Experimental animation of the Tao in 3D

Exploring Representation of the Tao in 3D (Part #9)

Prior experiments: As noted above, one insightful approach to such animation is that of Lance Skelly (Sling Yang, 3D CAD Model Library, 4 March 2013), explicitly inspired by that of Dave Goetsch Yin-Yang Animation, 24 January 2013), as indicated below. Rather than referring to the Tao symbol as such, these explore the yin-yang dynamic, also highlighted in a variety of video presentations. The "interpenetration" metaphor is especially intriguing given its cognitive implications.

Screen shots of experimental 3D animations of Tao symbol
Dave Goetsch, Yin-Yang Animation (2013)	Lance Skelly, Sling Yang (2013)

Animated version in 3D CAD Model Library	Animated version in 3D CAD Model Library

Animation possibilities of existing design metaphor: The 3D model which is the theme of this argument employs a particular design metaphor which merits further development and refinement. However the elements by which the model has been constructed also suggest the possibilities for their animation (in addition to simple rotation of the whole, as indicated). Possibilities include:

an animation in which the component elements are separated, variously juggled, and then recombined in order to suggest the nature of the disconnectivity and incomprehension which so obviously prevails -- and the puzzling cognitive challenge of fitting them together (Governance as "juggling" -- Juggling as "governance" Dynamics of braiding incommensurable insights for sustainable governance, 2018).
introduction of dynamic gradients of shading (as indicated above) to suggest how the components could be better understood as standing waves and/or flow patterns in relation to the holes in the symbol
use of methods in which the mesh of the wireframe rendering is treated as flexible rather than rigid -- potentially consistent with the manner in which a "mountainous topography" is built up and progressively eroded (down to the flat 2D representation)
animation of the ("rubberised") flexible mesh of the four half-curved cones in a rhythmic pattern -- potentially reminiscent with the expansion and contraction of the four chambers of the human heart
animation of the colouring of the four curved half-cones -- between 4-coloured distinctiveness to a 2-coloured form (as indicated in separate models above)
an animation in which a 3D model is engendered from the 2D variant by other transformation processes
a more complex animation integrating the 3D elements of the other symbols with which it can be associated (as tentatively indicated above)

Animations of higher dimensionality: Further possibilities to be considered derive from an appropriate assumption that any representation of the concept of the Tao merits recognition in terms of higher dimensionality than 3D or 4D. Such possibilities can usefully be explored in the light of the questionable relationship between use of sphere and torus in constructing the 3D model. The point is usefully emphasized by the following animation (below centre), notably featuring in a previous discussion (Topological Clues to a Memorable 12-fold Systemic Pattern, 2011).

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

The question would then be whether this type of transformation is effectively the characteristic dynamic in use of both sphere and torus in the model. The question applies both to the larger ends of the curved cones and to the encompassing sphere of the model -- then to be considered in terms of a hypersphere -- whether or not the torus takes the form of a horn torus (as mentioned above). Notably missing from models of lower dimensionality is the possible relation between the holes and the insights offered by the paradoxical Klein bottle, which features so extensively in the arguments from a cognitive perspective of Steven Rosen (Topologies of the Flesh, 2006; Dimensions of Apeiron: a topological phenomenology of space, time and individuation, 2004; Quantum Gravity and Taoist Cosmology: exploring the ancient origins of phenomenological string theory, 2017).

Of related interest is whether a reconciliation of use of sphere and torus (given their contrasting dimensions) could be explored by representing and positioning the smaller tori otherwise:

at the larger end of each cone, aligned with the spine of the cone (rather than at right angles to it) -- suggesting a "mouth-like" function through which information is "digested down the spine", or "excreted" from it
combining the conventional orientation of the torus with a second torus at the larger end of the cone (at right angles to it) -- thus achieving dynamically the spherical form of the end of each cone

The right-hand image above is included to indicate the potential relevance of the current design preoccupations of the ITER nuclear fusion project, as discussed seperately (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). In that spirit the relevance of higher dimensionality to addressing psychosocial divisiveness merits consideration in the light of the "big tent" metaphor, as argued separately (Global Brane Comprehension Enabling a Higher Dimensional Big Tent? 2011).

"Courtship" dynamics? The assumption can be explored that features signifying the Tao can only be comprehended as separated in some way, rather than than through the subtlety of their integration (Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018). The curved-cones of the 3D models above can then be animated in relation to one another -- as with couples in a dance, or in the dynamics of courtship, even that of birds.

