Torc-bearing, Playing-ball, Scoring and Nesting

Imagining Toroidal Life as a Sustainable Alternative (Part #10)

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Torc-bearing: The possibility of any form of "toroidal embodiment" calls for examination in the light of the remarks above with respect to familiarity with the torc, ring, necklace, bracelet and the like. Whereas these are variously worn, there is a curiously vital distinction to be made between:

• "torc-bearing" as an indicator of honour, high office, holiness, or the like
• "torc-bearing" as a mark of servitude, property, bondage, and even slavery (in the past)

There is a strange conflation of these distinctions in that a sash may be worn both by the president of a country and by a doorman -- with the former declaring a degree of servitude to the people, and the latter being "in service". A chain may be worn as a "chain of office", but also by a "prisoner in chains". This conflation is also evident in the use of rings as an indication of high office (the Pope, royalty -- or a Mafia chieftain) as well as being an indication of exclusive property and eternal fealty, as with a wedding ring or a fraternity ring.

Further confusion is evident in enthusiasm for the use of rings in the ear, nose, lips, and otherwise -- through piercing -- possibly as an indication of membership of an exclusive group. visibly distinctive from others and as such a strong affirmation of identity.

Torc-bearing may thus be recognized as a means of holding, containing and possessing value, whether in monetary or symbolic terms (as honour and a mark of respect). There is however little sense of what might "flow" within such devices as a toroid, a ring of toroids, or a chain of toroids -- with the possible exception of their use as circlets of prayer beads. As static, solid devices they can only potentially echo what might be otherwise associated with a halo. Even in the form of a tiara or crown, there is little sense of the dynamics between what is symbolized by its component parts (however extensively bejewelled), as argued separately (Imagining further implications: helical coil, toroidal knot or crown? 2019).

To the extent that torc-bearing is an indication of "high-flyers", it is far from clear what cognitive functions associated with its structure do indeed "enable flight" -- or how the significance with which they are imbued might do so. This empowerment does however continue to be explored in science fiction and fantasy.

More problematic is the case in which servitude requires some form of torc-bearing, In such cases the individual wears it much as with the classic reference to an "albatross round the neck". A "chain of office" may also be experienced as indistinguishable in many respects from imprisonment "in chains".

Playing-ball and "being in the loop": Torc-bearing suggests a curious relationship to playing-ball -- especially in a toroidal framework. Whatever the sense of of torc-bearing, the bearers are expected to "play ball", namely to conform to a particular pattern of behaviour (and an associated pattern of thinking) usefully indicated in this case by the circularity of the toroidal form.

In both cases the dynamics are effectively constrained by the torus as a "playing field" -- especially when it takes the form of a circular running track in an arena. Also of relevance to that understanding is the sense of "being in the loop" (Keep Me in the Loop, TalkEnglish; How to Stay "in the Loop", MindTools; Feedback Loops: All About Being "In the Loop"e;, ReturnPath, 29 December 2015).

Failure to "play-ball", and to be constrained by the implicit rules, is then perceived as systemically threatening to the integrity of the collective -- even dangerously so. Being "out of the loop" may be a consequence of systemic failures (P. Shanley and C. Lopez, Out of the Loop: why research rarely reaches policy makers and the public and what can be done, Biotropica, 41, 2009, 5; Mark Gongloff, Trump's Iran Plan: everyone's out of the lLoop, Bloomberg, 21 June 2019).

Sexual connotations of "scoring": The form of the torus is then especially suggestive of the focus on "scoring" in that context. This may be transformed into a focus on scoring goals, as in the many ball games having as objective to get the ball into a goal -- whether a net, ring, or otherwise (Baseball metaphors for sex, Wikipedia). There are only too obvious parallels to the sexual analogue for which "scoring" is a very common metaphor -- if not "balling" (69 Common Phrases In Sports That Sound Like Sex Terminology, PGP, 30 September 2014; The 19 Greatest Sports-Related Sex Euphemisms, TotalProSports, 21 July 2010). Widely recognized in many contexts is the sense of being "scored against", typically framed as having been "fucked" -- a process determining psychosocial dynamics thereafter in the priority given to "settling old scores". Of some relevance are the number of references to people being "raped with a baseball bat" an to its use in other forms of torture.

