Imagining a mnemonic device of requisite higher dimensionality

Local Reality of Overcrowding -- Global Unreality of Overpopulation (Part #15)

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5-fold systemic clues: The spherical pentagram presentation also draws attention to the similarity with the the classic Chinese 5-fold Wu Xing pattern (mentioned above) -- a reminder that the systemic links in that pattern (as presented in 2D, below left) are spherical -- not planar. A polar extreme of any mace-vajra could also be designed as a toroidal complex derived by adapting the 2D features of the Wu Xing into a 3D configuration of tori (as shown below). Such links are oversimplistically understood as straight lines; they are curves or arcs around a sphere -- potntially even of a hypersphere.

Chinese 5-phase Wu Xing cycle experimentally depicted as a configuration of tori in 3D (Animations of spheres moving through tori as systemic links; models rotated on x-axis. Correspondence to 2D image evident during the rotation)
Classic 2D representation	Wireframe rendering (spheres moving within tori)	Solid rendering (spheres moving over tori)
Adapted from Wu Xing entry in Wikipedia Interaction arrows: black=generating; white= overcoming	Virtual reality variants: x3d, wrl. Video variants: mp4 (left), mp4 (right) Other design parameters could be used for diameter/colour/speed of spheres, and direction/speed of rotation Transparency could be changed. Spheres could be replaced by distinctive Platonic polyhedra

As a menomic device, one of the merits ot the configuration is the extent to which different features of its geometry can be imagined as axes of rotation and manipulation. As with the animations above, these could be understood as implied by those demonstrated in baton twirling, quarterstaff, or kendo -- and even rope spinning (Rope Spinning: Flat Loop Tricks, YouTube, 2018; Short clips from Ropers Get-To-Gather 2014, YouTube). One possibility, for example, is to consider that pairs of spheres of the 3D Wu Xing could be understood as dumbbells, whose ("twirling") movement is constrained by the particular torus in terms of which they can be rotated.

For mnemonic purposes, the elements of the structure can be considered as visible or invisible (as suggested by the animation below centre). In terms of alternative perspectives, the 3D structure can then be considered as offering views from different angles, depending on the relative rotation of the dumbbells (as suggested below right). A related mnemonic argument has been developed separately with respect to use of Rubik's Cube (Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful, 2017).

Toroidal Wu Xing in 3D (screen shot)	Variations in pentagram visibility (animation)	3D Pentagram in perspective (example)

As argued above, the Wu Xing pattern might be usefully be understood as a form of 5-fold hypercycle. This lends itself to the configuration presented as an animation (below centre). Speculatively, the primary complementarity is indicated outside that framework (as a diagonal), consistent with the role of the dipole (as mentioned above). 5 other elements of the BaGua pattern (incorporated together in a possible 8-fold hypercycle above) are indicated as part of the 5-fold hypercycle pattern, with a sixth placed at the centre.

This mnemonic approach has the advantage of drawing attention to the perspective of the observer in "grasping" cognitively the hypercycle -- an extra-systemic sixth position -- as with any "grasp" of a mace-vajra or a baton-twirler. This recalls the argument of Terrence Deacon (What's Missing from Theories of Information? 2010). Together these elements emphasize through their animation that the elusive requisite comprehension of challenging systems is dynamic rather than the dangerously simplistic conventional implication that it is static, as emphasized separately (Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018).

Vitruvian man/woman (animation) (multi-coloured variant)	Indicative mapping of BaGua elements onto 5-fold hypercycle (animation)	Alchemical representation of the mysterious (plasma) fluid moving within the toroidal vessel above

As indicated in the animation (above left), the cognitive appeal can be further understood in the light of the aesthetic proportions of an animated form of the classic Vitruvian Man of Leonardo da Vinci (C. Lance Harding, Mysteries of the Vitruvian Man, Academy of Sacred Geometry, 2014). As variously illustrated in the latter, this is in itself suggestive of an imaginatively sophisticated mace-vajra design.

The focus of this argument has been on the complementarity between local and global, each effectively "mysterious" from the perspective of the other. This is usefully emphasized by the strangeness of the Taoist alchemical symbol (xuanpin) for the so-called valley spirit, or mysterious feminine, as widely discussed (Embodying topological succinctness beyond questions, 2014; Shuren Wang, Returning to Primordially Creative Thinking: Chinese wisdom on the horizon of "Xiang thinking", 2018; Evgueni A. Tortchinov, The Doctrine of the "Mysterious Female" in Taoism, 1997; Ellen M. Chen, In Praise of Nothing: an exploration of Daoist fundamental ontology, 2010).

