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30 March 2020 | Draft

Cognitive Engagement with Spike Dynamics of a Polyhedral Coronavirus

Alternation between assertive arrays and systemic patterns of comprehensible coherence

-- / --

Eliciting imaginative thinking from coronavirus of relevance to governance
Framing an "opponent" otherwise: befriending coronavirus?
Enactive engagement with otherness
Reframing the coronavirus to elicit new thinking*
Dynamics of raising and lowering spikes in polyhedral configurations
Symbolic configuration of disparate strategic elements?
Patterns of systemic relationship from an "internal" perspective
Distinguishing coherent patterns of strategic N-foldness -- from 8-fold to 80-fold
Global plan, doughnut, torus, helix and/or pineapple?


The presentations here follow from an argument previously made (Reimagining Coronavirus in 3D as a Metaphor of Global Society in Distress: crowning pattern that connects spiky organisms, satellite constellations, nuclear explosions, and egomania? 2020). There it was suggested that there were insights to be gained from the form of the coronavirus in 3D. In particular this highlighted the possible isomorphism between the configuration of spikes on the viral form and psychosocial forms potentially characterized in terms of "spikes". This approach was framed as consistent with the original inspiration of the Society for General Systems Research.

Of some relevance to the seemingly unusual comparison made there is the focus of an interview with Jeffrey Lewis (John Krzyzaniak, How the coronavirus outbreak is like a nuclear attack: An interview with Jeffrey Lewis, The Bulletin of Atomic Scientists, 20 March 2020).

The virtual reality 3D models elaborated in the previous paper lend themselves to further development in order to explore such possible isomorphism -- especially as triggers to imaginative reflection on possibilities for engagement with spiky forms, as might be generically understood.

Whether or not the unusual dynamics presented in the models (previously and below) above enable and reinforce "new thinking" of relevance to engagement with the coronavirus remains to be seen. The models are of particular interest in ordering the relationships between global strategies which could each be understood as configurations of a certain number of assertive "spikes". Examples include the 8-fold set of the UN's Millennium Development Goals, the 16(+1) set of Sustainable Development Goals, and similar strategic patterns of greater or lesser complexity. These lend themselves to experimental mappings on polyhedra, as discussed separately (Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful, 2017; Time for Provocative Mnemonic Aids to Systemic Connectivity? Possibilities of reconciling the "headless hearts" to the "heartless heads", 2018).

As noted in the previous argument, many viruses take polyhedral form and may well be described as icosahedral viruses (D. P. Wilson, Protruding Features of Viral Capsids Are Clustered on Icosahedral Great Circles, PLoS ONE, 11, 2016, 4). In that light, and on the basis of information available, the preliminary experimental models of the coronavirus presented earlier were assumed to have 72 or 74 spikes. As 72, this would be consistent with the special coherence of 72-fold patterns in human cognition, whether in mathematical terms or in the light of various traditions (see Wikipedia 72 (number)). Traditional understandings of that coherence can therefore be drawn into imaginative reflection on the engagement with a 72-fold virus, or with other configurations of strategies of that order.

Given the psychosocial emphasis (as detailed previously), the following explorations are based as much on science as aesthetics -- therefore allowing for poetic licence, despite any controversy in that regard. The assumption made in this exploration is that strategic reflection at this time can ill-afford the niceties of the conventional separation between disciplines. These seemingly enable the emergence of crises and the inhibition of "new thinking" in that regard. Argued otherwise, what perspectives are to be assumed irrelevant to a crisis of crises in which coherent response is only to be found at the price of "conceptual lockdown" -- requiring a form of "cognitive lockstep" to ensure that everyone follows the same script?

The question proposed in the earlier paper was whether and how the form of the coronavirus might help people to think fruitfully in new ways in preparation for future crises. How can humanity be enabled to imagine approaches more appropriate to the complexity of crises and distinct from the approaches which have engendered them? The possibility is considered further through suggestive 3D animations emphasizing the global coherence that is seemingly so lacking at this time -- despite promotion of "globalization'.

Eliciting imaginative thinking from coronavirus of relevance to governance

Although the following common quotations are allegedly from Albert Einstein, efforts to clarify their source by Alice Calaprice (The New Quotable Einstein, 2005), have only indicated that they correctly paraphrase his thinking:

For example, as noted by Ian Goldin and Robert Muggah (The world before this coronavirus and after cannot be the same, The Conversation, 28 March 2020):

With COVID-19 infections now evident in 176 countries, the pandemic is the most significant threat to humanity since the second world war. Then, as now, confidence in international cooperation and institutions plumbed new lows.... Even as we attend to the countless emergencies generated by COVID-19, we need to think deeply about why the international community was so unprepared for an outbreak that was so inevitable. This is hardly the first time we've faced global catastrophes.... A global Marshall plan, with massive injections of funding, is urgently needed to sustain governments and societies.

