Solving a problem by using what you know: a physicist looks at a problem in ecology

摘要

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap physics (e.g. chemistry, engineering, geology) but also true in any endeavour where mathematical modelling may contribute insight to the solution of problems (e.g. timing of traffic lights, efficient ways to seat passengers on airplanes, whether it is better to walk or run in a rain shower). The second idea concerns an approach to problem solving. Before some people try to solve a problem, they think they first must learn everything that is known about the subject. However, sometimes an effective approach is to declare, ‘I'm going to solve this problem with what I know now!' I see a relationship between this approach and the idea of back-of-the-envelope calculations, which many of us appreciate. Of course there are limitations to this method, but I believe that such an aggressive approach to a problem—uninfluenced by the methods everyone else has used—can be productive. This paper describes such an approach to a real-world problem, using only what is known by the teacher of the introductory, calculus-based physics course. The intent of this paper is to encourage students and teachers of physics to look for unconventional areas, outside of physics, where they might use the techniques they have learned to solve problems