention by analogy to plasma. Of related potential interest is some analogue to Feynman diagrams (Potential of Feynman Diagrams for Challenging Psychosocial Relationships? Comprehending the neglect of an unexplored possibility, 2013).
metabolic pathways, as with wiring diagrams, involving psychosocial analogues to the operation of the 20 amino acids -- as a form of "cognitive metabolism". This would constitute a dynamic form of concept map or semantic map
mandala, as constituting a mirror (a "looking glass"), or a means of framing the "rabbit hole", as a focus for attention. This metaphor is suggested by the design symmetry of the drilled truncated cube
Borromean ring configuration in three dimensions (below left). It is set experimentally within the drilled truncated cube (below right) to suggest the existence of processes discussed below.

Borromean rings in 3 dimensions
Borromean rings in 3D as logo of the International Mathematical Union (see Wolfram Mathematica animation)	Animation of rings indicatively positioned within the drilled truncated cube (all faces transparent; lines coloured as above)

The relevance of Borromean ring configuration to various authors is fruitfully discussed by Levi R. Bryant (author of Difference and Givenness: Deleuze's Transcendental Empiricism and the Ontology of Immanence, 2008) in a blog text on Borromean Machine-Oriented Ontology: strange strangers, and alien phenomenology (Larval Subjects, 24 July 2012). In the latter Bryant notes:

What Latour articulates is thus a sort of Borromean knot, organized around the real, power and interest, and the discursive. In Lacan's final teaching everything changes. Where before the symbolic held pride of place, subordinating the real and imaginary to its structurations, now the three orders (real, symbolic, imaginary) are on equal footing without one dominating the others. The key to the borromean knot is that the three rings of string are tied in such a way that no ring is directly tied to the other. If one ring is severed, the other two slip away because they aren't directly attached to one another like a chain. Each order thus has its own autonomy....

The domain of the imaginary is the domain of what Bogost has called "alien phenomenology", what Jakob von Uexkull called "ethology", and what I have called "transcendental empiricism". Alien phenomenology explores the phenomenological worlds of other entities, or what Morton has called "strange strangers". In contrast to traditional phenomenology, it is not a phenomenology of these entities, but a phenomenology of how these entities encounter the world about them. It is not a phenomenology of how things are given to us -- though all of that is retained -- but a phenomenology of how the world is given to these beings. It is what Luhmann, Maturana, and Varela called "second-order observations"; an observation not of a thing, but of how that being observes. Alien phenomenology thus suspends the unquestioned totalizing tendency of the way in which we encounter the world.

Bryant's arguments are placed in a post-phenomenological context by Tom Sparrow (The End of Phenomenology: metaphysics and the new realism, 2014).

Resonance hybrid: It is appropriate to note the recognition of the core structure of bases / codons. Given the recognition of the circular form of the benzene molecule as fundamental to organic compounds and life, the fact that its circulate structure takes the form of a resonance hybrid is especially significant. It could be considered a primary example of fruitful loopery -- especially in the light of its dynamic nature, in contrast with early efforts to describe it in terms of mechano-linearity. Indicative arguments in support of this from a biological perspective are those of Abir Igamberdiev (Dynamics and Mechanisms of Oscillatory Photosynthesis, Biosystems, 2011)

There is a case for exploring the possibility that such a structure -- of more complex form -- could be fundamental to the effective configuration of the 64 elements within the toroidal drilled truncated cube. Being fundamental to life through the pattern of codons, there is a logical elegance to that more complex pattern in three dimensions -- especially as a resonance hybrid.

Drilled truncated cube of 64 edges with opposite features on the structure identically coloured
Animation of 180 degree inversion/rotation	Animation of multiple inversions/rotations

Dynamic mapping implications: As a resonance hybrid this would then suggest that the attribution of codons (or hexagrams) to particular portions of a fixed structure needs to be reframed in dynamic terms. There is then a sense in which oscillation is fundamental to any mapping. With respect to attribution of hexagrams, this would notably follow from the secondary title of the I Ching as the Book of Changes, or Book of Mutations.

Whilst a particular relationship may be appropriate between opposite portions of the structure (as indicated above), oscillation may involve "flipping" or "switching" of attributions between those positions (as recognized in the case of hexagrams). This is best illustrated by animations of systematic inversion..

The variety of possibilities of inversion, especially as suggested by that between hexagrams, points to the possibility of reframing attributions based on the four bigrams or any codon correspondence.

Cognitive fusion: Placing the subjective locus within the "drilled hole" of the structure offers the suggestion that this is the attentive focus for "creative fire" (following Hofstadter and Sander, 2012).

It is in this sense that a form of circulation within (and around) the toroidal tube can be considered as potentially enabling "cognitive fusion", as separately argued in the light of the design constraints for the ITER nuclear fusion reactor (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). The ITER magnet system comprises 18 superconducting toroidal field and 6 poloidal field coils, a central solenoid, and a set of correction coils that magnetically confine, shape and control the plasma inside the vacuum vessel. The question is how some such analogue might apply in the case of the controlled flow and focusing of attention, as might be suggested by the alchemical metaphor of circulation of light, discussed separately (Circulation of the Light: essential metaphor of global sustainability? 2010). It is with the alchemical framing that the traditional Chinese quest for the elixir of immortality was associated.

As discussed separately (Engaging with Globality through Cognitive Circlets, 2009), cognitive fusion is understood within a military context as the integration of two technologies, temporal event correlation and case-based reasoning (G. Jakobson, L. Lewis and J. Buford, An Approach to Integrated Cognitive Fusion, 2004). This forms part of a more general concern with "information fusion" which is the focus of a journal (Information Fusion: an international journal on multi-sensor, multi-source information fusion) and of the International Society of Information Fusion, with its own fusion conference series and its Journal of Advances in Information Fusion. In the spectrum data, information, knowledge, wisdom, this explores considerations that might be considered a precursor to knowledge fusion (cf Richard Scherl, Introduction to Knowledge Fusion and Representation, 2004). This has been defined by Anthony Hunter (Fusion Rule Technology: a knowledge fusion framework for structured reports, 2006) as:

the process by which heterogeneous information from multiple sources is merged to create knowledge that is more complete, less uncertain, and less conflicting than the input. We can view knowledge fusion as a process that creates knowledge. Knowledge fusion can also involve annotating the output information with meta-level information about the provenance of the information used and the mode of aggregation.

The question is the extent to which the "information" or "knowledge" focus bridges the gap to psychoactive engagement with that knowledge, even to its embodiment following the arguments of such as George Lakoff and Mark Johnson (Philosophy In The Flesh: the embodied mind and its challenge to western thought, 1999). For such cognitive fusion, the unusual questions of complementarity and self-reflexivity, dematerialization and virtualization, coactive contextual relations, and the role of myth and symbol making can be specifically addressed through the analogy to nuclear fusion.

Animation indicative of the locus/focus of awareness within the drilled truncated cube (as engendered in terms of the 6 octagonal faces)	Animation suggestive of the dynamics of expansion/contraction of awareness in relation to a point of focus (as contained within the toroidal configuration)

Magnetic field rotation? Display of various circles, associated with the geometry of the drilled truncated cube (above right), also suggests further reflection in terms of their possible rotation, as explored with respect to Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). The suggestion there was reinforced by the following animation of the Sri Yantra of the Shri Vidya school of Hindu tantra --, consistent with reference to the mandala metaphor above.