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Potential significance of a Fibonacci spiral formation
Adaptive Hypercycle of Sustainable Psychosocial Self-organization (Part #5)
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There are of course a variety of spiral forms that might be used in a configuration like Fig. 2 in order to maximize (or optimize) visibility of hexagram conditions to each other. In a web environment users might, as noted, be offered the possibility of dynamically shifting between those forms.
A further consideration in any design choice follows from the possibility of embedding in the design other mnemonic triggers, as previously argued (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007). In the light of such considerations:
- it is appropriate to recall the "solar" metaphor so important to governance of many cultures down the ages. Arguably "global" could benefit from a metaphor of equivalent significance at this time -- especially given the inability to manage changing climate as a result of global warming.
- the solar metaphor is of course also characterized in its depictions by "rays". It is potentially fruitful to use the "houses" as indications of "ways of knowing" -- configured to suggest an "eightfold way of knowing".
- a particular spiral recognized to be fundamental to the organization of nature, and to human design preferences, is that based on the Golden Ratio -- namely the Fibonacci spiral. Such proportions are notably fundamental to what is valued in "sacred geometry", if only its aesthetic qualities:
- Ronald W. Neperud and Ronald C. Serlin report on its importance for children's design preferences (The Fibonacci Sequence: proportional and semantic bases of children's aesthetic preferences, Studies in Art Education, 1984).
- Others report on the relevance of such forms for learning (J. Burg, A. Lausier and V. Strokanova, Motivating Learning and Creativity With Fibonacci, Fractals, and Phi, 2004).
- A study by Marcel Danesi (The Fibonacci sequence and the nature of mathematical discovery: a semiotic perspective, Sign Systems Studies, 2005) looks at the serendipitous discovery of the Fibonacci sequence as the answer to a puzzle designed to illustrate the efficiency of the decimal number system as one of those episodes in human history which show how serendipity, semiosis, and discovery are intertwined. The author shows how the sequence has significant implications for the study of creative semiosis, since it suggests that symbols are hardly arbitrary products of human reason, but rather unconscious probes of reality.
- the spiral is of course widely valued as symbol, model and metaphor of psychosocial development. It is notably fundamental to the spiral dynamics associated with the integral theory of Ken Wilber and the AQAL quadrant system, as mentioned in the introductory paper (Don Edward Beck and Christopher Cowan, Spiral Dynamics: mstering values, leadership and change, 2005)
As noted above, there is a case therefore for exploring how the Fibonacci spiral might be used to configure the relationship between the "houses" of conditions of change. There is the possibility that such design properties might enhance psychoactive engagement with the patterns of change, for reasons previously presented (Topology of Valuing: psychodynamics of collective engagement with polyhedral value configurations, 2008). Such a combination of imagery responds to the challenge of combining the developmental dynamic of the spiral with the invariance of the pattern of changes as a whole. It is in this sense that the result has the potential of increasing the accessibility of insight into the nature of any adaptive hypercycle and its significance for sustainable psychosocial organization.
The importance of insights to be derived from order in nature has been highlighted by Christopher Alexander (The Nature of Order, 2003-4) and further explicated with regard to his current research (Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole. International Journal for Unconventional Computing, 5, 2009).
Alexander's current program was the subject of earlier commentary (Harmony-Comprehension and Wholeness-Engendering eliciting psychosocial transformational principles from design, 2010), itself expressed through the challenge of designing a "magic carpet" of relevance to governance (Magic Carpets as Psychoactive System Diagrams, 2010). A diagram such as that above might be understood as exploration of the possibility of a cognitive "magic carpet". As an approach to "braiding discourse" it may be seen as a response to the challenge of discourse in cyberspace (Interweaving Thematic Threads and Learning Pathways: Noonautics, Magic carpets and Wizdomes, 2010). Given Alexander's defining role with respect to design, of relevance to what follows is the focus of his current research on "geometric adaptation".
Framed as a cognitive design problem, in the light of the explorations of Christopher Alexander, a consideration is how to strike an interesting compromise between incorporating both symmetry and symmetry-breaking so as to enhance memorability and psychoactive engagement.
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