Comprehension of Requisite Variety via Rotation of the Complex Plane


Anthony Judge | Laetus in Praesens – TRANSCEND Media Service

Mutually Orthogonal Renderings of the Mandelbrot Set Framing an Eightfold Way


15 Jul 2019 – Faced with global crises, it is useful to recall the variants of the well-known insight: There Is Always a Well-Known Solution to Every Human Problem — Neat, Plausible, and Wrong. How many of the advocated global strategies can be recognized in that light?

There is no lack of recognition of the complexity of “strategic space” within which the articulation and display of strategies could be compared metaphorically to the competitive challenge faced by flowers (Keith Critchlow, The Hidden Geometry of Flowers: living rhythms, form and number, 2011). Missing is any sense of the requisite complexity within which otherwise incommensurable strategies may need to be embedded in order for their collective coherence to become comprehensible.

The tendency to organize any such articulation into multiple sections — multi-petalled “strategic flowers” — can then be compared with the branching 3-fold, 5-fold, N-fold patterns in the animations presented separately (Dynamics of tank comprehension and enclosure, 2019). The “bullet points” by which an articulation is presented could then be usefully compared to the seeds of such flowers — as with the UN Sustainable Development Goals. Metaphorical reference to “tanks” can be made in order to demonstrate the strategic challenge of interrelating the many relatively closed contexts in which strategy is variously envisaged (Tank Warfare Challenges for Global Governance: extending the “think tank” metaphor to include other cognitive modalities, 2019). That argument can be further developed.

The complex plane, from which strategic patterns can be understood mathematically to emerge, is indicative of a complex context in which stable patterns of various branchings emerge in various positions — with unstable patterns emerging outside the boundaries, as remarkably rendered by the fractal order of the Mandelbrot set with its fascinating aesthetics. There is however little collective understanding of the complexity of that strategic space or of how the relationship between any such patterns is indicative of the possibility of larger coherence — however that is to be comprehended. This is the challenge of governance, whether democratic or otherwise, as previously argued (Sustainability through the Dynamics of Strategic Dilemmas — in the light of the coherence and visual form of the Mandelbrot set, 2005; Psycho-social Significance of the Mandelbrot Set: a sustainable boundary between chaos and order, 2005; Imagination, Resolution, Emergence, Realization and Embodiment: iterative comprehension ordered via the dynamics of the Mandelbrot set, 2005).

There is no lack of recognition of the increasingly surreal nature of governance processes at this time (Surreal nature of current global governance as experienced, 2016). This sense is reinforced in daily media coverage of the extraordinary lack of coherence of governance at all levels of society — chaotic is a common descriptor — matched by ever-increasing polarization of factional discourse, together with the proliferation of fake news of every kind (Varieties of Fake News and Misrepresentation, 2019).

The spirit of the times is indicated by UK preparations for a non-deal Brexit, with scenarios including chaos at the ports, chaos in food and medicine distribution, chaos in care staff recruitment and chaos as financial markets shift to the EU. However, as argued by Simon Jenkins with respect to the leadership offered by Boris Johnson:

Yet ask Johnson’s small band of more sophisticated no-dealers, and a different justification begins to emerge. It lies in the theories of creative disruption espoused by the postwar economist Joseph Schumpeter and his followers. To them, occasional bouts of chaos are necessary. As during wars, recessions and Thatcherism, Britain needs a therapeutic shock to jolt it into a new karma, a new inner greatness…. As Thatcher showed, even creative destruction demands crisis management. Johnson’s politics seem more in tune with the wilder shores of chaos theory. In one gaffe after another, he has been the butterfly whose wing-beat can effect an unpredictable storm. While the chaotic forces of no deal whirl ever faster, his bland shrug of the shoulder becomes the “strange attractor“around which they mysteriously cohere. As with Donald Trump, anarchy can mean bad things, good things, absolutely any things. (Trump created a storm over Kim Darroch. Boris Johnson will bring a hurricane, The Guardian, 11 July 2019)

Arguably there is a need for a more complex “container” for the subtleties of such complexity. It is intriguing that the “planar” language is reflected in the widespread reference to “plans” and “planning” (by which a “Flat Earth” understanding is reinforced), or otherwise in reference to the “field” with which they are associated — as one preferred metaphor for any academic discipline or specialization. With respect to the argument regarding “tanks”, the boundary offered by the Mandelbrot set is usefully suggestive of that between the orderly stable space within the tank and the chaotically unstable condition outside it. Potentially of greater interest is the sense in which the positions within the Mandelbrot sense boundary, with which the patterns are variously located, themselves constitute tank boundaries — with that of the Mandelbrot set as a whole then constituting an elusive meta-pattern encompassing and containing all such patterns — effectively a “meta-tank”, a “tank of tanks”, or a tank container.

As yet, the amazing insights promised by the Mandelbrot set could readily be said to have been less than useful, notably in the light of efforts to apply them to financial governance — especially before and after the subprime mortgage crisis (Horace Campbell, Fractals and Benoit Mandelbrot: lessons for society, Pambazuka News, 21 October 2010; Alejandro Nadal, Understanding Instability: Mandelbrot, fractals, and financial crises, Triple Crisis, October 2010; David Orrell. Fractal Finance, World Finance, 4 January 2011; Christian Walter, The Mandelbrot programme and the pragmatic programme, Chance and Finance, 3 November 2015; Tren Griffin, Benoit Mandelbrot’s Ideas about Investing and Markets, 25iq, 9 December 2017). Tentatively this could be understood as a consequence of the restrictive narrow focus on the conventions of a singular complex plane — when mathematics has already envisaged higher dimensional extensions.

One approach to considering the relevance of such complexity is to develop further the earlier argument regarding the need for variously oriented planar frameworks for “tanks” of distinctive nature, notably mutually orthogonal planes. Naively, as an exploratory illustration to that end, the complex plane in which the Mandelbrot set is conventionally rendered could be subject to rotation on its two axes — the axis of real numbers and the axis of imaginary numbers. The Chinese yin/yang notation of unbroken and broken line can then be used to distinguish the real and imaginary characteristics of 8 distinctive octants (rather than 4 “quadrants”), thereby framed in a multiview projection.

The exercise is of potential relevance to climate change strategy since the traditional Chinese 8-fold BaGua notation is comprehended through specific use of weather-related metaphors, as previously explored (Enhancing Strategic Discourse Systematically using Climate Metaphors: widespread comprehension of system dynamics in weather patterns as a resource, 2015; Weather Metaphors as Whether Metaphors, 2015). There is a degree of irony to the fact that human understanding of the subtleties of the weather enables direct engagement with it in a period when ever more powerful supercomputers are seemingly required to comprehend the global complexity of climate.

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