Cyclic dynamic of emergent order versus States of emergency ordered spasmodically

Global Challenge of the Global Challenge (Part #10)

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Cycles of inter-transforming polyhedra? Following Stafford Beer, an interesting assumption with respect to polyhedra could be that the edges are indicative of transactions, lines of communication, or systemic conceptual relationships. Rather than assuming an institutional need to move from a primitive early stage (egg or chrysalis) to a final desirable later stage (butterfly), each stage may be valued for its particular strategic advantages in a continuing cycle.

The question is then how to understand the phase transitions between the stages -- as helpfully rendered comprehensible in the case of sets of polyhedral shapes. The cycle of shapes may then be understood in terms of a dynamic toroidal container for the succession of phases. The number of such phases to be distinguished is a matter for future exploration. In the examples below the focus is on the "regular" Platonic polyhedra and the "semi-regular" Archimedean polyhedra -- each constituting a particular approximation to spherical, understood as "global".

Cycling of polyhedra between phases contained by a torus (indicative animations)
5 Platonic polyhedral phases	13 Archimedean polyhedral phases

Dynamic justaposition of tori: The argument may be taken further by interrelating the separate cycles above, each contained there within a separate torus. In the animation below (far left), the 5-fold cycle is positioned within a smaller torus above a larger torus holding the 13-fold pattern -- viewed in cross-section showing the different polyhedral forms emerging periodically. Some provisional degree of complementarity between the dynamics of the Platonic and Archimedean variants derives from a table by Keith Critchlow (Order in Space, 1969).

The juxtaposition of the tori frames a 3D heart pattern variously evident in the two central animations, as discussed separately (Cognitive heart dynamics framed by two tori in 3D). The animation on the far right presents the two tori in an interlocking dynamic, also discussed separately (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006).

Animations indicative of possibilities of packing global complexity comprehensibly
Superposition of 2 tori with circulating polyhedra (outlining a 3D heart pattern)	Possible complex dynamics between superpositioned tori	Possible multi-level "stacking" of counter-rotating tori (multiple 3D heart patterns)	Alternative interlocking dynamics of two tori
Combination of separate animations above (viewed in cross-section)	Adaptation, with permission, of animation by Wolfgang Daeumler (Horn Torus)	Adaptation of X3D and VRML models (kindly prepared by Sergey Bederov of Cortona3D	X3D and VRML models (kindly developed by Sergey Bederov of Cortona3D).

As indicated below, further possibilities of this nature are considered separately (Psychosocial Implication in Polyhedral Animations in 3D: patterns of change suggested by nesting, packing, and transforming symmetrical polyhedra, 2015; Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? 2015).

Configuration in three dimensions of Platonic and Archimedean polyhedra (indicative animations)
4 Platonic polyhedra configured around tetrahedron	12 Archimedean polyhedra configured around truncated tetrahedron
Animations prepared using Stella Polyhedron Navigator

Periodic emergence versus Periodic emergency: Understood otherwise, in dynamic terms, the animations above suggestive ways of thinking about contrasting shapes and modes of organization emerging periodically from a more fundamental pattern. The "new shape" is then to be found in the periodic pattern rather than in any particular shape emerging for a period over time. Such potential emergence recalls the argument for a potential configuration (Wanted: New Types of Social Entity: the role of the "potential association", 1971).

There is a curious relation to be explored between an "emergency" and the process of emergent response, most notably through "emergency plans" elaborated in terms of "emergency prepardeness" in an effort to anticipate surprises calling for emergency management. In a period of unrelenting crises, the argument here effectively focuses on the capacity to respond to the challenges of governance through emergent reordering of structures and communication channels -- readily enabled (in principle) by information systems.

Rather than the focus on spasmodically ordering a state of emergency, the focus is then on the cyclic pattern within which order emerges as appropriate. The question is the number and variety of the plans considered appropriate to an emergency, and the conditions under which they are variously activated and deactivated. Of particular interest in a period of continuing crisis is the duration of any state of emergency, as well as the number and variety of such states that have been declared.

