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Unusually succinct interweaving of systemically significant symbolic patterns?


Higher Dimensional Reframing of Unity and Memorable Identity (Part #7)

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Of unexpected potential relevance is the configuration variously presented in the animations below. This has been named as the octahex ring by Glen Whitney (Math Monday: Hole New Polyhedra, National Museum of Mathematics, 2017). Much more complex variants -- as Stewart Toroids -- are indicated by Robert Webb (A Genus-41 Stewart Toroid)

Memorable mapping possibilities of an octahex ring of 12 octahedra
Configuring 108 edges (20 types) with 72 faces (12 types) and 36 vertices (6 types)
72 faces coloured by 12 face types Association of 72 "demonic" sigils with faces Association of 72 "demonic" sigils with faces
72 faces coloured by 12 face types Association of 72 demonic sigils with faces Association of 72 demonic sigils with faces
Animations generated with the aid of Stella 4D

The comments by Whitney (with regard to the polyhedral ring structure and the central hole) invite further consideration in the light of the continuing debate regarding the so-called doughnut model (Kate Raworth, Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist, 2017), as separately discussed (Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009; Exploring the Hidden Mysteries of Oxfam's Doughnut: recognizing the systemic negligence of an Earth Summit, 2012)

The traditional pattern of 72 problematic (wicked, demonic) strategic functions, complemented by pattern of 72 remedial (angelic) functions -- as discussed earlier -- could be usefully mapped for mnemonic purposes onto the 72 faces of the ring formation. The animation could allow for alternating between the two mappings.

The polyhedron is a compound of 12 octahedra -- of mnemonic value in relation to the many 12-fold articulations of strategic relevance (Checklist of 12-fold Principles, Plans, Symbols and Concepts, 2011). It is of particular interest in that any pattern of 108 distinctions can be associated with its edges, as with names of deity or related recitation on circlets of beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000). Of further potential interest is the manner in which the edges interweave in cycles around the structure. The edges are of 20 distinct types, recalling the tendency to distinguish 20-fold patterns of strategies (Requisite 20-fold Articulation of Operative Insights?, 2018).

As a mnemonic nexus of potential strategic significance, the ring structure of 36 vertices also merits exploration in the light of 36-fold patterns variously deemed to be of relevance to governance. These are discussed separately from various perspectives, notably as a means of interrelating the array of narratives, plots, agendas, stories and conspiracy theories (Thirty-six Dramatic Situations faced by Global Governance?, 2022). In terms of memorability, the dramatic situations are those to which people are notably exposed through the daily diet of news and entertainment, whether or not the pattern as a whole is comprehensible.

With respect to the pattern of 36 dramatic situations, and especially from a governance perspective in this period, how might this relate to the Chinese insight into 36 stratagems? This is a unique collection of ancient Chinese proverbs that describe some of the most cunning and subtle war tactics, presented metaphorically as "luring the tiger":

In addition to that Chinese example, other traditional 36-fold articulations are noted by Wikipedia.

The configuration invites further consideration as indicative of processes which could be associated with it. The animation on the left below highlights the 20 distinctive types of within the pattern of 108 edges. Of potential interest is whether subsets of edge types, or particular combinations of edges, could be understood as indicative of circuits or pathways around the configuration -- effectively as contrasting "metabolic pathways", as separately discussed (In quest of metabolic pathways of global governance? 2020; Pattern of value interrelationships implied by "metabolic pathways"? 2018).

The central animation below offers an indication of how the 36 "dramatic situations" might be associated with the pattern of 36 vertices -- with the implication that "narratives" might interrelate them as suggested by the hypothetical pathways of the animation on the left. The titles of the familiar "situations" are those of Georges Polti's 36 Dramatic Situations (Changing Minds), as reproduced separately (Dramatic situations in narrative and stories -- plus or minus thirty-six? 2022). Of obvious interest is how these might relate in cognitive and systemic terms to the pattern of 36 stratagems of Chinese tradition, each typically described metaphorically. How the pattern invites comprehension as a whole is clearly of relevance to the challenge of global govenance. Given the familiarity engendered by the ritual practice of recitation of the 108 "edges", how this might "translate" into intuitive familiarity with the pattern as a whole is a metter for further consideration.

