Topology of the Possible: 1 The Field of Possibility — Relational Foundations

Possibility is often treated as abstract, an inert set of outcomes waiting to be realised. From a relational perspective, however, possibility is neither passive nor separable from the systems it informs; it is a field — dynamic, structured, and co-constitutive. A field of potential does not exist independently of the relational patterns that give it shape. Just as a river’s current is inseparable from the contours of its bed, so too is possibility inseparable from the relational topology of the worlds in which it may emerge.

In this conception, a possible state is not a discrete entity but a locus of relational tension. It is defined not by its singularity, but by its contrasts, alignments, and interdependencies with other loci. Potentialities exist along gradients: some are dense and accessible, others diffuse and latent. The field is patterned by both enabling and constraining forces; it is structured but not determined. Each instantiation — each actualisation — constitutes a perspectival cut into this field, revealing both the realised path and the remaining latent potential.

Relational ontology offers a lens for understanding these dynamics. Systems are not mere aggregates of components; they are theories of structured possibility. Their individuation is perspectival, contingent upon the alignment of local and global potentials. A possibility is not “there” waiting to be selected; it emerges through the interaction of the system’s constraints, histories, and relational affordances. In this sense, the field of potential is simultaneously expansive and contingent, emergent and patterned.

This relational field is inherently multi-scalar. Some potentials manifest at the micro-level of an individual’s capacities or choices, while others arise only at the meso- or macro-level, contingent upon the interactions of collectives, environments, or symbolic systems. The field is not homogeneous; it is stratified, gradated, and responsive. Resonances occur when local potentials align with broader systemic inclinations, amplifying certain possibilities while suppressing others. Dissonances indicate conflict or misalignment, revealing boundaries within the field of potential itself.

Crucially, the field of possibility is not simply a temporal projection. While potential is often imagined as “what could come,” its structure is always present, interwoven with past, present, and emergent futures. Possibility is a medium in which temporalities fold and overlap, in which constraints are sedimented and anticipations are embedded. A field of potential is, therefore, a living, relational topography — an ongoing negotiation between what is and what could be, between emergence and limitation, between continuity and novelty.

By attending to possibility as a relational field, we shift focus from outcomes to dynamics. The emphasis moves from what will or might happen to how potential is patterned, constrained, amplified, and phased. In this light, every actualisation becomes a lens, a cut through the field, revealing the contours of potential that remain unseen, yet operative. Understanding these contours is the first step in mapping the topological dimensions of possibility itself.