Formalizing a pineapple model of governance through zonagons and zonohedrification?

Coronavirus -- Global Plan, Doughnut, Torus, Helix and/or Pineapple? (Part #7)

Polyhedral abstractions? The insights relating the Fibonacci patterning of natural order to that of the pineapple, and to the implications for governance, are primarily allusive, if not particularly elusive. A valuable clue is however offered by the various procedures for the geometrical transformation of polyhedra. These are notably include truncation, stellation, dualization, compounding, and zonohedrification. Giving rise to zonohedra, the latter is of particular relevance to any formal modelling of the pineapple, as variously presented by George W. Hart (Zonohedrification, The Mathematica Journal, 7, 1999, 3; Zonohedrification).

The faces of a zonohedron take the form of zonagons -- polygons with an even number of equal sides and opposite sides parallel -- which are fundamental to tiling a space and therefore to attribution of territory (Paul Stephenson, Tiles from Coverings; István Hargittai, Symmetry: Unifying Human Understanding, 2014; From the Rhombic Enneacontahedron to an All-Kite Polyhedron, Robert Loves Pi.Net, 15 February 2020). Of further relevance to the challenges of governance are particular zonohedra namely the rhombic dodecahedron and the rhombic triacontahedron to which particular attention was initially given by Jean J. Pedersen (Collapsoids, The Mathematical Gazette, 59, 1975, 408).

Oppositional geometry and logic? Given the challenge of opposition in governance, the relevance is evident in that these polyhedra feature notably in the issues framed from a logical perspective by oppositional geometry, as discussed separately (Oppositional Logic as Comprehensible Key to Sustainable Democracy: configuring patterns of anti-otherness, 2019; Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity: Eppur si muove -- biomimetic embedding of N-tuple helices in spherical polyhedra, 2017). The first is the geometric dual of the cuboctahedron whose remarkable properties were a particular focus of Buckminster Fuller. The second is a dual of the icosidodecahedron. Both duals are Archimedean solids. Fuller is especially famed for his development of geodesic domes whose design principles he related to challenges of global management of resources (Synergetics: Explorations in the Geometry of Thinking, 1975; Operating Manual for Spaceship Earth,1968).

"Strategic baskets", basket weaving and swirl patterns? It is appropriate in this context to recall the importance that continues to be attributed to "strategic baskets" as a model of relevance to governance. Especially significant in this respect has been the role of the The Three "Baskets" of the Helsinki Final Act of the of the Conference on Security and Co-operation in Europe (1975), a declaration sgined by 35 countries in an attempt to improve relations between the Communists and the West. As described in Recapturing the Spirit of Helsinki: the OSCE reflects on the past to shape its future (OSCE Magazine, October 2005), this encompassed three main sets of recommendations, commonly referred to as "baskets"(with a fourth that dealt with procedures to monitor implementation, and to plan future meetings):

The first set ("Basket I") related to politico-military aspects of security: principles guiding relations between and among participating States (the "Decalogue"), and military confidence-building measures.
The second set ("Basket II") concerned co-operation in a number of fields including economics, science and technology, and the environment.
The third set ("Basket III") dealt with "co-operation in humanitarian and other fields" -- a formula covering human rights issues under the headings of "human contacts", "information", "co-operation in the field of culture" and "co-operation in the field of education". It also included a specific set of recommendations related to Mediterranean issues

Of relevance is why the traditional form of a basket had such appeal with respect to governance at that critical time. Although its use at the time could be considered simplistic, there is a case for arguing that the intuitive appeal can be related to traditional techniques of basket weaving common to many cultures.

Of particular interest is the technique giving rise to especially attractive patterns of swirl baskets and coiled basketry. A single swirl may indeed curve to the right or to the left (Sun Swirl Basket, Ten Thousand Villages; Tutorial: Make a coiled raffia basket; 13 May 2015; Jill Choate, A Study in Spirals: how to make them happen, 8 March 2017). Double and triple swirl patterns are characteristic of traditional symbols, notably the Japanese tomoe.and the Western triskelion. These recall the swirling pattern familiar in pineapple spikes.

Basketry offers a much-valued metaphor in traditional cultures (Samuel Suina, Basket as Metaphor: Weaving the Basket, Indigenous Educational Models for Contemporary Practice, 2017; Colin Dickey, Shapes of Native Nonfiction: 'The Basket Isn't a Metaphor, It's an Example', Longreads, August 2019). The Commission on Environmental, Economic and Social Policy of the International Union for Conservation of Nature has framed its preoccupations in terms of three Knowledge Baskets, noting that:

The term 'knowledge baskets' is inspired by the Maori tradition of the God Tane's ascent through the twelve heavens to bring back to earth, three baskets of knowledge... For IUCN's work on knowledge baskets and flagship products, the term knowledge basket is a metaphor for working in a holistic way, valuing ethical respectful and reciprocal relationships as well as investing in the human social and cultural dimensions of environmental knowledge. Baskets have meaning across indigenous cultures, almost of all of whom have traditions around using baskets for functional earthly purposes as well as for sacred purposes....

Use of the term 'knowledge basket' marks an important milestone in IUCN, as it involves not only incorporating a traditional knowledge concept into IUCN's policy framework but also provides greater scope for people throughout the global indigenous conservation community to contribute to IUCN's important scientific work.

Clearly missing from use of basket as a metaphor for strategic governance is whether account might be taken of the structuring potential, and aesthetic appeal, of single or double swirl patterns -- in contrast to baskets lacking such features. How, for example, might such swirling have informed The OSCE Concept of Comprehensive and Co-operative Security (Organization for Security and Cooperation in Europe, 2009)? The question relates to the conflation at that time between metaphorical ":baskets" and metaphorical "pillars" --with the latter metaphor continuing to dominate strategic thinking in Europe (Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference, 2008). Such use of questionably coordinated "pillars" can clearly be related to the argument here with respect to "spikes". In basketry an equivalent to pillars is evident as a structural feature, especially in the absence of a swirling pattern -- then resulting in a stack design.

Curiously, but appropriate to the present period, global governance might well now be described as a "basket case" -- as used with respect to an institution or country in a bad condition or difficult situation, whether economically, financially or otherwise (Philippe Legrain, Europe's No Basket Case, International Economy, 17, 2004). It was originally used for a soldier missing both his arms and legs, who needed to be literally carried around in a litter or "basket". Given such understanding of a supporting container, does any proposal for a Marshall Plan raise the question of how such a "basket" should be designed?

Ironically, in a period of urgent worldwide quest for a vaccine to respond to COVID-19, "basket design" is employed metaphorically to describe a key methodology for the evaluation of a single drug for multiple indications (Mark Chang, et al, Innovative Strategies, Statistical Solutions and Simulations for Modern Clinical Trials, CRC Press, 2019; Kristen M. Cunanan, et al, Basket Trials in Oncology: a trade-off between complexity and efficiency, Journal of Clinical Oncology, 35, 2017, 3; Jay J. H Park, et al, Systematic review of basket trials, umbrella trials, and platform trials: a landscape analysis of master protocols, Trials, 20, 2019, 572).