The animation on the right below highilights the possibility of pathway through the configuration of 12 octahedra -- through their centres -- with the implication that it is their contrasting which ensure the coherence and viability of that pathway. The design challenge is reminiscent of that required for the electromagnetic control of plasma in a nuclear fusion reactor, as discussed separately (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). Of some relevance in that context is recognition of the challenge of controlling "snake-like" instabilities in the circular dynamic, given their association to the archetypal Ouroboros (Integrating Ouroboros and Yi Jing as Fundamental Symbols in 3D, 2021; Circulation of the Light: essential metaphor of global sustainability? 2010).

Potential mapping applications of polyhedral octahex ring
108 edges distinctively coloured as 20 edge types Association of 36 vertices with "dramatic situations"
(indicative)		 Animation of sphere passing along a twisting pathway through the configuration
Octahex ring: 108 edges distinctively coloured as 20 edge types Association of 36 vertices with dramatic situations Sphere passing along a twisting pathway through octahex ring
Animations generated with the aid of Stella 4D Adaptation of animation by Sergey Bederov of Cortona3D

Question to ChatGPT: I have a polyhedral ring composed of 12 octahedra, with 108 edges (20 types), 36 vertices (6 types), and 72 faces (12 types). Can you suggest how subsets of edges might form pathways spiralling around the configuration in comprehensible patterns

Creating pathways that spiral around a polyhedral ring composed of 12 octahedra requires an understanding of the geometric configuration and connectivity between the octahedra. Given the complexity, with 108 edges of 20 types, 36 vertices of 6 types, and 72 faces of 12 types, we'll approach this by considering the symmetry and the spatial arrangement of the octahedra.

Here are some suggestions for forming spiraling pathways around the configuration:

  • 1. Identify Symmetry Axes: First, identify the axes of symmetry through the arrangement. These axes can guide the creation of spirals that maintain a coherent pattern as they wrap around the structure. Given the polyhedral ring's specifications, it's likely that there are multiple axes around which spirals can symmetrically loop.
  • 2. Edge Classification and Selection: Given the 20 types of edges, classify them based on their orientation relative to the symmetry axes. Select edges that are parallel or nearly parallel to these axes for the spirals. This selection ensures the pathways will follow a coherent direction as they spiral around the configuration.
  • 3. Vertex Connectivity: Utilize the 6 types of vertices as pivot points for the spirals. Vertices where more edges converge are strategic points to transition the pathway from one octahedron to the next or to change the direction of the spiral. Mapping out these vertices can help in visualizing the pathway's progression.
  • 4. Pathway Patterns: Develop pathway patterns based on edge and vertex selection. For a simple spiral, choose a starting edge and follow connected edges that gradually ascend or descend around the ring. For more complex patterns, consider alternating between different types of edges or incorporating zig-zag motions between vertices.
  • 5. Spiral Direction and Layering: Decide on the direction of the spiral (clockwise or counterclockwise) and whether the pathway will be single-layered or multi-layered. Multi-layered spirals can add depth to the configuration and create more intricate patterns. Ensure that the transitions between layers are smooth and logical.
  • 6. Simulation and Visualization: If possible, use 3D modeling software to simulate the pathways. This tool can help in visualizing the spirals and ensuring they follow a comprehensible and aesthetically pleasing pattern. Adjustments can be made more easily in a virtual environment before finalizing the design.
  • 7. Iterative Design: Given the complexity, the design process will likely be iterative. Start with simpler spirals and gradually increase complexity. Experiment with different edge types and pathways, noting which configurations produce the most visually appealing and comprehensible patterns.

The creation of these pathways requires a blend of geometric understanding, creative design, and possibly computational tools for visualization and optimization. The final design should ideally highlight the unique structure of your polyhedral ring, creating a visually stunning and geometrically interesting object.

Question to ChatGPT: Having experimented unsuccessfully with such possibilities to some degree, further consideration can be sought from the use of such pathways for mapping psychosocial analogues to metabolic pathways. Of potential relevance, for example, is any mapping of the 36 vertices in relation to both the 36 stratagems of China (and their relevance in the Game of Go) and the 36 "dramatic situations" identified as familiar by Polti. The 108 edges are of course a major feature of popular mala bead recitation of the names of deity. The question is how these indications might be reconciled in memorable pathways of relevance to strategic coherence

Integrating psychosocial analogues with the geometric structure of your polyhedral ring presents a fascinating and complex challenge. By considering the 36 vertices in relation to both the 36 stratagems of China (and their application in the game of Go) and the 36 "dramatic situations" identified by Georges Polti, along with the significance of the 108 edges akin to mala bead recitation, you're essentially seeking to create a multidimensional mnemonic device that not only serves as a visual and structural representation but also embodies strategic and narrative coherence. Here's how these elements might be reconciled into memorable pathways:

  • Mapping the 36 Vertices
    • Stratagems and Dramatic Situations: Each vertex can be associated with one of the 36 stratagems and one of Polti's dramatic situations. This dual mapping allows each point on the polyhedral ring to represent a specific strategic or narrative principle. The challenge is to ensure that each vertex's dual meanings harmonize or create meaningful juxtapositions that can enhance strategic thinking or storytelling.
    • Visualization and Symbolism: For each vertex, create symbols or icons that encapsulate the essence of the corresponding stratagem and dramatic situation. These symbols can serve as visual cues to facilitate the recall of the strategic or narrative principle represented by each vertex.
  • The 108 Edges as Pathways
    • Mala Bead Recitation Analogy: Just as mala beads are used for meditation and recitation, the 108 edges can represent a journey through various states of consciousness, strategic thinking, or narrative exploration. The edges could symbolize transitions between stratagems, dramatic situations, or a combination of both, reflecting the interconnectedness of different strategies and narratives.
    • Creating Pathways: Develop pathways that link vertices in sequences that reflect logical or thematic progressions of stratagems and dramatic situations. These pathways can be designed to mimic the flow of a game of Go, where strategic positioning and territory control mirror the interplay of different strategies and narratives.
    • Memorable Patterns: Integrate patterns that reflect the cyclical nature of mala bead recitation, such as repeating certain sequences of stratagems or dramatic situations to reinforce their memorability. These patterns could also mirror strategic or narrative cycles, such as the rise and fall of fortunes in a story or the ebb and flow of advantage in strategic contexts.
  • Integrating the Elements for Strategic Coherence
    • Narrative and Strategic Frameworks: Use the frameworks of the 36 stratagems and Polti's dramatic situations as a guide for creating comprehensive pathways that span the entire structure. These pathways can be designed to tell a story or outline a strategic journey, with each step marked by a vertex and its associated principles.
    • Interactive Exploration: Consider the polyhedral ring as a three-dimensional board game or narrative exploration tool. Players or users could navigate the structure, making strategic or narrative decisions at each vertex, guided by the associated stratagem and dramatic situation.
    • Educational and Reflective Tool: Beyond its complexity, the polyhedral ring can serve as an educational tool for learning about the 36 stratagems, Polti's dramatic situations, and their applications in strategic thinking and storytelling. It can also serve as a reflective tool for meditation, allowing users to contemplate the interconnectedness of strategies, narratives, and the cyclical nature of life and conflict.

Incorporating these psychosocial analogues into the polyhedral ring's structure offers a rich, multi-layered approach to understanding and navigating complex strategic and narrative landscapes. The key to success in this endeavor lies in the careful selection and integration of symbols, pathways, and patterns that resonate with the user, fostering deep engagement with the underlying principles.

Question to ChatGPT: Reference has been made in this exchange to George Polti's set of 36 dramatic situations and to the Chinese set of 36 stratagems (whose relevance to the Game of Go has been noted). Is it possible to detect correspondences between these two sets -- and to recognize the manner in which they might be indicative of memorable systemic pathways. Given the skills of AI in Go, is there any record of the use of the 36 stratagems in training AI.

Exploring potential correspondences between Georges Polti's 36 dramatic situations and the Chinese 36 stratagems, and their relevance for creating memorable systemic pathways, involves diving into the thematic and strategic essence of both sets. While Polti's situations focus on universal narrative themes that drive human stories, the 36 stratagems offer tactical approaches often used in warfare, politics, and by extension, games like Go, where strategy plays a pivotal role. Despite their different contexts, both sets encapsulate patterns of human behavior and strategic thought that can indeed intersect and offer insights into complex interactions and decisions.