Such sentiments are expressed otherwise by Bill Gates (How We Must Respond To The Coronavirus Pandemic, TED Talk. 29 March 2020). Whilst physicists have struggled for decades over insights into unity as physically understood in terms of many dimensions, the global unification implied by "we" and "plan" seemingly calls for little thought in that regard. The language of politicians prevails, namely that "we are all in this together", without addressing that many of us do not accept the superficial thinking behind such slogneering. The fact that the world population is not appropriately mobilised by such language -- and what "we must do" from one perspective or another -- remains a profound mystery to those who have called for it so vainly over many decades (International Community as God or Sorcerer's Apprentice? Strategic chaos in the absence of an interlocking temporal pattern of longer-term cyclic processes, 2015).

New thinking? Much is made of the need for "new thinking" with respect to a global civilization in crisis (Richard A. Slaughter (Ed.), New Thinking for a New Millennium: the knowledge base of futures studies, 1996; Edward de Bono, New Thinking for the New Millennium, 2000; William J. Williams, New Thinking for a New Millennium: the processes and application of abstracting, 2000). The implications have been highlighted separately (Re-cognition of higher orders of insight through "new thinking", 2104; Eliciting new thinking, 2009) .

It would seem that some such possibility is being explored otherwise as "joined-up thinking" (Rick Lewis, Joined-up Thinking, Philosophy Now, Nov/Dec 2014; Chris Frith, Neuroscience: Joined-up thinking, Nature, 2014; Philip Delves Broughton, Joined-up thinking, Financial Times, 8 June 2011; Joined-up Thinking, Lloyd's News, 1 December 2014; EU development policy needs joined-up thinking, say MEPs, European Parliament News, 25 October 2012). How is this form of integrative thinking enabled within the world wide web?

The challenge could be framed otherwise. Each year one might ask what is the "new thinking" to which governance is currently attentive? What new thinking has emerged from which disciplines -- or from the UN, from the OECD, from the EU, from NATO -- as might be a focus in their annual reports? How is such "new thinking" to be recognized and ranked? Should precedence be given to the thinking emanating from those most highly ranked -- a function of the Almanach de Gotha in determining order of precedence on diplomatic and social occasions?

The coronavirus pandemic is reinforcing that long-expressed call for "new thinking" -- even those articulated by authorities (Annan calls for 'new thinking' in Mideast process, The Irish Times, 22 February 2002; Gorbachev's New Thinking, Foreign Affairs, 1 February 1989), or as articulated by the Cambridge Trust for New Thinking in Economics. Bluntly stated, few official reports are characterized by the quality of imagination attractive to larger proportions of the population.. The point has been separately argued (Engendering 2052 through Re-imagining the Present, 2012) -- which took the form of a review of an essentially unimaginative report presented to the Club of Rome (Jorgen Randers, 2052: a Global Forecast for the Next Forty Years, 2012).

Curiously it is innovators in technology who offer highly imaginative frameworks, most obviously manifesting in interactive gaming, virtual reality, the prospect of space exploration, and the like. They then function, to some degree, as surrogate officiants. They too may fantasize about their role in enabling more fruitful governance -- a more fruitful marriage between problematique and resolutique (John R. De La Mothe, Science, Technology and Global Governance, 2014; Benjamin Barber, Dysfunctional Nations, Rising Cities: the opportunity facing Silicon Valley, 2015 State of the Valley Conference; Jonathan Visbal, Governance Lessons from Silicon Valley, Bloomberg Business, 13 May 2008).

Physicists proudly refer to the much-quoted statement by Niels Bohr in response to Wolfgang Pauli: We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough. To that Freeman Dyson added:

When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope! (Innovation in Physics, Scientific American, 199, 1958, 3)

Faced with global crises and social chaos, the question with regard to the much-sought "new thinking" with respect to "global governance", and the "governance of globalization", is whether any theory is "crazy enough" -- as may well be essential. In this light the newly announced UK initiative for high-risk innovative research, frames the question whether the requisite "craziness" will be inhibited by the same mindsets that have inhibited it previously (UK to launch £800m 'blue skies' research agency. The Guardian, 12 March 2020; Dominic Cummings calls for 'weirdos and misfits' for No 10 jobs, The Guardian, 3 January 2020).

Correspondences, analogy and metaphor as insight catalysts: Within the conventions of the various disciplines, correspondences and analogies between domains tend to be viewed with suspicion in the quest for articulations which are natural to the particular domain -- and make no reference to other domains. Of interest in this respect are the various theories of correspondences (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007). Therein, as Variations on any "theory of correspondences", the following are discussed:

  • Metaphor and analogy
  • Isomorphism
  • Homology
  • Cobordism
  • Correlation
  • General system
  • Isophor
  • Design
  • Parallelism in rhetoric
  • "Magic"
  • Symbolism
  • Archetypal psychology
  • Synaesthesia
  • Transdisciplinarity
  • Psycho-cultural equivalence
  • Mutuality of affection
  • Value-centred "equivalence"
  • Spiritual equivalence

The latter clarification was elaborated in the light of the role of correspondence in a fundamental mathematical discovery with regard to the so-called monster group (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

A valuable discussion of the related nature of analogies has been made by Douglas Hofstadter and Emmanuel Sander (Surfaces and Essences: analogy as the fuel and fire of thinking, 2013), as a further development of Hofstadter's earlier work (Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995) and an extension of his seminal work on music and self-reference (Gödel, Escher, Bach: an Eternal Golden Braid, 1979). The importance of metaphor is specifically highlighted with respect to the creativity of Albert Einstein.

