Reframing an eightfold way by entangling imagination and reality?

Comprehension of Requisite Variety via Rotation of the Complex Plane (Part #4)

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Eightfold way? There is of course no lack of references to an "eightfold way" with which a pattern of octants might be appropriately associated. These include frameworks as fruitfully diverse as:

• Noble Eightfold Path, understood as the set of Buddhist practices leading to liberation from samsara, namely the painful cycle of "rebirth" (Eightfold Path, aka: Eightfold Way; 5 Definition(s), Wisdom Library). Any particular understanding of the meaning of rebirth can be usefully challenged by the variety of ways in which it may be understood (Varieties of Rebirth: distinguishing ways of being "born again", 2004). Of relevance to the strategic challenge of governance, and the cycles of violence which have yet to be transcended, is the insight of George Santayana: Those who cannot remember the past are condemned to repeat it.
  
  
• Particle-physics theory: the eightfold organizational scheme for the class of subatomic particles known as hadrons that led to the development of the quark model. (Murray Gell-Mann and Yuval Ne'eman, The Eightfold Way, Benjamin, 1964).
  
  
• Hydrodynamics of dissipation: Felix Haehl (The Eightfold Way to Dissipation: classification of hydrodynamic transport, Duke University, 2016 )
  
  
• Symbolic logic: (Jonathan P. Cummings, Sy-David Friedman and Assaf Rinot, The Eightfold Way, Journal of Symbolic Logic, 83, 1, 2018; pdf). The mutual independence of three central combinatorial properties in set theory can be demonstrated by showing that any of their eight Boolean combinations can be forced to hold under particular conditions.
  
  
• Hyperbolic geometry: The Klein Quartic Curve fundamental to hyperbolic geometry can only be visualized by approximation in 3D, inviting an 8-fold commentary (Silvio Levy, The Eightfold Way: the beauty of Klein's Quartic Curve, Cambridge University Press, 1999)
  
  
• Modal dichotomies of philosophy: Douglas Ian Campbell, The Eightfold Way: why analyticity, apriority and necessity are independent, Philosophers' Imprint, 17, 2017). These can be combined to produce a tri-dichotomy of eight modal categories.
  
  
• Policy analysis: (Eugene Bardach, A Practical Guide for Policy Analysis: the Eightfold Path to more effective problem solving, 2000)
  
  
• Data-driven business: Eightfold Way To Data-Driven Business
  
  
• Deliberation dialogue: Peter Mcburney, David Hitchcock and Simon Parsons (The Eightfold Way of Deliberation Dialogue, International Journal of Intelligent Systems, 2002)
  
  
• Coaction cardioid: Edward Haskell (Full Circle: The Moral Force of Unified Science, 1972)

The assumption in assembling such seemingly disparate 8-fold patterns is that there are cognitive constraints and biases in determining patterns of N-foldness, as discussed more generally (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980; Comprehension of Numbers Challenging Global Civilization, 2014). These would be consistent with the arguments of George Lakoff and Rafael E. Núñez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000). Examples are indicated by the following:

• Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources (2011)
• Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights (2018)
• Examples of 9-fold patterns (2016)
• Examples of 5-fold patterns (2019)

The Chinese pattern of trigrams, known as BaGua (as employed in the image above), can be understood as indicative of an 8-fold way, especially given its traditional circular configurations suggestively termed the "BaGua mirror". Usefully recognized as barring any eightfold way is an understanding of an eightfold fence, recognized as central to Japanese cultural identity. One of Japan's first recorded poems, in the imperial anthology Kojiki from the early eighth century, celebrated an "eightfold fence" separating Japan from other lands and peoples, a realm where the gods dwelled (Michael Auslin, Japan's Eightfold Fence, American Affairs, 1, 2017, 3). Symbolic significance is variously attributed to eight-gatedness, as with the eight gates of Jerusalem, or of Heaven. Such a pattern is evident in the description of Stephen Prothero (God Is Not One: The Eight Rival Religions That Run the World -- and why their differences matter, 2010).

Eastern martial arts tend to distinguish eight "directions of unbalancing" (Kuzushi in Judo and Kendo) These may be associated with eight compass directions (in two dimensions) in which an opponent may be moved so as break their balance. In three dimensions they might be understood as the eight corners of a cube within which the fighter is centered. In Aikido these eight directions are understood as ways to move one's body (Unsuko), to move one's opponent (Kuzushi), or to throw one's opponent (Tsukuri). The eight directions and five postures have been combined in different martial art traditions through movements, techniques, "energies", "gates", "stances" or "powers" (cf Michael P. Garofalo, Thirteen Postures of Taijiquan: Eight Gates and Five Directions, 2005; Michael P. Garofalo, Cloud Hands Taijiquan and Qigong Guides, Bibliographies, Links, Resources).

