Sean and Paul and the Beauty of Theories

Posted on September 22nd, 2009 by ryan.

Here’s a great exchange of ideas, the first from Paul Krugman in the NY Times regarding the failings of economists to foresee the recent implosion:

As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth. Until the Great Depression, most economists clung to a vision of capitalism as a perfect or nearly perfect system. That vision wasn’t sustainable in the face of mass unemployment, but as memories of the Depression faded, economists fell back in love with the old, idealized vision of an economy in which rational individuals interact in perfect markets, this time gussied up with fancy equations. The renewed romance with the idealized market was, to be sure, partly a response to shifting political winds, partly a response to financial incentives. But while sabbaticals at the Hoover Institution and job opportunities on Wall Street are nothing to sneeze at, the central cause of the profession’s failure was the desire for an all-encompassing, intellectually elegant approach that also gave economists a chance to show off their mathematical prowess.

And then some commentary from Sean Carrol, writing on my favorite physics blog, Cosmic Variance:

Without knowing much of anything about the relevant issues, I nevertheless suspect that this moral might be a bit too pat. Sure, people can fall in love with beautiful theories, to the extent that they overestimate their relationship to reality. But it seems likely to me that the correct way of understanding all this, once it’s properly understood, will look pretty beautiful as well. General relativity is widely held up as an example of a beautiful theory — and it is, when understood in its own language. But if you put the prediction of GR in the Solar System into the language of pre-existing Newtonian physics (which you could certainly do), it would look ugly and ad hoc. Likewise, Newton’s theory itself is quite elegant, when phrased in the language of potentials on a fixed spacetime background; but if you express the theory in terms of differential geometry (which you could certainly do), it looks like a mess. Sometimes the beauty/ugly distinction between theoretical conceptions is more a matter of how well we understand them, and less about their intrinsic qualities.

So my counter-hypothesis would be that it wasn’t beauty that was the problem, it was complacency. If you have a model that is beautiful and works well enough, you’re tempted to take pride in it rather than pushing it to extremes and looking for problems. I suspect that there is a very beautiful theory of economics out there waiting to be developed, one that understands perfectly well that individuals aren’t rational and markets aren’t perfect. One that has even more impressive-looking equations than the current favored models! Beauty isn’t always a cop-out.

Both those links are well worth a full read (the NY Times one is fairly long – schedule a cozy evening for it). In the spirit of dialogue, my feeling is that both Paul and Sean are coming at this from opposite ends of a single phenomena; well defined systems which involve feedback loops quickly become chaotic at larger scales. This is true for weather (we understand the basics of fluid dynamics and thermodynamics, but weather forecasts will never be very accurate), it’s true for the scale shift from quantum to relativistic, and it’s true for enormous economic systems. In other words, beautiful theories can both be true and useless – it’s all a question of scale.

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