Once we recognise locality as the hidden protagonist, its ubiquity becomes striking. Systems that succeed perfectly within their frames appear across domains — from perception and imagination to physics and computation. And in each case, the same principle holds: lawfulness is local; worldhood is not guaranteed.
Lawful in the Small
Consider any system that exhibits internal consistency and adherence to rules:
-
A visual construction obeys the geometry of its elements, even when the overall composition defies inhabitation.
-
A model of the cosmos produces predictions that are precise, reliable, and testable within its operational frame.
-
An AI system continues to generate fluent outputs, maintaining coherence token by token.
In each instance, nothing goes wrong locally. Every transition, every move, every computation follows its designed constraints. Precision is absolute, optimisation is achieved. Local lawfulness reigns.
Global Non-Integrability
And yet, the systems cannot always be composed into a coherent global whole. The impossibility emerges not from failure, but from the tension between perfectly lawful local frames and the demand for universal closure.
-
Geometric forms can be perfectly lawful step by step yet impossible to inhabit as a whole.
-
Cosmological measurements can be internally consistent while producing discrepancies when extrapolated to a global model.
-
AI outputs can satisfy local coherence while generating hallucinations when treated as globally referential.
This is non-integrability: lawful behavior that cannot be integrated into a single, stable, inhabitable world.
Locality as the Lens
Understanding these phenomena through locality clarifies a subtle but profound point: what seems like anomaly, error, or hallucination is often nothing of the sort.
-
It is not that the system is broken.
-
It is not that the world is misrepresented.
-
It is that the system never promised global coherence, only local lawfulness.
Recognition of this principle prevents the reflex to “repair” or force integration, which, as we have seen, is the true source of artefacts.
Across Domains, One Principle
By seeing locality as the common thread, we can:
-
Abstract lessons across domains without collapsing distinctions.
-
Predict where global incoherence will appear even in systems that are flawless locally.
-
Orient ourselves effectively without assuming worldhood.
Whether in the patterns of impossible constructions, the limits of cosmological inference, or the fluency of AI systems, the principle is consistent: lawfulness is local; expectations of global closure are artefacts of our own framing.
The Implication
Locality is not a limitation to be overcome; it is a diagnostic lens. Recognising it allows us to see structure where conventional failure criteria see only anomaly, and to navigate systems that are locally impeccable but globally uninhabitable.
The next question naturally follows: why do we so easily assume global coherence, and how does that assumption produce artefacts?
That is the focus of the next post in the plateau series.
No comments:
Post a Comment