Beyond the Linear Approximation

Abstract

If you happened to be good at math in high school, chances are you liked the subject. If you’re naturally gifted with a racket in your hand, it wouldn’t surprise me if you enjoyed playing tennis or squash. Personal success, it seems, focuses the mind like little else. Sometimes this rule also applies to entire disciplines. A perusal of old physics textbooks, for instance, quickly suggests that our discipline had been harboring a love affair with all things linear. Not that linear systems are very common in nature. No, linearity is the rare exception and not the rule. Rather, fact is that physics has had a lot of success with linear systems. They yield to mathematical analysis, and this analysis in turn allows for precise predictability. It’s not surprising then that in physics linear systems soon became the model children, the teacher’s pets. In textbooks they received most, if not all, the attention.