The Semiotic Geometry of Networks: Series Preface and Overview

Preface

System networks began as maps of choice — diagrams of potential within a system of meaning. But every map construes not only what is possible, but how possibility itself is imagined. The shape of a network is therefore not neutral: it encodes a geometry of construal, a tacit theory of relation and potential.

This series explores that geometry. It asks what different network forms — branching, nested, and cyclic — reveal about the kinds of meaning and reality they make possible. A branching network construes differentiation: one potential dividing into alternatives. A nested network construes inclusion: potentials enfolded within larger contexts. A cyclic network construes continuity and reflexivity: potential re-entering itself.

By reading network geometry semiotically, we open a bridge between systemic functional linguistics, relational ontology, and category theory. The network ceases to be a static diagram of options and becomes a topological construal of meaning itself — a geometry of readiness, alignment, and emergence.

Overview

The Semiotic Geometry of Networks explores how the shape of a network construes meaning, moving beyond traditional representations of choice to consider the topology of potential itself. Across five posts, the series examines three core geometries — branching, nesting, and cycling — and their integration into hybrid forms that capture the dynamics of readiness, alignment, and actualisation.

Key insights include:

1. Branching construes differentiation (either/or), structuring potential through contrast and perspectival cuts.

2. Nesting construes inclusion (both/within), structuring potential through context, containment, and inherited readiness.

3. Cycling construes recurrence (both/again), structuring potential through feedback, reflexivity, and temporal continuity.

4. Hybrid topologies integrate these geometries, producing networks capable of complex, adaptive, and emergent construals.

5. Topology as semiotic field: the arrangement of nodes, edges, and loops shapes not only what can be realised, but how potential itself is imagined and constrained.

By reading network geometry as semiotic, this series positions the system network as a general framework for understanding the relational organisation of potential and meaning across language, social systems, biology, and physics.