I’ve been learning some physics from Allan Adams and some physics students here at MIT, and I’ve suddenly realized that there are a lot of contextual tricks I take for granted when I’m doing physics, which make the physicists’ lives easier and sometimes really irritates the mathematicians. The first two examples I can think of is differentiating under the integral and never checking convergence, though both of these really fall under the bigger umbrella of assuming everything is well-behaved (which probably accounts for 80% of the mathematical gripes I’ve seen against physicists). Now, I’m a happy supporter of this “wishful thinking” practice: to use a programming analogy, I think of this habit as the lazy evaluation version of having good definitions, and as a lover of Python generators I totally appreciate the idea of saying “we’ll figure out the right definitions later since they actually exist.”

One of the most common physical tricks, however, is not of this category. It is the curiously natural framework: “we have a consistent idea of units.” Here’s a perfectly sound argument to get something that is not entirely obvious: Read More…