This "spirit" may be fruitfully considered as corresponding to the plasma (an unusual state of matter) -- a mysterious "feminine" fluid -- circulating in the "valley" formed by the ITER nuclear fusion reactor. It could however be considered as a form of systems diagram of the cognitive processes of ITER-8 and the challenge of cognitive fusion and its comprehension (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006).

It is intriguing to note a degree of relation between the three rings in the Taoist symbol above and how Dante Alighieri describes the three rings (tre giri) of the Holy Trinity in Paradiso 33 of the Divine Comedy (Arielle Saiber and Aba Mbirika, The Three Giri of Paradiso XXXIII, Dante Studies, 131, 2013, pp. 237-272). The rings are discussed separately in terms of interlocking Borromean rings from which the images below are reproduced (Borromean challenge to comprehension of any trinity?, 2018; Comprehension of Unity as a Paradoxical Dynamic: metaphors reframing problematic engagement with otherness, 2019). The perception of local from global, and vice versa, can indeed be seen as one of problematic engagement with "otherness".

Representations of Borromean rings
Toroidal version	3 Möbius strips (animation)	5-fold Borromean rings
Reproduced from Kauffman (2006)	Video (mp4); Virtual reality (x3d; wrl)	Reproduced from Chanberland and Herman (2013)

Could the Wu Xing dynamic be considered in terms of the pattern of 5-fold Borromean rings discussed separately (Marc Chamberland and Eugene A Herman, Rock-Paper-Scissors meets Borromean Rings, Grinnell College, 2014)? Such questions are relevant to the current pattern of global (or local) strategic dilemmas implied by the elements of the Wu Xing pattern.

Use of the Tao symbol as a mnemonic device
	"Valley spirit" ?
Images adapted from Snoring of The Other: a politically relevant psycho-spiritual metaphor? (2006)

The animations above follow from related experiments in visualization which suggest other possibilities (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017; Circular configuration of cognitive phases framing toroidal experience? 2017; Psychosocial Learnings from the Spiral Form of Hurricanes, 2017; Concordian Mandala as a Symbolic Nexus: insights from dynamics of a pentagonal configuration of nonagons in 3D, 2016). Possibilities with regard to use of the Möbius strip can be related to the Ouroboros, given the above use of a torus (Complementary visual patterns: Ouroboros, MÖbius strip, Klein bottle, 2017; Experimental animations in 3D of the ouroboros pattern, 2017).

Relative movement of elements, with cognitive implication suggested by optical effects: As currently designed, no relative movement between the elements of mace or sceptre is incorporated. Again this reinforces the sense of stasis associated with mace-based governance -- a characteristic of global reporting, as discussed separately (Dynamic Transformation of Static Reporting of Global Processes: suggestions for process-oriented titles of global issue reports, 2013). Possibilities might include:

• translation (of Möbius complexes) along polar axis
  • to encompass central sphere
  • to penetrate and fill 3D end structures (whether crown, heart-pattern, polyhedra, or otherwise)
• rotation
  • of Möbius strand complexes (as shown above), whether in same direction or in a counter direction
  • of any 3D end structures
• speed
• slower, with more meditative connotations
• faster, such as to suggest a sinusoidal effect

Relative dimensions of elements: Of potential significance is the relative size of the mace-sceptre of Western inspiration (possibly requiring two hands) in comparison with that of a vajra of Eastern inspiration (potentially enfolded within a hand in mudra rituals). With respect to the elements of such symbols, possibilities include:

• strand complexes:
  • thicker / thinner
  • shorter / longer
  • more / less transparent
  • as wireframe variant
• central sphere:
  • larger / smaller
  • more / less transparent, notably in the light of any dynamics through which it is understood as emergent, namely as a cognitive lens enabling insight through optical metaphors (potentially inverting the image of global from local, and vice versa)

Rotation of mace-vajra as a whole: Arguably a mace is most typically raised or lowered vertically with respect to its polar axis, prior to being placed horizontally on a stand. It is unclear that such movement is held to be of any significance for governance (with the potential exception of rituals associated with Black Rod in parliamentary assemblies). Other possibilities include:

• rotation in horizontal plane, typical of animated depictions of a centrifugal governor by which the speed of an engine is controlled
• rotation in vertical place, as is most characteristic of baton twirling by a drum major(ette)

Transformations: Information technology now offers new kinds of support for imaginative exploration of the role of a mace-vajra symbol through morphing transformations:

• Complementary forms:
  • Vajra-Bell: Of particular significance, the ghanta can be recognized as having one end of a vajra expanded into bell-shape, whilst the other retains the form of the other vajra extremity. Various approaches can then be envisaged to morphing a vajra end into a bell-shape.
  • Sceptre-Orb: A mace of simpler form may well have one end in the form of a sphere. Clearly the expansion of an end into that form can be readily envisaged, as with the "absorption" of the complete length of the mace into that orb (and the possibility of reversing that process).
• Mace to Fasces: Of potential interest, especially given the highly controversial symbolic implications, the single "rod" of a mace can be readily multiplied to constitute the set of rods characteristic of the form of the fasces symbol. The central axe of the latter is of course reminiscent of the function of the mace as a weapon through which law and order is enforced.
• Möbius strip to Klein bottle: In the effort to emphasize a seemingly essential "cognitive twist" between incommensurables (such as local-global, or ny relation to otherness), the example above makes use of the Möbius strip. Of further potential interest interest is the manner in which the more challenging form of a Klein bottle is made by stitching together two Möbius strips of opposite chirality (How is a Klein bottle made of two Möbius strips? Quora, 2016; Konrad Polthier, Imaging Maths: inside the Klein bottle, Plus, 1 September 2003). This possibility raises the question as to how the local-global polarity might be understood as "separated" or distinguished by the strange form of a Klein bottle, if paired Möbius strips in the example above were represented by such a form. Conversely, what is then lost if the Klein bottle is reduced to Möbius strips -- and further, to the simply rod-like form of a mace-sceptre?
• Wu-Xing to Torus: Given the 5-fold distinction of the senses by which the proxemic dimension of this argument was introduced, there is a case for relating this tentatively to the classic Chinese 5-phase articulation known as Wu Xing. This conceptual scheme is used in many traditional fields to explain a wide array of phenomena, including the succession of political regimes -- or the of planets of significant gravity (Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012; Memorable dynamics of living and dying: Hygeia and Wu Xing, 2014). As typically presented in 2D this could be explored as a cross-section of the 5-fold array of elements by which the polar shaft of the mace can be depicted (in one of the examples above). There is the further possibility of presenting it in 3D with the links between the 5 elements taking toroidal form (as shown above) -- then to be understood as a transformation into a configuration at each end of the mace.

Higher dimensionality? Is it too readily assumed that an adequate symbol for global governance can be appropriately designed in 3D? The introduction of animation above already suggests that the subtlety may need to make use of 4D. The mace-vajra of the future may require a higher order of connectivity to reinforce comprehension appropriate to the challenge, as discussed separately (Envisaging NATO Otherwise -- in 3D and 4D? Potentially hidden faces of global strategy highlighted through polyhedra, 2017; Beyond dispute in 5-dimensional space: Pentagramma Mirificum?, 2015).

The manner in which twirling of a baton-mace is so intimately related to the direction of music also suggests that wider comprehension of higher dimensionality may depend on the memorable connectivity offered by recognizable patterns in music, as separately argued (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). As a much-valued symbol, the role of the anthem bears consideration in this respect -- as with the provocative case for its reversal, given the current crisis of governance (Reversing the Anthem of Europe to Signal Distress: transcending crises of governance via reverse music and reverse speech? 2016). The subtle insights of Omar Khayyam, as a famed poet of a tent-making family, suggest that the comprehension and design of a "big tent", seen as necessary for effective interfaith discourse, needs to be understood otherwise (Global Brane Comprehension Enabling a Higher Dimensional Big Tent? Strategic implication in encompassing nothing and coming to naught, 2011; Philip Clayton, Seeking Common Ground in 'Big Tent' Christianity, The Huffington Post, 9 January 2010).

As implied by the case for a Quintuple Helix model of innovative governance (mentioned above), and reference to "MACE" as a European meta-data project, any requisite mace-vajra may well need to be be a symbol of higher dimensionality. Clues in that respect are to be found in the 4D analogues of polyhedra, known in 4D as polychora (with variants of yet higher order), as discussed in more detail:

Visual representations of globality of requisite variety for global governance Four-dimensional requisite for a time-bound global civilization? Comprehending the shapes of time through four-dimensional uniform polychora Five-fold ordering of strategic engagement with time

Five-fold cognitive dynamics of relevance to governance? Decision-making capacity versus Distinction-making capacity From space-ship design to time-ship embodiment as a requisite metaphor of governance

A valuable context for consideration of the 5-fold Wu Xing framework is offered by Xiaoying Qi (Paradoxical Integration: globalised knowledge flows and Chinese concepts in social theory, University of Western Sydney, 2011). If higher dimensional subtlety is indeed required, then paradox is more than likely to be a feature of it, as argued separately (Comprehension of Unity as a Paradoxical Dynamic: metaphors reframing problematic engagement with otherness, 2019). However Qi makes no explicit mention of that framework, despite extensive discussion of the concepts of wu and wuwei. Instead Qi indicates that knowledge flows can thus be part of what has been characterized by global cultural flows, analyzed by Arjun Appadurai in terms of "five dimensions": (a) ethnoscapes; (b) mediascapes; (c) technoscapes; (d) finanscapes; and (e) ideoscapes (Grassroots Globalisation and the Research Imagination, 2001).

