Dynamic reframing of the cognitive challenge of memorable configuration

Coherent Reconciliation of Eastern and Western Patterns of Logic (Part #11)

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There is indeed the possibility that the "Eastern" and "Western" configurations can be memorably reconciled in the light of insights from polyhedral combinatorics. Rather than a focus on correspondences between invariant configurations, another approach merits consideration in the light of the cognitive challenge and that of sustainable governance.

Dynamic relationships: Whether arrayed in 2D, 3D or more, the challenge can be understood metaphorically as one of dynamic adjustment of the forces associated with the configuration of polarities to ensure that a central focus is maintained "sustainably" (on average) -- however much there is momentary deviation from it in a variety of directions. In a sense it is that dynamic displacement which reflects "desirable" diversity around the central focus (in 2D, 3D, or more).

The possiility can be understood as featuring in various studies (T. Kunii, et al, Visualizing Highly Abstract Mathematical Concepts: a case study in animation of homology groups, Multimedia Modeling, 1993; Vassil Sgurev and Vladimir Jotsov, Method for Interpretation of Functions of Propositional Logic by Specific Binary Markov Processes, Recent Contributions in Intelligent Systems, 2016). One indication to that effect is the work of Jeffrey Z. J. Zhen (mentioned above):

The entire framework is described using 4 levels of hierarchy: n variables, 2ⁿ states, 2²ⁿ functions, and 2ⁿ!2²ⁿ logic functionals. Under the proposed framework, it is possible to determine higher level function complexity by analysing lower levels of organisation characteristics. These characteristics can be determined quite accurately because the symmetry conditions of variable and state organisations have invariant logic functions and a corresponding logic functional organisation. More symmetrical arrangement at state level creates more symmetrical permutations within the function space. Lower level properties are highly influential on the higher level properties of function components within a logic functional space. The proposed framework provides a logic foundation to describe complex binary systems using lower level properties, making analysis of systems more efficient and less calculation intensive. Different global coding schemes are discussed and typical two-variable cases of logic functionals are illustrated (Variant Logic Construction Under Permutation and Complementary Operations on Binary Logic, Variant Construction from Theoretical Foundation to Applications, 2019)

Design metaphors: Various metaphors can be used to illustrate the dynamic. A melody or a sonnet can frame a memorable pattern of connectivity between associations. This could be achieved through a configuration of colours in a colour wheel, understood dynamically as a colour cycle. The followng speculative animations use the lauburu symbol of Basque culture in relation to variants of the BaGua pattern, as discussed separately (Improvisation in Multivocal Poetic Discourse: Basque lauburu and bertsolaritza as catalysts of global significance, 2016).

Experimental rotation of alternative Lauburu patterns over alternative BaGua patterns
Anti-clockwise over King Wen pattern	Clockwise over Fuxi pattern

A related design challenge is the magnetic containment within a toroidal fusion reactor of nuclear plasma to ensure that it does not come into destructive contact with the walls of the container -- an archetypal "container for what cannot be contained". The ITER nuclear fusion reactor uses 18 "D"-shaped toroidal field magnets placed around the vacuum vessel to produce a magnetic field whose primary function is dynamically to confine the plasma particles. 6 ring-shaped poloidal field coils are situated outside of the toroidal field magnet structure to shape the plasma and contribute to its stability by dynamically "pinching" it away from the walls. 18 superconducting correction coils are inserted between the toroidal and poloidal field coils tol compensate for field errors caused by geometrical deviations due to manufacturing and assembly tolerances. Two non-superconducting coil systems inside of the ITER vacuum vessel provide additional plasma control capabilities.

Constraining "the uncontainable" through the magnets of the ITER tokamak design (as presented for illustrative purposes; note inclusion of a human figure as an indication of scale in left-most images)
Toroidal field magnets	Poloidal field magnets	Correction coils	In-vessel coils
Reproduced from The ITER Tokamak Magnets (ITER, 2013)

Thirty-five nations are collaborating to build ITER -- the European Union (plus Switzerland and the UK) is contributing almost half of the cost of its construction, while the other six members (China, India, Japan, South Korea, Russia and the USA) are contributing equally to the rest. Construction began in 2010 and the original 2018 first plasma target date was put back to 2025 by the ITER council in 2016. (ITER delays revision of project's timeline, World Nuclear News, 27 June 2023).

Speculative design: Given the potential of technomimicry, and as an indication of the challenges of attention control and focus, the ITER system of plasma control can be explored as a metaphor for the dynamics of sustainable governance (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). A case can be made for shifting from global geometry to that of a torus (Imagining Toroidal Life as a Sustainable Alternative: from globalization to toroidization or back to flatland? 2019).

As a speculative design exercise, the cuboctahedron and drilled truncated cube (discussed above) can be combined dynamically (below) to create a form of toroidal "container" inspired by the ITER design (above). Within that framework a torus of associations -- corresponding to that of nuclear plasma -- can be set to rotate. The pattern of images is derived from the much-cited set of 10 Zen bulls (or 10 ox-herding images) -- with its cognitive significance discussed separately (Circular configuration of cognitive phases framing toroidal experience? 2017). Consistent with the magnetic containment of the ITER design, the animation could be further developed by animating a counter-balancing dynamic between opposing triangular elements of the configuration.

Indicative configuration of a pattern of opposing functions as a container for a sustainable process (nesting a toroidal process within a dynamically integrated framework of cuboctahedron and drilled truncated cube)
wireframe view ("side")	wireframe view ("top")	selected faces non-transparent
Interactive 3D variant

Following the dynamic design constraints illustrated by ITER, a further possibiity is to build into the configuration a dynamic corresponding to that of the controlling role of counteracting "magnets" -- in this case the 8 BaGua elements, discussed previously and configured on opposing triangular faces of the cuboctahedron. Their complementarity offers an indication of the counterbalancing role of complementary cognitive functions with which those elements are associated. This is suggested by a typical array of alternative metaphors, indicated in the following table. Usefully to be emphasized is the elusive cognitive modality implied by the various metaphors associated with each element -- perhaps to be best understood as an aesthetic synthesis. The Chinese logograms are used in the following example

Use of complementary logograms in the above framework (opposing logograms are darkened and highlighted in the dynamic)

Interactive 3D variant

Technical note: Whilst there is considerable flexibility in modifying the above model in the X3D-Edit software used, a major challenge (for novices) is the counter-intuitive association of rectangular logogram images with the triangular sides. This involves iterative adjustment of the 4 parameters of the TextureTransform node, about which the application notes: The visible effects of these transformations might appear reversed because the image changes occur before mapping to the geometry. This can make the process seem counter-intuitive. As remarked by ChatGPT from which guidance was sought:

The process can indeed be more of an art than a science, especially when dealing with complex shapes like a cuboctahedron. Each software has its quirks and ways of handling transformations, and what works in one scenario may not apply universally. This "artistic" aspect of 3D modeling often requires a lot of experimentation, intuition, and patience. Successful texturing is frequently achieved through trial and error, and understanding the peculiarities of the software you're working with.

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