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The curious feature of the above progression of geometrical metaphors, with which identity and intentionality is variously associated, is the manner in which they encompass "nothingness" to an increasing degree. By implication necessarily, they effectively provide a container for "nothing"-- increasingly dissociated from "anything". An emerging sense of "nothing" is therefore implied by use of the metaphors as vehicles for individual or collective identity.
This is not evident in the case of a "point" simply made, with no implied contextual referents -- although "nothing" may indeed be implied as a context, with "nothing" then serving as an unusual container for "something". Nor is it evident in the case of a "line". With a polygon, this effectively surrounds "nothing", at the centre of which a common "point" is now implied -- as in the case of triangle, square, or other symmetrical 2-dimensional forms, however many "sides" they may have. The process effectively offers a first insight into the "nothing" so contained and defined -- culminating in that containment by a circle.
Through the form of a cylinder, the nature of that "nothingness" becomes more mysterious when recognized as a "hole", 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 Philsophy). They seeks to answer two basic questions: Do holes really exist? And if so, what are they? Philsophers would typically like to expel holes from their ontological inventory. Arguing in favour of the "existence" of such absences as full-fledged cognitive entities, the authors examine the ontology of holes, their geometry, their part-whole relations, their identity, their causal role, and the ways they are perceived. In cylindrical form holes are centred on an implied axis, with which a "point" can only be associated dynamically -- or as a succession of "points". In a sense there is no "point", except as possibly implied by that at the circular start of the "hole" and at its projection into the circular end (as a "target", at "the end of the tunnel").
A central "point" is more powerfully implied by a polyhedral configuration offering a 3-dimensional container for "nothing" -- with subsidiary "points" at the centre of each of the interlinked polygons composing that polyhdron, each a container for "nothing". A polyhedron can be explored as a configuration of holes.
Complexification of the polyhedron ensures increasing approximation to a sphere -- effectively a seamless container for "nothing" at which its engendering "point" is centered. Curiously, as a result of this complexification to seamlessness, the superficial "nothings" associated with the polygons at the surface are effectively eliminated. The surface of the sphere is then an englobing seamless "something" -- surrounding "nothing" -- with a seemingly inaccessible "point" at its centre, namely the engendering "point" of the sphere.
The fundamental role played by geometrical metaphors in articulating initiatives and sustaining worldviews is discussed separately (Identity, Possessive World-making and their Transformation Dynamics). Those geometrical metaphors imply an intimate, but unexplored, cognitive relation to "nothing". This is less evident in the widespread use of those metaphors in sustaining individual and collective identity, as well as strategic initiatives. It has however become dramatically "apparent" in the existential consequences of global crises in which people widely recognize that they are left with "nothing" and can hope for "nothing" in their future.
In the midst of the eurozone crisis, a valuable insight into "nothing" is offered by the historian Andrew Roberts (Europe's 'proud empire' is entering a cul de sac of history, Financial Times, 17 February 2012):
Nothing is inevitable. It was the first truth I was taught as a Cambridge undergraduate in the 1980s, and it has been italicised and underlined for me by everything I have learnt since.... The whole of human history is testament to the fact that vast sections of mankind can seem to be progressing towards what looks like an established goal, only to get sidetracked into cul-de-sacs, sometimes for decades, occasionally for centuries. So why do we still assume that an eventual return to any significant economic growth in the European Union is inevitable?
For it was the leading thinkers of the... historical determinist school who infected mankind with the concept that we were "progressing" somewhere, moving towards a fixed, positive future point. In economics, that idea is encapsulated in the assumption of economic growth as a kind of manifest destiny, almost the birthright of the species. All too often we see growth as something to be taken for granted as a natural part of the human condition; the rule rather than the exception. [italics added]
Roberts' introductory sentence (inadvertently) offers an ambiguous interpretation. The promised consequences of growth are indeed not inevitable and other outcomes may well be foreseen. However, interpreted otherwise, it is the inevitability of "nothing" which merits reflection in that this is already evident to many in some measure -- with the possibility of its widespread manifestation as the availability of resources diminishes ever more rapidly. "Nothing" is then unavoidable -- like the "death and taxes" characteristic of current austerity programmes to rectify incompetent governance.
As noted with respect to the explorations of physics (Configuring the Varieties of Experiential Nothingness), the notion of "nothing" (and of how the "universe" is engendered from a "point"), is now a fundamental preoccupation -- however obscure the reasons for which it is discussed. As noted there, at a time when many are faced with the experience of some form of "nothing", physicists are giving increased recognition to the fundamental role of "nothing" in relation to cosmology and the emergence of "everything" (Lawrence Krauss, A Universe from Nothing: why there is something rather than nothing, 2011; John D. Barrow, The Book of Nothing: vacuums, voids, and the latest ideas about the origins of the universe, 2002). The integrative implications are separately discussed (Fundamental integrative role of nothing -- the ultimate remainder?, 2011). For Krauss, space and time come from "nothing", understood as an extremely unstable state from which the production of "something" is virtually inevitable. A major meeting of physicists and cosmologists highlighted unresolved issues in that respect (Lisa Grossman, Death of the Eternal Cosmos, New Scientist, 14 January 2012).
