Knightly journeys in quest of global sustainability (and immortality)

Implication of the 12 Knights in any Strategic Round Table (Part #7)

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Constraining implications of 12-foldness: One approach to these questions -- from a systemic perspective -- is to return to the constraint of 12-foldness and the geometry this may imply. Aspects of this approach have received considerable attention from Arthur Young (Geometry of Meaning, 1976) and from R. Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975).

Fuller offers greater insight in terms of geometrical complexity, as discussed separately (Geometry of Thinking for Sustainable Global Governance, 2009). Young offers greater insight in terms of distinctive functionality, as variously suggested (Characteristics of phases in 12-phase learning-action cycle, 1998; Typology of 12 complementary strategies essential to sustainable development, 1998). From a cybernetic perspective, both are complemented by the work on syntegrity of Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994) as variously summarized (Allenna D. Leonard, Team Syntegrity Background. 2002; J. Truss, et al., The Coherent Architecture of Team Syntegrity: from small to mega forms, 2003).

Spherically symmetrical polyhedra: With respect to geometry, the issue is how a 12-fold pattern might be represented -- beyond the integrative implications of the traditional round table. The approaches of Fuller and Beer are especially significant in highlighting the nature of globality through their reference to spherically symmetrical polyhedra. It is then appropriate to suggest that the Knights travel variously around a spherically symmetrical polyhedron -- a virtual form indicative of functional globality. The distinct patterns of their journeys -- with their interweavings and consequent learnings -- might then be recognized in terms of distinct polyhedra. This argument has been highlighted in considering the relevance of polyhedral mappings to governance (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008)

The argument can be taken further in functional terms if it is assumed, as argued by Beer, that it is such configurations which are of cybernetic significance. Global forms onto which the 12 Knights, and their journeys, might be mapped then include the following.

Icosahedron with 12 vertices (Images generated by Stella Polyhedron Navigator)
Icosahedron folded into global form	Icosahedron unfolded into flat form

In the above case the Knights could be explicitly associated with distinct vertices. Whereas in the following case they could be associated with the domains represented by the distinct faces -- with a Knight located virtually at the centre of each face.

Dodecahedron with 12 faces
Dodecahedron folded into global form	Dodecahedron unfolded into flat form

Beer focused his cybernetic argument on the icosidodecahedron with 32 faces (of two types), 60 edges, and 30 vertices -- emphasizing the variety that could be associated with the vertices. The cube and octahedron (Platonic forms like the icosahedron and the dodecahedron) each have 12 edges. Restricting the focus here to the more fundamental Platonic forms, the pattern is as follows.

Pattern of characteristics of the set of spherically symmetrical Platonic forms
	Tetrahedron	Cube	Octahedron	Dodecahedron	Icosahedron
Edges	6	12	12	30	30
Faces	4	6	8	12	20
Vertices	4	8	6	20	12
Total	14	26	26	62	62

Great circle pathways: One possibility is then to assume that the quest of any one Knight is delineated (or mapped) by the great circle pathways around such polyhedra -- with which a vertex or face is associated (according to the form selected for the mapping). The explicit "linearity" of the journey may however be broken (or take implicit form) -- as when a face must be "crossed", perhaps to be understood as requiring an explicit diversion around the edges of that face in order to get back onto the circular pathway.

Here the circularity of the path -- and the closure with which it is associated -- is suggestive of an integrative journey circumscribing the whole and returning to the point of departure. With respect to any knightly quest, this recalls the poetic lines of T. S. Eliot: We shall not cease from exploration / And the end of all our exploring / Will be to arrive where we started / And know it for the first time.(Little Gidding, 1942).

