Number 21/Measurement & inference/Theory
The Scale Band Width
The quantity
The ratio of scales over which a theory retains most of its predictive accuracy before errors exceed a stated tolerance.
01Why it matters
It makes the domain of applicability a measurable property rather than a caveat, and lets competing theories be compared on band width as well as accuracy.
02Expected value
Narrow bands for theories built on a single mechanism, wide for those aggregated over many.
03How it would be measured
Test a theory's predictions across a range of scales and locate where error crosses tolerance.
04What would refute it
Uniform accuracy across all scales would make the band infinite and the concept unnecessary.