Physics Envy and All That
| Steven Postrel |
We often hear (sometimes on this blog) that mainstream economics suffers from an excess of mathematical modeling. Supposedly, math is distracting, or misleading, or limits the questions one can study. Occasionally it is asserted that math serves the purpose of disguising the triviality of one’s thoughts, or that it serves as a guild’s protectionist barrier against the worthy but unschooled. In my view, all of the same critiques may apply to any use of technical language (say in philosophy); one can find examples of all of these pathologies even when no math is involved.
Our problems, when they occur, do not lie in our tools but in the quality of our ideas, and our honesty in expressing them. And given the extreme difficulty in thinking clearly or precisely without mathematics about things like supply and demand, or optimal investment, or contingent contracts, or network structure and growth, I’m more than willing to entertain mathematical approaches. At least I can figure out what people’s assumptions are. (Of course, once you have the mathematical intuition down, it’s a good idea to try to translate your new understanding into verbal form, as long as everyone understands that something is always lost in translation.)
Critics of mathematics in economics, however, rarely come to grips with these specific issues of problem solving and understanding. (I have yet to hear, for example, an explanation of how diminishing or increasing marginal returns makes sense in anything but a mathematical context.) Instead, they employ a tactic that I think Phillip Mirowsky pioneered, accusing economists of suffering from “physics envy.” The idea, phrased to have an insulting Freudian resonance, is that economists aren’t smart enough to be physicists but like to play dress-up by adopting (what they think are) similar formal methods as their more-prestigious colleagues. Every now and then we hear the Feynmanesque “cargo-cult science” accusation that economists are like primitive Pacific islanders building grass control towers (mathematical models) and expecting real airplanes (scientific truth) to land.
Some people appear to think that the historical process by which math came into economics has a bearing on the accuracy of this smear. If Walras was influenced by contemporary works in physics, then the charge of physics envy is supposed to be proven somehow. This is a simple genetic fallacy, since the context in which someone gets an idea (say general equilibrium) has little bearing on the idea’s validity. The structure of the carbon atom supposedly came to its discover in a dream, yet historians of chemistry don’t talk about “shaman envy.”
But beyond this fallacy, the physics envy accusation is silly on its own terms. John von Neumann knew a fair amount of math and physics, and it didn’t seem inappropriate to him that economists should be using math — he complained that they didn’t use sufficiently sophisticated math (back in the 1940s), and would have laughed at the idea that the subject was somehow not suitable for formal modeling. Do ethologists have “economics envy” when they apply game theory or individual optimization methods to animal behavior?
The whole point of math is that lots of substantively different problems have similar formal properties. Exponential functions describe compound interest and they also describe radioactive decay (obviously, with a sign reversed). It would be an absurd example of Harold Bloom’s “anxiety of influence” if economists abjured exponential discounting to avoid accusations of physics envy. (Since exponential growth was one of the first formal ideas to be used in economics, by Malthus, it is an appropriate example.) Black and Scholes didn’t know that their partial differential equation for option pricing had something to do with the physics of freezing lakes — it just turned out that way.
So the next time someone pulls out the “physics envy” card, don’t be intimidated. They’re bluffing and playing a weak hand.