20th May 2007
Challenges to Comprehension Implied by the Logo
of the Union of Intelligible Associations
The pattern above, used as the logo of the Union of Intelligible Associations initiative, is the result of the search for an image corresponding to the complexity of the thousands of interrelated entities profiled within the Encyclopedia of World Problems and Human Potential. As such it was used on the cover of a presentation of that knowledge management initiative in its final phase.
Mandelbrot fractal: The image is a graphic representation of the M-set or Mandelbrot set (link includes detailed graphics), well-known to mathematicians associated with the complexity sciences. It is named after Benoît Mandelbrot who (re)discovered it. He recognized repeating patterns on all scales in numerous phenomena. The image is constituted by a set of those points -- representing complex numbers -- in the complex plane that form a fractal. The M-set fractal corresponds to the simplest nonlinear function -- but is also as complicated as a fractal can get. It distinguishes the simplest boundary between chaos and order. The aesthetic beauties of the fractal can be endlessly explored in great detail using a variety of software packages. The image above was generated from the Xaos package (developed Jan Hubicka, Thomas Marsh, Zoltan Kovacs and others, and now part of the part of the GNU Project and hosted by SourceForge).
Pattern language: Dissipative systems, and the M-set, 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. 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. Typically however the resolution is of four types:
The possibilities of the M-set were seen as a means of providing a form of map or index to the entities profiled in the databases of the Encyclopedia -- offering a new organization of chaos that respected the dynamics of the relationship between chaos and order. Further discussion of these possibilities is offered in:
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 their detail ("when two or three are gathered together in my name, there am I").
The pattern language is of significance because it enables agonizing psycho-social dilemmas, such as employment vs unemployment (environment vs employment, "affairs of the heart", etc) to be addressed in new ways -- unconstrained by the conventional binary logic and the logically excluded middle. In effect it is a language for exploring the viable patterns of the "middle way". It gives form, space and locus to particular dynamic resolutions of strategic dilemmas. The viability of these patterns, and the challenge to their comprehension, arises, however, from their characteristic dynamic -- in contrast with the stability normally sought in non-dynamic resolutions to such dilemmas.
Real vs Imaginary / Positive vs Negative: The complex numbers are positioned on a complex plane (of which the image above is one representation) in terms of two axes. By convention, the "real" dimension is represented on the horizontal axis (x-axis), whereas the "imaginary" dimension is represented on the vertical axis (y-axis) -- as shown in the Wikipedia entry. For the purposes of the logo, the axes have been rotated 90 degrees to the right -- with the positive-real below (and the negative-real above), whilst the positive-imaginary is to the right (and the negative imaginary to the left). Given the widely remarked resemblance to a meditating figure, this rotates the image from "sleeping" to "seated". Seen as a Buddha figure, this has notably given rise to "Buddhabrot" representations, using a special graphical rendering technique (Melinda Green, The Buddhabrot Technique; image; video) that reinforces the possibility of using astrophysical models to encode the universe of knowledge (Towards an Astrophysics of the Knowledge Universe: from astronautics to noonautics? 2007) .
The challenge of the Union of Intelligible Associations was to interrelate disparate sets of conceptual entities -- such as organizations, problems, strategies, values, state of awareness and development, metaphors, meetings, legal instruments (treaties, etc) -- of significance beyond the preoccupations of individual nations. The following table could be used to extend the mathematical understanding of real-imaginary/positive-negative -- beyond that of the complexity sciences -- honouring some of the self-referential challenges of complex adaptive systems (Consciously Self-reflexive Global Initiatives: Renaissance zones, complex adaptive systems, and third order organizations, 2007).
A more generic "Mandelbrot set" could then be understood as the result of mapping the features of complex collective reality (notably the entities profiled by the Union of Intelligible Associations) onto a complex plane in terms of their real-imaginary, positive-negative characteristics. Some features falling outside the boundary between chaos and order -- the boundary of the set as depicted -- would then be understood as "un-intelligible", and not forming part of collective reality. This generic reframing relates the positive-negative polarization much more closely to that evident in Taoist understandings of "creative"-"receptive". The polarization "real"-"imaginary" also then relates more closely to the subtleties of enactivism and the embodied mind (see Documents relating to Polarization, Dilemmas and Duality; Documents relating to Existential Engagement and Embodiment)
Languages and epistemological frameworks: However the question then becomes what language or epistemological framework is appropriate to representing and navigating such a complex reality (see Documents Relating to Language). A more insightful response is that no single language is adequate to this task (Navigating Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms through movement, 2002). It might be hoped that a set of complementary frameworks would be appropriate -- notably as caricatured elsewhere (12 Complementary Languages for Sustainable Governance, 2003). Better formulated distinctions of this kind might be made in terms of Ken Wilber's AQAL, Magoroh Maruyama's mindscapes, or other systems (Systems of Categories Distinguishing Cultural Biases, 1993; Richard E Nisbett, The Geography of Thought: how Asians and Westerners think differently...and why, 2003).
On this point, and in addition to the above author's, the work on a biocultural paradigm merits attention (Maria M Colavito. The Heresy of Oedipus and the Mind/Mind Split: a study of the biocultural origins of civilization, 1995; Antonio T de Nicolas, Religion: the last weapon of discrimination and the bio-cultural corrective, 2007; Neurobiology, Communities, Religion: a bio-cultural study, 1998). This is valuable, whether in terms of the challenging interplay of five modules of the human brain or of the need for distinct, but complementary, languages to order experience of richer significance. Particularly relevant is the challenging fluidity through which the neural networks associated with distinct brain modules must necessarily be employed.
Such arguments point to the real challenge of intelligibility -- a comprehension barrier or "glass ceiling" inhibiting more comprehensive insight.
Complementary emergent initiatives: This is one justification for reframing such challenges within the framework of four emergent complementary initiatives that might be understood as embodying to some degree the epistemological challenges of the above table:
As with the Mandelbrot set, the challenge is the exploration of the interface between chaos and order. In this sense a potentially more interesting way in which to envisage the emergent initiatives "engendered" by the "Union of Intelligible Associations" as associated with zones on the complex plane within the boundaries of the set.
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