Effectively continuous means: the grain exists, but you can’t resolve it.
Interpretation
A thing can be discrete “in itself” yet still look continuous to a finite observer when the smallest differences are below the observer’s resolution.
A working definition:
- X is effectively continuous for observer S iff, at S’s resolution and time horizon, X cannot be reliably distinguished from a continuum description.
This is the “reciprocal” face of effective infinity:
- effectively infinite: you can’t reach the edge (upper bound invisible)
- effectively continuous: you can’t resolve the grain (lower bound invisible)
Clarifying Questions
Gaps & Inconsistencies
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