Dynamics of raising and lowering spikes in polyhedral configurations

Cognitive Engagement with Spike Dynamics of a Polyhedral Coronavirus (Part #6)

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)

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:

Experimental Visualization of Dynamics of the European Parliament in 3D (2019)
Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful (2017)
Envisaging NATO Otherwise -- in 3D and 4D? (2017)
Eliciting Memorable Spheres and Polyhedra from Hyperspace (2015)
Metascience Enabling Upgrades to the Scientific Process: beyond Science 2.0 in the light of polyhedral metaphors? (2014)
Coherent Value Frameworks: Pillar-ization, Polarization and Polyhedral frames of reference (2008)

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:

independently and randomly
in groups, such as might be suggested by the mode of locomition of sea urchins
to different heights, with some spikes being of greater length thasn others
rythmically
with distinctive coloration
such as to focus internally rsther than externally

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)