The Topology of Potential

Topology of Potential: A Bridge Between Quantum Physics and Systemic Functional Linguistics

In both quantum physics and systemic functional linguistics (SFL), systems are described in terms of potential: the field of possibilities from which actual instances are drawn. In quantum physics, this potential is formalised as a probability amplitude distribution—the wavefunction—which encodes the likelihoods of different observable outcomes. In SFL, meaning potential is represented by system networks of choices, where each choice (or feature) has a probability of instantiation, shaped by contextual variables and prior instantiations. While these fields are worlds apart in content, both are fundamentally concerned with the structuring of potential, and the constraints that govern how potential is actualised. This shared concern invites a transdisciplinary metaphor: the topology of potential.

From Possibility to Probability

In SFL, a system network is not merely a logical tree of options; it is a structured and dynamic architecture in which pathways are probabilistically weighted. The probability of a given feature being instantiated is shaped by the context of situation (field, tenor, mode), the co-selection of features in the current instance, and patterns from prior instances. Thus, the meaning potential is a probabilistic field, not a flat space of logical possibilities.

More precisely, we might describe the system network not simply in terms of scalar probabilities, but as comprising probability distributions—wavefunction-like structures that reflect not only the likelihood of particular features, but the interdependence and interference among them. Each system and feature can be understood as contributing to a distributed, context-sensitive probability amplitude, which constrains the shape of potential instantiations. This opens the door to treating meaning potential in SFL not as a list of discrete alternatives, but as a continuous, overlapping field of weighted options—more akin to a probabilistic waveform than a logical menu.

Similarly, in quantum physics, the wavefunction encodes a space of probabilities—complex amplitudes whose squared magnitudes determine the likelihoods of outcomes. This space is not defined by absolute positions or states, but by the relative amplitudes and phases of potential outcomes, including nonlocal correlations such as entanglement. What unites these systems is that the actual (text, measurement outcome) is drawn from a potential that is already structured.

Topology as Meta-Structure

Topology concerns itself with the qualitative structure of a space: continuity, connectedness, boundaries, holes, and invariants under deformation. When applied to potential—not as physical space, but as the structured space of probabilities—topology becomes a meta-description of how potential is organised. It characterises what remains invariant across transformations or perturbations to the local field.

In quantum physics, topological quantum computing exploits precisely this kind of invariance: some quantum states maintain their information even as they undergo local changes, because the information is encoded in global topological features such as braiding of anyons. These features are robust against noise because they are not defined locally but by the structure of the probability distribution as a whole.

In SFL, while system networks are not typically framed topologically, one can speak of attractors, constraints, and pathways of higher or lower probability—structures that shape how likely particular instantiations are. If these probabilistic patterns show stability across contexts, then they function as topological invariants of the system: meta-structural constraints on how meaning potential unfolds. Understanding system networks as probability distributions—rather than discrete branches—allows us to frame these invariants as emerging from interference patterns, amplitude modulations, and field-like organisations within the meaning space.

Topology Without Space

This account does not presuppose a reified spatial manifold. In both the quantum and linguistic domains, space and time are not independent containers in which processes unfold; rather, they are dimensions of actualised instances, emerging from structured potentials. In this ontology, topology does not describe physical geometry but the structured organisation of probability within a system. It is a grammar of potential, not a map of space.

Conclusion: Toward a Semiotics of Potential

By describing system networks and wavefunctions as topologies of potential, we highlight a shared logic across domains: that systems constrain not only what is possible but how likely it is, and that this constraint has a structure that can persist across local transformations. This opens the way for a theory of potential as structured, probabilistic, and topological—a semiotics not only of meaning, but of probability itself.

This move does not collapse the distinction between physics and linguistics, but instead offers a higher-order abstraction: the topology of potential as a conceptual bridge between semiotic systems and physical ones, between instantiation and measurement, between the actual and the possible.