Some examples are given below -- characterized by distinctive patterns of separation, rotation and cyclic rate. The asymmetric variant on the extreme right could be framed as more "problematic" -- especially when the dance is simplistically framed as between "good" and "evil".

Experimental animations of paired elements of 3D Tao symbol (solid and wireframe renderings)


Using "droplets" extruded according to the model of Sergey Bederov (above)

Given the emphasis above on the "valley spirit" by which opposites are separated, such animations are indicative of means of distinguishing patterns of connectivity and disconnectivity -- prior to the "consummation" of which the Tao is then necessarily the epitome. The horn-like phases in some of the animations are consistent with bull mythology, sacred cows (protected by the constitution of India today), and the role of cow goddesses (most notably Hathor in ancient Egypt). Others recall the continuing fascination with breasts, noted above with respect to the "valley spirit". Arguably it is the manner in which these forms intimate the subtlety of the Tao which is the primary factor in their attraction.

Dancing the Tao? The variety of patterns in animations such as those above might readily follow from the possible axes of rotation in the geometry of the construction of the Tao symbol in 2D. One approach to this understanding is illustrated in the schematic animation (below centre) -- in 2D and without use of any black/white distinction. Further insight may be obtained from rotation of each pattern, as in the corresponding images in the animation (left and right below). These recall interest in the so-called flower of life and the study of flowers by Keith Critchlow (The Hidden Geometry of Flowers: living rhythms, form and number, 2011) following his various studies of patterms..

"Dancing of the Tao"?
4-fold Rotation of pattern on right	Animation of steps on a square	3-fold Rotation of pattern on left

Widely employed, the dance metaphor is especially appropriate in implying and embodying an elusive synthesis dynamically, whether as understood in terms of a "Yin-Yang dance" or as "Dancing the Tao". One such s understanding has been explored in the light of the work of Ursula Le Guin (Sandra J. Lindow, Dancing the Tao: Le Guin and Moral Development, Cambridge Scholars Publishing, 2012). The metaphor is employed in theatre and actual dance (Dancing Tao). The process of dance notation merits reflection from a "Yin-Yang" perspective -- even as a square dance. A related understanding is evident in the explanation of modern physics and quantum phenomena by Gary Zukav (The Dancing Wu Li Masters, 1979).

In the case of the animation in which black and white are distinguished, this recalls the remarkable insights of Nikola Tesla into the role of the rotation of a magnetic field of opposite charges in dynamos and motors (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). Rather than the current preoccupation with "positive", through the deprecation of the "negative", this suggests a fruitful transcendent relationship between them through cyclic dynamics -- as with electrical processes dependent on both.

The current cultivation of the "positive" in governance of any kind could then be seen as a desperate effort to walk on one foot -- assumed to be the "right" one -- without recognizing that sustainability is achieved by walking on two feet (at least). As is only too evident in modern democracies, the capacity for the necessary alternation could be unfortunately compared with hopping, limping or various handicaps (Policy Alternation for Development, 1984). History is likely to see the desperate effort to ignore or deprecate the "other foot" as laughable or tragic (Framing the Global Future by Ignoring Alternatives, 2009; Considering All the Strategic Options -- whilst ignoring alternatives and disclaiming cognitive protectionism, 2009).

Tracing the Tao symbol dynamically? Of some interest to any animation of the encompassing horn torus (rendered transparent in the 3D models presented) is the dynamics of Lissajous curves, as indicated below from the interactive animation by Wolfgang W. Daeumler. This is framed as an "intellectual game to reveal engrams of dimensional thinking and a proposal for a different approach to physical questions". The classic 2D Tao symbol could be understood as bearing a valuable resemblance to the forms traced dynamically in this way -- with that symbol then to be understood as a 2D static projection of those dynamics.

Lissajous curve on horn torus
Clockwise rotation	Anti-clockwise rotation

Derived from the interactive animation of Wolfgang Daeumler (Horn Torus and Physics: 'Geometry of Everything').

Given the relevance of the Möbius strip and Klein bottle to complex comprehension, as argued by Steven Rosen, it is noteworthy that these forms are themselves intimately related to the Lissajous curve. (cf. Elsa Abbena, et al, Modern Differential Geometry of Curves and Surfaces with Mathematica, 2017).

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Experimental animation of the Tao in 3D