Suppose therefore that, contrary to general assumptions, the early patent office procedures were indeed fundamental to Einstein's creative process, as argued separately (Einstein's Implicit Theory of Relativity - of Cognitive Property? Unexamined influence of patenting procedures, 2007). In the case of Ludwig Wittgenstein, such a seemingly "ridiculous" possibility has been extensively argued by the philosopher Susan G. Sterrett (Wittgenstein Flies a Kite: a story of models of wings and models of the world, 2006).

Biomimicry and technomimicry: These naturally follow from any understanding of correspondences and analogy. The issue of mimesis is addressed by the theoretical biologist Robert Rosen (Essays on Life Itself, 2000):

...mimetic approaches have been pursued over the years and indeed go back to prehistoric times (where they were expressed in terms of the occult notion of sympathies and embodied in "technologies" of sympathetic magic). In our own country, the same underlying concepts appear under the rubric "artificial" (as in artificial intelligence and artificial life). (pp. 132-133)

As the imitation of the models, systems, and elements of nature for the purpose of solving complex human problems, biomimetics has been fundamental to development of flight technology (Janine M. Benyus, Biomimicry: innovation inspired by nature, 2009; Akhlesh Lakhtakia, et al., Engineered Biomimicry, 2013). Technomimicry, by which one technology is developed through some degree of imitation of another, is less readily recognized in principle, however much it may be a feature of practice.

Both are a source of further insight, separately or in combination (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011; Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014).

General systems research and sympathetic magic: As noted above, the argument here is especially inspired by the approach of general systems theory, most notably promoted by Ludwig von Bertalanffy (General system theory: a new approach to unity of science, Human Biology, 23, 1951).

The quest for new insight, across the conventional boundaries by which it is inhibited, is usefully framed by an early editorial in Zygon: Journal of Religion and Science (16, 1981, 2). Zygon is interested in weaving together the multicolored strands of ideas and practices of religious traditions and the contemporary sciences. The focus of the issue, and the editorial, exploes the contemporary insights of systems theory for developing a tapestry that portrays human nature, society, and the rest of nature as a dynamic whole.

In view of this current exploration it is interesting to reflect briefly on two of the many ways in which human beings have tried to weave together different aspects of human experience, in order to feel more at home in the world and to exert some control over humans and the system of nature.

The first is the ancient idea of "imitative magic," an offshoot of "sympathetic magic" made famous by Sir James G. Frazer. This understanding of how things are related makes intelligible such diverse phenomena of tribal religion as the technology of voodoo, in which, for example, an image of a person is manipulated to control the actual person, and the various rainmaking practices, in which, for example, boulders are rolled down hills to simulate thunder or blood is dripped on the ground to assist sympathetically the natural production of rain. Similarly Elisha instructed the king to shoot arrows out of a window and then to go to strike the ground with them, in order to insure victory over the enemy (2 Kings 13:14-19). One might even wonder if sympathetic magic serves as a hidden assumption behind the Christian Lord's Supper, in which by partaking of bread and wine one enters into union with (communion) the body and blood of Jesus as the Christ.

The second way, that of scientific inquiry, has severed the type of causal connection postulated by sympathetic and imitative magic. Nonetheless, the attempt to weave out of our experiences a sense of unity that leads to some human control or influence continues in the making of analogies and the building of models by taking images or concepts from one area of experience and applying them to another. The Bohr planetary model of the atom and the billiard ball model in the kinetic theory of gases are two common, historical examples...

However, the building of models by generalizing from one area of human experience to the universe as a whole is always problematic. This is seen in the traditional problem of the relationship between the material and the mental. On the one hand, materialistic philosophies generalize physical models, developed through attempts to understand mechanistically the nonhuman aspects of the universe, to living forms. On the other hand, philosophers such as Alfred North Whitehead generalize the introspective experience of the human mind as having both a "physical" and a "mental" pole to all of existence, even to the atoms and the stars?

"Magic" may therefore be variously understood. Those skilled in any art or science are notably valued when their solutions to a challenge are described as "magic". Loosely defined, a social (or romantic) occasion is typically most highly valued if it is "magical". Some such understanding is widely promoted in marketing products and services.

