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Challenging mechanistic thinking: contribution of complexity sciences


Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors (Part #15)


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The above discussion in terms of geometrical forms readily encourages understanding of polyhedra as models -- configured together here as a kind of mega-model, possibly to be understood as a meta-model. This would be to forget the complexity of the global attractors that were the point of departure: the problematique, the resolutique, the imaginatique and the irresolutique -- and the challenge of the global identique.

The understanding of "union" as a polar contrast to the variety of "associations" may be usefully explored in terms of the boundary between order and chaos. The Mandelbrot set (M-set) fractal is a mapping of the simplest nonlinear function -- but is also as complicated as a fractal can get. It distinguishes the simplest boundary between chaos and order. It is recognized as the simplest non-trivial example of a holomorphic parameter space. In the search for solutions to complex equations, experiments with iterations by computer have highlighted intricate global properties related to nonconvergence and the stability of convergence.

The early confidence that complexity studies would have much to offer governance of complex systems appears to have largely dissipated -- without fully exploring their potential, except perhaps by the intelligence services. There has been a reversion, in relation to complexity, to what Edgar Morin (Pour Sortir du XXe Siecle, 1981) described as mono-factor thinking (cf Promoting a Singular Global Threat -- Terrorism: Strategy of choice for world governance, 2002). In particular the M-set offers a surprising higher order pattern that reconciles the challenge represented by the incommensurability of "real" and "imaginary" dimensions -- exemplified by complex numbers and their positioning on the real and imaginary axes fundamental to the visual representation of the M-set (see Fig. 6).

Dissipative systems, and the M-set, indeed offer a language through which to explore and identify viable patterns of sustainable relationship between essentially incompatible modes of behaviour or anti-thetical modes of thinking -- "union" vs "associations". It is these which are typically fundamental to the strategic dilemmas in pyscho-social systems -- whether intrapsychic, interpersonal or intergroup. It is the continuing search for the resolution of these dilemmas that characterizes the dynamic of such systems (cf Configuring Strategic Dilemmas in Intersectoral Dialogue: Summary of analysis on the occasion of Earth Summit, 1992)

As discussed elsewhere (cf Sustainability through the Dynamics of Strategic Dilemmas: in the light of the coherence and visual form of the Mandelbrot set, 2005), this approach offers a pattern language to explore the complexities of the periodic resolution to strategic dilemmas -- the space of "not-this, not-that" (the neti neti of Sanskrit). The emergent patterns there are those which characterize a multitude of dynamically stable experiential resolutions of strategic dilemmas. These dynamic resolutions can be depicted (through the M-set) as characteristic patterns of great variety. The set of all such patterns (the M-set as a whole) is of a coherent form that is reflected in many ways (isomorphically) in its detail.

Fractal representation of Mandelbrot set
NB: Conventionally the complex plane is represented with the x-axis as the real dimension and the y-axis the imaginary dimension [more]. Here that representation is rotated 90 degrees so that the negative portion of the real axis is at the top
Fractal representation of Mandelbrot set
Generated by Xaos: realtime fractal zoomer
truncated dodecahedron icosidodecahedron truncated icosidodecahedron truncated octahedron rhombicosidodecahedron rhombicuboctahedron truncated tetrahedron truncated cuboctahedron truncated icosahedron cuboctahedron truncated cube snub cube

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