Physics versus Math

May 19, 2015

You might think that my undergraduate degree is the kind of thing I’d remember. But if so, you’d be wrong.

A colleague noticed that in my post about protecting the norms of science, I wrote that I had an undergraduate degree in physics, but my CV says (correctly) that my undergraduate degree from the University of Chicago is a B.S. in Math. I was a physics major for most of my time there, and physics was the focus of my coursework. Here’s how I ended up with a math degree. 

During the first lecture for a course on experimental methods that was required for the physics degree, the professor, James Cronin, tried to offset the bias toward mathematical theory that we picked up in our other physics courses by saying that whenever possible, he avoided the use of math. “If I had to calculate the area under a curve,” he said, “I’d plot the function on graph paper, cut out the area under the curve, and weigh it.“ I was such a math snob then that I decided instantly to drop the course.

Because I had enough courses for the B.S. in Math, I switched to being a math major just in time to graduate. Cronin subsequently won a Nobel prize for his work on experiments that found evidence of violations of CP-symmetry. 

If you are an undergraduate thinking about studying economics in graduate school, I’d strongly recommend a physics degree, or at least lots of physics courses. Math is a tool, but math courses do not teach judgment about how to use this tool to make good abstract mental maps of real world terrain. Learning about models in physics–e.g. the Bohr model of the atom–exposes you to time-tested models that found a good balance between simplicity and insight about observables. Familiarity with many good models is the best way I know to develop a sense for how to take full advantage of the “map-terrain” relationship when you want to develop your own mental map of some new region.

Finding the right balance in map making seems to be something that we infer by recognizing patterns from many examples. It is not something we can learn by memorizing some check-list for good model building; or writing down some postulates for map-making and then proving some theorems about good maps; or blogoviating about what the opaque writings of some revered dead person might teach us about map making. Pure reason, which math sharpens, does not get you very far in learning how to use pure reason. At some point, you have to get out of your own head.

My diagnosis in the mathiness paper–that growth theory is broken because it suffers from a persistent disagreement analogous to the one between advocates for the geocentric and heliocentric models of the solar system–is based on a belief that when science is working well, it leads to agreement. I picked up this idea from the “verbal tradition” at the University of Chicago. Someone who knew him from his time at Chicago said Enrico Fermi claimed that “science is a process for resolving disagreement.“ 

The quote stuck with me because it was so provocative. For years, I thought it had to be wrong. Surely Robinson Crusoe could do science all by himself. 

I still believe that on the map side of the map-terrain relationship, one person working in isolation can prove a logically correct mathematical theorem. But I have come to believe that the only reliable knowledge about terrain comes from group consensus. Individual humans are not sufficiently self-aware to filter out their own biases.

If dogs had different kinds of brains, they might understand calculus and Newtonian dynamics. If humans had different kind of brains, maybe they could have perceptions of the world that are not biased. But we have to work with what we’ve got.

I wish it were needless to say but it is not: the kind of group consensus that a cult generates is no better than the judgment of the revered leader. What true science requires is a consensus that is hammered out among people who know how to think independently and are not afraid that they’ll be bullied if they disagree with their elders.

I still love the beauty of math, but I have lost the arrogance of youth, that confidence that one person working alone can discover true knowledge about terrain.

If I had it to do over, I would take the experimental methods course from Cronin.