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Containing the deadly question driving the quest
Implication of the 12 Knights in any Strategic Round Table (Part #13)
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Use of "round table" implies a quest. This in turn implies a "question" of some form, namely something for which an answer is felt to be required. In modern terms, question and answer may well be recognized in terms of problem and solution -- especially in relation issues of global governance. In any mythical context, the problem may take the form of a puzzle or a riddle. It can be argued that the challenge of global governance is characterized by a complex puzzle, poorly defined -- perhaps better understood as a challenge to the nature and process of conventional definition and the consensus it is believed to require. Reference may well be made to a complex of dilemmas for which a key may be desperately sought (Configuring Strategic Dilemmas in Intersectoral Dialogue, 1992).
These elements, confusions and associated illusions, are usefully dramatized in the tale of The Quest of the Holy Grail. The ancient Celtic myth, which Matarasso notes underlies that tale, has as key features the extraordinary dangers of the quest and the key question to be asked in order to heal the king and to free the kingdom from its enchantments.
In the dynamics of a round table, it is therefore valuable to explore how an underlying "question" determines and engenders the "quest" of the participants. This is especially the case if a key to the redeeming nature of the "answer" lies in how that "question" is understood. It is appropriate to note that in modern round table processes the question and quest may be variously conflated with assumptions about the nature of a required answer. This framing may obscure the challenge to comprehension typically characterized by a riddle or a puzzle. Participants may variously believe that they already have the answer -- if only others would subscribe to it.
Such an assumption constrains the dynamic by implying that a participant has already "got it" -- namely is in possession of the answer. The transformative danger of the implicit question may then only be experienced to a degree in the form of disagreement amongst the participants -- a dynamic which may well be considered as unfortunate and best designed out by suitable facilitation. The tale offers clues to the engagement with the "pre-emergent" question -- challenging prior belief and the sense of identity.
Framed in this way, with the "answer" as possession of the Holy Grail -- understood to be the goal of the quest -- the answer is then itself problematic . The tale challenges the possibility of any conventional capacity to possess it -- even to "grasp it" (Beyond Harassment of Reality and Grasping Future Possibilities: learnings from sexual harassment as a metaphor, 1996; Paradoxes of Engaging with the Ultimate in any Guise: living life penultimately. 2012). Sustainability merits consideration in that light. Implications that the Grail may take the form of some kind of container can then be interpreted as indicative of the possibility that sustainability itself may require an unusual form of container. Insights from the design of nuclear fusion reactors are suggestive in this respect, as separately argued (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006).
As one form of container, there is the further possibility that the very form of a round table may be usefully challenged by an appropriately "deadly" question, as separately argued (World Futures Conference as Catastrophic Question: from performance to morphogenesis and transformation, 2013).
In reflecting on the possible nature of a "spherical round table", the geometrical argument above can be taken further in the light of the challenge of sphere packing -- understood as the spherical arrangement of the distinctive cognitive significance of the 12 Knights. This can be represented by the following image derived from Keith Critchlow (Order in Space: a design source book, 1969, p. 39). Here 12 of the Archimedean polyhedra are arranged in their most regular pattern, a cuboctahedron, around a truncated tetrahedron -- the latter two completing the total of 14 such polyhedra (as discussed in Union of Intelligible Associations: remembering dynamic identity through a dodecameral mind, 2005).
| Cuboctahedral configuration of Archimedean polyhedra |
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Arrows indicate the succession of truncations from 1 to 6 in each case. | |
Successive truncations of octahedron | Successive truncations of icosahedron |
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Each element of the configuration above can be considered as implying a question -- of which an associated Knight is bearer or embodiment through his "problematic" behaviour. The polyhedra each offer a basis for distinctive cognitive mappings -- perhaps to be compared to metabolic pathways. The dynamic relationship between the polyhedra has been extensively explored by Buckminster Fuller through the cuboctahedron -- which he termed the vector equilibrium (now an inspiration for various explorations). The "truncations" might be interpreted as forms of cognitive reductionism.
In the light of the argument above, it is useful to contrast, as "containers" in the following pair of images, the 2-dimensional, 12-fold round table with that of the 3-dimensional cuboctahedron -- the vector equilibirum indicated above. Of particular interest is how the 4 3-fold and 3 4-fold patterns are represented in the 2-dimensional case and then "expanded" from that "flattened" conflation into an articulation as 8 3-fold and 6 4-fold in the 3-dimensional form.
| 12-fold pattern distinguishing the 4 3-fold and the 3 4-fold constitutive patterns | |
| In 2-dimensions (typical of zodiacal representations) | In 3-dimensions (as a vector equilibrium) |
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Arthur Young (1976), as developer of the Bell helicopter, devoted considerable attention to the 2-dimensional pattern and its mnemonic relationship to the zodiac -- in his quest for a "psychopter", as discussed separately (Engendering a Psychopter through Biomimicry and Technomimicry, 2011). Buckminster Fuller focused on the 3-dimensional cuboctahedron and its phases of transformation (Vector Equilibrium and its Transformation Pathways, 1980). Of particular interest is the twisting nature of that transformation and its potential cognitive significance (Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004; Twistedness in Psycho-social Systems: challenge to logic, morality, leadership and personal development, 2004).
| Great circle pathways relating 12 "knights" on cuboctahedron | |
| Circles distinguished by pathway colour (without distinguishing directionality) | Circles distinguished by arrow colour (assumptions made regarding directionality) |
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The following images present the cuboctahedron unfolded as a 2-dimensional net -- and partially folded into the 3-dimensional form depicted above. Folding the map combines external features.
| Use of cuboctahedron as a concept map relating the 12 "knights" and their journeys | |
| Cuboctahedron as unfolded net | Cuboctahedron net partially folded |
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There is of course the possibility of using more complex forms onto which to map even more detailed articulations of "knights" and their "journeys", as discussed and illustrated separately (Topological Clues to a Memorable 12-fold Systemic Pattern, 2011). One especially interesting form is the drilled truncated cube -- one of the Stewart Toroids (Cognitive implication of drilled toroids, 2011). This has 32 faces (of 5 types) and 32 vertices (of 4 types). Of particular interest is that it is somewhat unique amongst polyhedra in having 64 edges (of 9 types). These allow it to be used to provide a 3-dimensional concept map of the 64 conditions of change denoted by the hexagrams of the I Ching (Transformation Metaphors: dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). If understood to be a cognitive container, this is particularly interesting in the light of its structure as a ring -- or an approximation to one. The ring, like the grail, is a traditional focus of quests.
| Comparison of cuboctahedron with drilled truncated cube | |
| Cuboctahedron | Drilled truncated cube (omitting 4 octagonal faces) |
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Switching metaphors, it is appropriate to note that Keith Critchlow has developed his own insights in terms of flowers (The Hidden Geometry of Flowers: living rhythms, form and number, 2011). This metaphor is explored separately (Flowering of Civilization -- Deflowering of Culture: flow as a complex experiential dynamic, 2014). The language of flowers notably featured in the dynamics of courtly love between knight and lady. Curiously, but as might be suspected, many sources focus on the primary set of 12 perfumes.
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