Torus as a mapping surface

Enabling Wisdom Dynamically within Intertwined Tori (Part #3)

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The particular relevance of the torus as a mapping surface has been discussed separately (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011; Complexification of Globalization and Toroidal Transformation, 2010;  Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: Transforming a matrix classification onto intertwined tori, 2006).

Of potential significance in that connection is the assumed association between "thinking globally" and the apparently global form of the planet. The latter can of course be understood as a special kind of space-bound illusion. In orbiting around the sun in space-time it could be more fruitfully understood as a torus. With respect to the organization of cognition, there is now evidence to suggest that music is organized toroidally within the brain (cf Memorability: musical clues to psychosocial system sustainability, 2006). The sense of a mental "hole in the head" recalls advocacy of  self-trepanation (notably by Bart Huges) as a procedure towards some form of "enlightenment" (Charles G. Gross, A Hole in the Head: more tales in the history of neuroscience, 2009). A neat example of misplacecd concreteness?. The toroidal halo in depictions of the"holy" and the "enlightened" offers other associations.

In terms of mappings however, it might be provocatively asked whether the global brain needs a (cognitive) "hole in the head" -- especially given the connectivity constraints on the efficient design of (distributed) computer memory and the comparative advantage of 3D torus interconnectivity. As argued by Giovanbattista Mattiussi, et al. (The 3D Torus architecture and the Eurotech approach):

The ability of supercomputers to progressively run jobs faster meets the computational needs of both scientific research and an increasingly higher number of industry sectors.... Despite being available for quite a while, the torus architecture has now the potential to surge from niche application to mainstream. This is because, like never before, we face nowadays some severe challenges posed by a raising number of nodes. The problem, before being one of performance, is one of topology and scalability. The more a system grows, the more fat tree switched topologies show limits of cost, maintainability, consumption, reliability and, above all, scalability. Connecting nodes using a 3D Torus configuration means than each node in a cluster is connected to the adjacent ones via short cabling. The signal is routed directly from one node to the other with no need of switches. 3D means that the communication takes places in 6 different "directions"... In practical terms, each node can be connected to 6 other nodes: in this way, the graph of the connections resembles a tri-dimensional matrix.

The increasing importance attached to supercomputers, and such configuration. is unfortunately not matched with respect to global governance by the quality of what might be termed "superquestions" which might otherwise have been addressed to them (Superquestions for Supercomputers: avoiding terra flops from misguided dependence on teraflops? 2010).

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