Eliciting significance from symbol dynamics in 2D and 3D

Cognitive Implications in 3D of Triadic Symbols Valued in 2D (Part #2)

The point of departure for this exploration has been consideration of rotational dynamics of the triskelion, illustrated below, as previously presented with respect to reframing "wheels of governance" (Central pattern generators and higher order values? 2017).

Rotational wheel-like animations of the triskelion

Rotations generated from images in Wikipedia

The argument has been variously developed with respect to other symbols considered to be of fundamental significance in some way:

enneagram: This was explored in terms of the recognition by Stafford Beer, with respect to management cybernetics, of the embedding of the (seemingly 2D) enneagram within the 3D icosahedron, which he describes as emerging from collaboration with Joseph Truss -- in a chapter on The Dynamics of Icosahedral Space (Beyond Dispute, 1994, pp. 196-209), as discussed separately (Imagining the nature of cognitive "flight" in terms of the enneagram, 2014)
lauburu: Various animations have been produced as separately indicated (24-fold Pattern Implied by Dynamics of the Lauburu in 3D, 2016). The relevance of the lauburu was noted with respect to experimental animation of the Smith Chart in Modulating cognitive transformations: electrical metaphors and semiconduction (2012) and Wave-language potentially implied in encodings elaborated by cultures (2013). These animations related to further commentary (Improvisation in Multivocal Poetic Discourse: Basque lauburu and bertsolaritza as catalysts of global significance, 2016)
swastika: Animations of the counter-rotation of the two forms of the swastika were presented with that of the triskelion (Central pattern generators and higher order values? 2017), noting the cognitive significance of the implied dynamic (Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012). The dynamics can be discussed in relation to that of other patterns (Cross, swastika variants and lauburu, 2008) as a feature of the Sustainability through Magically Dancing Patterns (2008)
Star of David: The relation of this symbol to the 3D form of the Merkabah is separately described (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017). This notably explored the 2D Star of David as reinforcing dangerous cognitive reductionism and the Richer pattern of significance through complexification of the Star of David. The animations of mappings onto the Star of David was also presented. Of particular interest at this time is the symbolic reconciliation with the 5-fold Islamic Star (Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks, 2012).
pentagram: A key contribution to understanding of navigation around the globe -- between 2D and 3D perspectives -- has been the mathematical formulation Napier's rules for right spherical triangles. These were associated with a simple 5-fold structure later termed the Pentagramma Mirificum. Arguably such thinking has implications for psycho-social understandings of globality, as previously argued (Global Psychosocial Implication in the Pentagramma Mirificum: clues from spherical geometry to "getting around" and circumnavigating imaginatively, 2015). There is then a strong case for exploring how the geometry of "stars" may frame thinking in some poorly recognized way -- potentially to be informed by neglected insights concerning the mathematics of globality. There is a curious parallel with respect to health and healing between the pentagonal Wu Xing pattern, as a fundamental Chinese concept, and the Pythagorean symbol of the Hygiea (Beyond dispute in 5-dimensional space: Pentagramma Mirificum? 2015). That there is a degree of sensitivity to such pentagonal symbols is evident from the concern which can be aroused in the media by their inversion and association with questionable rituals.
torus / helix: Although 3D forms in their own right, whether as individual symbols, or combined in relation to a spiral form, these can be explored as potentially of relevance to the form of a mandala in 3D, given its particular cognitive significance (Visualization in 3D of Dynamics of Toroidal Helical Coils: in quest of optimum designs for a Concordian Mandala, 2016; Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012)
Mandelbrot set as visually rendered: As with the set of Borromean rings, although not widely recognized, 2D representations of the Mandelbrot set are considered by mathematicians as offering especially valuable insight into the fractal organization of complexity. Various renderings in 3D also exist. The possible psycho-social significance can be explored (Psycho-social Significance of the Mandelbrot Set: a sustainable boundary between chaos and order, 2005; Understanding the Monster through the Mandelbrot set -- Moonshine connectivity? 2007).

The possibly of unexplored implications of the use of such symbols at the present time is evident in the case of The Pentagon, or the logo of NATO. These therefore lend themselves to exploration of how they might be understood through forms of higher dimensionality (Envisaging NATO Otherwise -- in 3D and 4D? Potentially hidden faces of global strategy highlighted through polyhedra, 2017). Whereas mapping, most notably of the globe, focuses on projection from 3D to 2D, the latter addresses the seemingly unexplored challenge of inferring a 3D form from one in 2D (Explanation as interplay of projection and "conjection"? and Surrogates of "conjection" as an unrecognized cognitive process?).

There is particular value in exploring triadic symbols such as the triskelion -- beyond that noted above -- namely the manner in which it is implied by the relation between the three primary Abrahamic religions. Necessarily a matter of great controversy, it is their conflictual relations which are so characteristic of current global dynamics, as may be variously discussed (Root Irresponsibility for Major World Problems: the unexamined role of Abrahamic faiths in sustaining unrestrained population growth, 2007; Systemic Reliance of World Religions on Human Sacrifice: covert use of fatal conflict to ensure vital resource management, 2014).

Curiously, beyond the motivation of any of the Abrahamic religions (despite efforts at interfaith dialogue), the triadic nature of their relationship goes systematically unexplored, as can be otherwise reframed (Triangulation of Incommensurable Concepts for Global Configuration, 2011). There is seemingly no symbol of that relationship as a whole, irrespective of the existence of distinctive geometric symbols for each of them.

Another approach to the challenge of these divisive times is through identifying a pattern through which a variety of such conventional symbols might be interrelated (Dynamic Exploration of Value Configurations: interrelating traditional cultural symbols through animation, 2008; video).