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Reframing a strategic attractor as a vortex involving a cognitive twist

The-O Ring and The Bull Ring as Spectacular Archetypes (Part #5)

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Mysterious nature of "holes": As separately discussed (Towards the Systematic Reframing of Incomprehension through Metaphor, 2012), a hole is the metaphor of choice for teaching the theory of general relativity. As a hypothetical topological feature of spacetime, for which there is no observational evidence, they predict the possibility of a "shortcut" through spacetime (Marcus Chown, Intergalactic subway: all aboard the wormhole express, New Scientist, 12 March 2012). Use of the comprehensible term "hole" inhibits recognition of the cognitive challenge of their multidimensional nature -- essentially unvisualisable and to that extent incomprehensible.

As a challenge in their own right for ontology and epistemology, bounding "nothingness" by "holes", invites richer insight (Roberto Casati and Achille C. Varzi, Holes and Other Superficialities, 1994; M. Bertamini and C. J. Croucher, The Shape of Holes, Cognition, 2003). As a metaphor, what then might a wormhole offer as an incomprehensible "shortcut" through communication space, in the light of the forms of (in)comprehension by which this is characterized -- and the probability that the nature of that shortcut would necessarily be incomprehensible within the framework of conventional experience? Holes are at the borderline of metaphysics, everyday geometry, and the theory of perception (as summarized in the entry on holes in the Stanford Encyclopedia of Philosophy). The confusing associations between hole, whole and holy follow from this -- further confounded by the unfathomable implications of budgetary holes.

How do "holes" function as attractors -- especially with respect to the fascination of sexuality and intercourse? Appropriate to the manner in which the feminine may be "negatively" framed, Casati has elaborated what might be understood as a complementary study (Shadows: Unlocking Their Secrets, from Plato to Our Time, 2004). Such considerations can also be related to the significance of "nothing" at the present time, especially in terms of what people are offered for their future and can hope to anticipate (Emerging Significance of Nothing, 2012).

Integral spiral dynamics: A widely appreciated combination of fourfold integration is that associated with the AQAL 4-quadrant configuration (on the left below) and development through the complementary experiential quadrants by a spiral dynamic (as suggested by the schematic on the right below). AQAL theory is fundamental to the integral movement, as inspired and articulated by Ken Wilber, which constitutes an interface between transpersonal psychology, ontology, epistemology, and methodology. Spiral dynamics is a dynamic model of human development and of meme-carrying systems as introduced Don Beck and Chris Cowan (Spiral Dynamics, 1996). There are numerous complex images of both AQAL and spiral dynamics (accessible on the web) -- alone and in relation to one another -- most seemingly subject to questionable intellectual property restrictions (governing the competitive presentation and promotion of these models). As with any motivation to copyright a religious symbol, such restrictions are an interesting challenge for social change (Future Coping Strategies: beyond the constraints of proprietary metaphors, 1992).

Schematic illustrating the AQAL system Schematic suggestive of the Spiral Dynamics seystem

The images together suggest the developmental convergence on a particular kind of "target" -- but with little indication in the images of what happens when the "target" is achieved as a "goal". There is of course some implication that the target is better understood as a form of portal or doorway -- a "hole", potentially more consistent with the configuration of a torus. The images usefully raise the challenge of how the "theos" might be related to the AQAL quadrants and how "The O-ring" encircling them is recognized, given progressive experiential learning through spiral dynamics.

Toroidal thinking? As an attractor for strategic initiative, there is a sense in which any target functions as a form of vortex -- suggested to some degree by the images above. Any use of "target" then mistakenly renders static what is fundamentally a dynamic -- as implied by any quest for sustainability, namely a sustainable dynamic. Furthermore, if "target" is to be used as a strategic metaphor, it is useful to recognize that whatever is targetted may not be as static as might be preferred, as argued with respect to use of military metaphors (Enhancing Sustainable Development Strategies through Avoidance of Military Metaphors, 1998).

The dynamics may be explored through representations based on a torus. One approach is through the strategic game-playing associated with so-called Knight's move thinking, as partially indicated by the image on the left below (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011; Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012). It is appropriate to note that although "Knight's move thinking" is appreciated in game-playing (as in chess), it is specifically deprecated as a thought disorder -- the move of the knight in chess is then used as a metaphor for the unexpected, and illogical, connections between ideas (irrespective of the success to which these may lead).

