Readiness — Potential Made Accountable: 2 When Readiness Collapses: Singularities Revisited

1. Singularities Through the Lens of Readiness

In classical and modern physics, singularities are often treated as points of infinite density, curvature, or probability—locations where the world appears to break down.

From a relational perspective, these are not ontological extremes. They are moments where a system’s readiness has collapsed:

• Ability → 0: the relational structure can no longer support further actualisations.

• Inclination persists: the formal system continues to prescribe evolution along collapsed axes.

The result is formal divergence: the mathematics “blows up,” but the world has not become infinite. Instead, the system is signalling the exhaustion of relational capacity.

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2. Readiness and Known Pathologies

We can see the same pattern across multiple domains of physics:

1. Gravitational singularities

   • Black hole centralities or big bang points arise when spacetime curvature and mass-energy compress potential space to zero.

   • The formal equations continue to demand a solution, but relational capacity no longer exists.

2. Wavefunction collapse

   • Linear evolution (inclination) persists, but the relational conditions needed to support indefinite superposition (ability) are exhausted by measurement or interaction.

   • Divergence manifests as the so-called “collapse problem,” signalling the need for a shift in construal.

3. Renormalisation and infinities

   • Formal divergences in quantum field theory are responses to the mismatch between inclination (formal evolution) and actual relational capacity.

   • Renormalisation can be interpreted as a corrective: restoring effective potential axes where readiness has been mismanaged.

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3. Infinities as Epistemic Diagnostics

Traditionally, infinities at singularities have been interpreted metaphysically: “the universe is infinite here” or “physics fails absolutely.”

Relationally, we reinterpret them as epistemic diagnostics:

• They indicate where the current construal no longer has the relational capacity to support further actualisation.

• They are not claims about reality itself, but flags for epistemic responsibility.

• Recognising this turns mathematical pathologies into practical guidance: when a model signals divergence, we must examine what relational resources remain and what shifts of construal are necessary.

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4. Readiness as a Predictive Lens

Treating readiness explicitly allows us to:

• Predict where over-closure will occur before formal divergence becomes numerically extreme.

• Design modelling strategies that avoid unnecessary metaphysical extrapolation.

• Clarify the boundary between formal mathematics and relational reality.

Singularities, in this light, are not cosmic catastrophes, but information about the horizon of applicability.

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5. Conclusion

Reframing singularities in terms of readiness dissolves their metaphysical mystique:

• Ability collapse is local and relational, not universal.

• Divergence signals the mismatch between formal inclination and relational capacity, not infinity.

• Models gain epistemic accountability without sacrificing formal power.

In the next post, we will turn to mathematics itself, examining how inclination can be encoded without accounting for ability, and why formal divergence proliferates precisely where mathematics is most internally coherent.