Examples of cyclic 48-edged and 64-edged dynamic configurations

AI-enabled Mapping and Animation of Learning Pathways (Part #14)

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The following examples are an attempt to address the question of how to strike a balance between a representation of the complex of insights (relevant to the crisis of the times) and its comprehensibility, memorability and communicability.

Cyclic configuration offered by the 48-edged rhombicuboctahedron: Using the set of 48 koans and 47 micronutrients, the previous exercise explored the following mappings (Rendering a 48-fold set of insights memorable through visualization, 2024). Two AIs responded there to the speculative challenge of suggesting correspondences between the two sets.

Indicative mapping of 48 koans and micronutrients onto Archimedean polyhedra
48-edged Rhombicuboctahedron mapped with 48 koans		48-vertex Truncated cuboctahedron mapped with 48 koans
Produced with the aid of Stella4D

Of further interest was whether the polyhedral articulation could be rendered of greater value in cognitive and learning terms, notably in relation to comprehensibility and memorability of a relatively complex pattern and its potential dynamics. As a computer programming exercise in 3D visualization, it was this further exploration which was undertaken with the aid of AI -- initially ChatGPT and subsequently Claude (Sonnet variant). As a learning exercise in its own right, the difficulties encountered are described below.

The result of the exercise took the following form for which the set of 48 Zen koans served as examples. The images offer a sense of the dynamics of 48 "insight messages" circulating in different cycles -- presented as "tunnels" following the geometry of the 48-edged rhombicuboctahedron. The animation successively highlights those tunnels, or eliminates them. The animation is an illustration of the mapping previously envisaged with respect to koans and micronutrients with implications for potential implications for international, interfaith, intercultural and interdisciplinary discourse (Facilitating Global Dialogue with AI? 2024).

48-edged rhombicuboctahedron with 6 8-fold cycles variously highlighted (48 koan messages moving along cyclic pathways as examples) [GIF animation]
Cycle highlighting suppressed	All cycles highlighted	Selective highlighting of one cycle
Prepared with X3D-Edit using a model from Stela4D with the aid of AI

Cyclic configuration offered by the 64-edged drilled truncated cube: As a further exploration of the modelling exercise illustrated above, the approach was applied to the drilled truncated cube, given previous discussion of its value for mapping the 64 hexagrams of the I Ching and the genetic codons . (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015). Together with that mapping, the polyhedron could also be used for the 48 koans as presented above, and as previously discussed (Relating configurative mappings of 64 I Ching conditions and 48 koans, 2012).

In the animation exercises below the polyhedron is used as a framework to configure and suggestively render coherent the dynamic between complex arrays of insights.

• The animation on the left uses the design metaphor of the exercise with the 48-edged rhombicuboctahedron above. The 64 hexagrams are presented on disks circulating around the 6 external octagonal pathways of the polyhedron. The message on each disk changes to another hexagram at each bend in the octagonal pathway. The 48 koans are presented on disks circulating around 8 internal hexagonal pathways, with the message on each disk changing to another koan at each bend in the hexagonal pathway.
• The central animation rotates the traditional Shao Yong circle of hexagrams within the 64-edged framework, indicating the transformations between the hexagram-encoded conditions, as discussed separately with more complex versions of the animation (Framing Cognitive Space for Higher Order Coherence: toroidal interweaving from I Ching to supercomputers and back, 2019)
• The animation on the right exploits the manner in which the polyhedral framework frames the toroidal pathway basic to the ITER tokamak design for a nuclear fusion reactor in which plasma is constrained to circulate by a configuration of magnets preventing its contact with its physical container (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). Speculaion regarding the challenge of "cognitive fusion" and coherence is suggested by the use of the toroidal pathway to contain the classic set of Zen ox-herding images, as discussed separately (Dynamic reframing of the cognitive challenge of memorable configuration, 2023; Zen of Facticity: Bull, Ox or Otherwise? 2017). The dynamics of the toroid offer associations to the archetypal Ouroboros, as separately explored (Integrating Ouroboros and Yi Jing as Fundamental Symbols in 3D, 2021)

Examples with 64-edged drilled truncated cube (64 hexagram messages moving along 8-fold pathways cyclic pathways, 48 koan messages moving along 6-fold pathways)
6 8-fold cycles and 8 6-fold cycles variously highlighted [GIF animation]	Rotation of Shao Yung circle of hexagrams [GIF animation]	Rotation of Zen ox-herding images
Prepared with X3D-Edit using a model from Stella4D with the aid of AI

Of potential interest is the recent video by the Laboratory for Experimental Museology  offering experience of a tokamak (Alfredo Carpinetti, Fly Inside A Nuclear Fusion Reactor Thanks To This Spectacular Simulation, IFL Science, July 2024).