Distinguishing the global knightly journeys in terms of the set of spherically symmetrical Platonic forms
	Tetrahedron	Cube	Octahedron	Dodecahedron	Icosahedron
Journey pathways	6	12	12	30	30
sub-global journeys (strategic quests)	4 disparate sub-global (3-phase) journeys imply 12-foldness only through their bidirectionality -- but with each phase common to 2 domains	8 disparate sub-global (4-phase) journeys imply 12-foldness through their unique directionality -- but with each phase common to 2 domains	8 disparate sub-global (3-phase) journeys imply 12-foldness through their unique directionality -- but with each phase common to 2 domains	12 disparate sub-global (5-phase) journeys expess 12-foldness through their implicit common focus delineating a domain of unique orientation -- but with each phase common to 2 domains	20 disparate sub-global (3-phase) journeys express 12-foldness through their explicit junction points between 5 distinct global journeys -- but with each phase common to 2 domains
global journeys (strategic quests)	3 global journeys, in each of which only one phase is explicit, separated by 2 intermediary diversions between other domains	4 global journeys, each with two contrasting phases, separated by 2 intermediary diversions between other domains	4 global journeys, each with two contrasting phases, separated by 2 intermediary diversions between other domains	5 global journeys journeys, each with two contrasting phases, separated by 4 intermediary diversions between other domains	5 global journeys journeys, each with two contrasting phases, separated by 2 intermediary diversions between other domains.
Unique domains (orientation / identity)	4	6	8	12	20
	12-foldness is expressed through the conflation of 4 orientations (with implicit central identities)	12-foldness is expressed through the conflation of 2 parallel orientations (with implicit central identities)	12-foldness is expressed through the conflation of 3 orientations (with implicit central identities)	12-foldness is expressed explicitly through the 12 distinct orientations (with implicit central identities)
Unique perspectives (worldview)	4	8	6	20	12
	each perspective conflates 3 orientations and implicit worldviews to express 12-foldness				12-foldness is explicitly expressed by the junction points between the 5 global journeys

Non-linearity of journeys: The non-linearity of such knightly quests, and its importance in ensuring strategic continuity and coherence, recalls the importance attached to so-called Knight's move thinking in chess, and the equivalent in the game of go (Predictability and pattern-breaking: the Knight's move, 2011; Knight's move thinking: appreciated or deprecated, 2012; Insights from Knight's move thinking, 2012; Alternative representations: Knight's move, Swastika and BaGua ? 2012; Stratagems and ploys characteristic of Knight's move thinking, 2012).

As noted in those discussions, there is great irony to the fact that knight's move thinking is considered to be a thought disorder in medical practice, denoting a lack of connection between ideas as being indicative of illogical loosening of associations (Knight's move thinking, General Practice Notebook). This contrasts with its other uses as a metaphor for the much valued capacity to perceive relevant connectivity despite the unexpected and illogical. A knight figures prominently for that reason in many insignia and badges of the U.S. Military Intelligence Corps -- whom only political activists would characterize as suffering from a pathological thought disorder.

The ambiguity variously associated with illogicality, non-linearity and recognition of a higher order of connectivity (than is implied by "orderly" conventional thinking) suggests that the quests of the knights merit consideration in those terms. This is especially the case if interpreted with respect to globality, collective sustainability and personal immortality in their most integrative sense. Of relevance is any premature closure on a "holy grail" in the light of the argument of Paul Prew (The 21st Century World-Ecosystem: systemic collapse or transition to a new dissipative structure? 2003):

If social sciences are to advance, they must relinquish their hopes of scientific credibility in their quest for the holy grail of linear causality and begin reorienting research to include the ideas being generated in what has been called the "new sciences".

The concern has been articulated otherwise by Henry Mintzberg (The Rise and Fall of Strategic Planning, 1994). He concludes that strategy cannot be planned because planning is about analysis, whereas strategy is about synthesis. Prew notes similar arguments by Richard E. Lee (Imagining the Future: Constructing Social Knowledge after "Complexity Studies", 1998)

The point may be suggestively made otherwise in that the Knights of the Round Table are considered the exemplars of the medieval knight-errant who wandered the land in search of adventures to prove hischivalricvirtues, either in knightly duels (pas d'armes) or in pursuit ofcourtly love. Whilst "errant" may be associated with wandering, it is also suggestive of a pattern of "error-making" meriting appreciation, as argued by Donald N. Michael in terms of the "requirement for embracing error" (On Learning to Plan and Planning to Learn, 1973):

More bluntly, future-responsive societal learning makes it necessary for individuals and organizations to embrace error. It is the only way to ensure a shared self-consciousness about limited theory to the nature of social dynamics, about limited data for testing theory, and hence about our limited ability to control our situation well enough to be successful more often than not.

The argument might be extended to the appreciation of the challenges that humanity has engendered (Celebrating the Value of Deadly Problems Worldwide, 2008).

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