Further 3D design possibilities and metaphors

Integrating Ouroboros and Yi Jing as Fundamental Symbols in 3D (Part #9)

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Toroidal embodiment and being a torus? It follows from previous efforts to present symbols of importance with which fundamental values are variously associated (Eliciting Insight from Mandala-style Logos in 3D: interactive engagement with mandalas and yantras in virtual reality, 2020; Cognitive Implications in 3D of Triadic Symbols Valued in 2D, 2017; Reconciling Symbols of Islam, Judaism and Christianity, 2017).

In the light of the challenge of experiencing oneself (or society) as well-rounded, as argued above, is experiencing oneself as a torus just as feasible (if not more so) as experiencing oneself as global or spheroid in some way? The arguments of an earlier section suggest that there is an intuitive appreciation of circlets and ring formation. These could be said to have as much credibility as a global form -- if not more. It could be useful to explore the history of the discovery, appreciation and use of the ball in comparison with the necklace or bracelet -- especially given the importance attached to that of the wheel. (Toroidal embodiment, knottedness and being a torus? 2019)

Association of Ouroboros with 64 interrelated conditions of change encoded by the I Ching	Animation of helical coils embedded within helical coils indicative of an engendered "magnetic field"	Suggestive animation of circulation of relationships based on BaGua trigrams

Toroidal representation Zen ox-herding images: The approach developed here could be further adapted to any set of coherent set of symbols, as illustrated separately in the case of the Zen ox-herding images (Circular configuration of cognitive phases framing toroidal experience? 2017) forming part of a more general discussion (Zen of Facticity: Bull, Ox or Otherwise? Herding facts and their alternatives in a post-truth-era, 2017)

In terms of comprehensibility and memorabilty, of interest is the possibility of presenting the pattern of "bulls" within a torus (as shown below, left). For comparison, and in contrast with those above, te same approach may be used for any potential correspondence with the BaGua trigram pattern (below right). Such a depiction, especially when animated, evokes other ways of thinking about both in dynamic rather than static terms, as phases in a cycle rather than as stages in a linear progression. The representation is also helpful in suggesting the manner in which the phases may coexist, if only potentially, rather than each being superceded by the next. Any assumption of non-reversibility of time may also be called into question.

Variants of the animation may then enhance imaginative consideration of this possibility, as implied by other variants which could be produced (as noted below).

Animation of simplest torus as container for dynamic cognitive relations
10-fold pattern of Zen bulls	8-fold BaGua pattern of trigrams
(also video, wrl and x3d versions)	(also video, wrl and .x3d versions)

Options for disk dynamics within the torus -- with cognitive implications

rotation of torus with disks in fixed position (and reversal of that rotation)

spin disks on their axis in a fixed position within the torus

disks moved independently through the torus whether in a coordinated manner or randomly

move disks such that some are periodically merged/conflated (thereby reducing the number of distinctions made)

rotate disks in a fixed position such as to function as valves (opening and closing) in relation to notional circulation through the torus

increase/decrease diameter of disks

move disks across torus -- inserted into new positions (as with Earlier and Later Heaven arrangements of BaGua)

Use of the torus usefully frames the question as to what might be understood as circulating through the "tunnel", as can be variously discussed (Circulation of the Light: essential metaphor of global sustainability? 2010; Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). The forces channelled through the major axis are well-illustrated metaphorically in the case of electromagnetism with the operation of a solenoid.

Toroidal version of the Zodiac: Use of the symbolic language associated with the Zodiac has long been deprecated by science and religion despite its popular appeal as a meaningful framework. As noted above, of particular interest is the adaptation of that framework as a "Rosetta stone of meaning" to indicate principles of control and navigation of a vehicle from an engineering perspective (Arthur Young, Geometry of Meaning, 1976). This is discussed separately (Criteria for a Rosetta stone as a meta-model?; Geometry of meaning and cognitive embodiment?, 2016).

It is appropriate to note the care with which Young develops his argument from the abstractions of the physics of movement required in the control of a vehicle such as a helicopter. The terms from the zodiacal framework are only then attributed to offer a degree of qualitative comprehensibility to the distinctions he makes for which he repeatedly notes the inadequacy of words -- given the manner in which they can be variously interpreted and understood. Emergence of deeper understanding is of course characteristic of any learning process -- which may last many years.

As a focus of astrology, the Zodiac lends itself to an adaptation similar to that above with Yi Jing hexagrams. As noted earlier, one approach would be to use a Star of David representation of hexagrams as a framework for 12 Zodiac signs positioned around a torus.