  • Detecting Correspondences: To detect correspondences between Polti's dramatic situations and the 36 stratagems, one would need to analyze the underlying principles and objectives of each set:
    • Common Themes: Both sets explore themes of conflict, resolution, ambition, strategy, deception, and human relationships, albeit from different angles. For example, a stratagem focusing on deception and surprise could relate to a dramatic situation involving treachery or a secret being discovered.
    • Strategic and Narrative Dynamics: By examining the strategic goals behind a stratagem and the narrative thrust of a dramatic situation, one can identify parallels in how obstacles are approached and overcome, whether through cunning, strength, sacrifice, or alliance.
  • Indicative of Memorable Systemic Pathways: The correspondence between dramatic situations and stratagems could serve as a foundation for designing systemic pathways that are both memorable and effective:
    • Storytelling as a Strategic Tool: Embedding strategic lessons within narrative contexts can enhance memorability and applicability. For instance, a pathway designed around the theme of overcoming adversity might combine a relevant stratagem with a dramatic situation that illustrates this theme, such as "Disaster" (Polti) with "Besiege Wei to Rescue Zhao" (stratagem), emphasizing indirect approaches to solving problems.
    • Learning and Decision-Making Frameworks: By mapping these correspondences onto decision-making frameworks or learning models, individuals and organizations can navigate complex scenarios more effectively. This approach leverages the narrative to internalize strategic principles, much like how parables and fables have been used historically to impart wisdom.
  • AI and the 36 Stratagems:
    • Regarding the use of the 36 stratagems in training AI, particularly in the context of games like Go, there's no widely cited record of these stratagems being explicitly used as a training dataset or framework. AI models like AlphaGo develop their proficiency by playing numerous games against themselves and learning from vast databases of human-played games. They optimize their strategies through reinforcement learning, a process that doesn't explicitly teach the AI about human stratagems but rather allows it to discover efficient strategies through trial and error.
    • However, the principles underlying the 36 stratagems and similar strategic frameworks could implicitly emerge in the AI's gameplay as it learns to recognize and apply the most effective tactics for given situations. AI's capability to identify and exploit patterns could lead to strategies that resemble those found in the 36 stratagems, even if the AI isn't directly trained on them. The exploration of explicit incorporation of such stratagems into AI training could offer fascinating insights into strategic thinking and its application in complex decision-making environments.

The intersection of narrative situations, strategic frameworks, and AI capabilities presents a rich field for further exploration, potentially offering novel approaches to understanding and navigating the complexities of human and AI interaction, strategic planning, and storytelling.

A 36-fold pattern variously recognized invites further reflection in the light of the much-studied "thirty-six officers problem" and, more generally, that of mutually orthogonal Latin squares. Curiously it may also relate to detection of analytical criteria (Stefan Schandelmaier, et al, A systematic survey identified 36 criteria for assessing effect modification claims in randomized trials or meta-analyses, Journal of Clinical Epidemiology, 113, September 2019). In the light of the challenges of classifying potential failures of viable systems, more speculative is the possibility that the relevant systemic insight is associated with 2x36, as discussed separately (Mnemonic clues to 72 modes of viable system failure from a demonic pattern language, 2016).

Question to ChatGPT: In an earlier response you precautiously declined to suggest any specific systemic correspondences between the 36 dramatic situations and the 36 Chinese stratagems. Are you nevertheless able to suggest speculatively a tentative set of correspondences. The possibility is of further interest in the light of the mathematical challenges of the much-studied " thirty-six officers problem" and the identification of 36 criteria for assessing effect modification claims in randomized trials or meta-analyses

Creating a speculative set of correspondences between Georges Polti's 36 dramatic situations and the Chinese 36 stratagems is an intriguing intellectual exercise that blends narrative theory with strategic thinking. The challenge lies not just in the thematic alignment but also in respecting the unique cultural and historical contexts from which each set arises. Given these considerations, let's embark on a speculative, creative endeavor to explore potential alignments between these two sets, keeping in mind that these correspondences are interpretative and intended to inspire further thought rather than definitive mappings.

Speculative Correspondences

  • Supplication (Polti) with Hide the Dagger Behind a Smile (Stratagem): Both involve situations where one party seeks mercy or help from another, potentially with underlying intentions.
  • Deliverance with Besiege Wei to Rescue Zhao: Situations of rescue or relief from a threat, using indirect methods or distractions.
  • Crime Pursued by Vengeance with Kill with a Borrowed Knife: The act of seeking revenge or justice, possibly through the use of another's hand or resources.
  • Vengeance Taken for Kindred upon Kindred with Loot a Burning House: Exploiting a situation of internal conflict or turmoil within a group or family for personal gain.
  • Pursuit with Make a Sound in the East, Then Strike in the West: The dynamics of chase and escape, with the pursuer using deception and diversion to capture the target.
  • Disaster with Create Something from Nothing: Facing a calamitous event and the need to innovate or fabricate solutions to survive or overcome adversity.
  • Falling Prey to Cruelty or Misfortune with Cross the Sea Under Camouflage: Enduring hardship or misfortune, with survival depending on stealth or disguising true intentions.
  • Revolt with Openly Repair the Gallery Roads, But Sneak Through the Passage of Chencang: An uprising or rebellion, with strategies that involve misdirection or hidden maneuvers.
  • Daring Enterprise with Steal the Beams and Replace the Pillars: Undertaking a risky or bold venture, where success requires clever substitution or undermining foundations in secrecy.
  • Abduction with Exchange the Roles of Guest and Host: The act of kidnapping or taking someone against their will, where power dynamics are inverted or manipulated.