Given the manner in which sporting metaphors are also used with respect to war (scoring against the enemy), together with the sexual implications of war, this complex of associations has been variously examined and criticized:

• David G. Winter and Otto Rank: Circulating Metaphors of Sexuality, Aggression, and Power: Otto Rank's Analysis of "Conquering Cities and 'Conquering' Women", Political Psychology, 31, 2010, 1 pp. 1-19)
• Valentina Georgieva: Military Language and Sexual Language (Research Work of the Russian Universities, 54, 2015, 11)
• Kelly Oliver: Women as Weapons of War Iraq, Sex, and the Media (Columbia University Press, 2010)
• Maria Eriksson Baaz and Maria Stern: Sexual Violence as a Weapon of War?: Perceptions, prescriptions, problems in the Congo and beyond (Zed Books, 2013)
• Lisa Wade: War as Sexual Domination (Sociological Images, 14 June 2008)
• Deborah Roffman: The Power of Language: baseball as a sexual metaphor in American culture (SIECUS Report, 19, 1991, 5)

As described by Roffman (1991), the baseball metaphor is "insidiously powerful, singularly effective, and very efficient…as a vehicle for transmitting and transferring to successive generations of young people all that is wrong and unhealthy about American sexual attitudes". As noted by Malcolm Potts and Thomas Hayden (Sex and War, ReadHowYouWant, 2011):

Explicitly sexual metaphors also often emerge in accounts of warfare... It's no wonder some authors suggest that warfare sometimes seems to be a surrogate for sex, but we suspect the connection is more basic: Both sex and war fulfill profound male evolutionary drives, so it's not surprising they might come to serve as metaphors for one another. (p. 109)

Obvious correspondences are to be recognized between "shooting" in ball-games and metaphoric use of that term to refer to the ejaculation of sperm -- then readily to be compared to firing bullets in any conflict situation and the "transformation" they are anticipated as accomplishing in the other.

"Pizza" versus "Doughnut": The extensive preoccupation with such use of baseball metaphors for sex has evoked consideration of the desirability of alternatives of greater subtlety (Carly Dreyfus, To Slide or to Slice? Finding a Positive Sexual Metaphor, Scarleteen, 4 May 2009). This concern has been given a particular focus through a TED Talk by Al Vernacchio (Sex Needs a New Metaphor, here's one TED Talk, March 2012) evoking much further commentary (Sexual-Intimacy Metaphor to Abandon Baseball Terminology, Embrace Gymnastics Every Three Weekly, 25 February 2013).

As an alternative to baseball as a framing of sexual intercourse, one widely discussed metaphor has been the pizza (Helen Walters, Let's talk about sex -- and pizza: Al Vernacchio at TED2012, TED Blog, 2 March 2012; Why Pizza (Not Baseball) Should Be the Metaphor We Use for Sex, HelloFlo; Sex and Pizza: sex needs a new metaphor -- not baseball, Roger Williams University). Given the importance associated with the doughnut metaphor in framing the strategic challenges of the times (as discussed above), history may recognize that it is more than extraordinary that the pizza metaphor should have been proposed within months of the promotion (via Oxfam) of the doughnut metaphor for economics. (Let them eat cake?)

Given the extent to which sport, notably as exemplified by baseball, has also infiltrated the framing of warfare -- especially the associations to targetting -- it could then be asked whether it is imagined that warfare should also be framed in term of the joys of pizza consumption (Bruce Mazlish, The Joy of War and the Future of Humanity, New Global Studies, 4, 2011, 3; Julia Welland, The Joy of War: Embodied, Affective and Everyday Pleasures, Balsillie School of International Affairs, 2017; John-Paul Jordan, Joys of War, 2018).