As noted above, a more precise understanding of what makes such occasions magical was the focus of "natural magic" or "sympathetic magic", notably promoted by Marsilio Ficino (B. Copenhaver. Natural magic, hermetism, and occultism in early modern science, 1990) and contrasted with "demonic magic". As understood by its current practitioners (notably neo-pagans and wiccans), the "magical art of correspondences", based on an underlying theory of "correspondences", is held to be the basis of magic itself. These correspondences are considered to be hidden relationships among entities within the universe -- especially between human beings and the external world. They are understood as:

Framing an "opponent" otherwise: befriending coronavirus?

It is curious that there is so little familiarity with the range of modes through which any "other" may be framed, especially when the default is to frame the other as an "enemy". This limits the ways of thinking about the other, especially if there is urgent need for a creative remedial response to a sitation readily framed and experienced as disastrous. Discerning the variety of others is also problematic when there is an unquestioned need for an enemy and the clarity of any strategy framing eradication (Eradication as the Strategic Final Solution of the 21st Century? 2014).

The need for an enemy as a means of ensuring strategic coherence has been evident in response to the Devil, to Communism, to Socialism, to Capitalism, to Terrorism -- and now to the Coronavirus (Mark Shields, Needing an 'Enemy', Creators Syndicate, 26 August 2017; Andre Chavez, The United States' Need for an Enemy: a study of the form, function, and evolution of the necessity of opposition since 1765, GRIN Publishing, 2015; Howard F. Stein, The Indispensable Enemy and American-Soviet Relations, Ethos, 17, 1989, 4; China's Need for an Eternal Enemy, Asia Sentinel, 9 October 2006).

In his acknowledgement of the death of US national security adviser Zbigniew Brzezinski, the economist Paul Craig Roberts argues that: The most important truth of our time is that the world lives on the knife-edge of the American military/security complex's need for an enemy in order to keep profits flowing. (Zbigniew Brzezinski. Foreign Policy Journal, 3 June 2017).

Variety of "opponents", "enemies" and "challenges"? Recognition of a certain variety of "opponents" is characteristic of sports, game theory and artificial intelligence, most obviously in business and military strategy. Online game design actively seeks a greater "variety of enemies", for example. The question is whether a broader variety of "opponents" merits recognition as a source of insight into a wider variety of modes of engagement.

The question could be asked even more generally in terms of the variety of "othernesses" with which engagement might be required. Various approaches can be noted:

Cultural categories of otherness: As a challenge of perception, of some value are the variety "othernesses" distinguished by some Systems of Categories Distinguishing Cultural Biases (1993). The following systems are discussed there:

System of Magoroh Maruyama
System of Geert Hofstede
System of Kinhide Mushakoji
System of Will McWhinney
System of S Pepper
System of Mary Douglas
System of Howard Gardner
System of W T Jones
System of Emmanuel Todd

That of the philosopher W. T. Jones distinguishes seven "axes of bias".(The Romantic Syndrome: toward a new method in cultural anthropology and the history of ideas. The Hague, Martinus Nijhoff, 1961)

Enactive engagement with otherness

Each form of otherness naturally tends to evoke a particular pattern of response. The question is how to elicit new modes of response transcending the limitations of traditional patterns -- notably as may be suggest by the engagement with coronavirus. Some possibilities are discussed in the following:

Unusual possibilities, to which some may have recourse in response to coronavirus, or which may be cited as an inspiration, include the following, in no particualr order and potentially mutually entangled:

In the spirit of the argument here, these might be better configured visually, as tentatively indicated in the Venn diagram in 2D below. This has the necessary implication that the cognitive modalities variously overlap in whats which might be determined in the future. It is the underlying common experiential modality which is necessarily beyond any simple form of explication and is readily to be considered hyperdimensional. A 3D version would evoke other reflections more consistent with integrative global understanding.

Framing subtle engagement with otherness

Together or separately, these might be recognized as forms of cognitive enactivism, as separately discussed (Enveloping Development through Cognitive Enactivism: engaging with climate change by changing apprehension of climate, 2009; Cognitive Implications of Lifestyle Diseases of Rich and Poor: transforming personal entanglement with the natural environment, 2010). Response to the coronavirus pandemic, given the strategic confusion and misinformation, could be seen as variously analogous to an information disease, as speculatively explored (Memetic and Information Diseases in a Knowledge Society: speculations towards the development of cures and preventive measures, 2008).

Reframing the coronavirus to elicit new thinking

The earlier paper used the following depictions of the coronavirus as a basis for triggering imaginative reflection.

Depictions of the coronavirus
Ultrastructural morphology exhibited by coronaviruses. Note the spikes that adorn the outer surface of the virus, which impart the look of a corona surrounding the virion, when viewed electron microscopically. Images combined from a 3D medical animation, depicting the shape of coronavirus
as well as the cross-sectional view. Image shows the major elements including the
Spike S protein, HE protein, viral envelope, and helical RNA
Representation of the coronavirus in 3D Cross-sectional representation in 2D of the coronavirus in 3D Cross-sectional representation in 2D of the coronavirus in 3D
CDC/ Alissa Eckert, MS; Dan Higgins, MAM
/ Public domain
Reproduced from Wikipedia / CC BY-SA

As indicated by the subtile of the earlier paper, emphasis was placed on visual transformation of the coronavirus in order to associate with other "spiky" patterns discussed in detail there (Reimagining Coronavirus in 3D as a Metaphor of Global Society in Distress: crowning pattern that connects spiky organisms, satellite constellations, nuclear explosions, and egomania? 2020). The following is one such example in which the association with polyhedral forms was emphasized. Analogous patterns were cited there from the global form of certain plants and animals (Global "spiky-prickly" indications of a "pattern that connects", 2020).

