Cognitive implication of toroidal forms and dynamics

Topological Clues to a Memorable 12-fold Systemic Pattern (Part #3)

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[1a] Enabling structure: Toroidal forms, as derived from the circle and intimately related to the sphere, are used here as a surface with which cognitive content can be associated -- onto which it can be variously mapped. Examples, as partially illustrated below, include:

• rose windows, mandalas and yantras -- in which cognitive three dimensionality and an empty centre are implied
• circlets of prayer beads (rosaries, Hindu prayer beads, Buddhist prayer beads, Islamic Misbaha) with whose individual beads cognitive significance is associated, as separately discussed (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000)
• new understanding of communication form and medium through mapping onto a torus (Michael Schiltz, Form and Medium: a mathematical reconstruction, Image [&] Narrative, 6, 2003), as discussed separately (Beyond the plane of Möbius: form and medium in terms of the calculus of indications, 2007; Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011)
• *** DNA stairway
• *** music, tonnetze
• (Spherical configuration of interlocking roundtables: Internet enhancement of global self-organization through patterns of dialogue, 1998)
• (Spherical Configuration of Categories to Reflect Systemic Patterns of Environmental Checks and Balances, 1994)
• Harald Jockusch and Andreas Dress. From Sphere to Torus: a topological view of the metazoan body plan, Bulletin of Mathematical Biology, 2003, 65, 1,pp.57-65[text]

Varieties of toroidal representation
Kalachakra Mandala (from Wikipedia, enlargement)	Torus (from Wikipedia)	Global Underground Map (see enlargement)

[1b] Transformative dynamic: Complementing its role as a mappable "surface", a toroidal form is significant both as a "container" for processes involving flow, and for the vortexes associated with certain flow patterns, as for example:

• vortexes and toroidal patterns of fluid flow and associated flow-based technologies (Enabling Governance through the Dynamics of Nature: exemplified by cognitive implication of vortices and helicoidal flow, 2010), most notably in the light of the work of Viktor Schauberger (Nature As Teacher: how I discovered new principles in the working of nature, 1998; Energy Evolution: harnessing free energy from nature, 2000). Also (Lars Johansson, Curt Hallberg and Morten Ovesen, Self Organizing Fluid Technique in the Footsteps of Viktor Shauberger. Vortex World, 1997; Alick Bartholomew, Hidden Nature: the startling insights of Viktor Schauberger, 2005; Jane Cobbald, Viktor Schauberger: a life of learning from nature, 2009). The cognitive implications have been notably explored by Mihaly Csikszentmihalyi (Finding Flow: the psychology of engagement with everyday life, 1998; Flow: the psychology of optimal experience, 1990)
• toroidal flow as the basis for "implosion technology", as summarized by Josef Hasslberger (Dynamic Hydropower: the "suction turbine" or "jet turbine" of Viktor Schauberger, 1993). This implosion technology is variously reported to have been the basis for the development of a flying disk (known as a Repulsine), now the focus of efforts to reconstitute it (Alfred Evert, Schauberger - Repulsine - Redesign, 2008).
• (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011)
• necessary toroidal design of nuclear fusion reactors and, through technomimicry, the possibilty of "cognitive fusion" in analogous "containers" (Complementarity and Self-Reflexivity: between nuclear fusion and cognitive fusion, 2006; Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006)

• rotation:
• cycling
• rotating

Varieties of toroidal representation
Animation of blame game of Knight's moves on torus	Sphere / Torus transformation	Toroidal design of fusion reactor (from Wikipedia)

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