Direction of propulsion in a global context -- as enabled by configuration of symbolic stars

Engaging with Elusive Connectivity and Coherence (Part #6)

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Direction, navigation and control: What "direction" of movement does a symbolic star imply in a global context: inward? outward? Where is the psychosocial system to go? Clearly some happily frame the response in terms of travelling "to the stars". For others it is some understanding of delocalization to globalization. There is also a degree of understanding of "inner space". A case can also be made for a degree of mirroring between outer and inner exploration (Global potential for living sustainably "outside-inside", 2013). Where indeed are we aspiring to go? Per ardua ad astra?

Greater clarification can be given to the response in terms of the requirement for navigation in 3D, as exemplified by control of spacecraft in orbit or control of vessels underwater. These clarify the need for propulsion in three mutually orthogonal directions. This is achieved by jets in space although use tends to be made of propellers underwater -- either set at right angles to each other, or capable of being oriented. Related solutions are evident with helicopters and drones.

Orthogonal dimensions: The argument here assumes that the three rings discussed in relation to the Borromean condition, so elegantly analyzed in relation to the three rings of the Divine Comedy (Saiber, 2013), bear some relation to any understanding of mutually orthogonal directions -- whatever their cognitive implications.

Given the constraint on the non-planar nature of a 3-ring Borromean condition, the question is then how three helices (as the alternative) might best be presented in a mutually orthogonal configuration. This is a challenge to representation in this web format, to topology (given issues of design optimization), to aesthetics, and to comprehension. Additionally, how might any such configuration be comprehended?

Multiple loops: As one approach to this possibility, the 3-looped helical representation above can be tentatively complemented by two other helical loops -- all in mutually orthogonal configuration. By allowing each helix to rotate, arguably they may move into or out of a Borromean condition -- or that specifically distinguished above as a (3,3)-torus link. This could then suggest that the Borromean condition is only met transiently -- an appropriate possibility in its own right. In this 3D virtual reality animation, the movement is not constrained -- loops can move through each other.

Rotation of 3-looped helices around mutually orthogonal Cartesian axes (animations)
Single loop (z-axis)	Two loops (x and z axes)	Three loops (x,y and z axes)

Technomimicry? Beyond the wheel and the propeller, rotation of a single axis has been fundamental over the past century to the generation of electricity through dynamos and its use in electric motors. It is appropriate to ask whether the thinking of Nikola Tesla, as the key figure in that development, has implications for rotation around mutually orthogonal axes -- beyond that of operation of the gimbal, as illustrated in the previous discussion (Potential implications of alternation and rotation in psychosocial fields, 2014; Insight into global dynamics through Tesla's focus on the sphere, 2014).

Of particular interest are the potential consequences of rotation of such a psychososocial "magnetic field" on three axes rather than one. The possibilities are evident in the light of the heavy investment in toroidal reactors for nuclear fusion (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006).

Toroidal possibility: The following animation is suggestive in that respect. Of interest is the possible modification to parameters, notably the dimensions of the tori in relation to each other, and the rate of rotation of ech helix, especially at higher speed.

Three mutually orothogonal tori with a 3-loop helix moving over each of them (animation on right)
Video (mp4). Interactive virtual reality (x3d, wrl)

The configuration and dynamics recall those of the connections made and broken in a commutator and in the design of 3-phase electric motors.

Interlocking tori: Consideration can also be given to the relative movement of interlocked tori, as reprodiced below from a related discussion (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006).

Screen shots of a dynamic virtual reality model of intertwined tori (click on each variant to access and manipulate in 3D; in the free Cortona VRML viewer, right click for preferences to switch from/to the "wireframe" presentation)
	Red torus has a vortex (smoke ring) dynamic in the model
	Blue torus has a wheel-like dynamic in the model
VRML animation by Bob Burkhardt		X3D and VRML models (kindly developed by Sergey Bederov of Cortona3D).

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