Another approach is through recognition that the associated complexity is better understood through the dynamic of two intertwined tori, as indicated by the image on the right below (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: Transforming a matrix classification onto intertwined tori, 2006).

Knight's move thinking mapped onto a torus

Intertwined tori

Requisite "cognitive twist"? As noted earlier with respect to the tabular and cubic arrays, both any O-ring or torus readily imply a comprehensible simplicity -- a dangerously oversimplistic form of closure. They obscure the cognitive challenges implied by the contrasting orientations which engender the tetrahedron. It is in this sense that a more complex mapping surface is more appropriate. This is suggested by the twist in a Möbius strip (on the right below). Mapping the "theos" onto a torus -- emphasizing the mnemonic suffix (discussed in the first part of the paper) -- offers the suggestion that any "portal" through the central hole in the torus (indicative of the O-ring) may be effectively blocked by an "article", usefully to be seen as a cognitive mindset common to the "theo" modalities in their engagement with reality. The definite article -- "the" -- is the most frequent word in English.

Suggestive toroidal configuration of "theos"
sensation, intuition, thinking, feeling

Möbius strip
(image reproduced from Wikipedia)

The twist in the Möbius strip may be used as a means of mapping the relationship between the four "theos", as suggested by the images below. These necessarily imply a form of O-ring.

Möbius strips used to map relationships between two sets of "theos"

Embodying complexity?
This approach map be taken further by combining the two images above, increasing the implied complexity of the implicit O-ring. The image on the right derives from a discussion of the possibility of mapping strategic challenges onto a form of complex plane as suggested by mathematics (Imagining the Real Challenge and Realizing the Imaginal Pathway of Sustainable Transformation, 2007).

Interrelation of 2 Möbius strips as an appropriately
complex configuration of the 4 "theos"
Interrelating problematique, resolutique, "imaginatique" and "irresolutique" in terms of real and imaginary

Dynamics of BaGua and Knight's move: A further possible development (of the image on the left above) is to associate a configuration of 4 Möbius strips (in the image on the left below) to incorporate insights deriving from the BaGua pattern of "theos" (as discussed in the first part of the paper). The challenge cognitive (dis)connectivity of the BaGua pattern could be seen as reflected in the (dis)connectivity of Knight's move thinking, as represented in the animation on the right below, and separately discussed (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2007)

Representation of BaGua
embodied within four interwoven Möbius strips
("Earlier Heaven" arrangement )
Animation of 8 of the Knight's moves in chess
(suggestive of the dynamics of both the blame game
and Knights of the Round Table)

Octopedal insight? Of possible relevance to the challenge implied by the schematic of cognitive functions on the left, is current work in artificial intelligence on how to design an octopod -- notably the issue of how it avoids typing itself in knots (Nir Nesher, et al, Self-Recognition Mechanism between Skin and Suckers Prevents Octopus Arms from Interfering with Each Other, Current Biology, 2014; Katherine Harmon Courage, How to Build a Robot Octopus, Scientific American, October 2013).

From an implicit ring to implicit globality: Further to the point made above, the question is how to enable comprehensibility of ever higher dimensionality -- without reinforcing simplistic comprehension at any stage. The images above use the Möbius strip (singly or in configuration) to imply a subtle form of O-ring. This might be more fruitfully understood as implying a spherical/global form related in complex ways to a toroid. These possibilities can be further suggested by the following animations -- reminiscent to some degree of the dynamics of intercourse, through the "O-ring" in quest of the "egg", thereby engendered -- as discussed separately (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011)

"Degeneration" of a torus into a sphere
(animation reproduced from Wikipedia)
Clifford torus
(animation reproduced from Wikipedia)

The above animations are indicative of the challenge of thinking about the relation between externality/explicate/objectivity and internality/implicate/subjectivity as may be associated with "theo-science" (theory/theorem) and "theo-belief" (theology/theosophy). This relation can be variously discussed (Psychosocial Implication of Without Within, 2013; ¡¡¿ Defining the objective ∞ Refining the subjective ?!: Explaining reality ∞ Embodying realization, 2011).

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