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.

More like this

It's not clear to me what Krugman is arguing against in that line. I do agree that his main target in the article is the freshwater concepts and ideas...seductively beautiful, but, perhaps not correct. However he specifically calls out "clad in impressive-looking mathematics." (Later he makes a dig at physicist level math.) To me that's just silly. As Eric points out, it's not at all clear that good mathematics isn't what is holding back economics. See for example his talk at the Perimeter Institute . Just as we shouldn't damn string theory just because it has "sophisticated" math (there are other reasons to damn it!) I think we shouldn't damn ideas in economics just be cause it has "sophisticated" math (plus sophistication is in the eye of the beholder. Calculus was once pretty sophisticated, but would you argue that applying calculus to economics (biology, etc) is wrongheaded?)

You have a brain, training in analytic thinking and problem solving, and you can write. That puts you WAAAAY out on the high end of Blogworld.

I happen to know an economist who consulted with hedge funds concerning those debt swaps that were supposed to insure against (hedge your bet) bad things. He always takes exception to physics papers, including ones like Eric talks about, because they never state their assumptions in the sort of clean set of mathematical axioms his school of economics (freshwater, I believe) favors. He would complain that we would never say whether the functions we were talking about had Lebesgue measure, for example. It drove him nuts that we just went ahead and saw if it worked. It was clear to us that economists like him did not really care if their math worked, because they could not do controlled experiments to see if it worked.

It really did seem to be about the beauty of the argument, not something messy like the "drag crisis" in turbulent flow or spontaneous symmetry breaking. Krugman nailed that aspect of their "theory" work perfectly. And I saw his remark about physicist-level math as more of a slam on the sophistication of the theories used by the economists.

By the way, they know quite a lot about the job market and the psychology that underlies an increase in the unemployment rate as you leave a recession, because people reenter the job market. What they don't seem to realize is that there actually was a bad recession in 1983 and minor ones since, because their theory says recessions don't happen. Seriously. That is what it says. It is practically an axiom. Of course, physicists and mathematicians know what to do when A implies B and B is provably false: you reject A. This is not what they do in Chicago.

By CCPhysicist (not verified) on 08 Sep 2009 #permalink

Okay, a swimming pool can have a deep end and a shallow end. But are my ex-professorships insufficient to parse: "high end blogosphere"? Spheres have ends? High and low WHAT?

I'm okay with TRUTH and BEAUTY. But, despite his Nobel, New York Times writings, and debate with Charles Stross, I'm not clear on what Truth and Beauty are to Krugman.

But maybe he's bashing Quants rather than the quantitative? Bashing Econophysics rather than Physics? I don't know.

Maybe it's a week and a half of forest fire smoke inhalation, but my mind is all fuzzy here.

Your throw-away line reminded me of a good topic you or Matt might take up: How the "3D movie" polarized glasses work. They use L and R circular polarizers, which is why you don't have to hold your head vertical at all times in the theater.

Krugman misses the point. Theories about economics are actually theories about power. Sure, the freshwater and saltwater economists phrase their arguments in terms of marginal utilities and differential equations, but they are arguing about economic and political power.

Astronomy was once like this, which is why the heliocentric model and arguing about mountains on the moon was considered a political challenge. Of course, this was in the 16th and 17th century.

Genetics in the Soviet Union had a similar problem with the rise of Lysenko and his politically correct theory of inheritance.

Remember, the scientific revolution only happened once, and only in one particular society at a particular time. Usually science, because of its relentless search for truth, gets strangled in its crib, just as most searches for truth get strangled in their cribs.

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.

I'm not an economist, so I'm happy to express an opinion in this corner of the blogosphere.

I don't think Krugman was writing about the large amounts of data that have built up, but rather that the theory was mathematically elegant, but built on unrealistic assumptions. It could be made more complicated (perhaps adding gauge theory), but if the assumption that everybody is rational is kept, the whole thing is still utterly unrealistic.

Sometimes I see the same thing in ecology: theoreticians build these wonderful castles in the air, but it's obvious that they have no connection to reality: there was a lot of fuss about chaos in the 80s, and spatial pattern formation in the 90s, but it ignored the simple fact that the environment changes in time and space. The empiricists largely got on with their work, and only looked at the theoretical stuff for the pretty pictures.

