The Secret Pathway between Configurations of Otherness?

TRANSCEND MEMBERS, 24 Nov 2025

Anthony Judge | Laetus in Prasesens - TRANSCEND Media Service

Mnemonic Geometry Clues on How to Kiss-Touch and Make-Up

Introduction

24 Nov 2025 – Discourse between disparate domains: There is ever more indication that civilization is faced with a major difficulty in facilitating the engagement between disparate domains. This has long been evident between religions whose insights regarding transcendental unity and harmony do not translate into the relationships between their respective adherents. The pattern is very similar in the case of academic disciplines, between the sciences and the humanities, and between contrasting philosophies. Inter-faith, inter-disciplinary, and inter-ideological dialogue have become exercises in tokenism and virtue signalling with little effective results in practice.

The difficulty is otherwise evident in the relationship between people of different “types”, most notably that between people of different personality type — despite the efforts in team building. Understood otherwise there is an analogous difficulty in the relation between logic and emotion, or of physicality and intuition — however framed (Interrelating Multiple Ways of Looking at a Crisis, 2021; Ways of Thinking, Perception and Analysis, 2001; Ways of looking at ways of looking — in a period of invasive surveillance, 2014). Typically this is handled by favouring one or the other in a particular context — even to the exclusion of the others. The challenge has been partly framed and addressed by the various methods of Edward de Bono (Six Thinking Hats, 1985; Six Frames For Thinking About Information 2008). Their uptake has not responded to the development of the problem — especially to the conflicts it engenders.

Mathematics and geometry? In this situation it is therefore curious to explore whether mathematics and geometry have insights to offer — acclaimed as they are as offering the most sophisticated understanding of relationships.

A point of departure is the depiction by science of the relation between two contrasting modalities, of which there are many images.The most obvious is a magnet with fields of force between two poles. This is echoed to a degree by images of right and left brain as related through the hypothalamus. With respect to civilization, this frames a question regarding the hypothalamus and the corpus callosum (Corpus Callosum of the Global Brain?: locating the integrative function within the world wide web, 2014)

Whilst there are many images for a 2-fold relationship, somewhat less evident are the depictions of 3-fold relations. Although in this case imagery of knots and the like — most notably Celtic knots, the trefoil and the trefoil knot — frames such understanding. This is especially imbued with a degree of mystery in religious references to any trinity of deities. However although these may well be depicted in two dimensions, it frames the challenge of the form which any 4-fold relationship might take. In this case reference may be made to four-leaf clover and to more complex Celtic knots and related patterns — even to to the cinquefoil and beyond. Such petal and leaf arrangements clarify the distinction between a degree of unity in which all are linked at a common central point — an illusion of unity to which many vainly aspire in psychosocial organization — and other forms of coherent interrelationship (Keith Critchlow, The Hidden Geometry of Flowers: living rhythms, form and number, 2012). .

“Kiss-touch”: The approach taken here is to explore with AI the pattern of relationships between 4 modalities of any kind — as a point of departure highlighted as of special significance (Comprehension of Singularity through 4-fold Complementarity, 2024; AI-enabled Mapping and Animation of Learning Pathways, 2024). This may be readily depicted by placing a fourth orange on top of a configuration of 3 oranges touching one another in a triangular configuration — a pattern which is widely comprehensible in stacking fruit or cannon balls. Their specific points of contact are commonly referenced in design terminology as a “kiss-touch . It evoked an early discussion by Isaac Newton with David Gregory in 1694 regarding the “kissing number”, namely the maximal number of equal size non-overlapping spheres in three dimensions that can touch another sphere of the same size (Oleg R. Musin, The Kissing Problem in Three Dimensions, 13 June 2005).

The specific phrase “kiss-touch” is less common as a lexical unit, but it is transparently descriptive — especially in scientific or technical settings — of the moment or locus where two objects meet gently, as in sphere packing, billiards, or gears. It conveys both the delicacy and the exactness of such a contact, borrowing directly from these historical senses of physical and metaphorical closeness. Thus, as used in geometry or packing theory, “kiss-touch” is a natural extension of the established metaphorical and physical meanings of “kiss” as a light, precise contact. As such it featured in the descriptions of tensegrity structures and geodesic domes by Buckminster Fuller, who explored ideas around points of contact, interaction, and energy transfer. This relates closely to the geometric notion captured by “kissing” spheres in mathematics and physics (Synergetics: Explorations in the Geometry of Thinking, 1975)

As the specific point of transition from one sphere or domain to another — from one “language” to another — the question is then how best to understand the pattern of transitional pathways between four such domains — or more — when such domains are in close touch with one another in communication terms (Pathways in Governance between Logic, Emotion, Spirituality and Action, 2024) . Aspects of the question naturally invite geometrical and other commentary from mathematics, but the concern here is the relevance of such insights to psychosocial interaction. In this light the question relates to the quest for a Rosetta Stone to enable such transition, as discussed previously (Integrative implications of the Rosetta Stone, Philosopher’s Stone and Diamond, 2025).

