Globalization: playing ball, self-reflexivityand self-penetration?

Dynamics of N-fold Integration of Disparate Cognitive Modalities (Part #15)

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The spherically symmetrical polyhedra to which is reference is made above correspond to different degrees of approximation to a sphere -- to the globe which features so prominently in discourse about globalization. As an integrative concept and symbol its implications are a challenge to cognitive engagement.

One approach is through recognition that its subtle complexity is reflected in a strange manner in the design of balls used in ball games world wide. The stitching pattern on the association football offers one example -- given that this takes the form of a truncated icosahedron (Understanding Sustainable Dialogue: the secret within Bucky's Ball? 1996). Another example is offered by the baseball / tennis ball curve  discussed below.

Why would a global civilization associate the fundamental symbolic value of integration (and "unity") with the process of striking a ball competitively?

Baseball curve / Tennis ball curve: Whilst the form of the Mereon Trefoil is somewhat difficult to remember, its visual complexification is evident to a degree in the transition from the simple trefoil knot (below left) through the curve which is a prominent feature of the seam of every tennis ball and baseball (below centre). Both the trefoil knot and the 2D image of the baseball curve are a feature of traditional Celtic knots.

Comparable animations englobing a sphere?
Trefoil knot	Baseball / Tennis ball seam curve	Mereon Trefoil
Adaptation of an X3D model produced by Sergey Bederov	Interactive 3D variant	Adaptation of an X3D model produced by Sergey Bederov (Interactive version in X3DOM)

The parameters by which the three can be visualized could be explored as related, although the point is made that variants have been proposed for the baseball curve (Dean Allison, Ricardo Diaz, and Nathaniel Miller, Generalized Baseball Curves: Three Symmetries and You're In! Loci, MAA Mathematical Sciences Digital Library, September 2008, 2866). It is discussed by Robert Ferréol (Bicylindrical Curve, 2018) as the intersections between two cylinders of revolution, otherwise known as a Steinmetz curve. The complete Jitterbug dynamic, with which the Mereon Trefoil has been associated (as noted above), can be defined mathematically as following elliptical paths defined by four intersecting cylinders.

The dynamics associated with the tennis ball/basketball curve are discussed and illustrated separately, notably in relation to the form of a baseball cap (Non-linear pathways curving  between octants, 2020; Systemic and cognitive implications of baseball cap framing? 2020). An interactive 3D model is presented allowing users to modify the parameters of the baseball curve (designed by Sergey Bederov of Cortona 3D) -- in the context of speculation on Negligence of a "global wave" from a "wavelet" perspective? (2020).

In his above-mentioned discussion of the Mereon Trefoil, Louis Kauffaman (2003) presents a valuable illustrated discussion of the traditional Chinese Wu Xing pattern of 5 elements, in a section titled (From The Five Elements to the Petersen Graph and the Dodecahedron). In a separate discussion on the cognitive challenges of proximity in relation local versus global, a concluding section argued that the linking lines in the Wu Xing pattern (left, upper) could each be more appropriately represented as a torus (Imagining a mnemonic device of requisite higher dimensionality, 2019). The animation of a 3D model (left, below) offers an indication of this.

However, in the light of the use above of a sphere to indicate degrees of comprehension, variations in systemic (in)comprehensibility of the disparate elements of the Wu Xing pattern are indicated in the other animations below -- in each case with wireframe alternates to indicate what is hidden.

Degrees of comprehension of 5-phase Wu Xing cycle experimentally depicted as a configuration of tori in 3D (Animations of spheres moving through tori as systemic links)
Wu Xing pattern in 2D and 3D	Minimal systemic comprehension	Conventional systemic comprehension	Partial in-depth comprehension
Virtual reality variants: x3d, wrl. Video variants: mp4 (left) Other design parameters could be used for diameter/colour/speed of spheres, and direction/speed of rotation Transparency could be variously changed. Spheres could be replaced by distinctive Platonic polyhedra

Juggling: Curiously juggling could be recognized as a non-competitive form of playing with a ball -- with the challenge being the competence of the juggler. Given the archetypal challenge of the Gordian Knot, the complementary cognitive relevance of knotting and juggling merits consideration (Mapping grossness: Gordian knot of governance as a Discordian mandala? 2016; Governance as "juggling" -- Juggling as "governance": dynamics of braiding incommensurable insights for sustainable governance, 2018). The latter concluded with discussions of:

• Determining the requisite number of patterns, partners and "balls" in governance
• Acquiring a "sense" of 12 modalities for viable system awareness?