The current situation is further complicated by recognition of a degree of "threat level" requiring a "readiness condition" which may endure for some time -- if not permanently. For example, five graduated levels of readiness (or states of alert) are specified for the U.S. military within the DEFCON system: from 5 (least severe) to 1 (most severe). Similar systems exist in other countries. Curiously their determination is primarily influence by the immediacy of the threat rather than any catastrophic eventiality in the longer term. In this sense the eventual disaster of climate change or resource exhaustion are treated as comparable to detection of an asteroid calculated to strike the planet decades in the future. These do not register as "threats" calling for emergency response.

Morphogenesis: The toroidal animation of forms presented above is consistent with the depiction (below left) of the distinction of only four phases of emergency management. This can be usefully contrasted with familar understanding of the life cycle of a "butterfly" and its implications for the complex subtlety of psychosocial morphogenesis (Enabling morphogenesis and transformation through catastrophic questioning, 2013; René Thom, Structural Stability and Morphogenesis, 1972).

Contrasting understendings of "emergency" and "emergent"
Cycle of phases in emergency management	What is the "shape" of a "butterfly"?
Reproduced from Wikipedia	Cyclic combination of images above

Given increasing recognition of the insights from biomimetics, what might be learned from a butterfly about the governance of morphogenesis?

Could this be fruitfully informed by reflection on the famous Chinese tale of the butterfly dream of Chuang Tzu -- wondering if he was a man who dreamed of being a butterfly or a butterfly dreaming of being a man? Many dramas highlighting the theme of transformation have been written about the tale (Kuang-Ming Wu, The Butterfly as Companion: meditations on the first three chapters of the Chuang Tzu, SUNY, 1990).

With respect to governance of morphogeneiss, an appropriate contrast can be made with respect to many transformations in geometry (as an "explicate order") -- possibly to be recognized as "tinkering" -- and the dynamic of underlying holomovement characteristic of an "implicate order", as articulated by David Bohm (Wholeness and the Implicate Order, 1980; Explicate and implicate order). As noted in the former (p. 202):

In the interests of clarity, we shall therefore reserve the word transformation to describe a simple geometric change within a given explicate order. What happens in the broader context of implicate order we shall then call a metamorphosis. This word indicates that the change is much more radical than the change of position of orientation of a rigid body, and that it is in certain ways more like the changes from caterpillar to butterfly (in which everything alters in a thorough going manner while some subtle and highly implicit features remain invariant).

Nesting alternative shapes approximating to "global": Rather than understanding alternative shapes to be cycling "through" a torus, or configured "around" a "seminal" or "foundational" shape (as above), they can be understood as nested in relation to one another -- as with the potential forms of a "butterfly" in process of metamorphosis. As an animation in virtual reality, that on the left (below) offers a suggestive "pumping" dynamic, usefully compared with the original inspiration of Johannes Kepler on the right. The latter is perhaps to be more fruitfully understood as a "global" understanding of the solar system..

Nesting 5 Platonic polyhedra octahedron, icosahedron, dodecahedron, tetrahedron, cube (Version as video animation of "pumping" action (.mov); access to X3D variant)
Rhombic Triacontahedron (green) as a nesting framework (virtual reality variants static: vrml or x3d; mutual rotation: vrml or x3d; "pumping": vrml or x3d; videos: "pumping" mp4; "rotation" mp4)	Polyhedral model of solar system of Johannes Kepler in Mysterium Cosmographicum (1596)
Developed with X3D Edit and Stella Polyhedron Navigator	Reproduced from Wikipedia entry

The animation on the left is discussed separately in more detail (Nesting polyhedra to enable comparison of patterns of discourse, 2015; Relative movement of nested Platonic polyhedra: pumping and rotation, 2015). The latter introduces more complex animations of significance to global comprehension (Rotation and pumping of nested Chinese "puzzle balls" as symbolizing "worlds-within-worlds", 2015)

Cognitive embodiment of globality? The "pumping" dynamic in the nesting animation on the left (above) suggests an understanding of the emergence of different patterns of order -- their "explication" or unfoldment -- from an inner implicate order. This process can be related to understandings of the embodiment of mind, as articulated by George Lakoff and Mark Johnson (Philosophy In The Flesh: the embodied mind and its challenge to Western thought, 1999), and other authors, as discussed separately (Embodiment of Change: Comprehension, Traction and Impact? 2011; Inplanation: multiversal embodiment through the Ouroboros, 2012; Embodying topological succinctness beyond questions, 2014; ¿ Embodying a Way Round Pointlessness ? 2012).