These speculative correspondences are meant to illustrate the potential for thematic and strategic resonance between Polti's dramatic situations and the Chinese stratagems. They highlight how narrative elements can intersect with tactical approaches, offering a rich tapestry for exploration in various fields, including literature, game design, strategic planning, and psychological studies.

The mention of the "thirty-six officers problem" and the identification of 36 criteria for assessing effect modification claims in randomized trials or meta-analyses adds another layer of intrigue to the number 36, suggesting a broader symbolic or structural significance that could be explored in diverse contexts. These mathematical and methodological frameworks provide yet another dimension through which the interplay of narrative and strategy can be examined, potentially revealing deeper insights into the patterns and principles that underlie human thought and behavior.

Question to ChatGPT: Given the recognized relevance to the Game of Go, and the demonstrated skills of AI in that game, at what stage is it to be expected that AI will be able to suggest coherent mappings rather than procedures whereby they might be elicited otherwise. The question follows from the acknowledged ability of AI to engender new materials and molecular configurations

The evolution of AI in complex decision-making and creativity, as demonstrated in games like Go and in fields such as material science, points towards a future where AI could indeed suggest coherent mappings directly, integrating complex datasets and abstract concepts. The leap from procedural guidance to generating innovative, coherent mappings involves several advancements and considerations:

  • Current State: AI in Games and Creativity:
    • Games like Go: AI, notably through algorithms like AlphaGo, has demonstrated superior skill in Go by learning from vast datasets of games and through reinforcement learning, where the AI plays against itself to improve. This process does not directly translate to creating mappings but shows AI's capability in strategic thinking and pattern recognition.
    • Material Science and Design: AI has been used to predict new materials and molecular configurations by analyzing patterns in data, learning from known chemical properties, and applying these to generate predictions about new materials. This involves understanding complex relationships and predicting outcomes based on vast datasets.
  • Transition to Generating Coherent Mappings
    • Abstract Concept Integration: Moving from procedural suggestions to direct mappings requires AI to understand and integrate abstract concepts from diverse domains (e.g., psychosocial theories, strategic games, and narrative structures). This involves not just pattern recognition but also the creation of new patterns that make sense across these domains.
    • Advancements in AI Models: The development of more sophisticated AI models that can handle multi-modal data (text, symbols, visual cues) and understand their interrelations is crucial. These models would need to excel in associative thinking, drawing connections between seemingly unrelated concepts.
    • Interdisciplinary Training Data: The AI would need access to a broad and deep dataset encompassing game theory, narrative theory, psychology, and other relevant fields. The challenge lies not just in the quantity of the data but in its quality and the AI's ability to draw meaningful insights from it.
    • Creative and Strategic Reasoning: AI would need to advance in areas of creative and strategic reasoning, going beyond learning from existing data to generating novel, yet coherent, solutions to complex problems. This involves a leap from reactive to proactive AI, capable of innovation rather than just optimization.
  • Expected Timeline: Predicting a precise timeline for when AI could achieve this level of sophistication is challenging due to the rapid pace of technological advancements and the varying degrees of complexity in the tasks. However, several indicators suggest that we are moving closer:
    • Rapid Advancements in AI: The pace of advancement in AI capabilities, particularly in deep learning and neural networks, suggests significant progress could be made within the next decade.
    • Interdisciplinary Research: Increased focus on interdisciplinary AI research, integrating cognitive science, computer science, and other fields, is laying the groundwork for more sophisticated AI models.
    • Custom AI Solutions: Development of custom AI solutions for specific interdisciplinary applications, including those that require complex mappings and integrations, is becoming more common.

In summary, while current AI excels in structured environments with clear rules and objectives, like Go, and in generating predictions within well-defined domains, such as material science, the ability to suggest coherent mappings across abstract and diverse domains is on the horizon. It will likely evolve as AI models become more advanced in understanding and integrating complex, abstract concepts, potentially within the next decade or so, depending on the pace of research and technological breakthroughs.

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