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.

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?

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)

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 separate\ly (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 "now" and "feeling alive". It could be consistent with transcending the conventional binary modality (Transcending Simplistic Binary Contractual Relationships, 2012). In that sense "now":

• is neither question nor answer, as with any associated sense of identity (Am I Question or Answer? 2006)
• exemplifies neither "feeling alive" nor "feeling dead" (as discussed in the main paper)
• is neither a preoccupation with "knowing" nor with "not-knowing"
• offers neither a sense of "nothingness" nor with "fullness" (plenitude)

Memory aid: Provocatively -- and with the poetic licence appropriate to going down the "rabbit hole", and given the quest for mnemonic catalysts -- it may be appropriate to explore aesthetic twists, transformations and resonances between focal terms of this discussion through imaginative word play, consistent with the riddle by which the sense of "now" may be characterized. This is partially suggested by the essay of William S. Huff (Homonym, Homonym and Homonym, and Other Word Pairs, Symmetry: Culture and Science, 1992). The terms variously related through such devices might then include:

Mnemonic exercise in configuring thematic elements

With respect to memory aids, there is a certain elegant appropriateness to the possibility of using the common football as a mapping surface. This is all the more so in that the game of football, and the attention it attracts worldwide, is especially emblematic of the experiential preoccupations with the feelng of "being alive" in the moment -- with the "now" which is the focus of this exploration. There is of course a degree of irony to its "global" form and the manner in which it is so desperately kicked around -- globally. Conversely, to have "won" in the process significantly enhances the sense of "feeling alive" -- whereas losers are readily framed as "dead".

Experiential sense of "now"? A major limitation in the above argument is the descriptive nature of the articulation of the existential experience of "now". This may be partially remedied through questioning in the moment:

• which "now" characterizes the moment? --- with some sense that a distinction is possible between modalities of "now" that have been previously recognized, and therefore enabling a mode of engagement to be framed
• what "now"? -- with the contrasting sense that an as yet unrecognized modality is emerging (one possibly previously unknown) -- essentially a surprise, with the potentially catastrophic implications as framed by Nassim Nicholas Taleb (The Black Swan, 2007; Antifragile, 2012)
• how "now"? -- namely consideration of how best to reconfigure in the moment to "handle" the situation (without "grasping" it inappropriately) -- well described by the need for strategic nimbleness, so as best to dance with an emerging reality
• when "now"? -- namely a focus on timing enabling appropriate engagement with the emerging moment -- entrainment by it, going with the flow, knowing when "the time is now"
• where "now"? -- namely a recognition of the subtle directionality implied by the moment -- a sense of the "way things are going" and any direction of shift
• why "now"? -- namely a sense of implication within the dynamics of a more encompassing context
• who "now"? -- namely a sense of who one is becoming, or the role one is taking on for the moment

These experiential indicators are rendered even more subtle through the question pairing discussed above -- and the experience of "now" with respect to any continuum, most obviously where-when (with its correspondence to space-time). Various metaphors may be used to frame the moment in which the questioning applies, and the potentially relevant skill sets:

• piloting a helicopter, discussed above as the preferred metaphor of Arthur M. Young (developer of the Bell helicopter), who applied the associated insights to the development of a "psychopter" as the "winged self" requiring an analogue to "seat of the pants" skills in the moment (Geometry of Meaning, 1976). As discussed separately (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011), from a decision-making perspective his approach is potentially of relevance to any discussion of a 12-fold pattern of question-pairs.
• navigating hyperspace, as imagined by writers of science fiction -- the art being to sense, imaginatively, the quality of the complex space in the moment and to reconfigure information inputs so as to be able to "swim", "climb", "tunnel" or "fly" through it, whichever was most metaphorically appropriate (Engaging with the Inexplicable, the Incomprehensible and the Unexpected, 2010)
• martial arts, variously attentive to the practice, the articulation and the philosophy of engagement with an unpredictable, challenging "other" in the moment (Ensuring Strategic Resilience through Haiku Patterns: reframing the scope of the "martial arts" in response to strategic threats, 2006).
• dancing with a pearl of wisdom, as exemplified by elusive dynamics of the dragon dance of Chinese culture. More generally, engagement with the movement of light through precious stones, and especially through the further insight offered by the mythology of the diamond (Patterning Archetypal Templates of Emergent Order: implications of diamond faceting for enlightening dialogue, 2002).
• game-playing, as most notably explored from a cultural perspective by Hermann Hesse (The Glass Bead Game, 1943). As discussed separately, some strategically transformative use of games is now made by communities, somewhat in that spirit (Imaginal Education: game playing, science fiction, language, art and world-making, 2003). Potentially most suggestive, given the paradoxes explored, is the fictional account by M. A. Foster (Gameplayers of Zan, 1977). The experiential potential of game-playing is powerfully argued by James P. Carse (Finite and Infinite Games, 1987).
• humour, as offering a widely recognized existential engagement with the moment, especially since humour may be framed by a leading question. Humour featured as an early theme of artificial intelligence (Marvin Minsky, Jokes and their Relation to the Cognitive Unconscious, 1980). The unusual approach, using it to reverse engineer the mind, could fruitfully explore humour in terms of the dynamic framing offered by questions, given their fundamental role in framing jokes (Matthew M. Hurley, et al., Inside Jokes: using humor to reverse engineer the mind. 2011). Whilst the study raises questions as to "what" humour is, and "why" it is enjoyed -- identifying twenty questions that a humor theory should be able to answer -- it does not address the role of questions in relation to humour. The integrative potential of humour, as a universal human trait, has been discussed separately (Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005).
• cognitive exoskeleton, as offering a cognitive analogue to current development of the powered exoskeleton. This approach to patterns of questions could be understood as implied by that of Edward de Bono with respect to "thinking hats", "action shoes", and more generally (Six Frames For Thinking About Information, 2008).

