Beauty’s Just Another Word I’m Never Certain How to Spell

Like every other blogger with a political opinion, I read Paul Krugman’s essay on economics last week, and tagged it for Saturday’s Links Dump. And while I appreciate Eric Weinstein calling me out as part of the “high end blogosphere,” I’m not sure I have much to say about it that is useful. But, since he asked…

Twitter’s interface makes it almost impossible to go back and figure out what the hell was going on even a few days ago, but going through Eric’s feed, the crux of the matter seems to be that he takes issue with Krugman’s claim that “the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.” Eric argues instead that it is “the BUTT UGLY part of economics that just brought the world to the brink.” He then goes on to claim that gauge theory is required to explain inflation in a more realistically-modeled world, which I think is connected to the earlier statements because he (Eric) believes that gauge theory is mathematically beautiful. I think that’s the idea, anyway– my track record at predicting what Eric is actually trying to say is not good.

As a low energy experimental physicist, I don’t have enough experience with gauge theory to have an opinion of its aesthetic value. I think, though, that the problem here is a difference in the meaning of “beauty” for Eric and Paul Krugman. Isn’t that always the way?

Eric’s using “beauty” to refer to a sort of refined mathematical beauty that I have no appreciation of (being, again, a low energy experimentalist). In his view, the problem of modern economics is that the mathematics that macroeconomists were using wasn’t sophisticated enough.

Krugman, on the other hand, is referring to a more conceptual sort of “beauty.” There’s a certain kind of elegance to what Krugman calls “freshwater macroeconomics,” in honor of its mostly Midwestern proponents. There’s something kind of seductive about the simple rational-maximizer models they used, in which you can build up all sort of large-scale economic behaviors based on the idea that people know what they want, and will act in a rational manner to get it.

That kind of conceptual elegance is something I can appreciate a little more than the gauge theory end of things. You get the same sort of thing happening in fields like classical optics or statistical mechanics, where you can derive bulk properties from astonishingly simple assumptions about the uncountable trillions of atoms making up a sample. It’s really amazingly cool that you can work out, say, how polarized sunglasses work from the assumption that material objects are made up of tiny electronic dipoles that oscillate in response to an applied oscillating electromagnetic field.

As I said, I can appreciate this sort of conceptual beauty a little more than the more highly mathematical sort. Of course, it’s very important to remember that the approximations going into these models place very strict limits on their applicability. You can describe polarization by reflection using a very simple atoms-as-dipoles model of the interaction between light and matter, but that model is going to give you problems when you deal with light that is near a resonant frequency for the material in question. Because, in the end, atoms aren’t really tiny classical dipoles that oscillate nicely in response to nice, classical electromagnetic waves– both light and atoms are quantum objects, and behave according to different rules than classical dipoles.

Similarly, you’re going to have problems with a conceptually elegant mathematical model of an economic system when the millions upon millions of people making it up aren’t really spherical, frictionless, and perfectly rational maximizers of utility. This is the sort of beauty-related breakdown that Krugman is writing about.

Now, it may be that you can rescue your model by applying some more sophisticated mathematics to the problem, and it may be that what you end up with has Eric’s mathematical sort of beauty. I’m really not qualified to judge that for economics, but it’s true in physics– you can quantize the field, and quantize the atoms making up a material, and recover your original predictions as a large-detuning limit of a more complicated theory that will also describe resonant processes using the same higher-level theoretical framework. There’s a kind of beauty in that, to be sure, but I don’t think economics is there yet.

As for the larger issue of the state of economics as a discipline, all I can really do is repeat my joke from the links dump, namely that economics is the astronomy of the social sciences.

It’s actually a somewhat dated joke, as astronomy has become a lot more respectable these days. You can still get a sense of what I mean from watching a lot of astronomy talks, which are full of plots whose horizontal axes increase from right to left, and weird non-linear relationships between quantities. This is mostly historical, and happened because astronomers developed the ability to make measurements well before they developed the ability to interpret those measurements, and thus had to guess at what appropriate relationships might be. Later on, it turned out that the quantity they had chosen to measure was the negative logarithm of the temperature, or some such, but by that time they had been plotting things on funny axes for so long that they continue to do so to this day.

Economics, it often seems to me, is in the backwards-graphing stage. They’re piling up lots of data, and identifying some relationships between some of those data, but they don’t have a good handle on what’s really important. Which is how you can end up with an economic boom in which median real wages remain stagnant, or see the unemployment rate decrease because people have given up looking for jobs.

Somewhere down the road, somebody will figure out what they really ought to be measuring, which will turn out to be the negative logarithm of what they’re measuring now, or some such. The process may even involve highly technical mathematics that are beautiful in their own way, but they’ll keep plotting everything backwards just because.