Global configuration of circles as requisite pattern of interlocking cycles for sustainability?

Eliciting Patterns of Global Consensus via Tensional Integrity (Part #7)

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With respect to global governance, reference continues to be made to the archetypal Gordian Knot (Mapping Grossness: Gordian knot of governance as a Discordian mandala? 2016). The relevance to governance and strategy of a cyclic perspective can be variously discussed:

• Eightfold Configuration of Nested Cycles of Cognitive Transformations (2012)
• Adaptive Hypercycle of Sustainable Psychosocial Self-organization (2010)
• System Dynamics, Hypercycles and Psychosocial Self-organization (2010)
• Cognitive Cycles Vital to Sustainable Self-Governance  (2009)
• Characteristics of phases in 12-phase learning-action cycle (1998)
• Cycles of winning and losing (1995)

Faced with the challenges of economic cycles and environmental cycles, concern focuses increasingly on recycling and the circular economy for which there is a notable lack of memorable iconography. The conceptual challenge of global strategic articulation was characterized at the UN/ITU AI for Good Summit (as noted above) by the opening declaration of the ITU Secretary General -- backed by a tabular wall of SDG imagery, with no indication whatsoever as to how the implied strategies might be interrelated. Could ChatGPT have offered a more insightful opening address -- justifying the sense of threat articulated by leaders unable to do so?

Global cyclic imagery? By contrast, given the considerable popular importance of the Olympic Games, reinforced by its commercial, political and symbolic value, the appeal of the associated iconography merits particular consideration. There is considerable familiarity with the five interlocking coloured circles as emblematic of the Olympic Movement -- symbolic of a culminating aspiration for many. The five coloured circles were originally conceived as symbolic of the five continents (although seven continents are now distinguished).

The Club of Rome articulates its latest strategic proposal in terms of a pentagram of "five turnarounds", as illustrated below (Sandrine Dixson-Declève, et al. Earth for All: A Survival Guide for Humanity, 2022).

Earth4All initiative of Club of Rome
5-fold "turnarounds"	6-fold Transformational economics
Reproduced from Earth4All

As discussed previously, this follows a tradition of 5-fold articulations of fundamental significance, most notably that of the Chinese Wu Xing and the Hygieia of ancient Greece (Systemic configuration of highly disparate cognitive modalities -- in the light of 5-ring strategy? 2019; Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012).  A 5-fold pattern of "dimensions" has recently been articulated by the Inner Development Goals initiative to complement the "external" preoccupation of the UN's SDGs (Thomas Jordan, Inner Development Goals: background, method and the IDG framework, 2021). The configuration of these dimensions is discussed separately (Contrasting engagement with "goals" by the Inner Development Goals initiative, 2022).

The Borromean ring configuration is potentially of particular significance to global governance through its suggestion of a higher order of requisite complexity and cyclic interlocking (Borromean challenge to comprehension of any trinity? 2018; Requisite curvature: reconciling the Triple Helix, the Triskelion and the Borromean condition, 2018; Engaging globally with knots and riddles -- Gordian and otherwise, 2018)

Suggestive comparison of cycles of interaction
Rock-Scissors-Paper	Rock-Scissors-Paper-Lizard-Spock	Chinese 5-phase Wu Xing cycle	5-fold Borromean rings	Pentagonal Discordian mandala
Reproduced from Wikipedia		Adapted from Wikipedia	From Chanberland and Herma (2013)	Reproduced from Wikipedia

Significance is otherwise associated with a pattern of five circles, whether interlocking or not:

• five great circles of latitude: Arctic Circle, Tropic of Cancer, Equator, Tropic of Capricorn, and the Antarctic Circle (The Five Great Circles of Earth, YouTube). However, in geometric terms these are not "great circles", in contrast to those of longitude.
  
  
• in geometry, the five circles theorem states that, given five circles centred on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second intersection points forms a pentagram whose points lie on the circles themselves (Miquel Five Circles Theorem, Wolfram MathWorld; Miquel's Pentagram Theorem, Wolfram MathWorld). A related result in geometry, Miquel's theorem, concerns the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. The converse Miquel's Pentagon Theorem is in turn related to Miquel's six circles theorem. This states that if five circles share four triple-points of intersection then the remaining four points of intersection lie on a sixth circle. Variants in 3D are recognized.
  
  
• representation of the intersection of five circles is an option in Venn diagrams (Venn Diagram with 5 Circles for PowerPoint), which might have been adopted to articulate the Earth4All approach
  
  
• configuration of 5 circular arcs forming the so-called Pentagramma Mirificum fundamental to global navigation (Global Psychosocial Implication in the Pentagramma Mirificum, 2015)

Related 5-fold configurations of potential relevance include various cultural symbols (Five Fold Symbol Meanings 9 July 2019; Five Fold Celtic Meanings 3 February 2018). Consideration might also be given to the so-called circle of fifths as a way of organizing and comprehending the 12 chromatic pitches in music theory (as a sequence of perfect fifths). This might offer clues to the unexplained enthusiasm for 12-fold global strategic articulations (Checklist of 12-fold Principles, Plans, Symbols and Concepts, 2011).

Previous discussion has considered the contrast between 5-fold and 6-fold articulations, notably with respect to the cultures in conflict with which such articulations are fundamentally associated (Middle East Peace Potential through Dynamics in Spherical Geometry, 2012). There the focus was on engendering connectivity between seemingly incommensurable 5-fold and 6-fold conceptual frameworks.

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