Theory 09/Theory choice/Method
Explanations Fail at Their Own Scale
An explanation is only valid within a band of scales set by the ratio of its mechanism's characteristic length or time to the phenomenon's, and applying it outside that band produces confident errors rather than obvious ones.
01What is already known
Physicists know this as the breakdown of effective theories; biologists as the danger of extrapolating from model organisms; social scientists as the ecological fallacy. Each field has its own cautionary tale. The common structure — that error is silent at the boundary — is rarely stated as a principle.
02The mechanism
A mechanism explains by identifying the variables that dominate at a particular scale. Outside that scale, the neglected variables become comparable to the retained ones, and the explanation degrades. Crucially, it degrades continuously: predictions remain superficially plausible while becoming wrong, which is why the error is not self-announcing. The band width is set by how sharply the dominant variables dominate.
03Predictions
- Errors from applying a theory outside its band should be larger, and more confidently held, than errors from applying a wrong theory inside its band.
- Fields should show characteristic failure modes at specific scale ratios rather than random error.
- Explicit statements of a theory's scale band should reduce overconfident extrapolation more than adding caveats about uncertainty.
04Refutation
If extrapolation errors are equally likely at all scale ratios, there is no band and the principle is empty.
Take well-specified theories with known characteristic scales, and compare prediction error as a function of the ratio between the theory's scale and the target phenomenon's scale, across disciplines.