The relation to otherness, exemplified here by that between local and global, would seem to require forms of governance with a higher dimensional perspective -- given the highly problematic dynamics to which that relationship gives rise. There is a case for comparing the challenge to comprehension with that of the Principle of Complementarity regarding the relation between wave and particle in quantum mechanics. This would suggest that it is impossible to give due consideration of global and local perspectives at the same time. The need for a reframing of social and international relations with such an understanding has been articulated by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015). As mentioned above, does understanding of the paradox of "glocalization" require insights from understandings of nonlocality as framed by fundamental physics?

Physics is accustomed to the articulation of reality in 10 dimensions (Matt Williams, A universe of 10 dimensions, Phys.org, 11 December 2014). The latter notes the striking videos enabling visualization of 10-dimensionality (Thinking visually about higher dimensions, YouTube, 11 August 2017). Arguably the animation above of the 10-torus configuration in 3D of the Wu Xing offers another example.

There is some irony to the possibility that other modes of articulating psychosocial organization may be appropriate. One example might be that of wampum belts of the Iroquois Confederacy, given their equivalent in the symbolic sashes currently used as an indication of authority (Quantum Wampum Essential to Navigating Ragnarok: thrival in crisis through embodying turbulent flow, 2014; Penelope Myrtle Kelsey, Reading the Wampum: essays on Hodinöhsö:ni' visual code and epistemological recovery, 2014). The role of the as yet undecoded quipu in ensuring the integrity of the Andean civilization over an extensive period could be considered another example.

Is global governance currently exhibiting a high order of what might be termed "imaginative failure" -- as with the assessment of the ijntelligence failure in anticipation of 9/11. However speculative, given the transcendental, if not religious, significance accorded to symbols in the process of governance, there is clearly a case for exploring subtler modes of understanding the relation with any "other". The wave-particle complementarity would appear to offer valuable clues in that respect, as argued separately (Being Neither a-Waving Nor a-Parting: cognitive implications of wave-particle duality in the light of science and spirituality, 2013; Encountering Otherness as a Waveform -- in the light of a wave theory of being, 2013). Global and local perspectives may be appropriately understood as equally illusory -- each to the other.

Local Reality of Overcrowding?
Climbers queuing on Mount Everest (May 2019)	Crowd of refugees arriving in Malmo (Sweden)
Image which went viral, taken on 23 May by the climber Nirmal Pujra (AFP Photo; Project Possible) (Peter Beaumont, Why I won't be joining the queue at the top of Everest, The Guardian, 26 May 2019; Helier Cheung, Mount Everest: Why the summit can get so crowded, BBC News,24 May 2019 )	Copright by Reuters / TT News Agency; reproduced from Civil war or bright future? Sweden beckons more migrants with 'land of benefits' website as ex-Scania CEO predicts grave conflict (RT, 29 Oct, 2019) following account by Paulina Neuding (Bomb attacks are now a normal part of Swedish life, The Spectator, October 2019)

Imposition of Tourism Quotas -- Local Overcrowding?

15 Beloved Places Struggling With Overtourism (Canada Nast Traveler, 15 October 2018): Mallorca, Bali, Ecuador (Galapagos), Amsterdam, Boracay, Angkor Wat, Peru (Machu Picchu), Iceland, Bali, Dubrovnik, Santorini, Barcelona, Thai Islands, Mount Everest, Venice 8 Destinations Putting a Cap on Tourist Numbers (EscapeHere): Bhutan, Beijing (The Forbidden City). Australia (Lord Howe Island), Antarctica, Seychelles Tourism pressures: Five places tackling too many visitors (BBC News, 16 April 2018): Thailand (Maya Bay), Italy (Cinque Terre), South Korea (Jeju Island), Colombia (Caño Cristales) 17 Places That Have Been Ruined by Tourism (Reader's Digest) Europe Made Billions from Tourists. Now It's Turning Them Away (Time, 26 July 2018) Coping with Success: Managing overcrowding in tourism destinations (World Travel and Tourism Council / McKinsey, 2017): Heatmap of 68 cities in initial diagnostic The tourist attractions on top of your bucket list might not actually want you there (Quartzy, 13 December 2017) Some European Cities May Begin Limiting Tourism After Angry Backlash (The Huffington Post, 7 August 2017)

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