Model communication: These visualization experiments with various design metaphors raise the question as to how they might be usefully communicated, given the following constraints:

• when printed, the dynamics are necessarily lost, and potentially the colours
• when presented on the web, a major challenge is associated with the norms and protocols of different platforms and browsers:
  • GIF animations, necessarily non-interactive and potentially of unacceptable file size
  • MP3 videos, necessarily non-interactive and potentially of unacceptable file size
• constraints are partially by-passed through use of X3DOM framing of the X3D files. This was only partially successful, despite AI assistance, requiring further testing to ensure disk movement (Mapping Learning Pathway Dynamics in 3D with Rhombicuboctahedron, 2024; Mapping Learning Pathway Dynamics in 3D with Drilled Truncated Cube, 2024)
• enabling users to download the X3D files to explore them with appropriate viewers, and potentially to modify them further. This possiility may be further constrained by the inability of some viewers to process some files.

Model development possibilities: As experiments, the animations are necessarily a "work in process" inviting further modification -- potentially by those accessing the X3D files -- since these can be made with a simple text editor. Possibilities by which the aesthetics may be improved, with or without greater expertise, include:

• changes of colour to the "tunnels", to the "disks", and/or to the text (or images) carried by the disks. Alternative sets of complementary colours could be chosen
• changes of transparency to the "tunnels", whether to render them more transparent or far less so.
  • the changes could be made dynamically and/or progressively, to highlight particular tunnels
  • the changes could be made such as to render particular tunnels invisible
• changes to the dimensions (size of disks, radius of edges)m diameter of the tunnels, possibly selectively with respect to some
• changes to the polyhedral "skeleton":
  • increase/decrease the size of the spheres at the tunnel junction points
    
  • use different colours for the junction points
  • increase/decrease the diameter of the edges between the spheres -- possibly to that of the tunnels
  • increase/decrease the transparency of the spheres or edges
• changes to the relative rates of movement of the disks, whether for all of them or selectively; rotation of the whole structure -- or not
• the tunnels can be individually dissociated from the polyhedral configuration, whether selective and/or given a distinctive movement
• changes to the set (or clustering) of the text (or images) carried by the disks
  • with a sequential order in a given tunnel (Koan 1, Koan 2, etc)
  • clustering the messages thematically by tunnel -- with each tunnel then associated with a distinctive theme
  • use of images rather than text

With more skill, many of these changes could be incorporated as features of the model, allowing for user interaction rather than requiring changes to the model (with a simple text editor).

Considerable effort was invested in the variety of viewpoints from which the 3D configuration might be perceived -- a standard feature of 3D displays. A particular objective had been to offer a viewpoint which would track a disk as it moved along a pathway, enabling it to observe the switch in messages at each bend on a pathway. Although this is technically feasible, this was not successful -- despite considerable AI support.

Potential significance of the models: The design possibilities merit exploration as mnemonic preferences and triggers. Of particular interest is whether and how such animations clarify the challenge of comprehending complex sets of insights with respect to the strategic and cognitive coherence -- such as the 48 koans or the 64 hexagrams, or other 8-fold configurations (Comprehensible Configuration of 8-fold Psychosocial Patterns in 3D, 2024). The challenge might be compared to that of the use of circlets of prayer beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000).

Curiously the polyhedra recall the design of wearable crowns and their embedded jewels, given all the symbolism with which they are associated with respect to governance (Engaging with Globality through cognitive lines, circlets, crowns or holes, 2009; Metaphorical Geometry in Quest of Globality -- in response to global governance challenges, 2009). Related visualization experiments can be undertaken with respect to the complexity of the crown chakra (Satellite Constellation and Crown Chakra as Complementary Global Metaphors? 2020).

As stressed above, the animations suggest the dynamic relationships between multiple "ways of looking" -- especially given the traditional governance role of "the Crown" (Interrelating Multiple Ways of Looking at a Crisis, 2021). Of curious relevance to the 48-fold pattern, is that 48 is the number of great vows and promises made by Buddha to provide the ultimate salvation to countless beings. In Judaism, Torah wisdom is said to be acquired via 48 ways according to the Mishnah

Also intriguing is how any hypothetical "global brain" might be envisaged, especially given the possibility of interconnection of AIs (Envisaging a Comprehensible Global Brain -- as a Playful Organ, 2019; Imagining a Future Union of Artificial Intelligences, 2024)

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