Related correspondences might be usefully recognized in the movements associated with juggling, as variously clarified (Burkard Polster, The Mathematics of Juggling, 2003; Jochen Voss, The Mathematical Theory of Juggling, 2012; Jarold Jacob Tawney, Jugglinks: Tangling Together the Worlds of Knot Theory and Juggling, Ohio State University, 2001).

Selection of animations of 3-ball juggling patterns by one juggler (derived from juggling patterns in Wikipedia)
3-ball cascade	3-ball shower	3-ball columns	3-ball box	3-ball Mills mess	3-ball Burke's barrage
attribution	attribution	attribution	attribution	attribution	attribution

Self-reference and self-reflexivity: Juggling necessarily gives immediate insight to the juggler with regard to what current competence enables with respect to what is juggled -- sustainably. It could be described as the art of the possible in the light of recognition of limitations. This is far less evident in the case of knotting, whatever the degree of correspondence between juggling and knotting.

Sustaining the juggling process can be explored in the light of the different orders of feedback understood in cybernetic terms with respect to the operation of a viable system, as discussed separately (***). This has notably been articulated by Maurice Yolles (Knowledge Cybernetics: a metaphor for post-normal science, 2009; Organisations as Complex Systems: an introduction to knowledge cybernetics, 2006).

Whether in cognitive terms, or with regard to the challenge of a global civilization, competence in regard to self-reference is clearly problematic (Hilary Lawson, Reflexivity: the post-modern predicament, 1986; George Lakoff and Mark Johnson, Philosophy in the Flesh: the embodied mind and its challenge to western thought, 1999; Nassim Nicholas Taleb, Skin in the Game: hidden asymmetries in daily life, 2018). Framed by prefixes, it is the challenge of "intro-" (as in introspection), or of "sub-" -- namely subjectivity in contrast to objectivity.

There is however a case for using the embedding of symmetrical knots in a sphere (as above) as a means of representing the challenge visually. The animations variously show the relation of knot-like forms to a sphere. Even though the knots have a degree of symmetry in spherical terms, it is however clear that their relation to any "global" comprehension is problematic -- if the knot is to be understood as "grasping" and "holding" that form.

Superficiality: It is in this sense that the baseball curve appears most successful in containing the sphere. It achieves this by being essentially -- and elegantly -- superficial. It does not penetrate the sphere in any way, although it may appear to do so when the sphere is transparent. This is not the case with the trefoil knots. Each clearly penetrates and traverses the sphere, potentially implying greater cognitive depth and integration -- and a degree of requisite cognitive twist appropriate to any visualization of self-reference.

It can be readily argued that global civilization is "superficial" -- as it is widely understood and presented -- and becoming more so through a variety of processes usefully framed as "dumbing down". This is despite the fact that the dynamics of the ball games played globally imply an integrative depth to which allusion can only be made in passing through reference to the "spirit of the game". In that light civilization is essentially unconscious and simplistic in any claims to vital self-referential cognitive dynamics, as argued by John Ralston Saul (Unconscious Civilization, 1995). This could be understood as implied by the intuitive credibility accorded to conspiracy theories and hidden agendas (Inspiration, Conspiration, Transpiration, Expiration: towards a universal model of conspiracy theories, 2020).

Much is necessarily "unsaid:, as may be variously argued (Global Strategic Implications of the "Unsaid", 2003; Varieties of Tone of Voice and Engagement with Global Strategy, 2020). It is readily recognized that much occurs in an "underhand manner", "under the belt", "under the table", or "under the radar". Conventional models readily discount the potential consequences of such dynamics -- despite their significant consequences.

Penetration and invagination: In the animations of the two trefoil knots above, the curves are shown as "penetrating" the surface of the sphere (in its non-transparent phase) -- in contrast to the baseball curve, where this is not the case.

