Mathematical presentations of arguments, whether in science or economics, not only make [arguments] more compact and their complexities easier to follow than a longer verbal presentation would be, but can also make their implications clearer and their flaws harder to hide. For example, when preparing a landmark 1931 scholarly article on economics, one later reprinted for decades thereafter, Professor Jacob Viner of the University of Chicago instructed a draftsman on how he wanted certain complex cost curves constructed. The draftsman replied that one of the set of curves with which Professor Viner wanted to illustrate the analysis in his article was impossible to draw with all the characteristics that Viner had specified. As Professor Viner later recognized, he had asked for something that was “technically impossible and economically inappropriate,” because some of the assumptions in his analysis were incompatible with some of his other assumptions. That flaw became apparent in a mathematical presentation of the argument, whereas mutually incompatible assumptions can co-exist indefinitely in an imprecise verbal presentation.
From Thomas Sowell’s Basic Economics. I love this story. I’ve always loved a good bull-session. I remember in college trying to tell a friend (probably on more than one occasion) to write down their argument on paper, rather than allowing it to be a jumble of ideas existing entirely in one’s head. An incoherent thought can survive a long time in your own head; writing it down makes you confront any obvious inconsistencies. Everyone can benefit from this simple exercise: write down what you believe such that you might convince an honest skeptic; do NOT write as if you are preaching to the choir. Admittedly, some people are immune to this test and embrace any nonsense that spews forth from their pen or keyboard. “Diarrhea of the pen” can be fine, so long as you clean up after yourself.
Thomas Sowell is describing the next step in this process – converting your argument as far as is possible into a purely mathematical or logical statement. I applaud anyone who takes it that far. Sometimes nonsense passes the “state it in plain English” test, but then fails the “convert it to math” step. I am sometimes irritated with people who have expressed a strong opinion without going through any of these steps. I consider it rude to waste people’s time with half-baked nonsense. If you don’t have an informed opinion about something, you probably should spend more time learning and thinking about it and less time talking about it.