The challenge could be caricatured as determining the “kissing number” in configurations of collective domains — enabling them to “kiss and make up”. The challenge is exemplified in the case of the pattern of 8 major religions (Stephen Prothero, God Is Not One: the eight rival religions that run the world and why their differences matter, Journal for the Scientific Study of Religion, 50, 2011, 1). It is evident in any effort to reconcile the 8 forms of intelligence of multiple intelligence theory, or the contrasting personality types in team building

Of course others claim greater or lesser numbers than eight, and in the case of the disciplines, the Web of Science database includes 241 subjects of study, whereas Wikipedia lists 1475 fields, as noted by Ugo Bardi (Science and the Dragon: Redistributing the Treasure of Knowledge,  Organisms: Journal of Biological Sciences, 5, 2022, 2). The Mathematics Subject Classification offers 64 top-level topics, but with seemingly little concern for how mathematics might be more appropriately organized for their comprehension (Is the House of Mathematics in Order? 2000; Configuring the 64 disciplines of mathematics as a 64-edged drilled truncated cube, 2021).

Transitional manoeuvers: Ironically the question is somewhat analogous to the gravity assist maneuver of spacecraft, and by extension to the hypothetical Interplanetary Transport Network (ITN) — the collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. Given the challenging psychosocial relations within patterns of otherness, the need for an analogous ITN is discussed separately in terms of the Possibility of an “Inter-other Transition Network” (2012). This suggests the value of using mathematics to explore the relations between silos by which communication is currently dysfunctionally fragmented (Mathematical Modelling of Silo Thinking in Interdisciplinary Contexts, 2024). Ironically, given their training on data sets from multiple silos, AIs offer a unique resource in exploration of inter-silo relationships.

Curiously, as noted above, the psychosocial challenge is exemplified by the very narrow window through which smooth transition is possible between modalities such as logic and emotion — somewhat analogous to the 3 degrees declination in the final approach of a viable glide path for a landing aircraft. The requirement for a smooth transition is most obvious in the case of highway entry and exit ramps. A high degree of continuity is required for viable transitions between distinctive modes — rather than sudden (“step”) transitions. This suggests a questionable comparison with any effort in discourse at “Getting to Yes” (1981), and the experience of arguments by the silver-tongued that are almost “right” or “true” — as in courtship and grooming.

Artificial intelligence: The following exercise was initiated as an experiment in communication with AIs, firstly in clarifying the nature of the challenge in geometrical terms meaningful to forms of intelligence only progressively developing a capacity to visualize in 3D. However the experiment also helps to clarify the challenges to the possibility of inter-modal connectivity — for those cultivating particular modalities, and having minimal comprehension of how this might be effectively structured, whether in 3D or more.

The experiment takes place in a period which there is extensive media coverage of the disastrous potential of AI — whilst carefully ignoring the disastrous potential of “business-as-usual” and the possibility that AI might enable a new “Cognitive Renaissance” in which the dots are more appropriately linked together (From disorderly “collapse” to orderly “renaissance”, 2019) . A particular focus is given to AI-engendered “hallucinations“, carefully ignoring the hallucinations currently sustained in the course of “discourse-as-usual” — whether within”cults” or ensuring the integrity of silos (Lucy Osler, AI-induced psychosis: the danger of humans and machines hallucinating together, The Conversation, 18 November 2025). The extensive commentary by AI in this experiment has been minimally edited — with the exception of removal of characteristic flattery, ironically corresponding to that featuring in many forms of social discourse. Extensive editing could be envisaged for particular purposes.

The exchanges with AIs went through many stages indicative of miscommunication, false starts and assertions of impossibility. Unexpected positive result were however achieved and visualized in geometrical terms. The animations are potentially of far greater interest to most than the details of how they were achieved — and are necessarily far more readily comprehensible. This invites reflection on the implications for psychosocial engagement between disparate domains between which there are typically no bridging pathways (Remembering the Disparate via a Polyhedral Carousel, 2025; .Dynamics of N-fold Integration of Disparate Cognitive Modalities, 2021)

Quadripolartiy vs. Bipolarity? Ironically the challenge is exemplified by the traditional discontinuities in the relationship between the four elements: Earth, Air, Fire and Water — curiously now framed in terms of disconnection from nature (Human Intercourse: Intercourse with Nature and Intercourse with the Other, 2007). Physically their relationship can be represented in pressure-temperature phase diagram. Missing is any analogous representation of their psychosocial analogues (Characteristics of phases in 12-phase learning-action cycle, 1998).

Somewhat curiously, that pattern of traditional elements could be understood as echoed in the four traditional directions by which the geopolitical world has long been framed: North, South (“Global South”), East, and West. In the light of the tetrahedral model articulated in what follows, this quadripolar polar pattern is compared with that presented by the Centre for International Governance Innovation (S. Yash Kalash, The Quadripolar World: understanding Twenty-First-Century geopolitics, 4 June 2025) — contrasted here with that of the Swastika..

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