Enhancing coherence through spherical triangulation

Triangulation of Incommensurable Concepts for Global Configuration (Part #9)

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R. Buckminster Fuller has argued extensively regarding the fundamental importance of triangulation as the basis for the stability of structures, notably with respect to his application of spherical triangulation to geodesic domes (Synergetics: explorations in the geometry of thinking, 1975). He demonstrates the need for omnitriangulation as a fundamental requirement of system integrity:

Not until we have three noncommonly polarized, great-circle bands providing omnitriangulation as in a spherical octahedron, do we have the great circles acting structurally to self-interstabilize their respective spherical positionings

It is possible therefore that the integrity of psychosocial systems, and the connectivity of the "patterns which connect" of Gregory Bateson, involve an "omnitriangulated" emotional engagement. To that extent Bateson's mental focus on Mind and Nature: a necessary unity (1979) may be obscuring the need for an essentially emotional "glue" through which coherence is engendered and experienced -- as tends to be obvious from a depth ecology understanding as articulated by David Abram (Depth Ecology, 2002; The Spell of the Sensuous: perception and language in a more-than-human world, 1996). In discussing depth ecology (from the perspective of Abram and others) and the use of Merleau-Ponty's phenomenology in relation to reflection in a sensuous rationality, Chris Schlottmann (Embodiment and Embeddedness in Philosophies of Ecology: deep ecology, Confucian ecology, and Maurice Merleau-Ponty's phenomenology, 2002) argues:

A significant tension develops from integrating sensuousness with rationality. Sensuousness and emotion do not seem to have the quality of self-reflection, as intellect does. Sensuous rationality is therefore not subject to this corrective mechanism, and seems to be less verifiable.

The case for a metaphorical or cognitive architecture "beyond three" can be variously made (Spherical Configuration of Categories to Reflect Systemic Patterns of Environmental Checks and Balances, 1994). Its feasibility is increasingly evident in a web environment (Spherical Configuration of Interlocking Roundtables: Internet enhancement of global self-organization through patterns of dialogue, 1998). The cognitive "flatness" of a triangle may be provocatively called into question by mathematicians (Dionys Burger, Sphereland: a fantasy about curved spaces and an expanding universe, 1965; Ian Stewart, Flatterland, 2001), with the latter exploring non-Euclidean geometric implications.

The argument here however is that rather than "categories" configured by spherical triangulation, there is merit in considering the integrative implication of metaphorical languages so configured. To the extent that metaphors are traditional vehicles for wisdom, the possibility may be explored in terms of the design and construction of "wizdomes" in a web environment (Transforming Static Websites into Mobile "Wizdomes": enabling change through intertwining dynamic and configurative metaphors, 2007).

As envisaged there, the cognitive process of "wizdome building" is one of configuring knowledge elements such as to provide an integrative sense of perspective (in French une position de recul). This sense of perspective is however associated with a particular form of detachment (perhaps even in the Buddhist meditative sense) from the polarization and dualistic thinking characteristic of many modes of thought. These multiple polarities of the mundane world are then embodied in the structural elements of the wizdome as (overarching) vault "beams" basic to the creation of its central "space". These are fruitfully understood in terms of a spherical metaphor -- and architecturally as a form of dome. This is in effect the cognitive analogue to the geodesic domes of Buckminster Fuller.

The integrative implications of such curvature is what induces the necessary "cognitive fusion" as explored more extensively elsewhere (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006; Strategic Challenge of Polysensorial Knowledge bringing the "elephant" into "focus", 2008). Fuller's insight might be fruitfully developed in relation to the geometry of argumentation and proof, namely how to interrelate "lines" of argument that together make various "points". Of greatest interest is where this process shifts out of the plane (as characterized by "explanation") through the spherical triangulation that requires curvature such as to create the kinds of "volumes" required by the dialogue and discourse of the future (Geometry of Organizations, Policies and Programme, 1992).

Especially intruiging is the possibility that new forms of relationship may be found between complex metaphorical patterns, such as those of the I Ching and the Kama Sutra. The discovery of fullerenes ("bucky balls") as a new form of carbon, based on the spherical configuration of 60 carbon atoms, is indicative of such possibility, as separately discussed (Understanding Sustainable Dialogue: the Secret within Bucky's Ball? 1996). The configuration of I Ching hexagrams by József Drasny in his Yi-globe is suggestive in this respect.

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

As recently noted by Andreas Schöter (Chorand Spheres, Yijing, 2011)

This is, superficially, a completely different structure to that shown previously for the Receptive/Creative sphere. However, topology is concerned with the fundamental spacial properties of a structure, and in that case, the two Boolean structures are equivalent. Relating these structures back to the Boolean lattice: the first Chorand Sphere has 30 facets, so between them, both spheres have 60 facets. There are 240 facets in the complete Boolean lattice. So, 180 facets are hidden. These "missing" facets connect the two spheres together.

• vector equilibrium of metaphors ***
• "ascent" -- orbit -- flying

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