1. Why Singularities Feel Like Infinity
In physics discourse, singularities are almost universally described in the language of excess: infinite density, infinite curvature, infinite energy. The intuition is straightforward and compelling—something has grown without bound, overwhelming the capacity of the theory to contain it.
This intuition, however, is precisely backwards.
What appears as infinity is not an abundance of possibility, but the loss of it. Singularities do not arise because reality has become too open; they arise because the space in which further differentiation could occur has collapsed.
To see this clearly, we need to shift attention from quantities to potential space.
2. Potential Space as Structured Openness
Within relational ontology, potential is not an abstract reservoir of unrealised states. It is the structured openness between actualisations—the relational room that allows one construal to give way to another.
Potential space is:
not empty,
not arbitrary,
and not limitless.
It is shaped by the horizon within which construal is taking place. Each horizon stabilises certain distinctions while leaving others available for further differentiation.
Without potential space, nothing new can be actualised. With it, actualisation remains possible without exhausting the system.
3. Actualisation as a Cut That Preserves Differentiability
Actualisation is not the elimination of potential; it is a cut through it.
A successful cut:
stabilises a phenomenon,
renders it available for experience, modelling, or action,
and crucially, preserves further differentiability.
In other words, a well-formed actualisation does not close the system. It momentarily closes enough to be coherent, while keeping the horizon open enough for continuation.
This balance—temporary closure with preserved openness—is what allows sequences of actualisations to occur at all.
4. Singularity as the Collapse of Potential Space
A singularity occurs when this balance fails.
More precisely:
actualisation has proceeded in such a way that no further differentiability remains possible,
the potential space between actualisations contracts to zero,
yet the formal system continues to project further actualisation.
This is not openness pushed to an extreme. It is over-closure.
The system has cut itself into a corner.
5. Why Mathematics Responds with Divergence
Formal systems, especially mathematical ones, encode inclination: they specify how a system should continue if continuation is possible.
What they cannot encode is the collapse of the relational conditions that make continuation possible at all.
When potential space vanishes but formal inclination remains, mathematics has only one available response: divergence.
“Infinity” is not a discovery here; it is a symptom. It is what formal continuation looks like when there is no relational room left to move.
The equations are not revealing boundlessness in nature. They are signalling that they have been asked to continue without a horizon.
6. Over-Closure Masquerading as Excess
This is why singularities are so consistently misread.
Over-closure presents phenomenologically as excess:
quantities blow up,
limits fail,
behaviour becomes undefined.
But ontologically, the situation is the opposite:
no further distinctions can be drawn,
no new perspectives can be stabilised,
no additional actualisations can be meaningfully projected.
Infinity here names not too much, but nothing left.
7. Reversing the Intuition
Once potential space is made explicit, the intuition flips:
Singularities do not mark where reality becomes unbounded.
They mark where a particular construal has exhausted its horizon.
The breakdown occurs not in the world, but in the relation between a modelling system and the potential it presupposes.
8. Orientation to What Comes Next
If singularities arise from over-closure rather than excess, a pressing question follows:
Why do our most powerful formal systems repeatedly push toward this point?
The answer lies in how mathematics encodes inclination while remaining blind to the collapse of readiness.
That will be the task of the next post: to examine why formal systems cannot see their own horizon conditions—and why this blindness is systematically mistaken for ontological depth.
Singularities, then, are not windows onto infinite reality. They are mirrors reflecting the limits of a construal that forgot to check whether potential space still remained.
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