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13 October 2014 | Draft

Representation of Creative Processes through Dynamics in Three Dimensions

Global insight from spherical reframing of mandalas, the zodiac and the enneagram

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Global insight implied by circular representation
Spherical mapping of conditions traditionally associated with the zodiac
Relevance to change, learning and creativity
Transcending polar preoccupation
Imagining the nature of cognitive "flight" in terms of the enneagram
Meaningful cognitive navigation


The argument developed here derives from an exploration of the creativity of Nikola Tesla (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). There it took the form of a separate section (Insight into global dynamics through Tesla's focus on the sphere, 2014). The focus and scope of that section, with its speculative animations, justified its separate development in this document into which the contents have been transferred.

The concern here is with the learnings to be derived from spherical representation of cognitive dynamics -- especially in contrast to their representation framed in some way by a circle, as with mandalas, the zodiac or the enneagram.

Missing from the separate discussion of Tesla's creativity was his considerable interest in the sphere -- both in relation to his energy experiments, and to his understanding of the terrestrial globe. There is a case for relating these to the later explorations of Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975), as separately discussed (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009).

With respect to Tesla, it was suggested that his creativity might be fruitfully explored in the light of technomimicry, as illustrated by that of Arthur M. Young, designer of the Bell helicopter, and as separately discussed (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011). Young envisaged the possibilities of applying the principles of helicopter control -- notably involving challenges of rotation -- to the development of a "psychopter", or "winged self" (Geometry of Meaning, 1976; The Bell Notes: A Journey from Physics to Metaphysics, 1979). Possible understandings are discussed separately (Characteristics of phases in 12-phase learning-action cycle, 1998; Typology of 12 complementary strategies essential to sustainable development, 1998). If creativity through "biomimicry" has now been seen as an instance of "bio-inspiration", the possibilities of "technomimicry" might be better recognized through "techno-inspiration", in the light of the arguments of Jeff Karp (Kayt Sukel, What I'd ask Spider-Man, mascot of bio-inspiration, New Scientist, 14 October 2014).

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). 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, with which distinct stakeholders could be associated in any discourse.

The following argument explores a degree of confluence in the arguments of Young, Fuller and Beer when their implications in three dimensions are considered, especially when understood dynamically. This had been stressed with respect to Tesla's innovative capacity with regard to electromagnetism, more particularly in handling the polarity of positive and negative.

Global insight implied by circular representation

Maps of the world typically depict it as being flat, although the projections used may imply a global form that can remain difficult to imagine meaningfully. For many, including scientists, the "sun rises", even though the dynamics may be understood otherwise. The first edition of Thomas L. Friedman's The World Is Flat (2005) was given the first Financial Times and Goldman Sachs Business Book of the Year Award in 2005. The award recognizes one business book that provides 'the most compelling and enjoyable insight into modern business issues, including management, finance and economics.' Does this suggast a dependence on a fundamentally misleading perspective -- or one which is widely reinforced, as argued separately (Irresponsible Dependence on a Flat Earth Mentality -- in response to global governance challenges, 2008)?

8-foldness: There is extensive commentary on the BaGua circular configuration of trigrams according to the understandings of Chinese philosophy. These can be presented in animated form, as portrayed previously with regard to Tesla (Imagining a method for adapting Tesla's insights to a psychosocial context , 2014). Those circular animations were reproduced from Animation of Classical BaGua Arrangements; a dynamic representation of Neti Neti (2011) where they were presented with alternative configurations, also discussed otherwise (Unknown Undoing: challenge of incomprehensibility of systemic neglect, 2008).

12-foldness: With respect to Arthur Young's exploration of learning-action cycles in Geometry of Meaning (1976), it is appropriate to note his courageous attempt to relate these to the far more widely memorable understanding of zodiacal cycles (Zodiac: An Analysis of Symbolic Degrees by Eric Schroeder, 1982). Such bridging exercises are rare. Why is that?