Also noted was the tendency for viruses to take polyhedral form, as illustrated by the following image from a description of icoashedral capsids in Wikipedia.

Icosahedral form of adenovirus
Icosahedral form of adenovirus
Thomas Splettstoesser ( / CC BY-SA

It was in the light of such polyhedral configuration that it was decided to configure together the 72-spikes of the coronavirus as shown below.

Global configuration of mushroom-clouds on vertices of polyhedra -- simulating a coronavirus
72 vertices -- icosahedral symmetry (mp4; x3d) 74 vertices -- cubic symmetry (mp4; x3d)
Animation of solid variant
Screen shot of wire frame variant Animation of solid variant Screen shot of wire frame variant
Animation of global configuration of mushroom-clouds on vertices of polyhedra -- simulating a coronavirus Animation of global configuration of mushroom-clouds on vertices of polyhedra -- simulating a coronavirus Animation of global configuration of mushroom-clouds on vertices of polyhedra -- simulating a coronavirus Global configuration of mushroom-clouds on vertices of polyhedra -- simulating a coronavirus
Combination and adaptation of polyhedral and mushroom-cloud models separately prepared by Sergey Bederov of Cortona3D

The earlier paper emphasized that such global patterns of spikes, however they might be configured in polyhedral form, offered insights into psychosocial organization which could be considered analogous whether in terms of general systems theory or as mnemonic aids (Psychosocial "global implication" of a "pattern that connects"? 2020).

Dynamics of raising and lowering spikes in polyhedral configurations

The argument in what follows focuses on the possible dynamics of a global configuration of spikes as it might relate to a polyhedral configuration of edges. This possibility can best be communicated visually using animations in 3D as shown below. The dynamics might for example be compared with the raising and lowering of missiles around the globe in response to perceived levels of threat (or the lack thereof). The protective use of spikes in this way is for example evident in the quill erection of hedgehogs and porcupines. A human analogue might be recognized in the response to fear as "hair-raising". Such configurations of spikes also recall the design of naval mines and other weapons, as previously noted..

Animation of spike dynamics on selected polyhedra with 72 vertices (solid and wireframe variants)
Pentakis rhombicosidodecahedron Pentakis-snub-dodecahedron
Solid Wire Solid Wire
Polyhedral models kindly prepared by Sergey Bederov of Cortona3D, with animation timings slightly modified

As explained in the earlier paper, the information available on the coronavirus suggested a configuration of 74 spikes -- on average. That pattern is reflected in the model below. An argument was hower made for 72-spikes because of its significance in a variety of traditions and the geometric constraints of such a configuration, even in satellite constellations. That pattern is illustrated in the models above.

Animation of spike dynamics on a 6-frequency stellated geodesic sphere with 74 vertices
(solid and wireframe variants)
Animation of spike dynamics on a 6-frequency stellated geodesic sphere Animation of spike dynamics on a 6-frequency stellated geodesic sphere
Animated polyhedral model kindly prepared by Sergey Bederov of Cortona3D

As stressed in the earlier paper, of particular interest is how the "spikes" may be usefully recognized in relation to the challenges of governance. Thus they may be understood as the individual elements of a global strategy, as a configuration of global problems addressed by a global strategy. They might also be understood as the set of principles or values on which any such strategy was based -- by which it was informed. Similarly it might be understood as the set of values rendering any set of problems recognizable -- since in the absence of a value a problem is invisible and effectively non-existent.

It is from such a perspective that the manner in which a strategic configuration is ordered becomes of interest, namely how it is coordinated and rendered coherent as a whole -- in global terms. This perspective contrasts with the use of checklists to articulate strategies or sets of values. Examples are the UN's Sustainable Development Goals or the UN's Universal Declarationm pof Human Rights. Arguably, noably in the light of pandemic crisis, and others currently ignored, there is a case for some urgency in the quest for systemic coherence and new ways of thinking about it, as separately discussed (Time for Provocative Mnemonic Aids to Systemic Connectivity? Possibilities of reconciling the "headless hearts" to the "heartless heads", 2018).

Polyhedral mapping: Checklists -- as "to do" lists -- are inherently unmemorable, with little emphasis on their coherence or the manner in which they constitute a viable system. An alternative approach is to seek ways of mapping the elements of such checklists onto mind maps in 2D. The tendency is to avoid this, since there is indeed little understanding of how their elements are interrelated.

