Visual representations of globality of requisite variety for global governance

Enhancing Strategic Discourse Systematically using Climate Metaphors (Part #4)

The illustrations below are intended to elicit reflection on mapping surfaces of requisite complexity to encompass climate conditions. This follows the suggestion above that these might usefully correspond in terms of weather metaphors to the pattern of conditions in the Book of Changes, especially with respect to comprehension of the dynamics of changes from one condition to another -- which are the essential challenge of governance. The images give focus to the question as to what new form might a pattern of global coherence need to take in order to hold strategic developments of a similar complexity to the changes in weather and climate.

Beyond trends in opinion polls and ratings: What might correspond to the daily representation by meteorologists of air currents and temperature changes? Is there a need to comprehend patterns of complexity of a higher order? Should the imagination be challenged with regard to the adequacy of the conventional focus on globality understood as a sphere?

*Selected images of the Yi-globe* of József Drasny** reproduced with permission from The Image of the Cosmos in the I Ching: the Yi-globe (2007)

These images point to the possibility of a correspondence between the spherical organization of conditions of change and the more familiar understanding of how the Earth, as a globe, is exposed to light and darkness

Following numbers as a key to comprehensible patterns: In the visualizations which follow -- of forms with a symmetry which renders them memorable to some degree -- the quest for patterns of interest in this respect is guided by the principle of "follow the numbers". This is usefully to be compared with the widespread analytical approach framed by the catchphrase "follow the money".

The challenge would appear to be to frame binary preoccupations by subtleties of different order, as may be variously recognized. Thus 2 can be placed in a context of 4, of 8, of 16, or of 64. The pattern may be enriched through 3, giving 12, 96, 192, or 384, for example. Similarly these can be enriched by 5, giving 20, 30, 60, and the like. Polyhedra offer a means for giving memorable form to such patterns and the distinctions and relations between them, as separately argued (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009) in the light of the magnum opus of Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975-1979)..

It is on this basis that the following images and animations were prepared using Stella Polyhedron Navigator. The first is a toroidal polyhedron, one of the Stewart toroids. It is one of the few 3D polyhedra which has only 64 edges, if these are indeed to be considered of value to representation of the 64 conditions of the Book of Changes. Of some relevance is the implication that each of the following images can be readily inscribed within a sphere -- a circumsphere.

Drilled truncated cube of 32 faces (5 types), 64 edges (9 types), 32 vertices (4 types) [totalling 128=2⁷]
Animation with faces non-transparent	Screen shot of interactive force-directed version (with node labelling)

The variant on the right above resulted from exporting that on the left via a .OFF format, as described previously (Use of force-directed layout to elicit memorable polyhedra, 2015). The following images are those of several of the relatively few forms which have 64 vertices, if the conditions of change could best be associated with them. Together with that above, there are striking commonalities. The fact that it is of toroidal form suggests that the more fundamental understanding of "holes" might merit careful consideration, 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).

Selected polyhedra with 64 vertices based on a truncated tesseract
3D projection of the 4D polychoron Truncated tesseract ("Tat")	3D projection of the 4D polychoron Rectified tesseract ("Rit")
of 48 faces (7 types), 112 edges (15 types), 64 vertices (8 types)	of 64 faces (4 types), 96 edges (4 types), 64 vertices (4 types)

Cubes 4+3+1 (animation)	Cubes 8 (animation)
of 48 faces (4 types), 96 edges (6 types), 64 vertices (4 types)	of 48 faces (2 types), 96 edges (4 types), 64 vertices (4 types)

Prepared using Stella Polyhedron Navigator