Framing the interplay of leadership and misleadership

Framing the Interplay of Leadership and Misleadership: in the light of the coaction cardioid and the Mandelbrot set (Part #2)

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Greater clarity with respect to the interplay of leadership and misleadership can be achieved by drawing on arguments elaborated earlier (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005). There attention was drawn to the pattern of interactions highlighted by Edward Haskell (Generalization of the structure of Mendeleev's periodic table, 1972) in his work on the coaction cardioid (as discussed below). In its generic terms, the "governor component" is matched against the "work component" -- here corresponding respectively to leadership and followership. Schematically, using biological terms, this gave rise to Figure 3 (which follows the same pattern as Figure 1 in the main paper).

Edward Haskell's insights (as represented in Figure 3) have been very usefully (and extensively) adapted by Timothy Wilken (The Relationship Continuum, 2002) to an ordering of the spectrum of personal relationships: adversity -- neutrality -- synergy. Wilken equates "synergy" with "positive" and "adversity" with "negative", although there are questionable aspects to this equivalence (cf Being Positive Avoiding Negativity: management challenge of positive vs negative, 2005). Wilken's study reframes Haskell's above ordering in the following table, where "win" equates with "positive" and "lose" with "negative". Again this may be fruitfully related to the pattern of Figure 1 in the main paper. The conditions highlighted in Figures 2a and 2b might also be integrated into an elaboration of Figure 4.

Figure 4: 8-fold Pattern of Non-Neutral Relationships (Timothy Wilken)

In the earlier paper (in Figure 3 there) the representations above were related to the classical Ba Gua diagram of Taoism.

Haskell's original presentation of the above took the form of a cardioid cycle defined in relation to a circle (as seen in the figure below) of unchanging order (or entropy). The coaction cardioid turns

• into the zero-zero or scalar zero circle in the region of predominantly negative coactions (inturning, in Greek, is entropy) toward Alpha (in Teilhard de Chardin's terms)
• out of the circle in the region of predominantly positive coactions (turning out, in Greek, is ectropy) -- toward Omega (again in Teilhard de Chardin's terms).

The interactions, or "games", which reduce the degree of order (increasing entropy) are then within the circle, whereas those that increase the degree of order (decreasing entropy) lie outside the circle. The cardioid describes the "path" between these different conditions that is effectively associated with the sustainability of the system as a whole -- in which all interactions have a role to play.

Figure 5: Coaction cardioid (Haskell / Cassidy) Geometric representation of conditions in 8-fold Figure 3 [see also articulations by Wilken, pp. 157-161)

In the earlier paper it was argued that the cardioid may well function as a kind of value attractor (cf Human Values as Strange Attractors: Coevolution of classes of governance principles, 1993). In this sense it is perhaps more fruitful to look further at the way in which the different "games" as transactional patterns, define the contextual cardioid pattern -- namely the sense in which all the games need to be evoked in order for sustainability to hold. Figure 6 was used there to present this pattern.

Figure 6: Transactional game patterns defining a coaction cardioid (with traditional Taoist magic square numbering)

A subsequent paper (Sustainability through the Dynamics of Strategic Dilemmas -- in the light of the coherence and visual form of the Mandelbrot set, 2005) explored the above leads -- possibly primarily metaphorical -- as 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 possibility was subsequently explored with greater rigour by Kent Palmer (Is a Science of Nonduality possible? 2005) leading him to present this relationship as a "Haskell/Mandelbrot/Judge theory of nonduality".

Since the relationship between "leadership" and "misleadership" may indeed be understood in game theory terms -- whether or not it is indeed described as a "shell game", the presentation of Figure 6 may be adapted to that case, as in Figure 7 (notably based on Figure 1, in the main paper, here rotated 90 degrees).

Figure 7: Adaptation of the approach of Figure 6 to leadership and misleadership (highlighting the coaction cardioid, relevant to Figure 9, and the zones of synergy, neutrality and adversity)

By building further on these possibilities, greater insight may be obtained into the relationship between "leadership" and "misleadership", as suggested below by Figure 9. However, as suggested by the work of Palmer, rather than overlay the pattern of relationships with a simple cardioid, the conventional representation of the Mandelbrot set (M-set) is used -- of which one of many possible renderings is presented in Figure 8.

Figure 8: Rendering of Mandelbrot set using in- and out-colouring of image with Xaos to highlight complexity (axes have been rotated)

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Figure 8a: Illustration of alternative colouring conventions inside the M-set (suggestive of other understandings of the relationship between leadership and misleadership)

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Figure 8b: Progressive emergence of M-set through succession of iterations (suggestive of progressive clarification of understanding, through a learning process, of distinctions between forms of leadership and misleadership)
Iteration 0	Iteration 1
Iteration 3	Iteration 4
Iteration 6	Iteration 7
Iteration 9	Iteration 10
Iteration 12	Iteration 13
Iteration 15	Iteration 16
Iteration 18	Iteration 19
Iteration 21	Iteration 22

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