Physics has never been shy about borrowing from mathematics. It is less forthright about the price it pays for doing so. The discipline’s greatest conceptual triumphs owe their elegance to mathematical structure—but so do many of its most persistent confusions. Somewhere along the way, the formal scaffolding begins to imagine itself as the building; the behaviour of equations is quietly mistaken for the behaviour of the world. The result is a peculiar kind of ontological theatre: mathematical artefacts walk onstage dressed as physical entities, and physics applauds as though it has discovered something deep.
This series is about diagnosing that mistake.
1. The Central Problem: Conflating Formal Behaviour with Physical Structure
Modern physics often treats mathematical formalisms as if they were transparent windows onto reality. A function diverges, and we are told the universe becomes infinite. A symmetry survives gauge fixing, and we are told nature contains redundancy. A model under-specifies a situation, and we are told the world is “fuzzy.” A renormalisation trick works, and we are told nature secretly truncates itself at certain scales.
Each of these claims rests on the same underlying error:
The mathematical gesture is taken for an ontological revelation.
This is not physics; it is a failure of construal.
2. Mathematics Is Never Neutral: It Selects, Excludes, and Orients
In a relational ontology, every construal is a cut—a selective actualisation of potential from the system that grounds it. Mathematics is no exception. A mathematical model is not a passive representation but an active, inclined gesture toward the world. It foregrounds some possibilities, forecloses others, and takes a stance on how distinctions are drawn.
But physics rarely treats it this way.
Instead, the model is treated as a neutral medium, as though the structure of the formalism were simply revealing what is already there. In doing so, physics obscures the fact that the mathematics itself has a built-in inclination—an orientation toward openness or closure, toward under-specification or over-commitment.
This inclination shapes everything that follows:
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which distinctions the model amplifies,
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which it suppresses,
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where it overreaches,
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where it collapses.
When the formalism is pushed past its natural inclination, it generates artefacts: infinities, redundancies, collapses, divergences. And physics, forgetting that these arise from a particular cut, mistakes them for discoveries about the world.
3. Inclination: The Missing Conceptual Tool
To correct this, we need a concept that captures how a model leans—how it orients its own construal. That concept is inclination.
An inclined cut is never neutral. It always:
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opens in some directions while closing in others,
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coheres certain patterns while collapsing alternatives,
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invites particular continuations while resisting others.
Mathematics brings its own inclinations to the table.
And when physics forgets this—when it treats an inclined formal gesture as a literal description—what follows are the classic paradoxes it continues to misdiagnose as physical mysteries.
4. When Models Are Taken Too Literally, They Start Producing Monsters
The iconic examples are easy to list:
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“Infinities” interpreted as physical infinitude.
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“Singularities” reified as physical pinpoints where laws break.
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Gauge redundancies treated as actual surplus structure in nature.
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Renormalisation schemes mistaken for literal physical cutoffs.
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Wavefunctions read as states of being rather than generative constraints.
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Metric curvature taken as the intrinsic shape of spacetime itself.
Each is a case where formal behaviour is mistaken for ontological claim.
And each becomes solvable once we recognise that the mathematics is not revealing the world but expressing its own selective stance within it.
The failures are not empirical—they are construal failures.
When a model does something strange, what we learn is not “the universe contains strangeness,” but “the model’s inclination is showing.”
5. What This Series Will Do
This series, Cuts That Mistake Themselves, will examine these missteps one by one. Each post will analyse a familiar physics concept that has been inflated beyond its formal role and reified into a metaphysical claim. The goal is not to disparage physics but to sharpen it—to show how a relational understanding of construal can restore clarity where the discipline has tied itself into knots.
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Post 2 will show how the conflation of divergence with collapse arises from a failure to distinguish openness-inclination from closure-inclination.
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Later posts will examine gauge freedom, renormalisation, wavefunction ontology, spacetime geometry, and the myth of mathematical transparency.
The through-line is simple:
When physics mistakes the behaviour of its models for the behaviour of the world, it inherits paradoxes that were never the world’s to begin with.
6. Closing: Beginning the Undoing
Once we bring inclination back into view, the discipline’s deepest puzzles reveal themselves as misunderstandings of its own practices. The monsters were never in the universe; they were in the mathematics taken too literally.
This series is an invitation to that understanding.
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