Given the fundamental role of penetration as it relates to sexual intercourse, it is appropriate to explore the relevance of that metaphor -- understood as a prelude to engendering renewal, variously anticipated as a global Renaissance (Challenges of Renaissance: suggestive pattern of concerns in the light of the birth metaphor, 2003). No "penetration"; no "Renaissance"? In biological terms the intermediary processes are invagination and gastrulation -- inviting speculative reflection on their systemic implications:

• Invagination in psychosocial terms: understandings from web resources (2010)
• Engendering Invagination and Gastrulation of Globalization (2010)
• Complexification of Globalization and Toroidal Transformation: topological implications of invagination and gastrulation in embryogenesis (2010)

Violation, expletives, piercings, self-harm and inoculation: The future may recognize as extraordinary the degree to which the cognitive process of "penetration" and self-reference is now celebrated and cultivated "superficially" -- a process of pseudophilia:

• Violence: The current extent of violence, and anticipation of violence on a global scale, requires no comment. Violence in the media is now a fundamental requirement for entertainment. In order to be attractive (and marketable) such products tend to acquire credibility through a marked degree of violence. For example, those watching television are typically exposed to a daily diet of murders -- in addition to beatings, if not torture, rehearsed in much online gaming. This pattern curiously echoes what is deprecated as uncivilized in the Roman Empire of the past with its focus on violent games and gladiatorial combat. Entertainment echoes and celebrates the violence symbolized by missiles and their global trajectories.
  
  
• Rape: As a particular form of violence, the widespread incidence of individual rape calls for no comment. Curiously an analogous phenomenon has been recognized with respect to the rape of countries by other countries and institutions (Heather Cottin, The IMF rapes the world, Workers World, 7 July 2011; Matthew Rothschild, The IMF Chief's Rape Charge: metaphor for the IMF's abuse of power, Common Dreams, 16 May 2011).
  
  
• Self-harm and suicide: The pattern of violence and violation is now self-focused as indicated by the increase in self-harm, potentially taking an ultimate form in suicide. This frames the question as to whether countries -- and global civilization -- are now subscribing to this pattern, especially with the anticipation of civilizational collapse (Mind Map of Global Civilizational Collapse: why nothing is happening in response to global challenges , 2011).
  
  
• Expletives: The authenticity of discourse is increasingly indicated by use of "fuck", most obviously in popular films, seemingly as a reflection of discourse in the real world among real people. This contrasts with depiction of worlds -- "bubbles" -- in which no such reference is made, and in carefully censored formal discourse. As argued separately, strategies are elaborated and negotiated in contexts in which such expletives are characteristic -- only to be presented publicly through edited versions increasingly lacking any credibility (Mysterious Complementarity between Capitalism and Arsenalism: metaphors crucial to sustainability and the crisis of the times, 2020). Is the meaningful communication of significance possible without an implication of penetration? Most curious with respect to any intuitive call for self-reference is the common injunction "go fuck yourself" -- curious given the physical impossibility.
  
  
• Piercings: Arguably the fashionable appeal of body piercing as a distinguishing mark of identity and individuality can be recognized as symbolizing and embodying penetration -- and the authenticity it is held to imply (List of body piercings, Wikipedia).
  
  
• Inoculation: Current moves towards mandatory universal vaccination (in response to the COVID pandemic) merit recognition as a feature of the pattern highlighted by the previous points. They could be understood as a radically revised implementation of the essentially failed ambition towards universal indoctrination by the major ideologies and religions of the world.

The manner in which the curves of the trefoil knots dip beneath the surface of the associated sphere (in the animations above) -- seemingly to separate portions of the continuing curve -- merits recognition as echoing the strange interaction between a conscious objective world and an unconscious netherworld. As an underworld of subjectivity, this may be variously explored (Designing Global Self-governance for the Future: patterns of dynamic integration of the netherworld, 2010; Engaging with the Future with Insights of the Past, 2010). As the latter notes, interaction with the "underworld" has been of major importance in civilizations of the past. For the current global civilization, any such problematic preoccupation is primarily with regard to the underworld of organized crime.

The intuited reality, hidden below the surface of the sphere of conventional discourse, is most obviously experienced in terms of the widespread incidence of mood depression -- and the triggers this offers for the phenomena above. The irony is all the greater in the degree of correspondence with economic depression. The separateness indicated by the dipping of the curves below that surface is also curiously echoed by the attitude to otherness and especially to waste disposal (Unrecycled waste disposal as evidence for Planet Earth as a "shithole",  2018). Indifference to the world, as implied by the common corporate expletive "fuck the world", has the curious reactive consequence that the world will "fuck you back" in systemic terms.

It is in this context that the world is faced with the anticipation of a Great Reset -- a simplification by elites in highly controversial contrast to past dreams of a new Renaissance (Klaus Schwab and Thierry Malleret, COVID-19: the Great Reset, World Economic Forum, 2020). Missing is any understanding of how integration of any evoked "controversy" is fundamental to the paradoxical nature of the requisite cognitive twist in systemic terms, as discussed above (Missing "halves" of the Global Reset mandalas? 2020). How will the "netherworld" respond?

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