Aesthetic reconciliation of contrasting toroidal metaphors?

Imagining Toroidal Life as a Sustainable Alternative (Part #11)

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Missing with respect to both metaphors are the insights offered by the classic study by Gyorgy Doczi (The Power of Limits: proportional harmonies in nature, art, and architecture, Shambhala, 1981). Whether with respect to the preoccupation of the doughnut metaphor or the pizza metaphor, variants are to be recognized in the attraction of restraint in contrast to excess, as variously expressed, most notably in poetry (Richard Hoffpauir, The Art of Restraint: English Poetry from Hardy to Larkin, University of Delaware Press, 1991; Elaine P. Miller, Harnessing Dionysos: Nietzsche on rhythm, time, and restraint, Journal of Nietzsche Studies, 17, 1999, Spring; Arthur J. Clark, Culture and Restraint, Saint George, 13, 1910, 51).

There is a strangely appropriate possibility that the mutual constraint is fundamentally aesthetic, notably in the light of the arguments above regarding the cognitive organization of music -- intuitive, unconscious or not. Curiously it is "pizza consumption" which is far more closely associated with music than the planetary boundaries framing a "safe operating space" according to the doughnut metaphor. In poetic terms, the policy challenge could be framed in terms of "engagement" otherwise understood (Poetry-making and Policy-making: Arranging a Marriage between Beauty and the Beast, 1993; Poetic Engagement with Afghanistan, Caucasus and Iran: an unexplored strategic opportunity? 2009).

It is less than clear how the "planetary boundaries" were determined to be ninefold, but there is a strong case for associating them with mnemonic reminders to render them memorable to the widest audience. Examples might include:

• The extensive significance of nine in Norse mythology, most notably the nine worlds that are supported by Yggdrasil as the "World Tree" (Joshua J. Markby, Nine Realms of Norse Cosmology, Ancient History Encyclopedia, 20 December 2018). Ironically the Stockholm music label Acronym has separate recordings for both "Planetary boundaries" and "Yggdrasil" -- reinforcing any argument that the Stockolm Resilience Centre may have been influenced in some way in originally distinguishing nine such boundaries.
• The Nine Rings in the mythological fantasy of J. R. R. Tolkien (The Lord of the Rings, 1954), namely those of the Rings of Power that Sauron used to corrupt Men to his service; with those taking the Nine Rings becoming the Nazgul -- the "ringwraiths". Otherwise described in a poetic line as: Nine for Mortal Men doomed to die.
• Chinese Nine Linked Rings Puzzle (jiulianhuan), to which reference is made over centuries, with its current form requiring 341 moves (Albrecht Heeffer and Andreas M. Hinz, "A difficult case": Pacioli and Cardano on the Chinese Rings, Recreational Mathematics Magazine; Carolyn Pe Rosiene, et al, The Nine Rings Puzzle, 3 ways: a Rosetta Stone for programming paradigms, Research Gate, January 2012)
• Nonagonal symbol of the penultimate degree of Freemasonry
• Nine-ringed astrolabe (Karoly Simonyi, A Cultural History of Physics, CRC Press, 2012, p. 167)
• The manner in which nine rings are presented as key to deriving power from nuclear fusion (Nine rings to cope with ITER's powerful magnetic fields, Fusion for Energy, 13 November 2017; Magnetic System: nine rings to counter the force, ITER, 20 November 2017)
• Nine celestial spheres of heaven, notably as described in The Divine Comedy by Dante Alighieri, complemented by 9 circles of Inferno, and 9 rings around Mount Purgatory
• In the Samatha practice, common to many Buddhist traditions, there are nine stages of training the mind (nine mental abidings), by which to achieve appropriate concentration. These are understood as corresponding to the Ten Bulls of Zen tradition.

In the light of proposals for a pizza metaphor for intercourse, it is curious to note -- if not simply amusing -- a comparable 9-fold "segmentation", although 10 are listed by Wikipedia (The Nine Jade Dragon Exercises of Taoism; 9 Sex Positions That Will Get You Out Of Your Comfort Zone, Bustle; The 9 Best Sex Positions that Practically Guarantee an Orgasm, Women's Health).

Bluntly stated, the "Nine Rings" popularized worldwide by The Lord of the Rings are far more memorable to many than the "9 Planetary Boundaries". Many colourful depictions (available on the web) have been imaginatively presented regarding the relationship between Yggdrasil and the 9 realms of the gods -- notably in support of online gaming (for which the name Yggdrasil is used). A case could then be made for building the "Planetary Boundaries" into a comprehensive epic to be more widely appreciated -- as with the Kalevala or the Mahabharata. With respect to the argument above, the imagery of the Ten Bulls can be experimentally incorporated into toroidal animations to evoke imaginative reflection, as shown below. In the light of the above, there is some irony to the continuing debate over the classification of life into "kingdoms" or "domains" (Cavalier-Smith, Eukaryote Kingdoms: seven or nine? Biosystems, 14,1981) and to continuing debate over the eight or nine modes of intelligence to be recognized in theories of multiple intelligence.

Animations of Ten Bulls of Zen within a torus wrapped by a helix of 9 windings (9 Bulls moving within the helix; 8th Bull in the centre of the torus)
Vertical flip of bulls	Horizontal flip of bulls	Rotation of bulls
Adapted from Zen of Facticity: Bull, Ox or Otherwise? Herding facts and their alternatives in a post-truth-era (2017)

The animations above are clearly based on a particular design metaphor with regard to colour, rate of movement, nature of movement and directionality, helical windings and dimensions. Of the 10, the 8th Bull ("Both Bull and Self Transcended") has no image and was therefore placed in the centre; it could be removed. The helix of 9 windings is continuous -- but is potentially suggestive of both the distinctiveness of the 9 planetary boundaries and their connectivity. As interactive models in virtual reality, these parameters could be readily modified. In the earlier experimental animations, the classic images of the bulls were replaced by the trigrams of the Chinese BaGua system. Clearly the approach would allow the images to be replaced by the runes which denote the realms of the gods in Norse mythology.

Winding a torus as shown above is reminiscent of arguments regarding the Potential implications of alternation and rotation in psychosocial fields in the light of the remarkable insights of Nikola Tesla (Reimagining Tesla's Creativity through Technomimicry Psychosocial empowerment by imagining charged conditions otherwise, 2014). In any quest for widespread popular comprehension of the "planetary boundaries", the argument above emphasized the intuitive (if not instinctual) appeal of toroidal motion. To what extent is this reflected in the appeal of many carousel-like fairground rides -- "merry-go-rounds" -- to which the animations above then bear a fruitful resemblance? It is probable that carousels in Nordic countries would use the 9 gods of Norse mythology in their rides.

Experimental animations of 9-fold pattern of planetary boundaries inspired by the "World Tree" (Yggdrasil)
Solid variant	Wireframe variant

Design metaphors used in the above are a large blue torus opening and closing, with a circle of 9 spheres rotating through it. In addition, rings of 9 smaller spheres (similarly coloured) rotate around them -- suggestive of a form of recursion. A set of 9 thinner tori pass through a tenth sphere in the centre, with white spheres travelling through them. The design variously echoes arguments made above with respect to the requisite complexification of the doughnut metaphor (for the constraints on the planetary dynamic) and of the pizza metaphor (for the individual sexual preoccupation with scoring). The experiment frames the question of what alternative designs could be usefully explored, especially in the case of interactive virtual reality models.

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