Mnemonic Foundations of a Playable Topology of Global Coherence

TRANSCEND MEMBERS, 20 Apr 2026

Anthony Judge | Laetus in Praesens - TRANSCEND Media Service

From Alphabetic Memorability to Polyhedral and Toroidal Dynamics of a 26-Fold Pattern of Polyhedral Governance

Introduction

19 Apr 2026 – In the quest for coherence in a civilization increasingly fragmented in a variety of respects (even dangerously so), it is ironic to note that patterns of connectivity and coherence — long framed as polyhedra by geometry — are primarily known only to specialists and are distinguished by a variety of terms which are meaningless (even alienating) to most. The irony is all the greater in that the unmemorable names of the 26 polyhedra in a principal set of such patterns of coherence can be contrasted with the memorability of the known 26 letters of the alphabet common to many languages.

The challenge may be framed simply: can patterns of coherence as structurally rich as polyhedra be rendered as cognitively accessible and memorable as the alphabet? This could be compared with the early challenge of education, namely enabling children to engage with the alphabet as a pattern, typically through mnemonic chants, poems or song (Heidi Butkus, The Number 26 Song). It is questionable whether there is any focus on “learning patterns of coherence” otherwise, although it may be argued that popular enthusiasm for music and song could be seen in that light. Polyhedra are structurally powerful but cognitively opaque in contrast with the alphabet — cognitively trivial but universally memorable. The question is whether patterns of coherence as rich as polyhedra could be rendered as cognitively accessible as the alphabet.

It is curious that the influential insights into such polyhedral patterns has been associated in Western civilization with the much admired Pythagorean’s of Ancient Greece. That their engagement with them, as is well known, was intimately associated with their musical insights can be contrasted with the virtually total dissociation from music of modern geometry — as now studied and taught by mathematicians (Joscelyn Godwin, The Harmony of the Spheres: the Pythagorean tradition in music, 1992; Kitty Ferguson, The Music of Pythagoras, 2008). It is other disciplines which now make use of such patterns — as in music and dance, for example. Eastern cultures have however continued to cultivate a meaningful cognitive association between aesthetics and governance — where Western governance has limited its attention to aesthetics to decorative functions, most obviously in receptions at global summits and in the questionable role of the Anthem of Europe (Reversing the Anthem of Europe to Signal Distress, 2016).

The challenge for governance and any global strategy could then be caricatured by the phrase: “if it ain’t singable, it wont be credible, memorable or sustainable” — as argued separately (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). That possibility frames the question as to whether there is a need to explore how the basic 26-fold set of patterns of coherence could be rendered memorable — if only by association with the 26-fold set of letters of the alphabet, or by what any such “alphabet” may suggest. One obvious possibility is the use of memorable acronyms, as is the case with the multiplicity of national and international strategic initiatives — deprecated however through their incoherence as an “alphabet soup” (International Organization Abbreviations and Addresses, 1984). Such possibilities suggest that memorability may depend less on the complexity of the pattern than on the availability of a compact set of generative elements through which it can be traversed.

The exploration was therefore extended experimentally through interaction with multiple AI systems, not as sources of authority, but as probes capable of eliciting alternative framings and unexpected correspondences. In that sense the following exercise endeavours to elicit new possibilities with the aid of several AIs — renowned as they are for capacities in pattern recognition and articulation, but especially for drawing together disparate approaches of potential relevance to any such challenge. The possible “alphabetisation” of the basic 26 patterns of coherence recognized by geometricians was initially put to the Perplexity AI and then to DeepSeek. A more elaborated approach was then sought from Claude AI and ChatGPT — with which earlier approaches to the mattter had been sought (Conceptual Complexity Compactified within Fundamental Polyhedra, 2026).

The exchange with each AI focused initially on how familiarity with the 26-letter alphabet might be adapted to rendering memorable the set of 26 polyhedra as virtually unrecognized patterns of coherence. The exchange with Claude and ChatGPT then developed into consideration of the alphabetically encoded “operators” recognized by various “Western” disciplines — and the cognitive operations they implied — including Atkin’s Q-analysis, Deacon’s absentials, Laban notation, the De Bruijn torus, together with Neo-Riemannian and Conway transformations. A degree of correspondence was noted with articulations contrasting “Eastern” disciplines, including: Sefer Yetzirah, Natya Shastra, the Rasa, Mudra and Bhava systems, and others. That recognition is in accordance with the arguments of Susantha Goonatilake (Non-Western Science: mining civilizational knowledge, Encyclopedia of Life Support Systems EOLSS, 1999). The exchange concluded with a focus on the identification of a generic cognitive toolkit of transformational moves in the light of Neo-Riemannian transformations and the De Bruijn torus.