I wonder how many empirical economists (I guess this largely means economotricians) were looking at all this theory and saying "yes, but...". Shouldn't be too hard to spot them now, just look for the air of extreme smugness.

My take on Krugman's complaint is similar to Bob's: economists went to some trouble to construct elegant mathematical theories, but they never checked whether the underlying assumptions were valid, or even reasonable. Part of the problem is that it is difficult if not impossible to do the experiment in economics, whereas physicists can do (or at least envision) the experiment*, and any theory however mathematically elegant must fall by the wayside if it cannot predict the results of the experiment. Economists are only forced to abandon elegant-but-wrong theories after they precipitate market crashes, and even then it tends to be one-funeral-at-a-time progress.

*String theory is a likely exception here. Like economic theorists, string theorists have great difficulty predicting the outcome of controlled experiments. Often the relevant experiments, if they can be envisioned, cannot be feasibly implemented, which is the same problem economics has.

By Eric Lund (not verified) on 09 Sep 2009 #permalink

Is "Uncle Al" calling himself "Kaleberg" now? Just curious.

The beauty that Krugman is talking about in economics is very similar to the beauty of the two-dimensional Ising model. The Ising model is similar enough to realistic systems to be interesting, and aspects of it can be solved exactly. That solution exhibits highly nontrivial properties, which we know are, under the right circumstances, qualitatively similar to the behavior seen in real systems. The same statements could be made about a lot of economic models. Beauty here is something quite similar to mathematical rigor.

In physics, we have a pretty good idea what the underlying physics that describes more realistic ferromagnets is. In economics, we actually also have a pretty good idea what more realistic economic models should look like. Physicists have put a lot of effort into understanding the more realistic descriptions of collective phenomena. Economists have done a less adequate job analyzing the more realistic models of economic behavior.

There are a couple of reasons for this. One is probably that the economic systems are simply more complicated. The economists cannot be faulted for making less progress on those grounds. The economists are also less able to incorporate experimental insights into their analyses. Controlled experiments are difficult to impossible, and observational data on macroeconomics arrives only slowly. However--and here is where the economists really are to blame--they are also simply less receptive and less interested in the real-world data. Economists are drawn to one school or another by the general philosophy of the school. The schools have long track records or results, and most young scholars associate themselves with whichever school fits their preconceived notions about how the economy works.

Economists who chose the freshwater school because it agreed with their prejudices continue to work on the idealized, Ising-like models. They do this for two reasons. First, these models are tractable enough that they can actually get some results. Second, although they know that the models aren't perfect reflections of reality, they believe that they are "close enough." But that conclusion is mostly just based on intuition. The approximations involved in these idealizations are uncontrolled; it is not possible to quantify how close to reality the models are.

Beauty is never a good scientific argument because it is strongly observer dependent. While a perception of beauty is certainly a common motivation that drives many people, it isn't one that should enter a scientific discussion. Who says that the human sense for beauty should have anything to do with how Nature works? It's the same with religion. It might be an inspiration for some scientists, but it shouldn't enter the argument.

The point about gauge invariance however isn't so much its beauty as it's conceptual generality. It's no accident various forms of gauge invariance show up in very different places. It is in fact pretty artificial to stick with one particular (non-invariant) derivative just because it's the first one you encounter in high school. Whether or not gauge invariance in economics is actually useful however is a completely different question. While I tend to think it is probably correct to use proper parallel transport, I also think economics has much more severe problems than that.

The main difference (as I see it) between economists and the astronomers you mention is that there are many people who think the findings/theories/equations of economists have real-world application.

The longer they continue to be wrong in the way you describe (or in any other way, actually), the more their incorrect theories will be applied as monetary policy.

By Wilson Fowlie (not verified) on 09 Sep 2009 #permalink

As far as beauty in math and science, I love this quote from Wolfgang Pauli who had gotten annoyed at the constant declaration of "beauty = truth",

on the back of a postcard (or adverstisement, not sure which story is correct):
"This is to show that I can paint like Titian." (A big drawing of a rectangle) "Only technical details are missing."

In other words, a beautiful picture with incorrect details is pretty worthless.

By Lord Phat (not verified) on 09 Sep 2009 #permalink

It seems to me that economics is nothing like astronomy (or physics). Those comparisons actually annoy me quite a bit (sorry).

Economics is much more like biology. They still in the early days where the field should be dominated by naturalists, but have gotten delusional imagine themselves to be uncovering deep immutable laws.