A disposition of 12 complementary qualities in a circle has long been a feature of civilization and of integrative understanding, as can be variously explored, notably with regard to the enthusiasm for "round tables" (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011; Implication of the 12 Knights in any Strategic Round Table, 2014). This proclivity can be explored with respect to global governance (Eliciting a 12-fold Pattern of Generic Operational Insights: Recognition of memory constraints on collective strategic comprehension, 2011; Imagining Attractive Global Governance: questioning possibilities and constraints of well-boundedness, 2013; Enabling a 12-fold Pattern of Systemic Dialogue for Governance, 2011).

Navigation in three dimensions: It is curiously appropriate that Young's primary inspiration was navigation in three dimensions, as exemplified by his pioneering work on helicopter design. However, in endeavouring to generalize his learnings from that domain, he chose to associate his insights with the traditional circular representation of the zodiac. This raises the question of how that understanding might be augmented with respect to cognitive navigation by a representation of the zodiac in three dimensions as explored below. This is of course consistent with the original inspiration of the spherical disposition of the constellations around the celestial sphere.

Integrative animation: The following experimental animation -- in circular form -- integrates points made by Arthur Young, as variously described and discussed separately (Geometry of Meaning: Examples of Integrated, Multi-set Concept Schemes, Annex 1, 1984; Functional Complementarity of Higher Order Questions: psycho-social sustainability modelled by coordinated movement, 2004). Prior to its association with the zodiac, Young used a simpler circular representation in the light of the physics of controlled navigation from which his insights derived (Configuration of states, acts and relationships). Relating creativity of such as Tesla to widespread understanding of the zodiac is especially valuable as an aid to comprehension and reflection on the navigation of the conceptual universe -- of the noosphere.

Use of the symbolic language associated with the zodiac has long been deprecated by science and religion despite its popular appeal as a meaningful framework. It is appropriate to note the care with which Young develops his argument from the abstractions of the physics of movement required in the control of a vehicle such as a helicopter. The terms from the zodiacal framework are only then attributed to offer a degree of qualitative comprehensibility to the distinctions he makes for which he repeatedly notes the inadequacy of words -- given the manner in which they can be variously interpreted and understood. Emergence of deeper understanding is of course characteristic of any learning process -- which may last many years.

Animation suggestive of the experiential system of interwoven creative processes
-- creativity embodied in alchemical processes encoded by the forms of zodiacal signs
(adapted from Eliciting a Universe of Meaning:
within a global information society of fragmenting knowledge and relationships
, 2013)
Animation of 12 control processes as zodiac pattern

Positive and Negative: The animation above includes indication of the conditions traditionally considered "positive" or "negative". These are fundamental to the innovative developments of Tesla with respect to electromagnetism -- and the possible implications for corresponding handling of positively and negatively charged psychosocial conditions, as discussed in the preceding paper). As noted by Wikipedia with respect to "negative signs": No value judgment is attached to the terms negative or positive. They may be likened to polarities in a magnet: one side is positive and one side is negative. Neither side is "good" nor "bad" -- they are merely different. Signs associated with the negative are Taurus, Cancer, Virgo, Scorpio, Capricorn, and Pisces; those associated with the positive are Aries, Gemini, Leo, Libra, Sagittarius, and Aquarius..

Complementarity of complexity and simplexity: Use of the zodiac by Young as an explanatory metaphor highlights the complementarity inherent in the struggle between:

The complexity explored by science could well be "held" conceptually through rotational dynamics -- incorporating it into integrative models and mappings of a particular form. The necessary simplicity for its comprehension as a whole could well be addressed through a complementary preoccupation with simplexity -- remarkably exemplified by the sphere, with its global associations and implications.

Complexity is of course a focus by science on complex systems, most notably through the discipline of cybernetics. Of particular concern to the development of global civilization is the developing understanding of complex adaptive systems. The interest in "simplexity" is as yet far less well developed,