From 2D to 3D octant configuration: It is intriguing to note that many of the articulations of an 8-fold way take the form of checklists, potentially even the original Noble Eightfold Path of Buddhism. Those of physics imply some form of hyperdimensional configuration, as with those of symbolic logic. There is less emphasis on how any such pattern is to be comprehended as a whole -- with the cognitive engagement that might especially enable. However of particular relevance are the insights of oppositional logic (Guoping Du, Hongguang Wang and Jie Shen, Oppositional Logic, LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction, 2009; Fabien Schang, Logic in Opposition, Studia Humana, 2013). This is an extended system of classical propositional logic.

Of particular relevance is the use of 3D symmetrical polyhedral configurations to render the insights comprehensible (Oppositional Geometry: mathematics (and philosophy) of opposition; Alessio Moretti, The Geometry of Logical Opposition, 2009). Curiously, as with mathematics, these remarkable insights have seemingly had no detectable impact on the many conditions of opposition so characteristic of society at this time -- as discussed separately (Neglected recognition of logical patterns -- especially of opposition, 2017; Oppositional Logic as Comprehensible Key to Sustainable Democracy: configuring patterns of anti-otherness, 2018).

One approach to developing this argument, and the relevance of a rotational configuration of the complex plane, is through the Coaction Cardioid cycle of Edward Haskell (Full Circle: The Moral Force of Unified Science, 1972), further elaborated by Timothy Wilken (UnCommon Science, 2001).

Those indications resulted in the separate argument (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005). This included the following sections, notably taking account of the BaGua pattern:

Encoding indications of significance: The illustrative images there were of 2D form. In the light of the arguments above with respect to rotation of the complex plane, there is then a case for considering how 8 distinctive cognitive significance might be associated with the octants of the 3D configuration of Mandelbrot sets as cognitive contexts of particularly quality. Insights may be distinctively associated with the BaGua trigrams (or encoded by them) as with those of oppositional logic. How then might these relate to that configuration -- as suggested by their association with the octants in the image above (and below)?

Relation between octant configuration and mutually orthogonal Mandelbrot renderings

Imagination, fantasy and aesthetic coherence? With regard to the challenging allienation of abstract models, such as that on the left above, it is intriguig to recognize that the aesthetic complexities of the configuration on the right would not be unfamiliar to those engaging in widely popular online games of multiple levels in virtual worlds, for which level design is now a discipline in its own right. This includes the manner in which these may be segmented into domains or worlds governed by different characteristics, as with the 41 fantasy novels of Terry Pratchett's Discworld series.

Such complexity would seem to have a degree of intuitive appeal which is far from widely evident in models engendered by the policy-making environment. Of particlar relevance is the design preoccupation with dynamic game difficulty balancing, namely the process of automatically changing parameters, scenarios, and behaviours in a video game in real-time, based on the player's ability, in order to avoid engendering boredom in a player. This may include nonlinear gameplay. Given increasing levels of alienation from science and world news, it could be asked how these environments now compare to the engagement offered by gaming (Les Sillars, The Future of News, First Things, March 2019; Nic Newman, Journalism, Media and Technology Trends and Predictions 2019, Digital News Publications; Most young lack interest in politics: official survey, BBC, 21 February 2014).

With respect to the aesthetic appeal of the Mandelbrot set, further speculation is possible, given the manner in which it embodies the golden ratio as the convergence of the Fibonacci series (Holly Krieger, Fibonacci Numbers hidden in the Mandelbrot Set, Numberphile, 5 October 2017). The circumference of the visual rendering is characterized by what are termed "bulbs". These are distinguished by their periodicity. This raises the question as to how many bulbs there are, as discussed separately. If there is a degree of intuitive recognition of the coherence of the pattern represented by such a rendering, it could be asked whether this is somehow associated with the considerable value attached to prayer beads in many cultures. More specifically, is it possible that the number of beads in any such circlet is related to the bulbs and their periodicity? Thus there are: 6 bulbs of period 4, 15 of period 5, 27 of 6, 63 of 7, 120 of 8, 252 of 9, and 495 of period 10. Such numbers are of the order of various prayer bead circlets (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000).

Given the mysterious constraint on the neocortical cognitive limit to the maintenance of stable social relationships, at approximately 150 -- known as Dunbar's number -- could that also be related to that pattern of conceptual distinctions? This has been clarified by David Burkus (Dunbar's number doesn't represent the average number of social connections, Quartz, 8 August 2018). This notes that research has shown that the that the average (mean) network size of those surveyed was 611 people. Taken by itself, this number is dramatically larger than Dunbar's estimate. But while the mean network size was 611 contacts, the median was 472 contacts (period 10?). To a statistician this is a clear signal that the number of contacts in people's networks doesn't follow a normal distribution. Instead, network sizes may follow a power law (Tyler H. McCormick, et al, How Many People do you Know?: Efficiently estimating personal network size, Journal of the American Statistical Association, 105, 2010).

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