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Reframing nothing as a vital generative focus for sustainability
Now as the Ultimate Cognitive Strange Attractor (Part #14)
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Nothing: The argument has highlighted the association between the sense of "now" and the nature of "nothing" through suggesting that there is particular value in understanding any experiential focus in terms of a central "hole" -- implying a virtual centre rather than a central "point". The topological form most appropriate to this understanding is the torus -- in its most general terms. The toroidal Szilassi polyhedron is an exceptional form for the exploration of this possibility.
Mapping questions and question-pairs onto a toroidal form then "reframes nothing" in a way which is potentially more meaningful experientially -- especially in the light of the attention activated by a dynamic complex of questions. The potential significance of a hole has been succinctly highlighted in a classic Chinese quotation -- with which Stafford Beer's 30-fold icosahedral focus is consistent.
| Value of nothing |
| Thirty spokes share the wheel's hub; It is the centre hole that makes it useful. Shape clay into a vessel; It is the space within that makes it useful. Cut doors and windows for a room; It is the holes which make it useful. Therefore profit comes from what is there; Usefulness from what is not there. (Lao Tzu, Tao Te Ching). |
Framing nothing using more complex topological forms, by which experiential significance can be articulated, offers further possibilities -- of which the above quotation is indicative. The approach contrasts with the focus on changing from "something" to another "thing" without exploring the possibility that the role of "nothing" may offer richer possibilities. This applies to arguments for a paradigm shift and in the advocacy of alternatives as caricatured separately (Responsibility for Global Governance Who? Where? When? How? Why? Which? What? 2008). Centering on nothing may prove more viable -- and more consistent with a sense of "now" and immediacy, namely with life in the moment.
Of particular relevance is the relatively unexplored nature of holes and the attraction they exert -- hence the reference in the subtitle to going down the "rabbit hole", notably referring to the documentary (What the Bleep! Down the Rabbit Hole). In the latter case, the nature of the associated "nothingness" becomes more mysterious, as remarkably discussed 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 (as they summarize in the entry on holes in the Stanford Encyclopedia of Philosophy).
Expressed otherwise, it is not that global civilization needs a "hole in the head", but rather that a "hole in the mind" may elicit new forms of insight. Hence the case for a "whole in the globe". Humanity may be in a condition characteristic of some animals, namely under pressure to change skin or carapace -- in cognitive terms. Again the football is suggestive in that respect. It "works" because of "what is not there" -- in the terms of the Tao Te Ching. Of related relevance may be the arguments of Terrence W. Deacon (What's Missing from Theories of Information? 2010) and of Abraham Flexner (The Usefulness of Useless Knowledge, Harper's Magazine, 1939).
If the noosphere is to be understood as being encompassed by some analogue to the ionosphere -- so vital to global telecommunication and remote sensing -- it is then curiously appropriate to note that the use of so-called loop antenna for such purposes could be understood to be of toroidal form. Given the role of circlets of beads in many cultures, there is a certain charm to their comparison with the functions of such an antenna (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000). As a mapping of decision processes characteristic of the moment, a set of Szilassi polyhedra could be readily strung together as a memento of any so-called "string of decisions" -- or possibly of the challenge of any "vicious cycle" of decisions.
| Animation of implied "necklace" of Szilassi polyhedra "commemorating" instances of "now" -- past and future? |
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Beyond the simple movement represented above, a fuller animation is reminiscent of a flight of birds. Associating the polyhedra in this way is also reminiscent of Buddhist and Hindu metaphors of Indra's Net (or necklace) and its interest from a mathematical perspective as the continuous limit sets generated when pairs of generating circles touch (David Mumford, et al, Indra's Pearls: The Vision of Felix Klein, 2002).
Toroidal framings: The Szilassi polyhedron is presented above as offering unusual possibilities -- if only in terms of mapping. A previous exercise explored the use of another toroidal polyhedron, namely the drilled truncated cube (another of the Stewart toroids). This is unique in having 64 edges, suggesting the possibility of mapping the much-studied 64 conditions of change encoded by the system of I Ching hexagrams (Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012). Of interest in that respect is whether these constitute challenges to decision-making -- typically of "which" -- and how these relate to both questions and answers. The sections in that exploration are:
It is intriguing that engagement with "wisdom" can be explored through the questions which are the primary characteristic of each of the 48 koans of The Gateless Gate. In that culture they can, alternatively, be explored through the nature of the answers which are a primary characteristic of decision-making in relation to the conditions indicated by the 64 hexagrams of the I Ching (Transformation Metaphors -- derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997).
There is of course a degree of debatable ambiguity in this distinction raising the issue of the nature of question and answer in relation to wisdom. Potentially interesting is then the possibility of relating the mapping of 48 koans to a mapping of the 64 hexagrams of the I Ching (Relating configurative mappings of 64 I Ching conditions and 48 koans, 2012). This possibility suggests an extension of use of geometrical metaphors to integrate any polyhedral representation of questions (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009).
The names mapped into the image below derive from an extensive adaptation identifying the "causal loops" by which the conditions indicated by the hexagrams are traditionally related (as noted above).
| Drilled truncated cube with I Ching hexagram names associated with its 64 edges (reproduced from Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012, discussing mapping onto that form) | |
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Paradoxical focus of now: As with the attribution of questions and question-pairs to the Szilassi polyhedron, the attributions to the polyhedral form are necessarily tentative. Of particular interest in the Szilassi case is any choice made for the unpaired question of the seven -- the only one of the seven with a degtree of symmetry in its own right. It should of course be stressed that "now" is understood in relation to the toroidal hole that the polyhedron frames. This suggests that the choice of any unbalanced question is part of the experiential dynamic. It may emerge as unique in the moment.
Whilst a sense of "now" is framed by the configuration of questions, continuing consideration is required regarding the dynamic implied by that configuration -- as suggested above with respect to mapping onto the football pattern. One possible clue is offered by a degree of correspondence with the six-fold circular structure of the benzene molecule so fundamental to organic life. This is renowned for being dependent for its integrity on resonance -- leading to its recognition as a so-called resonance hybrid, as discussed separately (Patterns of Alternation: cycles of dissonance and resonance).
This is suggestive of the possibility that, from a cognitive perspective, the Szilassi configuration of questions might well be best understood as a resonance hybrd. This could be especially appropriate to the dynamic quality of the sense of "
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