If there is anything to be learned from physics, its more sophisticated insights into the relation between "nothing", a "point", and the emergence of a "universe", are worthy of the most careful consideration in the current context -- as the product of the creativity of those upheld as having the most "brilliant minds". How might such insight "inform" that relating to the strategic preoccupations making such extensive metaphorical use of geometrical forms? How might consideration be given to the neglected attention to the "nothing" implied by strategic use of those forms, as separately discussed (Global Strategic Implications of the Unsaid, 2003; Lipoproblems: developing a strategy omitting a key problem, 2009).
An example is provided by the insight of the premier cosmologist, Stephen Hawking (The Dreams That Stuff Is Made Of: the most astounding papers of quantum physics -- and how they shook the scientific world, 2011). With others he is preoccupied by the first second in the creation of the universe -- from a "point" -- using insights from the general theory of relativity and quantum mechanics towards the elaboration of a Theory of Everything. Of relevance to the above argument, he is widely quoted as saying: I avoid problems with a lot of equations or translate them into problems of geometry... I can then picture them in my mind.
A focus for these preoccupations is both the emergence of the universe from a "point" and the collapse of a universe back into a singularity -- at which "point" the density would be infinite and all the basic laws of physics would have broken down. This framing is suggestive of the conditions of "point making" as well as of the collapse of the emergent "worldview", potentially into some form of "singularity" (Emerging Memetic Singularity in the Global Knowledge Society, 2009). The argument with respect to the "breakdown" of the laws of physics is reminiscent of that with respect to "childlike" cognition in relation to "conventional thinking", as discussed separately (Requisite Childlike Cognition for "Heavenly" Integration? 2012) -- especially ironic in the light of continuing use of the legacy term "celestial mechanics".
Hawking has promoted the geometry of a ''no-boundary universe'', a finite, closed universe in the shape of a sphere -- in four dimensions. Expanding from a Big Bang to a maximum, it then contracts toward an eventual collapse -- the Big Crunch. Lacking a boundary, this would seem to require a "closed" universe. Others have promoted the geometry of an "open" universe -- resembling an open horn. Proposals have been made by physicists to reconcile these two distinct forms, as was done with the alternatives of the wave-particle duality -- by allowing for distinct "points of view".
Hawking has reframed the no-boundary universe with the aid of extra dimensions in space-time -- including an ''imaginary time'' running at right angles to real time. It could be shaped like a cone. Sliced horizontally, it would look like a circle, or a closed universe. Sliced vertically, it would be a parabola, or an open universe. The universe is thus open and closed, depending on how it is "viewed" (although it is unclear from what "points" this may be possible).
Are there insights to be gained by applying the geometry underlying such thinking to the "making of a point" and the emergence and collapse of a "worldview"? Of potential relevance are the insights into the "physics of meaning" of René Thom, as discussed separately (Semiophysics?). Given Hawking's imaginative use of conic sections to describe the universe and its origins -- notably in terms of a parabola -- there is a profound irony to the lack of exploration of Thom's insights into the semantic implications of conic sections, and notably the parabola (Paraboles et catastrophes, 1983).
Might understanding of the creation and form of any universe not be fruitfully "informed" by the catastrophes which were a focus of Thom's work (Structural Stability and Morphogenesis: an outline of a general theory of models, 1972)? Should "point-making" be explored as a catastrophe -- as with "universe-making"?
Further possibilities of sustaining identity, through the progression of geometrical metaphors, are implied by insights into the cognitive implications of paradoxical forms such as the Klein bottle -- and their relevance to the paradoxical challenges of physics, as explored by Steven Rosen (Bridging the "Two Cultures": Merleau-Ponty and the crisis in modern physics, 2009; The Concept of the Infinite and the crisis in modern physics. Speculations in Science and Technology, 1983).
What do such metaphors offer as possibilities for new understandings of the 2-dimensional territoriality of "turf wars" -- notably between the disciplines and in the Middle East? Can the significance of "Jerusalem" -- and the quarrelsome "worldviews" it engenders -- be reframed more fruitfully through such a metaphorical approach, as separately discussed (And When the Bombing Stops? Territorial conflict as a challenge to mathematicians, 2000)?
The geometrical challenge can also related to the legendary quest by alchemists for a container capable of holding the "universal solvent" -- that which can dissolve "everything". Expressed otherwise, this would be the form which could "contain" every kind of "point making" susceptible to dissolve it -- an appropriate framing of the challenge of global governance. The quest is echoed in that for an appropriate design to contain plasma in toroidal nuclear fusion reactors (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing, 2006).
NB: See separate presentation of relevant bibliographical references.
This work is licenced under a creative commons licence.