Another approach is to map the elemens onto polyhedra in 3D. Various exercises in this respect have been undertaken in the following:

Spike dynamics? Of what are the spike dynamics in the above animations suggestive? There is the obvious sense in which strategic spikes are raised in defence of integrity or in affirmation of identity -- echoing the defensive 2D pattern of "circling the wagons". Any assertive strategic declaration or set of organizational principles could be understood in 3D in this way -- although typically presented as a checklist in 2D.

Potentially of far greater interest is the complementary pattern associated with the lowering of the spikes to render explicit a polyhedral configuration. In systemic terms this can be understood as a pattern of feedback loops through which global integrity is both sustained and rendered comprehensible.

More intriguing still, as discussed further below, are the "internal" links within the body of the polyhedron -- necessarily also a feature of the pattern of feedback loops and its memorability. Are the "external" links associated with the lowered spikes to be considered more "objective" (and less controversial) than the "internal" links -- potentially more "subjective" and therefore more controversial?

The animated models above suggest many modifications in support of other reflections. Thus the spikes might be raised or lowered:

What strategic and aspirational insights might then be associated with such possibilities as a pattern language?

"Strategic priapism"? The configurations and animations offering a visual language in which to highlight both potentially excessive assertion and the absence of systemic consideration of necessary feedback loops.

The argument can be be made in terms of the proliferation of skyscrapers erected and the considerable psychological importance of having a "bigger spike" than others. This is evident within capital cities and between them. A simple mapping could for example be made of spikes onto vertices of a single polyhedron in the case of the 9-15 "Trump Towers" (with a further proposed) around the world (Aria Bendix, Here are all the Trump Towers that have been built, Business Insider, 25 January 2019). The polyhedron would then hold the set as a whole, implying a degree of global pattern coherence.

A similar visual exercise could be performed for the set of missile silos (or military bases), variously raised or lowered according to threat level. Of interest in this case is the sense in which the Permanent Members of the UN Security Council (and some other countries) each have a configuration of missile silos for the preservation of peace in the world. . The visual mapping could then be made in terms of several polyhedral forms.

Potentially more intriguing are patterns of virtual spikes associated with articulations of global strategies composed of various numbers of constituent elements, principleds or goals. These could be separately mapped onto distinctive polyhedra -- each such pattern to be recognized as a competing assertion of global intent. Especially interesting .is any recognition of the interrelationship between the spikes of a given set -- when the spikes are lowered as suggested by the animations above.

Use of "priapism" is of course provocative, and perhaps necessarily so, since the difficulty in the case of each set of spikes is that there is little recognition of the pattern they constitute when lowered. Given the promotional pressure, and the assocviated ego needs, there is little consideration of such an alternative configuration -- or of its vital role in ensuring the sustainability of the configuration. Use of the metaphor is appropriate given the manner in which it has notably been evoked in relation to the American presidency (Arnold Beichman, The President as Priapist, The Washington Examiner, 2 June 2003). As surprisingly noted by Salvatore Mangione (Physical Diagnosis Secrets, Elsevier Health Sciences, 2012):

If we look back at the American presidency, we might conclude that priapism qualifies as a White House occupational hazard, were it not for the fact that this condition is usually not associated with sexual desire. (pp. 489-490)

Symbolic configuration of disparate strategic elements?

In a section on Global connectivity as reinforced through symbolic configuration? in the previous paper, the recognized value of symbols in holding patterns of much-valued insights was noted. The question was raised regarding the requisite complexity at this time of a global configuration appropriate to the challenges of a civilization in crisis. Given the sense of a multifold crisis, seemingly simplified by the singular nature of the coronavirus pandemic, the use of the form of that virus as a clue to more complex configurations is arguable appropriate -- if only as a challenge to reflection.

By how many elements is it appropriate to assume that the global crisis is characterized at this time? The UN found it appropriate to shift from the 8-fold set of Millennium Development Goals (2000) to a 16(+1) fold set of Sustainable Development Goals (2016). Other reputable reports have proposed 14, 15, 16 and the like.***. None of these is organized in systemic terms, such as to highlight the interrelationships between their elements -- or to explain how different groups could favour different configurations, thereby undermining emergence of the global strategic coherence to which they each purport to aspire. Can it honestly be claimed that these articulations of strategic insight are adequate in a period of crisis with whose emergence the thinking they embody has been associated?

As a provocation, however controversial, there is therefore a case for exploring traditional configurations, which dare to imagine the need for higher numbers of focal preoccupations -- and which seek ways to render their configurations coherent and memorable. As noted above, the range of potential connotations of value, mathematical and otherwise, is usefully suggested Wikipedia (72 (number))

Traditional "Western" configuration: Any such pattern of coherence lends itself to further speculative exploration (Engaging with Hyperreality through Demonique and Angelique? Mnemonic clues to global governance from mathematical theology and hyperbolic tessellation, 2016). The following was developed from an argument there regarding an experiment in Hyperbolic reframing of the Demonique and Angelique of tradition. This has the merit of reflecting the qualitative distinctions in a pattern of 72, whereas the global configurations of spikes above only do so in terms of their geometrical orientation around the sphere.

