The most iconic example of this is the singularity.
It is here that physics’ forgetting is at its most dramatic: the point where the cut mistakes itself so completely that infinity (the refusal of limit) is equated with absolute closure (the imposition of limit). A divergence in a formalism becomes a metaphysical pronouncement about the universe collapsing into a zero-dimensional boundary.
This post examines how that mistake arises, why it persists, and how it dissolves once we take inclination seriously as the orientation of construal.
1. The Standard Story: Infinity Is Singularity
In textbook cosmology and general relativity, the logic runs like this:
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As a particular coordinate
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These divergences are described as “becoming infinite.”
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This is interpreted as a physical statement that the spacetime curvature or energy density is literally infinite.
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Therefore, the theory asserts a singularity: a place where the universe is infinitely dense and the laws break down.
This reasoning folds two incompatible construals into one:
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Infinity: unboundedness of a formal quantity.
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Singularity: total collapse of structure.
The result is a kind of conceptual Möbius strip—open divergence and closed collapse treated as the same phenomenon simply because they share the symbolic notation “∞.”
But in a relational framework, the contradiction becomes immediately visible.
2. Infinity and Singularity as Opposed Inclinations
In relational terms, neither infinity nor singularity is an entity. Each is a limit of inclination:
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Infinity marks the limit of openness-inclination—the model leaning so far toward unbounded specification that the distinctions it constructs can no longer be sustained coherently.
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Singularity marks the limit of closure-inclination—the model leaning so far toward over-determination that its structure collapses into an undifferentiable point.
These are opposite orientations of construal.
Their conflation occurs only if we forget that mathematics is not a lens but a cut—one with its own orientation. And when the formal behaviour is pushed past its natural inclination, the model generates pathological artefacts that physics mistakenly attributes to the cosmos.
3. Where the Conflation Begins: Reading Model Breakdown as Physical Revelation
The key move—made so frequently that physics no longer notices it—is this:
When the model collapses, interpret the collapse as a property of the world.
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The formalism is defined only for certain ranges of construal.
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We push it past those ranges.
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Divergence occurs.
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Instead of recognising this as formal overreach, physics labels it “a singularity.”
The result is a semantic slip:
model failure → reified as → physical event.
4. Why General Relativity Is the Perfect Stage for the Mistake
General relativity expresses gravitational phenomena through differential geometry—a mathematically exquisite construal that privileges smoothness, differentiability, and locality. These choices bring a specific inclination:
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toward continuous structure,
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toward local differentiation,
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toward smoothly evolving curvature.
When the ontology of the modelled situation exceeds these commitments—when the cut is leaned into regions where the formalism cannot sustain its own differentiability—the model responds with exactly the kinds of artefacts we see:
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curvature scalars blowing up,
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geodesics ending abruptly,
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volume elements collapsing to zero.
To call them “singularities” is to misidentify the residue of the cut as a feature of cosmology.
5. How Inclination Dissolves the Paradox
Once inclination is restored to the analysis, the apparent contradiction of “infinity as closed singularity” evaporates.
1. Divergence (∞) → a model inclined toward over-openness
The mathematics extends distinctions beyond where they can coherently be maintained. The divergence is a symptom of an over-opening of construal.
2. Singularity → a model inclined toward over-closure
The formal structure collapses because the construal over-specifies structure relative to the space of potential it is meant to articulate.
3. The conflation → a failure to distinguish these orientations
Physics treats the consequences of over-opening as the same as the consequences of over-closing because both produce a breakdown. The discipline treats the symptoms as ontological data rather than inclination-induced artefacts.
With inclination in view, we can re-describe what is happening:
The so-called singularity is not an infinitely dense point in the universe.It is the degenerate limit of a particular mathematical inclination,collapsing under the strain of its own commitments.
Just as a metaphor fails when taken literally, a formalism fails when taken outside its own relational horizon.
6. The Benefit of This Reframing
This reframing does not deny any empirical successes of physics. It does not rewrite cosmology. It simply removes a metaphysical mistake that has long distorted the discourse.
We gain:
1. Conceptual coherence
No more equating unbounded openness with absolute closure.
2. Diagnostic clarity
We can now see divergences as signs of mis-inclined construal, not cosmic catastrophes.
3. Methodological discipline
The separation between mathematical behaviour and world behaviour is preserved.
And above all:
4. The paradox disappears
The singularity becomes a limit case of a cut—not a feature of the universe.
7. Closing Gesture: What the “Singularity” Teaches Us About Construal
The singularity is the emblem of physics mistaking its mathematics for reality. Once we trace the problem to inclination, the drama quietens. There is no collapsing universe lurking at the centre of equations; there is only a model running out of space to differentiate.
The real revelation is not cosmological but methodological:
In the next posts, we follow this theme forward. Each will look at a case where an artefact of formal inclination was mistaken for physical truth—and what happens once we restore the cut to its rightful place as the generator of those artefacts.
And they disappear the moment we stop believing them.
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