{"id":3639,"date":"2009-09-08T20:12:04","date_gmt":"2009-09-09T03:12:04","guid":{"rendered":"http:\/\/dabacon.org\/pontiff\/?p=3639"},"modified":"2009-09-08T20:12:04","modified_gmt":"2009-09-09T03:12:04","slug":"weinstein-v-krugman-v-orzel-mathematical-elegance-death-match","status":"publish","type":"post","link":"https:\/\/dabacon.org\/pontiff\/2009\/09\/08\/weinstein-v-krugman-v-orzel-mathematical-elegance-death-match\/","title":{"rendered":"Weinstein v. Krugman v. Orzel (Mathematical Elegance Death Match)"},"content":{"rendered":"

Over at the most uncertain blog, he of uncertain principles (aka Chad) takes up a challenge posed by @EricRWeinstein<\/a> on twitter concerning Paul Krugman’s recent article on why economists got the economic crisis so wrong<\/a>. Since I know even less economics than anyone around here this seems like a great opportunity for me to weigh in (this is, after all, the blogosphere!)
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\nKrugman’s article is deceptively enticing, yet I find it disturbingly inadequate. In particular the critique is very much written as a just-so story, and there is very little in terms of concrete claims made nor of actual solutions proposed. In particular I bet I could write his article and come to nearly the opposite conclusion (that the freshwater economists got it right) by suitably cherry-picking quotes from the saltwater economists (Fish: read the article to see the definitions of these two groups.) Okay, maybe not, but something about the article feels more polemic than scientific. But the main subject of Chad’s post and of Eric’s twittering is one early paragraph where Krugman lays out the following hypothesis (emphasis below is mine):<\/p>\n

What happened to the economics profession? And where does it go from here?
\nAs I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.<\/b> 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.<\/p><\/blockquote>\n

Chad makes the claim that Krugman is essentially substituting “beauty” for the seductive ideas of the efficient market hypothesis, the capital asset pricing model, etc and that really he isn’t attacking beauty or mathematical elegance. Indeed later in the article we find:<\/p>\n

Armed with their new models and formidable math skills — the more arcane uses of CAPM require physicist-level computations — mild-mannered business-school professors could and did become Wall Street rocket scientists, earning Wall Street paychecks.<\/p><\/blockquote>\n

(Take that mathematicians and computer scientists: physicist-level<\/b> computations! To be fair he does not say that they are more or less difficult than mathematician-level computations. But really, Paul, mild-mannered business-school professors as physicists? You’ve got to be joking.)
\nBut I think what Eric was getting at in his tweets is something a bit different. In particular I think what Eric is reeling against is that Krugman’s line is a very anti-intellectual, and perhaps anti-progress statement for economics, which confuses mathematics and it’s utility in the world with mathematics used to gussy up a wrong hypothesis. This later is, of course, a cardinal sin for any who hold experiment, reality, and science dear, and certainly Krugman accuses the freshwater economists of fishing in such waters. But, Krugman also suggests that the way out of this is not to look for elegance and beauty and good mathematics:<\/p>\n

It’s much harder to say where the economics profession goes from here. But what’s almost certain is that economists will have to learn to live with messiness.<\/b> That is, they will have to acknowledge the importance of irrational and often unpredictable behavior, face up to the often idiosyncratic imperfections of markets and accept that an elegant economic “theory of everything” is a long way off.<\/b> In practical terms, this will translate into more cautious policy advice — and a reduced willingness to dismantle economic safeguards in the faith that markets will solve all problems.<\/p><\/blockquote>\n

Now I wouldn’t argue against Krugman’s specific recommendations in this paragraph (that one must incorporate irrationality an unpredictability), but he does strongly suggest that the messiness of human behavior is explicitly responsible for the inability of an “elegant” theory of economics. The problem with this statement is not whether its true or false (whether there is anyway to establish a grand unified theory of economics), but that it is an extremely anti-scientific view of the world.
\nConsider, by way of analogy, the following argument. (1) String theory involves sophisticated mathematics and is beautiful, (2) String theory does not seem to work as a grand unified theory, therefore (3) sophisticated mathematics should not be used to come up with the correct approach to quantizing gravity. Certainly I would consider this form of argument as flawed and I think Krugman is pushing himself strongly in this direction. Krugman argues: (1) there is a very beautiful and mathematically sophisticated theory of economics with the efficient market hypothesis as its cornerstone, (2) these theories appear to have not done well as a framework for understanding the current economic crisis, thus (3) we should abandon any search for elegant and mathematically sophisticated theories in economics.
\nJust to give one example of this, I would point you to Eric Weinstein’s talk<\/a> in 2006 at the Perimeter Institute (I’ll be visiting PI next week!) where he attempts to use gauge theory to discuss problems in computing price indices. Yeah, that sounds completely crazy, but if you watch Eric’s talk you might begin to understand why it’s not so crazy. In particular Eric argues that while we currently view gauge theory as something which only physicists can use, i.e. which only applies to the laws of physics, it’s not at all clear that this is true. Of particular importance was the discovery, for example, that gauge theories like Yang-Mills theory have an elegant geometric description in terms of fiber bundles. Eric argues (I think) that this elegant structure is really capturing deep mathematics: the unreasonable connection between math and physics which we do not understand, but which we have certainly witnessed emerge during the history of physics and mathematics many times. Thus should we really be surprised if the mathematics that describes our universe (which has fancy terms like principle bundle, pullback, etc.) isn’t actually useful to describe other components of our universe beyond the laws of physics?
\nOf course this leap feels extremely far: from gauge theory to economics? But really, we already have great precedence for leaps like this. Take for example the fancy mathematics of 1693: calculus. Calculus has a deep and wonderful releationship with Newtonian mechanics, yet today we apply it in many different fields: biology, social sciences, economics, etc. Yet we don’t question it’s applicability there, in large part, I think, because we are used to it. It does not seem odd to apply calculus to biology but it might have been quite a shock to anyone around in 1693!
\nOne can argue tell one is blue that “humans are different” and that “economics is about Homo sapiens and therefore intractable” but if there is any hope for economics, it seems to me, it is not to retreat away from mathematical sophistication. Sure, I agree, fancy math can hide bad economics (same thing holds in physics.) But fancy\/deep\/beautiful math can also help you go where others have not been able to tread. Math arising from physics has an especially surprising way of being relevant beyond the laws of physics. So retreat not, economists, from the shouting hordes of anti-math naysayers at the gates, but head over to your physics, computer science, and math departments, sit in on a class with a subject you don’t know, and maybe, just maybe, it will give you tools to understand why the hell my 401K got hammered last year.<\/p>\n","protected":false},"excerpt":{"rendered":"

Over at the most uncertain blog, he of uncertain principles (aka Chad) takes up a challenge posed by @EricRWeinstein on twitter concerning Paul Krugman’s recent article on why economists got the economic crisis so wrong. Since I know even less economics than anyone around here this seems like a great opportunity for me to weigh … <\/p>\n

Continue reading “Weinstein v. Krugman v. Orzel (Mathematical Elegance Death Match)”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[26,28,34,41,53],"tags":[],"class_list":["post-3639","post","type-post","status-publish","format-standard","hentry","category-economics","category-extralusionary-intelligence","category-go-ahead-waste-your-time","category-mathematics","category-physics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/posts\/3639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/comments?post=3639"}],"version-history":[{"count":0,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/posts\/3639\/revisions"}],"wp:attachment":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/media?parent=3639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/categories?post=3639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/tags?post=3639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}