Complementarity of 64-fold Sets as an Elusive Rosetta Stone?

TRANSCEND MEMBERS, 2 Feb 2026

Anthony Judge | Laetus in Praesens - TRANSCEND Media Service

Circumventing irresponsible authoritarian imposition of incoherent patterns of connectedness.

Introduction

A previous exercise explored the elaboration and visualization of a coherent 64-fold pattern for the Mathematics Subject Classification (MSC) which has used 63-64 top-level categories (Ordering the House of Mathematics from an AI Perspective? , 2026). The approach was adapted to the traditional set of 64 hexagrams of the I Ching — an early inspiration for the binary encoding fundamental to computer and AI operation. The methodology was then applied to the 64 genetic codons fundamental to the organization of DNA and life. It was speculatively adapted to the memorable organization of the elements of the Periodic Table of Chemical Elements of value to human life and to the organization of the 64 essential “arts” of human living — as traditionally articulated by the Kama Sutra. The sets were each mapped experimentally onto the 64 vertices of a hexeract (a 6-dimensional hypercube) as projected into interactive visualizations in 3D.

In each case consideration was given to identification of a 20-fold subset with particular “operational” functions, most notably in the case of the 20 amino acids (Rendering a 64-fold pattern dynamically comprehensible via 20-fold and 12-fold patterns, 2021; Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights, 2018). The question was the memorability of the smaller sets — suggested by a degree of familiarity in practice and how their coherence could be usefully visualized, notably as the 20 vertices of dodecahedron. The possibility of even greater recognition was then framed by the possibility of 8-fold and 4-fold mappings onto the cube and the tetrahedron respectively.

The exercise highlighted the relative incoherence of the organization of such sets in systemic terms, and the implication for both their comprehensibility as a whole and their memorability — notably with consequences for the challenges of coherent governance. Curiously the individual is confronted by authorities with conventional organization of such sets and what is effectively the righteous imposition of such chaotic classifications of key features of reality — a reality to which each is strongly encouraged to “subscribe” unquestioningly. Authorities are relatively indifferent in practice to that incoherence and to the challenges to comprehensibility and memorability, as previously argued.

Given the curious parallels between the choice of 64-fold sets in disparate domains and cultures, of interest is whether the individual is able to call into question the advocated “disorder” — possibly through the use of AI to consider how they might be fruitfully reframed for pedagogical or other purposes. Of interest in technical terms is the ease by which interfaces can now be designed as “mnemonic skins” through which to view legacy classifications. Many such “skins” can be envisaged, as with the choice of thematic design of browser interfaces offered to users. Such skins may reflect cognitive preferences as implied by ‘multiple intelligence theory introduced by Howard Gardner or the work of Geert Hofstede on cultural dimensions theory.

Further to the earlier exercise, of particular interest is how the method might be applied to religions, nations and disciplines where the same disorder is only too evident in a world faced with polycrisis — as with the irresponsible imposition of selective ordering by particular authorities. Faced with an estimated 10,000 religions, the possibility is suggested by the controversial study of Stephen Prothero (God Is Not One: The Eight Rival Religions That Run the World—and Why Their Differences Matter, 2010). Similarly, faced with some 193 members of the United Nations, of interest is the particular importance associated with the G7 / G8 and the G20 — and even the emerging multipolar pattern of the “Big Four” (USA, Russia, China, and another). In the case of disciplines presumably vital to the application of knowledge to a society in a condition of crisis, it is effectively unknown how many “disciplines” are recognized or call for recognition — with various authorities endeavouring to present a disparate array of unquestionable selective lists in to reinforce their particular agendas. Inspired by the Periodic Table, the possibility of a memorable pattern of ways of knowing was previously presented (Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order, 2009).

The challenge for any individual is how to engage with the confusion of arrays of “things” — often obscure — whose extent is held to be only comprehensible to experts tolerant of their complexity, however any array is variously claimed to be ordered. Few of the experts would claim to be able to name from memory all the nations or all the elements, for example, whether or not they may acknowledge their existence. This curiously echoes the situation in Ancient Greece where hundreds of deities were worshipped in addition to the 12 Olympians (List of Greek Deities). Some were adopted in Ancient Rome, as with the 12 Dii Consentes — some clustered as the 20 Dii Selecti, expanded to a set of some 67 “major deities”, or more (List of Roman deities). The Hindu deity concept varies from a personal god to 33 major deities in the Vedas,  to hundreds of deities mentioned in the Puranas. In the absence of general consensus of how any such arrays are to be memorably organized, or any evident collective motivation to achieve this, there is clearly a degree of freedom to explore new possibilities for doing so — beyond the use of circlets of 108 prayer beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000). In a civilization now characterized by a multiplicity of “problems”, there is some irony to the fact that Greek culture continues to make use of smaller circlets of “worry beads” — although each bead is not (as yet) typically associated with a particular problem.

As a conclusion to this exercise, a further possibility is envisaged, namely the implication that the set of 64-fold patterns of connectivity together constitute — through a degree of complementarity — the indication of an elusive “Rosetta Stone” of higher order, as previously discussed (Cognitive Fullerene as a Rosetta Stone for Patterns of Systemic Constraint, 2025; Integrative implications of the Rosetta Stone, Philosopher’s Stone and Diamond, 2025). The Rosetta Stone is a founding metaphor of the ambitious Langlands Program of mathematics (Kevin Hartnet, A Rosetta Stone for Mathematics, Quanta, 6 May 2024). Whilst the earlier method is applied here to the ordering of religions, nations and disciplines, there is the sense in which (together with the other instances) they might form a memorable 8-fold pattern, as previously considered from a metaphorical perspective (Selection of complementary metaphors, 2018).

One version of the visualization of that 8-fold complementarity includes the experimental sonification of the 64 vertices to enable the distinction between them to be recognized through a 2-tone chord associated with each of them — a distinction which may be easier recognize than through the eye or text labels.

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