Saturday, June 20, 2009

All models are wrong

.. but some models are useful (George Box et al, 2009, p.61). What makes a model useful? Some theories of science have made grand descriptions in terms of prediction, explanation etc, but it really comes down to a consensus. Today (June 20th) it is reported that the British Government has decided that the spelling rule “I before e except after c” should no longer be taught in schools because the large number of exceptions made it useless. Such a rule is of course one of observation rather than a law of nature, but on close inspection it is easy to find hidden qualifications to any law you care to mention.
Until very recently, many in the scientific community used to imagine that they were discovering the truth about how the physical world works. Whewell (1833, p.256) quotes Lagrange’s opinion “that Newton was fortunate in having the system of the world for his problem, since its theory could be discovered once only”. Now a lake can be discovered only once, but systems are merely constructed, and many refinements and re-interpretations will be possible. Twentieth century physics revealed unimaginable strangeness, needing many alternative and conflicting models to apply to quantum mechanics, diffraction, cosmology, etc., and there was some useful criticism of old notions such as “final causes” (basically, boundary conditions at infinity).
Many researchers in the late nineteenth and early twentieth century searched only for natural laws expressible in terms of differential equations. Since this search followed so closely after the development of the calculus it appears with hindsight that these men with a new hammer suddenly saw nails everywhere.
The same hindsight opens our eyes to the serious untruths in their “natural laws”: on close inspection a natural law does not actually apply everywhere, but only (um..) where it applies (e.g. in the absence of discontinuities, in a neighbourhood of the origin). To be fair, talk of truth or laws was mostly a habit of speech: the models described in these laws are useful in telling us what to expect in the sort of situation for which the model was designed. In other situations or on close inspection we might need a different or more refined model.
As with final causes, or the ether, models can be useful even when they conflict with other models (seem counter-intuitive) or don’t fit with current ideas of causality. For example, classical field theory remains useful, even though we know that action at a distance is impossible, and that there is a better model based on radiation. Non-existent lakes will eventually be removed from atlases, but models will continue as long as somebody finds them useful.

References:
Box, G. E. P; Luceo, A.; Paniagua-quinones, M. d. C. (2009): Statistical Control by Monitoring and Feedback Adjustment, 2nd ed. (Wiley) ISBN 0470148322
Whewell, W. (1833) Astronomy and General Physics: Considered with Reference to Natural Theology

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