The contrasting patterns help to frame reflection on whether the values, aspirations and strategies of humanity can be understood as encoded in the extensive reflection on a configuration of "angels" -- as noted in the discussiion giving rise to themapping. The "demons" to which they are opposed could be similarly seen as represented a corresponding configuration of sigils by which the "demonic forces" are understood to be bound or held in check. Modern termoinologhy would of course prefer a more neutral reference to "positive" and "negative" respectively -- although remarkably unwilling to articular the variety of positive or negatives forces from a strategic perspective.

Indication in 2D of the dynamic nature of a "hyperdimensional" crown-corona
Alternative experimental configurations alternating between the 72 angels and demons
Animation of 8 sets of 9
(enlargements for detail: angels / demons)
Animation of 9 sets of 8
(enlargements for detail: angels / demons)
Experimental configuration alternating between the 72 angels and demons Experimental configuration alternating between the 72 angels and demons
The allocation of sets to the star "tables" in the above schematics is based on the tabular form in which the 72 angel names (from the Shemhamphorasch) and the72 demonic sigils (from the Ars Goetia) are typically presented. The rows are presented "around the tables" in one schematic, and the columns are presented "around the tables" in the other. The sequence around the tables is questionable, demanding further consideration.

The question is how those configurations might be rendered comprehensible otherwise, inspired by the polyhedral form of the coronavirus --with its implications for systemic ordering vital to its integrity. The approach explored below for the model is to increase the width of the spikes and to place the symbols above on the ends, as shown below. .

Indication in 3D of the dynamic nature of a "hyperdimensional" crown-corona
3D Configuration of "positive forces " as 72 "Angel names" 3D Configuration of "negative forces " as 72 "Demonic sigils"
3D Configuration of   positive forces as 72 Angel names 3D Configuration of  negative forces as 72 Demonic sigils

Traditional "Eastern" configuration: Of corresponding relevance is the articulation of Chinese culture in the 64-fold pattern of hexagrams of the I Ching. An earlier circular configuration in 2D confirmed the reflection of  Gottfried Leibniz in inventing the binary coding system in 1689 -- now so fundamental to computing.

As presented on the right below, particular transformations between conditions of change, as denoted by the hexagrams, are indicated according to that coding system. Interpretative descriptions of each are provided separately. As a pattern indicative of a dynamic understanding of unity, it lends itself to experimental animations, as described separately (Dynamic Exploration of Value Configurations: interrelating traditional cultural symbols through animation, 2008). One variant is accessible in video format (Relating cultural symbols using dynamic I Ching configuration, YouTube).

Examples of circular configurations of 64 I Ching hexagrams
As communicated to Leibniz (1703) Indicating transformations between conditions
Circular configurations of 64 I Ching hexagrams Circular configurations of 64 I Ching hexagrams
By Unknown - Perkins, Franklin. Leibniz and China:
a commerce of light
. Cambridge UP, 2004. 117., Public Domain, Link
As used on this website, for which it was elaborated;
further details of the configuration are provided separately

Of relevance to the polyhedral approach adovcated here, the question is whether any such mapping can be fruitfully configured in 3D, as discussed separately (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015)

The pattern of 64 is nearly unique within that polyhedral context. However one interesting candidate is the toroidal drilled truncated cube with 64 edges -- with which any set of 64 elements could be associated. The issue is whether the manner in which they can be positioned on that framework constitutes a configuration which is meaningful in relation to particular cases, such as the codons or the hexagrams. Furthermore, is it possible that known constraints in the patterning in such particular cases can together offer guidance in the attribution of the distinct elements -- of relevance to each case?

Preliminary experiments with this polyhedron have been undertaken previously with respect to the hexagrams alone -- but only to get a sense of the possibility, as a "proof of concept" (Enabling Wisdom Dynamically within Intertwined Tori: Requisite resonance in global knowledge architecture, 2012). To be emphasized is the degree to which the Chinese codiing system is complemented by a detailed pattern of metaphors through which distinctions between the 64 elements are made, as well as the meaning which can be associated between the transformations between them -- inviting a variety of patterns of interpretation of relevance to governance (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). Again it should be emphasized that no comparable patterns have been articulated in memorable terms between the elements of sets of global strategies.

Drilled truncated cube of 64 edges with random attribution of hexagram names
(reproduced from Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012)

Selected faces transparent All faces transparent
Drilled truncated cube of 64 edges with hexagram names Drilled truncated cube of 64 edges with hexagram names
Animations generated with Stella Polyhedron Navigator

Possible use of this form as a means of interrelating genetic codons is illustrated by the following.

