Thursday, May 26, 2011

Poincaré's Take on Theories

I've always been interested in the ideas of mathematician and philosopher Henri Poincaré. While I have not read any of his philosophical work, his ideas as summarized by others have always resonated with me. Here's an excerpt from the Internet Encyclopedia of Philosophy on Poincaré's thoughts concerning the relationship between observations and theories (italics denote my emphasis).
According to Poincaré, although scientific theories originate from experience, they are neither verifiable nor falsifiable by means of the experience alone. For example, look at the problem of finding a mathematical law that describes a given series of observations. In this case, representative points are plotted in a graph, and then a simple curve is interpolated. The curve chosen will depend both on the experience which determines the representative points and on the desired smoothness of the curve even though the smoother the curve the more that some points will miss the curve. Therefore, the interpolated curve — and thus the tentative law — is not a direct generalization of the experience, for it ‘corrects’ the experience. The discrepancy between observed and calculated values is thus not regarded as a falsification of the law, but as a correction that the law imposes on our observations. In this sense, there is always a necessary difference between facts and theories, and therefore a scientific theory is not directly falsifiable by the experience.
Poincaré did not likely consider systematic errors in the reason for why observations did not match a theory, so it is interesting that a theory that does not match the experimental data precisely is not necessarily wrong.

How does the uncertainty principle tie into this argument?