There is a deep reason why economics is nothing like physics and a lot like biology. Economics and biology are both about complex adaptive systems. Meteorology would be an OK comparison too.

Krugman misses the point. Theories about economics are actually theories about power. Sure, the freshwater and saltwater economists phrase their arguments in terms of marginal utilities and differential equations, but they are arguing about economic and political power.

I would say that meteorology, physics, and biology all end up studying complex adaptive systems: spin glasses and the idea of frustration in general in physics for one example.
The big difference between econ and other adaptive systems is that in econ, conscious actors within the system react to knowledge of the system: new economic models are quickly incorporated and exploited by the players, and then superseded by models that take the previously exploited models into account. I'd only compare it to game theory, psychologists doing psychometrics on other psychologists, etc.

So economists (the ones that actually move markets, not just talk about them in retrospect) should be counted on to create/use models that maximize their own best (and probably short-term) interests. Those are only tangential to creating/using models that accurately portray risk: the tangent touches the line on the chart at the present day.

So what if your model correctly predicts a crash? Your job is to use the model that keeps money flowing into the system; using the "correct" model means you've failed and you're fired. Using the pretty model that says everything is fine leads to "success", at least as measured in economic terms. Take the bonus. You've only truly failed if you sunk that bonus into the assets you're pumping up.

hibob, good point

Though I would disagree. The complex adaptive systems physics (typically) deals with aren't really adaptive systems IMO. At best, they are the easy cases. The definitions are too fuzzy at this point to have a pitched battle about though ;)

The conscious feedback in economics is evil. Don't think we really need to invoke 'conscious', but there is a sort of emergent introspection which is at least different in quantity if not quality. Evolutionary biology has to deal with something similar though. Co-adaptation and environmental modification make the already neigh intractable "evolutionary dynamics in a multiple resource environment" problem all the more difficult (in a sort of combinatorial way.)

Your final point is brilliant though. I'd use the Y2K bug as an example. Just because (almost) nothing broke when clocks ticked over to 2000 doesn't mean that there was no bug to worry about. It more likely means that all the worries led to people actually fixing the problems before they exploded!
Y2K is a success story.

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.

In addition to the problem of needlessly annoying astronomers (;-) and demonstrating that you don't know very much about astronomy, I think your attempted analogy ends up making the opposite argument that Krugman was making -- and, since he's an economist, I suspect he has a better picture of his field than you or I would. Krugman was, I gather, arguing that postwar economics has been hobbled by an exaltation of theory over data, so that even fairly strong observational evidences (historical bubbles and crashes, including the Great Depression) got glossed over or explained away, because the (elegantly mathematical) theory of rational actors and market perfection had priority. It's not a problem of having lots of data (possibly measured in strange units) and little or no theory to interpret that data with -- it's a matter of trusting theory first, to the near exclusion of data. So even if your caricature of astronomy were correct, it's a poor analogy for economics!

More apt historical analogies might be possible. For example, one could point to 18th Century medicine: a field that had made some empirical progress over the past (e.g., much better anatomical knowledge than Classical or medieval times, including things like blood circulation), but which was still beholden to classical theories like the four-humors model, leading to the bleeding of patients to deal with fevers, despite the absence any real evidence that this helped.

Or, if you insist on slagging astonomy (;-), how about the 16th Century? Owen Gingerich has shown (e.g., in The Book Nobody Read) that while most astronomers of Copernicus' time either ignored or rejected his heliocentric model, they were quite impressed by what is to us pointless mathematical detail: specifically, the way Copernicus used combinations of uniform circular motions to replace the one blatant bit of non-uniform motion in Ptolemy's geocentric model, the equant.[*] (This was a technique which could be applied to both geocentric and heliocentric models, so his contemporaries could happily incorporate it into Ptolemy's model while while ignoring the weird heliocentric idea.) In other words, what mattered more than matching the observed data was ensuring that the theory was as mathematically beautiful as possible -- given that for both the ancients and for Copernicus and his contemporaries, perfection and beauty meant uniform circular motion.

Which neatly ties in with your comments about the ambiguity of "beauty" in mathematics and scientific theory.

[*] Copernicus may have based this on earlier work by Arab and Persian mathematicians in the 13th and 14th Centuries, although the exact route of transmission is unknown.