Kepler’s near discovery of the sine law: A qualitative computational model

Computational models offer an excellent tool for the study and analysis of scientific discovery processes. The study of failures provides an insight into the history and philosophy of science as valuable as the study of successful discoveries. Using a computational model I analyzed Kepler’s approach in formulating a quantitative law for refraction. Although Kepler ultimately failed in discovering the sine law, the model shows that his basic hypothesis as well as his approach by geometrical reasoning was a correct one. This went largely unnoticed by commentators on the history of optics. Based on this analysis I provide new evidence that Descartes and Snell found in Kepler’s main hypothesis everything needed to deduce the sine law by pure geometrical reasoning. Our computational model is based on geometrical knowledge as contrasted with previous quantitative approaches. It has been implemented as a Prolog program.