In this course we tried to blend software and science in an unusual way. By the end of the semester, the maxims had covered quite a wide range of topics. You may find some of them exaggerated or oversimplified. And, of course, while a few of these ideas may be new, I recognize that many have been expressed before. Here are my maxims.
Scientific progress occurs by revolutions and paradigm shifts on all scales.
If Kuhn had written The Structure of Scientific Revolutions after the popularization of fractals, he would never have dared to suggest there were just two. If no parameters in the world were very large or very small, science would reduce to an exhaustive list of everything. Science is the extraction of underlying principles from given systems, and engineering is the design of systems on the basis of underlying principles. A computational study is unlikely to lead to real scientific progress unless the software environment is convenient enough to encourage one to vary parameters, modify the problem, play around. If the answer is highly sensitive to perturbations, you have probably asked the wrong question.