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Cognitive Implications in 3D of Triadic Symbols Valued in 2D

Representations of the triskelion in virtual reality and implications for quantum consciousness

Cognitive Implications in 3D of Triadic Symbols Valued in 2D
Eliciting significance from symbol dynamics in 2D and 3D
Adapting 2D images to 3D: transformations of cognitive significance
Forms of the triskelion in 3D of potential significance
Quantum consciousness implications of fundamental symbol patterns
On being "walking wave functions" in terms of quantum consciousness?
Paradoxes of communicating fundamental insight through metaphor

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The argument here has been further developed separately (Psychosocial Learnings from the Spiral Form of Hurricanes: implications of the triple helix and the 3-fold triskelion as "cognitive cyclones"? 2017), to which the following is therefore an introduction.


A number of traditional symbols considered fundamental in various cultures have typically been rendered in two dimensions. They are to be found in architecture, flags, and a variety of insignia, and are much valued in terms of their significance. They can be understood as providing a collective cognitive focus, a source of inspiration, and may well be a catalyst for meditation. The question here is the further signifiance to which they may give rise when rendered in three dimensions rather than two. Exploration of the possibility is enabled by development in computer software, especially in anticipation of the widespread deployment of virtual reality devices.

The example explored here is the triskelion (triskele) or triple spiral, notably when based on interlocking Archimedean spirals. The symbol, also known as the "spiral of life", appears in many early cultures dating back to the Neolithic period, most notably that of the famed megalithic tomb of Newgrange in Ireland, built around 3200 BC. It has been the focus of many interpretations, perhaps most usefully that of Glenys Livingstone (Celebrating the Triple Spiral: a PaGaian Cosmology, PaGaian Cosmology, 2007). Traditional Asian versions of the triskelion include the Japanese Mitsudomoe, the Tibetan Buddhist Gankyil, and the Korean Sam Taegeuk (Triple Tomoe and Related Threefold Symbols, Pennine Tai Chi). Variants appear in church architecture and jewelry.

As a logo, modern usage includes that of Trisquel (officially Trisquel GNU/Linux), a Linux distribution, derived from another computer operating system, Ubuntu. It is the logo of Mankind 2000. As with the swastika, the triskelion may well be used by white supremacist groups, especially in countries where the swastika is banned. The triskelion form is specifically associated with the protein clathrin which performs critical roles in shaping rounded vesicles in the cytoplasm for intracellular trafficking. As names, both "triskelion" and "triskele" are associatrd with commercial products and services (if not trademarked).

Such a symbol is of particular interest given the cognitive importance attached to a number of triadic patterns. These include the semiotic triangle of meaning of Charles Ogden, the triangulated Oedipus complex of Jacques Lacan, the phenomenological epoché of Francisco Varela, and the Christian Trinity. Of particular interest is the triadic form of the logo of the Roerich Pact, namely the inter-American Treaty on the Protection of Artistic and Scientific Institutions and Historic Monuments (1935). This provides legal recognition that the defense of cultural objects is more important than the use or destruction of that culture for military purposes, and that the protection of culture always has precedence over any military necessity.

Especially appropriate to the argument here is that the 3-fold set of Borromean rings has been rendered in 3D and adopted as the logo of the International Mathematical Union in 2006. The set of rings is a famous topological link of three components. The rings have the surprising property that if any one component is removed, the other two can fall apart (while all three together remain linked). This so-called Brunnian property has led the rings to be used over many centuries in many cultures as a symbol of interconnectedness, or of strength in unity. It has been used in a medieval depiction of the Christian Trinity, for example.

Composed as it is of three interweaving Archimedean spirals, the triskelion could well be described as a triple helix. Although it is not used as the logo of the Triple Helix Association, it is appropriate to note the pattern of international conferences of that body since 1996. These seek to promote all aspects of the interaction between academy-industry-government in fostering research, innovation, economic competitiveness and growth.

The question is whether and how richer insight might be enabled by rendering two-dimensional patterns of significance into 3D, notably through recognition of the dynamics associated with any such topological transformation. To the extent that a two-dimensional pattern may be cognitively embodied in some way as a focus of identity, the "extrusion" of the pattern to engender a form in 3D is particularly intriguing. There is then the implication that the 2D pattern is an especially restricted projection of a richer and deeper sense of identity -- a limitation inappropriate to the times, and perhaps dangerously so.

There is the possibility that forms of connectivity that prove difficult in 2D, if not impossible, may be rendered comprehensible by renderings in 3D. This could be relevant to eliciting imaginative new thinking -- transcending the many binary framings by which intractable conflicts are currently sustained. What subtler insights can such 3D renderings "carry", engender and distinguish -- notably as a means of counteracting tendencies to their dysfunctional conflation in practice?

The transformation of perspective from 2D to 3D can itself help to frame consideration of the individual and collective implications of "quantum reality". Their credibility has been remarkably argued by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015). The possibility is all the more relevant because that argument is made from the perspective of one of the most prominenent scholars of international relations with a special focus on international security. He notably calls into question the conventional understanding of the division of the global system into "states", suggesting the need for a quantum model of human identity

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