The Semiotic Geometry of Networks: 1 The Geometry of Meaning

Every theory of language — and of reality — carries an implicit geometry. It organises potential into shapes: trees, layers, loops, or fields. Systemic Functional Linguistics has long favoured the network as its central image, but the network’s shape has rarely been treated as semiotic in its own right. It has been taken as a neutral representation of choice.

This post reopens that assumption. We ask: what does a network’s geometry construe about meaning?

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1. From representation to construal

In traditional SFL usage, the system network is a diagrammatic convenience — a way of representing options and dependencies. Yet from a relational ontological perspective, representation is itself construal: every depiction enacts a relation.

A branching network construes differentiation — potential sliced into exclusive paths.

A nested network construes inclusion — one potential contained within another.

A cyclic network construes reflexivity — potential that re-enters itself.

These geometries are not simply visual metaphors; they instantiate distinct logics of potential. The network does not depict choice; it enacts a theory of what it means for potential to become actual.

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2. Geometry as semiotic variable

Once geometry is treated semiotically, it becomes a meaning variable in its own right — as fundamental as delicacy or rank.

• Branching foregrounds exclusivity: choice as division, trajectory, decision.

• Nesting foregrounds dependency: inclusion, scope, contextual embedding.

• Cycling foregrounds continuity: feedback, recurrence, regeneration.

Each geometry thus carries an implicit ontology:

• branching assumes a directional flow from potential to actual;

• nesting assumes hierarchical containment;

• cycling assumes persistence through self-reference.

The choice of geometry therefore constrains the theory itself — shaping how we imagine potential, relation, and temporality.

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3. The semiotic horizon

If networks are geometries of construal, then semiotic systems differ not only in what they can mean but in how they imagine the structure of meaning.

• A grammar dominated by branching networks privileges choice and differentiation.

• A logic built on nesting (e.g., predicate logic, hierarchical semantics) privileges containment and scope.

• A processual model built on cycles (e.g., autopoiesis, feedback systems) privileges recurrence and self-organisation.

Each is a different geometry of meaning — a different worlding of potential.

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4. Beyond static diagrams

When we treat geometry as construal, the network becomes more than a static map. It becomes a semiotic field, a topology of relation that evolves with its use.

• Branches can fold into cycles, generating reflexivity.

• Nested structures can unfold into parallel branches, generating differentiation.

• Cycles can open into new branches, generating novelty.

Thus geometry is not fixed but transformative — meaning’s topology changes as systems interact, align, and re-enter one another.

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5. The conceptual move

This first post establishes a new stance:

The geometry of a network is itself a semiotic act — a construal of how potential relates to actualisation.

From this stance follow the next three explorations:

• Post 2: Branching networks and the logic of differentiation.

• Post 3: Nested networks and the logic of inclusion.

• Post 4: Cyclic networks and the logic of reflexivity.

We’ll then close by integrating them into a topology of meaning, showing how mixed geometries correspond to complex, evolving systems of construal.