Kuhn vs Copernicus

With respect to both planetary position and to precession of the equinoxes, predictions made with Ptolemy’s system never quite conformed with the best available observations. Further reduction of those minor discrepancies constituted many of the principal problems of normal astronomical research for many of Ptolemy’s successors… Given a particular  discrepancy, astronomers were invariably able to eliminate it by making some particular adjustment in Ptolemy’s system of compounded circles. But as time went on, a man looking at the net result of the normal research effort of many astronomers could observe that astronomy’s complexity was increasing far more rapidly than its accuracy and that a discrepancy corrected in one place was likely to show up in another.

Say you have a mathematical model that predicts some system you have no control over. All models and all measurements are wrong, so you’ll never get complete agreement between theory and observations. At some point, though, you’re sure enough about your measurements that you think the inaccuracy is in the model. You can always add ad hoc terms to a model. If you did regression, for example, you can add terms until you get a sufficiently good fit. Given enough degrees of freedom, you can fit to any finite number of observations, though I guess they didn’t have enough computing power to do this in the 15th century. Why is this kind of model complexity bad? It defeats the point of falsification, for one thing.

Even Copernicus’ more elaborate proposal was neither simpler nor more accurate than Ptolemy’s system. Available observational tests, as we shall see more clearly below, provided no basis for a choice between them. Under these circumstances, one of the factors that led astronomers to Copernicus… was the recognized crisis that had been responsible for innovation in the first place. Ptolemaic astronomy had failed to solve its problems; the time had come to give a competitor a chance.

The trouble with falsification is not just that every theory is false, it’s that just about every theory is demonstrably false. You can show that a particular method falls down and practitioners will no-sell this. Instead your burden is to show that the theory is no longer useful, which is a lot harder. On the other hand, falsification does win (usually, maybe) in the very long run: the eventual triumph of Copernicus over Ptolemy is because it fits observation better, even if that wasn’t clear in Copernicus’ time. Crisis generates theories, but in itself, it doesn’t determine which theory wins.