The choice of two of the primary junk food products as metaphors for the fundamental processes and challenges of society arguably merits extensive reflection. Especially curious is the choice of the one without a central hole as being more appropriately representative of sex. Are a doughnut and a pizza the best that humanity can be offered in order to engage with the challenges of the present and the future?

With respect to the argument above, the unexamined toroidal associations highlighted with respect to the segmented doughnut also merit consideration with respect to the geometry of the pizza -- notably as a consumer product, given the challenges of consumption framed by the doughnut model.

Toroidal attractor underlying sex, sport and war? This conflation of associations, so fundamental to psychosocial dynamics, suggests that the dynamics could be fruitfully configured together, as suggested by the images on the left below. Given the argument for toroidal representation, those on the right are more suggestive of the dynamics -- with any notion of "nesting" then suggested by the form of the torus as a whole.

Metaphorical nexus of fundamental psychosocial preoccupations
2D schema	3D animation	Alternative toroidal variants

As a symbolic nexus, the images on the right are also consistent with the preoccupation of space exploration and the associated space race -- targetting features of the solar system to establish possession thereof. Reaching the Moon and the planets can be readily understood as "scoring" in sexual terms, especially given the phallic associations of rocketry, as indicated by the poet W. H. Auden (Edward Mendelson, 'So Huge a Phallic Triumph': Why Apollo had little appeal for Auden, New York Review of Books, 12 August 2019).

Nesting: As noted above, the toroid also conveniently recalls one design for a space habitat -- effectively a new "nest" for the reproductive commitment of humanity, consistent with the strategic quest for a "safe operating space for humanity" -- at least for a highly selected proportion. The metaphors associated with the images on the right are necessarily only indicative of psychodynamic functions in relation to the toroidal dynamics -- recognizing that these are of dimensioality greater than three. In evoking attraction of the most fundamental kind, those dynamics are usefully recognized as a strange attractor. More strange ironically is the lack of comprehension as to how it functions as an attractor, and the simplistic explanations presented in that regard.

The toroidal dynamic, and the attraction it evokes, is therefore indicative of a complex relationship between achievement of "scoring" in the short-term (through possessive encroachment and penetration) and "encompassing" (namely possessing otherwise through "enclosure") such as to enable "nest building" and "reproduction" in the longer-term. The processes are necessarily instinctual to a high degree and as such elusive to conscious comprehension -- whether with regard to their manifestation in sex itself, in competitive sport, or in conflictual interactions. Advocacy of peace is then only attractive as a relief from such dynamics which tend to be inherently more engaging. How to compete with internet porn and media violence?

Mutual constraint by interlocking tori: The co-existence of two metaphors, lending themselves to recognition as toroids, suggests that they may be complementary in ways which merit careful examination. Specifically it could be asked whether the processes in each case suggest that the two tori are dynamically interlocked as suggested by the following animations. The dynamic could be recognized as representing a fundamental form of "intercourse" between two frameworks which are typically not appropriately associated. -- enabling further "pizza consumption"

Animation of a dynamic virtual reality model of intertwined tori
	Red torus has a vortex (smoke ring) dynamic in the model
	Blue torus has a wheel-like dynamic in the model
X3D and VRML models kindly developed by Sergey Bederov of Cortona3D (interactive 3D version)

The animations derive from a separate discussion (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006; Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011; Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018).

The argument can be further developed in the light of other ways of understanding interlocking. That on the left below is self-explanatory -- raising the question of the "bond" between the two tori. Those in the centre follow from the requisite complexity associated with 3-fold Borromean rings (as discussed above) -- however, in depicting a 7-fold equivalent, the point is raised as to whether a 9-fold interlinkage is required for the 9 planetary boundaries required for a "safe operating space for humanity". A wide variety of such links of various complexity is discussed by Slavik V. Jablan (Are Borromean Links So Rare? Forma, 14, 1999, pp. 269–277; coloured illustrations).

