Reimagining Meaning Potential as a Probabilistic Waveform: Toward a Topology of Instantiation

Reimagining Meaning Potential as a Probabilistic Waveform: Toward a Topology of Instantiation

Systemic Functional Linguistics (SFL) has long offered a richly contextual and stratified model of language. At the heart of its architecture lies the notion of meaning potential: the structured possibility of meaning that underpins every instance of language in use. But how we visualise this potential has deep implications—not only for how we understand language, but for how we might model it computationally. This post proposes a reimagining of meaning potential not as a tree of discrete options, but as a probability field—a waveform-like structure that varies continuously and contextually. This perspective may open the way to new mathematical models of language, and new advances in artificial intelligence.

The Standard View: System Networks and Discrete Choice

In traditional SFL descriptions, meaning potential is represented as system networks: structured arrays of features, typically presented as choice points in a tree. These features are selected under contextual conditions, yielding a patterned configuration of meaning that becomes the semantic content of a text. Selection is guided by contextual variables—field, tenor, and mode—which together define the register of a situation type: the region of meaning potential that is most likely to be instantiated.

While this model has been enormously fruitful, its representation of potential as a discrete menu of alternatives can obscure the fluid, overlapping, and probabilistic nature of real-world meaning-making.

A Shift in Perspective: Meaning as Waveform

We propose that instead of visualising the system network as a tree of discrete choices, we treat it as a field of probability amplitudes—a wavefunction of meaning. In this model, each system and feature is not a fixed alternative to be selected or ignored, but a distributed potential: a weighted possibility that resonates with others, interferes, co-patterns, and is modulated by context.

Each point in the system is a node of amplitude, not a node of choice. Probabilities are not fixed scalar values but distributions—reflecting interdependence, constraint, and systemic harmony. Like wavefunctions in quantum mechanics, these amplitudes can interfere constructively or destructively, depending on the surrounding configuration. What results is a topological surface of meaning potential: a landscape of constrained possibilities.

Example: Interference in Mood and Modality

Consider a speaker choosing between "You must go now" and "You could go now." Traditional SFL treats these as selections within the systems of Mood and Modality. But under a waveform model, these aren't fixed binary options. Instead, the features 'imperative' and 'possibility' interact as overlapping probability amplitudes influenced by tenor (e.g. relative power, distance). A deferential but urgent context might shift the distribution such that both 'must' and 'could' are likely, yielding tension or hedging in the final utterance.

A diagram might illustrate a 2D probability field, with modality values distributed along one axis and mood types along another. Context modulates the peak regions—showing how likely each configuration is to be instantiated.

The Role of Context: Modulating the Field

Crucially, the contextual variables of field, tenor, and mode function not as selectors but as modulators of the amplitude field. They reshape the topology of potential—raising the probability of some features, suppressing others, and shifting the contours of meaning toward certain regions. This shaping of the field by context is what defines register: the structured variation of meaning potential across semantics and lexicogrammar in a given situation type.

In terms of the cline of instantiation, we can say:

• At the potential pole, we find the full system of meaning as probability amplitude fields.

• At the midpoint, shaped by context, we encounter register: a constrained and modulated configuration of potential.

• At the instance pole, we encounter instantiation: the collapse of the amplitude field into a patterned meaning event.

Importantly, register is not a separate stratum, nor a thing-in-itself. It is the variation zone on the cline of instantiation, seen from the potential pole.

From Choice to Collapse: Rethinking Instantiation

If meaning potential is a waveform, then instantiation is not a choice but a collapse: a resolution of distributed possibility into actual configuration. It is shaped by:

• The constraints of context

• The harmony and tension among features

• The trajectory of unfolding meaning

This model allows us to account for:

• The fluidity of meaning, even within a single text

• The interdependence of features

• The emergent nature of coherence and pattern

It also offers a powerful analogy to systems in physics, where wavefunctions represent potential states, and measurement collapses them into actual outcomes.

A Bridge to the Brain: Edelman and the Material Substrate

This wavefunction model of meaning potential aligns naturally with Gerald Edelman's Theory of Neuronal Group Selection (TNGS). In TNGS, cognition arises from dynamic interactions among neuronal groups shaped by evolutionary and experiential selection. Meaning is not retrieved from a mental library but emerges from the interaction of complex, probabilistic neural circuits—just as a linguistic instance emerges from the waveform-like distribution of systemic potential.

Edelman's notion of reentrant signalling—where neural maps send signals back and forth to synchronise and stabilise—mirrors the process of systemic harmony in SFL, where systems co-pattern across strata. Both suggest a material basis for the probabilistic waveform: a distributed potential across neural groups that is modulated by context, interaction, and experience.

Implications for Modelling and AI

Treating meaning potential as a probabilistic waveform opens new doors for modelling language mathematically. It suggests that:

• Meaning is not discrete, but topological

• Context modulates a distribution, not a switchboard

• Instantiation is emergent, not mechanistic

Such a model could eventually inform AI systems that generate language not by selecting from fixed options, but by navigating a context-sensitive amplitude field—producing meaning as a dynamic waveform rather than a deterministic code.

Incorporating Edelman's ideas further grounds this potential in the material order of consciousness—allowing us to imagine AI systems that simulate not only linguistic competence, but something closer to semiotic emergence.

Conclusion: A New Topology of Meaning

By reimagining the system network as a waveform, we preserve the core strengths of SFL—contextuality, stratification, metafunction—while offering a new way to understand variation and potential. This perspective gives us a topology of meaning that is rich, dynamic, and mathematically tractable.

And it brings us one step closer to modelling language in ways that do justice to its fluid complexity—not just for linguists, but for machines that seek to mean.