firstname.lastname@example.org (Edward Green) writes: > >I used to think I saw a clear distinction, but now some of it is less >clear. This catastrophe occurred during a pointless argument in the >postmodern group about the significance of "a single data point".
Science rarely, if ever, relies on a single datum to overturn a theoretical prediction. A "data point" must have some error bars, and uncertainty or confidence level, associated with it which implies multiple measurements. A lot depends on how literally you take "single datum" (data are plural), which would probably be quite literally in a postmodern discussion.
The exceptions that come to mind are the old claims of an unchanging sky, disproved by the observation of planets or a supernova. Whether several observations of a single event, or a series of measurements of 'wandering stars' constitutes a single datum could be problematical. Major discoveries of wholly new phenomena can hang on a single experiment, but even Becquerel repeated his discovery of radioactivity.
>As we know, in the physical sciences we would hardly ever accept a >single observation as being a significant test of any theory. Yet in >mathematical logic we have the easy example that a single >counter-example is sufficient to overturn a theorem. A comfortable >distinction, but not well thought out, IMVHO.
A counter-example can overturn a theory as well, but the main difference is that mathematical consistency of a physical theory is only part of what we mean by a good theory, whereas it is all that we demand of a good theorem.
-- James A. Carr <email@example.com> | "They invented band!" http://www.scri.fsu.edu/~jac/ | Spectator at 1997 inaugural parade Supercomputer Computations Res. Inst. | commenting on the Macarena done by Florida State, Tallahassee FL 32306 | the Florida A&M Marching 100