Mathematization in the Sciences

The superb pictures of Jupiter and Saturn transmitted back to earth by Pioneer 11 impress me as a marvelous technological achievement. Even more impressive is that this was accomplished without several prior attempts. It is certainly the case that subsystems were tested, and that engineers benefited from their experiences with related systems. Nevertheless, the success of this effort in the absence of the usual testing and refinement is remarkable. Contrast this success with the notorious inaccuracy of economic forecasts—despite the best efforts of knowledgeable people and great (dollar) incentives for accurate predictions. We accept success, especially technological success, in the physical sciences and engineering as a matter of course. We are not surprised—disappointed, perhaps, but not surprised—by the lack of success in areas more closely related to the life and social sciences. It is common to say that we understand (or that someone understands) the science and engineering of space probes, but we do not have comparable understanding of the economy or of many biological or social systems. What is frequently meant is that there are good mathematical models for the physical sciences, but that the models used in the life and social sciences are not nearly as effective. Let us examine this idea in somewhat more detail.