Drilled truncated cube of 64 edges with random attribution of codon combinations
Animation with faces non-transparent Animation with faces transparent
Drilled truncated cube Drilled truncated cube
Animations generated with Stella Polyhedron Navigator

The juxtaposition above immediately raises the questions:

Illustration of geometric model changing between two possible capsids. A similar change of size has been observed as the result of a single amino-acid mutation ***

Patterns of systemic relationship from an "internal" perspective

The "superfcial: features of polyhedra, as characteristic of the animations above, literally obscure their internal complexity and its roles in ensuring their integrity -- and the sustainability of any mappings for which they are used. This is highlighted by the wireframe variant of the animations below/

Animation of small stellated dodecahedron 5+1 with 72 vertices (solid and wireframe variants)
Animation of small stellated dodecahedron 5+1 with 72 vertices Animation of small stellated dodecahedron 5+1 with 72 vertices
Animations generated with Stella Polyhedron Navigator

The argument can be presented other wisethrough exercises in mapping those insights which readily feature in global discourse. This can be suggested by the following "mind maps" -- both being suggestive of a need for a more comprehensive effort to interrelate insights of that nature.

Systemic map relating hope-mongering/doom-mongering to known/unknowns Indication of systemic relationships framing Refugees per Kiloton (tentative)
Systemic map relating hope-mongering/doom-mongering to known/unknowns Indication of systemic relationships framing  Refugees per Kiloton
Reproduced from Towards a bigger tent: recognizing responsible time horizons in cyclic terms? (2015) Reproduced from Evaluating the Grossness of Gross Domestic Product (2016)

Distinguishing coherent patterns of strategic N-foldness -- from 8-fold to 80-fold

The argument development here was partly inspired by the polyhedral form of many viruses. The variety is usefully illustrated by the following image in which they asre distinguished in terms of a triangulation number ("T-number").. The T-number is representative of the size and complexity of viral capsids (List of geodesic polyhedra and Goldberg polyhedra, Wikipedia).

Spherical capsids of various sizes are composed of 12 pentamers (represented as darkened pentagons) and a variable number of hexamers.
Ranjan V. Mannige and Charles L. Brooks III / CC BY

The mysterious question, as yet to be clarified, is why sets of strategies are constituted by authorities and experts (without comment or justification) by particular numbers of elements, exemplified by the UN's 8 Millennium Development Goals and the 16(+1) Sustainable Development Goals. The issue can be explored more generally (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980). The clearest approach to an explanation, itself controversial, is that of cognitive psychologist George Lakoff (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001).

The organization of viruses, as noted above, focuses on triangulation to which consideration is given separately (Triangulation of Incommensurable Concepts for Global Configuration, 2011). An exercise of interest here focuses on the 8-fold pattern as evident in both the UN's sets of goals (8 and 2x8) and in the more complex traditional configurations above (8x8 and 9x8). In the case of the Sustainable Development Goals, these are defined as having 169 "targets", with various numbers of targets per goals (see checklist), together with an associated set of some 230 indicators.

Polyhedral forms potentially valuable to comprehension of "factor-8" preferences and memorability of N-fold global strategies
(animations in preparation)
8 16 24 32 40

Is it a mere coincidence that 169 is 13x13 or is there some unexplored systemic significance to that? Some commentary is evident in the Final list of proposed Sustainable Development Goal indicators (E/CN.3/2016/2/Rev.1)) as developed by the Inter-Agency and Expert Group on SDG Indicators (IAEG-SDGs) noting that the list is composed of distinct 230 indicators. In the absence of clarification of this "to do" list, is the cognitive challenge of recogntion of this range from 169 to 230 to be compared to Dunbar's number. This is a suggested cognitive limit to the number of people with whom a person can maintain stable social relationships. Proponents assert that numbers larger than this generally require more restrictive rules, laws, and enforced norms to maintain a stable, cohesive group. It has been proposed to lie between 100 and 250, with a commonly used value of 150 (Comprehension of Numbers Challenging Global Civilization: number games people play for survival, 2014)

Global plan, doughnut, torus, helix and/or pineapple?

In response to the chaos of coronavirus and its expected aftermath, there is widespread quest for a "plan" (Selman Gebrekidan, The World Has a Plan to Fight Coronavirus, The New York Times, 12 March 2020; Ari Schulman, What's the Plan? Yes, the Covid-19 shutdown is necessary -- but it won't work without a vision of how it ends, The New Atlantis, 21 March 2020),). This is now being articulated in terms of a "Global Marshall Plan" (Isabel Silva, A new Marshall plan? MEPs debate coronavirus response, Euronews, 26 March 2020; OECD Secretary-General: coronavirus "war" demands joint action, 21 March 2020). The latter Commits policy support, saying efforts must have "Ambition of Marshall Plan, vision of New Deal"

Possibilities for an appropriate global strategic form, in the light of the above argument, are developed in a subsequent discussion (Coronavirus -- Global Plan, Doughnut, Torus, Helix and/or Pineapple? Zome modelling dynamics allowing for uncertainty in perception of order in governance? 2020).


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