The above indications can be considered as part of a more general set relating to movement -- potentially "down the rabbit hole" (Clues to Movement and Attitude Control, 2002; Navigating Alternative Conceptual Realities. 2002; Towards an Astrophysics of the Knowledge Universe: from astronautics to noonautics? 2006). With respect to a web-enhanced knowledge environment, further possibilities may be imagined (From Information Highways to Songlines of the Noosphere: global configuration of hypertext pathways as a prerequisite for meaningful collective transformation, 1996; Transforming Static Websites into Mobile "Wizdomes": enabling change through intertwining dynamic and configurative metaphors, 2007).

Is the Szilassi configuration suggestive of the cognitive organization of a "wizdome" as a form of vessel for the navigation of knowledge space -- or perhaps as a "magic carpet" -- as framed by the following animation? The alternative abbreviation -- as "whiz" -- suggests a complex of associations with WH-questions and the sense of "isness" which is a characteristic of "now" (The Isdom of the Wisdom Society: embodying time as the heartland of humanity, 2003).

Animation indicative of the "discovery" of a cognitive "magic carpet" emerging from a "wizdome"?

Relevant to use of the "carpet" metaphor here is the attention given to carpet design by architect Christopher Alexander in the seventh in a series of books on design, order and pattern (Notes on the Synthesis of Form, 1964; A Pattern Language, 1977; A Foreshadowing of 21st Century Art: the color and geometry of very early Turkish carpets, 1993). Surprisingly his work has had considerable influence on computer programming language design -- the essence of system comprehension. As discussed separately (Magic Carpets as Psychoactive System Diagrams, 2010), Alexander explores "carpet geometry" in terms of a set of 15 "transformations" (Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole. International Journal for Unconventional Computing, 5, 2009). He emphasizes the importance of geometric adaptation in order to enable comprehension of a higher order, as discussed separately (Harmony-Comprehension and Wholeness-Engendering: eliciting psychosocial transformational principles from design, 2010) The potential implications can be taken further (In Quest of a Dynamic Pattern of Transformations: sensing the strange attractor of an emerging Rosetta Stone, 2012).

Cyclopean symbolism of "nowing"? The following images offer an interesting contrast in relation to the above argument. For global society, the Eye of Providence (notably figuring on the reverse of the Great Seal of the United States and on the one dollar bill), has implications for the condition of the world at this time. The left-hand image portrays a barren landscape dominated by an unfinished pyramid of 13 steps, topped by the Eye of Providence within a triangle.

That pyramid, with its detachable triangle, is reminiscent of the Pyramid Ship -- a "Cheops class warship" -- of the alien Goa'uld, featuring in the widely disseminated Stargate series. It also recalls the ambitions of dissociated elites to abandon "planet Earth" for gated communities, and for other parts of the galaxy. The visible "gap" is then clearly significant.

The image on the right, however, positions paradoxical cognitive functionality -- in the "now" -- within the eye of the toroidal form of the Szilassi polyhedron. People may themselves have the possibility of functioning as "stargates" (People as Stargates: an alternative perspective on human relationships in space-time, 1996; World Introversion through Paracycling: global potential for living sustainably "outside-inside", 2013)

Symbolic locus of the Eye of Providence?
On the one dollar bill	Within the Szilassi polyhedron

Given the masonic symbolism typically associated with that of the Great Seal (left above), it is surprising to note that one of the easiest ways to remember the complex geometry of the Szilassi polyhedron is as a 3-dimensional version of the square and compasses (otherwise overlayed in 2 dimensions), so widely recognized as the symbol most identifiable with freemasonry. The space they enclose -- to which such significance is attached -- can be associated with the hole in polyhedron, especially since variants of the symbol include a broken circle within it (in the form of the letter G). The square and the compasses can be mapped onto the polyhedron in two ways, as indicated in the animations below. Whilst such projections are an aid to memory, they also encourage reflection -- as so ably demonstrated by the popular appeal of the Dan Brown novels (The Da Vinci Code, 2003; The Lost Symbol, 2009), and the array of questions of which they are a focus, challenging the frameworks of convention regarding the externalities of where-when and which-how..

Projection of the square and compasses of Freemasonry on the Szilassi polyhedron as a mnemonic aid
Variant A (animation around vertical axis)	Variant B (angled animation)

Paradoxical geometry: Of interest in making this contrast is the nature of the "pyramid" as a geometrical form in relation to the Szilassi polyhedron. The pyramid is not the simplest of the polyhedra, a 4-sided tetrahedron, as might be assumed; with the base, it is 5-sided. As noted above, the tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face. This has symbolic implications for the organization of the incommensurable worldviews of global society -- and a justification for its display in Reconciliation Place (Canberra) with the Mobius strip (as noted above). It is recognized that the next more complex polyhedron with equivalent properties has 44 vertices and 66 edges -- but it is not known whether such a polyhedron exists. The drilled truncated cube, featured above, is indicative of related mapping possibilities of cognitive significance (32 vertices, 64 edges, 32 faces).

The core experiential challenge is how cognition and identity are enabled and sustained by such geometry. Of relevance to this are the explorations of Douglas Hofstadter (I Am a Strange Loop, 2007) with respect to the Mobius strip, and also with respect to the Klein bottle by Steven M. Rosen (Topologies of the Flesh, 2006). The potentially paradoxical collective implications have been discussed separately (Sustaining a Community of Strange Loops: comprehension and engagement through aesthetic ring transformation, 2010). On the assumption that insight is not "cyclopean", the eye metaphor may also be represented in the following image of a Mobius strip (as was presented there).

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