Potential cognitive implications of toroidal helical movement

Visualization in 3D of Dynamics of Toroidal Helical Coils (Part #7)

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As stressed above, one purpose of this exploration is to determine whether the visualized dynamics in 3D are suggestive of fruitful ways of mapping complexity in 3D -- complexity which it is possibly difficult, if not impossible, to visualize in 2D. Some possibilities are discussed separately (Cognitive implication of toroidal forms and dynamics, 2011)

The issue here is whether the visual effects offer integrative insights enabling cognitive content to be associated comprehensibly with features of the configuration. As a "holy grail" for this exercise, the assumption is made that the Borromean condition -- if it can be engendered by a particular set of parameters -- may possibly offer particular insights into viability and sustainability.

Related metaphors: So framed it could then be said (for example) that the configuration is variously illustrative (or reminiscent) of situations in which the "balls" necessarily do not touch and could be understood as engendering a form of "Borromean condition". There is a shift in perspective to pathways defined dynamically -- pathways which are only "occupied" infrequently at any particular location. Examples include:

• a chemical molecule characterized by electron orbitals. This is especially suggestive because of the many possible cognitive implications of the wave-particle duality. Some have been discussed separately (as noted below)
  
  
• juggling a set of balls, as remarkably discussed by Burkard Polster (The Mathematics of Juggling, 2006) which fruitfully integrates perspectives regarding polyhedra (and their great circles), Hamiltonian cycles and distinctive complex juggling patterns (with an annex of stereograms of more complex Hamiltonian cycles). The author extends his argument to include the seemingly disparate domains of bell ringing and knot theory (including braid theory). Understood more generally these all reflect forms of dynamic interweaving -- all of which have long been appreciated as comprehensible in practice, notably through their aesthetics. (Some juggling demonstrations, 1998; Juggling demo, 1998; 46 Juggling animations, Wikimedia; X3D Robotic hand juggling primitives, 2014)
  
  
• any road network, as discussed separately (Being in the Flow on Strategic Highways and Byways: enabling sustainable self-governance through traffic signage, 2011)

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