The continuing existence of those traditions suggests that quantitative bias systematically obscures the harmonies of coherence that qualitative aesthetic appreciation can directly apprehend — leaving their deepest structural expression hidden in plain sight within the numerological traditions whose deprecation ensures they are never seriously examined

What begins as a mnemonic exercise through these exchanges — how to remember a set of 26 polyhedra — thus progressively reveals correspondences with transformation systems across mathematics, music, movement, and cultural traditions. In this progression, the focus shifts from naming to transformation, from classification to navigation, and from memory to playability. The question is no longer simply how to represent coherence, but how to move within it. This has implications for governance, where the challenge is not only to define coherent frameworks, but to render them cognitively accessible and operationally usable across diverse perspectives — whether patterns of coherence can be rendered navigable through a limited set of operations. In this light, the alphabet becomes not only a mnemonic device but a model for a generative system, suggesting parallels with transformation grammars in music, geometry, movement, and narrative.

If coherence cannot be rendered memorable and performable, can it be effectively enacted in governance? Could a small set of mnemonic or operational “alphabetic” forms render complex patterns of coherence navigable, memorable, and usable?

A note on method. The experimental use of AI in this context is itself an illustration of the rapid evolution of these platforms and of how they come to be shaped by the feedback that guides their commercial marketing. Early criticism focused on the irritation of excessive “algorithmic flattery” of users. How user “buy-in” is ensured and sustained is, as with any commercial service, a concern for the provider; how this evolves into a form of progressive “grooming” is a concern for regular users — whether or not it can be distinguished from the norms of ordinary social interaction. Traces of such framing are variously evident in the exchanges that follow, and could be further edited out for a variety of purposes; readers are invited to treat them as they would comparable framing in human interaction. As in earlier experiments with AI, it is the questions put to the systems that primarily feature in what follows — with the extensively detailed responses selectively accessible only where readers wish to consult them. Readers are of course free to pose the same questions — or others — to AI systems of their own choice, whether now or in the future when such platforms have further developed.

It is worth noting in this context that the substantial resources currently directed toward AI for targeting, surveillance, and adversarial applications proceed without any comparable investment in the cognitive possibilities that the following exchanges illustrate — the capacity of such systems to surface unrecognised correspondences, to hold disparate frameworks in productive tension, and to render complex patterns of coherence accessible across domains that governance discourse currently treats as incommensurable. The asymmetry of investment is itself a governance failure of the kind the exchanges below attempt to diagnose.

TO CONTINUE READING Go to Original – laetusinpraesens.org

Share this article: email mastodon facebook 🔗 copy link

DISCLAIMER: The statements, views and opinions expressed in pieces republished here are solely those of the authors and do not necessarily represent those of TMS. In accordance with title 17 U.S.C. section 107, this material is distributed without profit to those who have expressed a prior interest in receiving the included information for research and educational purposes. TMS has no affiliation whatsoever with the originator of this article nor is TMS endorsed or sponsored by the originator. “GO TO ORIGINAL” links are provided as a convenience to our readers and allow for verification of authenticity. However, as originating pages are often updated by their originating host sites, the versions posted may not match the versions our readers view when clicking the “GO TO ORIGINAL” links. This site contains copyrighted material the use of which has not always been specifically authorized by the copyright owner. We are making such material available in our efforts to advance understanding of environmental, political, human rights, economic, democracy, scientific, and social justice issues, etc. We believe this constitutes a ‘fair use’ of any such copyrighted material as provided for in section 107 of the US Copyright Law. In accordance with Title 17 U.S.C. Section 107, the material on this site is distributed without profit to those who have expressed a prior interest in receiving the included information for research and educational purposes. For more information go to: http://www.law.cornell.edu/uscode/17/107.shtml. If you wish to use copyrighted material from this site for purposes of your own that go beyond ‘fair use’, you must obtain permission from the copyright owner.

There are no comments so far.