1. The Problem with Singularities
In contemporary physics, a singularity names a point at which the theory fails: quantities diverge, predictions break down, and the mathematics no longer yields determinate results. This failure is routinely re-described as an extreme feature of reality itself—a place, moment, or state where nature becomes infinite, discontinuous, or opaque.
This move quietly transfers responsibility from the model to the world.
From the perspective of relational ontology, this is already a category error. Singularities do not announce an ontological abyss; they signal a breakdown in how readiness has been projected by a modelling system.
The task of this post is to show how singularities can be coherently re‑construed—without metaphysical inflation—by making explicit the relational conditions under which actualisation remains possible.
2. Readiness: The Condition for Actualisation
Within a Hallidayan, relational framework, readiness names the systemic condition that makes actualisation possible. Readiness is not a substance or force; it is a relational configuration.
Readiness has two subtypes:
Inclination — the orientation of a system toward further construal or action.
Ability — the capacity of the system, under current relational conditions, to enact that orientation.
Actualisation occurs only where both inclination and ability obtain. Remove either, and readiness collapses.
Crucially, readiness is always perspectival. It belongs to a system under a construal, not to the universe as such.
3. What a Singularity Really Marks
From this vantage point, a singularity is not:
a physical object,
a region of spacetime,
or an ultimate feature of nature.
A singularity marks a failure of readiness.
More precisely:
The formal system retains inclination: the equations continue to project further evolution or differentiation.
The relational conditions that sustain ability have collapsed: no further distinctions can be actualised.
The model nevertheless proceeds as if readiness still holds.
The result is mathematical divergence—"infinity"—not as a property of reality, but as an artefact of misprojected readiness.
4. Over‑Closure and the Vanishing of Potential Space
This failure can also be described in terms of potential space.
Relational ontology treats potential not as an abstract reservoir, but as the structured openness between actualisations. Actualisation is a cut through potential that stabilises a phenomenon while leaving further differentiation possible.
At a singularity:
the potential space between actualisations contracts to zero,
differentiation becomes impossible,
yet the formal system continues to demand further actualisation.
This is not openness without limit; it is over‑closure.
Infinity here does not mean boundlessness. It means the absence of relational room to move.
5. Why Physics Misreads the Situation
Physics inherits a powerful but hazardous habit: treating formal inclination as ontological authority.
When the mathematics says “continue,” physics assumes nature must comply.
But mathematics encodes inclination, not readiness. It cannot, by itself, register the collapse of ability. When ability fails, mathematics has only one way to respond: divergence.
Infinity is thus not discovered; it is generated.
6. Singularity as a Diagnostic, Not a Destination
Once re‑construed relationally, singularities become diagnostically valuable:
They identify where a modelling practice has exceeded its readiness conditions.
They reveal unacknowledged assumptions about continuity, differentiability, or persistence.
They mark the need for a shift in construal, not deeper metaphysics.
A singularity is a signal that the current horizon has been exhausted.
7. No Metaphysical Baggage Required
This reframing dissolves several long‑standing confusions:
No appeal to “infinite density,” “breakdown of spacetime,” or “edges of reality” is required.
No ontological drama needs to be staged at the limits of calculation.
No mystery remains once readiness is made explicit.
What fails is not reality, but a way of construing it.
8. Toward a Relational Practice of Modelling
If singularities are failures of readiness, then modelling practice must learn to ask a new question:
Under what relational conditions does readiness still hold?
This is not an empirical question alone, nor a purely formal one. It is a semiotic and ontological question about the legitimacy of projection.
Treating readiness as a first‑class constraint would allow physics to remain rigorous without becoming metaphysical—and powerful without mistaking inclination for inevitability.
Singularities would then be recognised for what they are:
not places where explanation ends,
but places where responsibility returns to the act of construal itself.
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