As with the insights into transformation derived from the butterfly dream of Chuang Tzu, both the nesting and the pumping dynamic are indicative of understandings of globality as both "outside" (namely explicate) and "inside" (namely implicate) -- a paradox fundamental to its comprehension (World Introversion through Paracycling: global potential for living sustainably "outside-inside", 2013). As a 4-dimensional process (at least), the 3D depictions in terms of a torus, and the nested variant, are better recognized as cognitively conflated.

The challenge of comprehension can be explored in relation to the "doughnut" of Oxfam (Exploring the Hidden Mysteries of Oxfam's Doughnut: recognizing the systemic negligence of an Earth Summit, 2012). The following animation of Hathor in the Egyptian then offers a provocative representation of the requisite cognitive dynamic. This suggests a strategic "third eye" of sustainability through a mythological complement to the Eye of Horus in that tradition, especially in the light of its symbolic importance in that era (Recognition of the Oxfam doughnut as a strategic "eye" for the "vision" of governance, 2012). The Oxfam doughnut has been incorporated there into a cycle, previously presented and discussed in simpler form (Embodiment of Identity in Conscious Creativity: challenge of encompassing "con", 2011). The subtitle of that document emphasizes the necessary cognitive vigilance to transcend the confidence games so typical of conventional approaches to strategic governance.

In quest of mnemonic catalysts using animations
Eye of Horus as suggestive of left-wing strategic oversight?	Hathor as suggestive of transcendent insight?	Eye of Horus as suggestive of right-wing strategic oversight?

Antifragility and Resilience? It is of course the case that there is a basic strategic preference for a particular shape as framework for regular (habitual) processes. It is this preference that is being called into question by the current period and its "surprises", as noted above in the description by Nassim Nicholas Taleb (The Black Swan: the impact of the highly improbable, 2007).

Of further relevance however is the sense in which a cycle of phase transitions may be understood as a shift from one mode of order to another -- and as such may be understood as "disorderly", or dependent on a disorderly transition. It is in this sense that "antifragility" of any particular shape is relevant, as recognized in the subsequent argument of Nassim Nicholas Taleb (Antifragile: Things That Gain from Disorder, 2012).

As suggested by the animations above, order is to be found at a higher level -- through the cycle framed by the implied torus -- rather than with respect to the requisite instability of the order of any particular phase. The principle of cybernetics relating to requisite variety of particular forms could merit generalization to include recognition of their requisite instability in dynamic systems terms.

This understanding is consistent with arguments for resilience and the adaptive cycle (Thomas Homer-Dixon, The Upside of Down: catastrophe, creativity, and the renewal of civilization, 2006; Judith Rodin, The Resilience Dividend: managing disruption, avoiding diaster, and growing stronger in an unpredictable world, 2015).

Designing "on the fly": A further consideration lies in recognition that in time of crisis a singular shape cannot be fruitfully designed in abstraction. In a sense it is partly engendered by the dynamics of the crisis and the responses to it. Mixing metaphors, the challenge is to enable the new by designing "on the fly". A remarkable example of this is provided by the science fiction account of engendering a space-time ship whose stability required that it be piloted during the process, with the aid of advanced game-playing techniques (M. A. Foster, The Gameplayers of Zan, 1977).

Global challenge of dynamics toroidally framed: The interaction between global and toroidal forms is remarkably illustrated by the following animation. An innovative response to the "global" challenge can then be seen as severely inhibited by preoccupation with a particular spherical phase in that cycle -- typically understood in static terms.

Torus-Sphere Transformation (animation)

Reproduced from Wikipedia; made by User:Kieff

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