The following experimental animation -- in circular form -- integrates points made by Arthur Young, as variously described and discussed separately (Geometry of Meaning: Examples of Integrated, Multi-set Concept Schemes, Annex 1, 1984; Functional Complementarity of Higher Order Questions: psycho-social sustainability modelled by coordinated movement, 2004). Prior to its association with the Zodiac, Young used a simpler circular representation in the light of the physics of controlled navigation from which his insights derived (Configuration of states, acts and relationships). Relating creativity of such as Tesla to widespread understanding of the zodiac is especially valuable as an aid to comprehension and reflection on the navigation of the conceptual universe -- of the noosphere.

The circular presentation of the table by Young in relation to his arguments with respect to the pattern of the Zodiac is presented on the left below -- tentatively augmented with the 15 fundamental concepts of Arnopoulos (2000), as discussed separately (Global insight implied by circular representation, 2014; Correspondences between juggling and governance, 2018).

Note that 3 of Arnopoulos's concepts have been set below, arguably because they do not lend themselves to direct experience in the same manner as the other 12. An animated variant on the right below is an effort to show how these are associated with the creativity held to be engendered by alchemical processes encoded by the forms of Zodiacal signs (adapted from Eliciting a Universe of Meaning: within a global information society of fragmenting knowledge and relationships, 2013).

Interrelationship of Zodiac as a "Rosetta stone of meaning" with sociophysics and alchemical processes (tentative)
"Rosetta stone of meaning" of Arthur Young associated with categories of sociophysics	Experiential system of interwoven creative processes using an alchemical metaphor (animation of the pattern on the left)

Toroidal implication of the enneagram: Clearly the arts associated with the Muses, as valued in the Greek and Roman civilizations, merit consideration as "gatekeepers" of the cognitive mirror. They are the personification of knowledge and the arts and the associated inspiration for literature, and science -- now celebrated in the role of "museums". The role of poetry is clearly recognized by them and related to that of astronomy -- surprisingly. Exploratively ("inploratively"?) they are configured below by attributing them, arbitrarily, to the classic form of the enneagram as discussed separately (Warp and Weft of Future Governance: ninefold interweaving of incommensurable threads of discourse, 2010). The pattern on the left is then superimposed on the Ouroboros in the image on the right

Configuration of the Muses on an enneagram suggestively associated with the Ouroboros

The paradoxical mirroring of a participatory multiverse -- without and within -- is appropriately noted by the title of a work by Joseph Campbell The Inner Reaches of Outer Space: metaphor as myth and as religion, 1986). However it is appropriate to note the pioneering work of Marsilio Ficino of half a millennium ago in writing what amounts to the imaginative reframing of everyday life: De Vita Coelitus Comparanda -- as described by Thomas Moore (The Planets Within: the astrological psychology of Marsilio Ficino, 1990), and separately discussed (Composing the Present Moment: celebrating the insights of Marsilio Ficino interpreted by Thomas Moore, 2001). The above argument follows from an earlier speculation (Being the Universe: a Metaphoric Frontier -- co-existent immanence of evolutionary phases, 1999).

Toroidal twisting and knotting: Consideration could be given to transforming the torus from its simple circular form by variously twisting it as implied by some traditional images of the Ouroboros.

Contrasting depictions of the Ouroboros -- and its associations with the infinity symbol

There are many depictions of more complex forms of the torus, most notably as a torus knot.

Indication of complex toroidal dynamics
Torus knot	Toroidal knot (animation)	Animation of vortex ring	Neo-Riemannian Tonnetz (animation of a toroidal view)
Michiel Sikma, CC BY-SA 2.5, via Wikimedia Commons	Adaptation of a model developed by Adrian Rossiter with Antiprism	By Lucas V. Barbosa - Own work, Public Domain, Link	By Davidwbulger - Own work, Public Domain, Link

torus with holes -- scales ****

Toroidal multiplication and interlocking: Such 3D possibilities can be extended by rotating and interrelating circles of hexagrams, as shown below left (Toroidal constraint -- nuclear fusion as metaphor of cognitive fusion, 2019). This formed part of a discussion of Framing Cognitive Space for Higher Order Coherence (2019). As indicated above, the significance of the crown metaphor is also evident in the cognitive role attributed to the crown chakra (Sahasrara) of Hinduism, discussed separately (Global Insight from Crown Chakra Dynamics in 3D? Strategic viability through interrelating 1,000 perspectives in virtual reality, 2020).

Indication of complex toroidal dynamics
Rotation of mutually orthogonal circles of 64 hexagrams	Crown chakra as a set of 20 moving rings of 50 "petals"	Crown chakra inversion of 20 moving rings of 50 "petals"	Gyroscopic movement of selected chkra rings of 50 "petals"
x3dom;video; x3d	x3dom; video; x3d	x3dom; video; x3d	x3dom; video; x3d

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