Alternative forms of interlocking?
Interlocked tori	Borromean rings in 3D	3 mutually orthogonal tori with a 3-loop helix moving over each	7-fold Borromean rings	9-fold Borromean rings
				Requisitely complex interlocking for the 9 planetary boundaries of the doughnut model ? and the pizza model
Michael Schreiber (Wolfram Demonstration Project, 2011)	Reproduced from Kauffman (2006)		Reproduced from Chamberland and Herman (2013)

Boundaries and limits: Curiously both the doughnut metaphor and the pizza metaphor call for attention to boundaries -- otherwise to be specifically recognized as limits, if not constraints, whether with respect to collective or individual behaviour. Strangely neither metaphor evokes sensitivity to the subtlety of limits in enhancing the attraction which would render them viable. As a representation of sex, the pizza metaphor only suggests a constraint on greed to enable a degree of sharing. The doughnut metaphor is primarily a technical device -- which might well be compared with a chastity belt for human civilization.

Of particular relevance is the sense in which the doughnut and the pizza dynamics, as systemically understood in collective terms, might well be mutually constraining. Excessively overriding the boundaries of one could well constrain the other in unforeseen ways -- like it or not. Thus does "too much pizza" endanger planetary boundaries; and does too much doughnut inhibit creativity?

The distinctive dynamics associated with the torus as represented above suggest that -- from a longer-term perspective -- they correspond to the balance widely extolled as the symbolic ideal of the relation balance between "Fatherhood" and "Motherhood" in the dynamic of the family. That obvious abuses in both cases are variously called into question at this time is relevant to this commentary and to the inadequately formulated understanding of that dynamic. The depiction of the Bottomean rings in 3D is intriguingly suggestive of the greater complexity of a viable marital bond than is potentially implied by the simplicity of the conventional wedding ring -- especially given the contrast to what only appears in 2D to be such a Borromean bond (as indicated earlier).

Post-Jouissance? There is a strange and ironic sense in which attachment to "scoring" in any manner (including pizza consumption) lends itself to the criticism by Lacanian paychoanalysis of the preoccupation with jouissance -- and especially with its sexual connotations As emphasized by the pizza metaphor, this could then be considered comparable to consumerism par excellence -- in a quest for the growth on which the economy of the collective is so dependent within the constraints of the doughnut metaphor.

However jouissance is to be understood, as articulated by Jacques Lacan, its further implications derive from his interpretation of the work of Sigmund Freud (Beyond the Pleasure Principle, 1920). This in particular is widely recognized as highly confusing in its own right. Jouissance has achieved a degree of appreciation in the radical arguments of Slavoj Zizek, (Lacan's Formulas of Sexuation, 1995; Metastases of Enjoyment: six essays on woman and causality, Verso, 1994) -- arguments which are themselves complex, confusing and highly controversial, perhaps appropriately so, given the subtlety of the matter -- "too close to the existential bone". The understanding has been further developed in a cross-cultural analysis in philosophical and psychoanalytic terms (Ashmita Khasnabish, Jouissance as Ananda: Indian philosophy, feminist theory, and literature, 2003).

The questions raised by jouissance are however relevant to imagining the nature of a "safe operating space for humanity" according to the doughnut metaphor -- challenged by the primary preoccupation of humanity with "scoring" as framed by the pizza metaphor. Is "post-jouissance" indeed especially associated with a death drive, whether individual or collective -- understood as  "opposition between the ego or death instincts and the sexual or life instincts".

Scoring own goals? Strangely, when framed in this way, it could be said that the problem for humanity and strategic governance is the extent to which the "scoring" -- in which there is such a heavy investment -- can be understood as a process of enthusiastically scoring "own goals". (Rowan Williams Amazon fires are a shameful indictment of our lust for excess The Guardian, 6 September 2019).

Given that metaphor, also of interest is the extent to which a player may try to throw a game by deliberately attempting an own goal -- suggesting that some may be endeavouring to do precisely that. A further irony is the extent to which the stitching pattern of balls used in association football is that of a truncated icosahedron -- a pattern of considerable significance to cognitive organization, as noted separately (Projective geometry of discourse: points, lines, frames and "hidden" perspectives, 2018).

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