**In the light of the coherence and visual form of the Mandelbrot set (Part #1)**

Introduction

Relationships between "incommensurables"

Thesis

Methodological approach

Challenging aspects of this exploration

Dissipative systems and their illusory continuity

Structure of the visual representation of the Mandelbrot set

Interpreting features of the M-set

Potential implications: orders of abstraction and "explanation"

Meshing mathematical and experiential understanding

Possible psycho-social significance of the M-set

Imagination, Resolution, Emergence, Realization and Embodiment: iterative comprehension

Potential implications for interdisciplinary and intersectoral initiatives

Managing intractable differences: relevance to particular polarities

"Real" vs "Imaginary"

Relevance to strategic dilemmas

Enhancing insight through audio-visual techniques

References

[Parts: Next | Last | All ] [Links: To-K | From-K | From-Kx | Refs ]

This exploration endeavours to frame the concerns of two earlier associated papers in terms of the insights of dissipative systems and the Mandelbrot set (hereafter referred to as the M-set). The first paper (*Being Positive Avoiding Negativity: management challenge -- positive vs negative*, 2005) was concerned with the appropriate handling of "positive" and "negative" from a strategic perspective and as a judgement on the relevance of feedback. The second paper (*Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship*, 2005) sought to demonstrate the importance of a set of 8 patterns of interaction in defining a coherent pattern within any system of relationships -- highlighting the role of the cardioid in that pattern, following the work of Edward Haskell (*Generalization of the structure of Mendeleev's periodic table*, 1972).

Given the prime importance of the cardioid in representation of the M-set, the argument that follows is initially descriptive in clarifying an explanation of dissipative systems in terms relevant to the strategic challenge of interpersonal and intergroup relationships of those papers. There is an extensive body of literature of varying levels of technicality that explains the M-set and related issues. The concern here is the potential relevance of those insights to contexts which have not as yet been a prime concern. Reference is therefore only made to the technicalities where they suggest insights of relevance to the strategic challenge that might otherwise go unrecognized.

The purpose here is to explore imaginative leads and framings -- possibly primarily metaphorical -- that may be a guide to more concrete interpretations. In that respect the isomorphism with Haskell's cardioid may bear a less than rigorous relationship to that discussed here. [This question is currently under investigation by Kent Palmer]

This approach is consistent with that advocated by Ralph H. Abraham (*Human Fractals: the arabesques in our mind*. [text]

tudents well-trained in mathematics as well as in a social or human science.To many pure mathematicians, especially those to whom fractal geometry itself is not mathematics but heresy, these applications of new mathematical ideas to anthropology will seem anathema, vulgarization, fractal evil itself. In my perspective, however, they are the first steps of a major paradigm shift, a critical renewal arriving in timely fashion, of an entire area of cultural studies. Let us encourage this trend, which could be advanced spectacularly by a new generation of students well-trained in mathematics as well as in a social or human science.

[Parts: Next | Last | All ] [Links: To-K | From-K | From-Kx | Refs ]