The pursuit of beauty and economic theory: friends or enemies?
I read this post on Aeon by Frank Wilczek this morning. I posted about it on Facebook but doing so did not make me stop thinking about it. I want to put some of these thoughts down here, as they relate to economic theory, what draws me to it, and whether the draw of beauty in the mathematics used in economic theory detracts from the theory’s value to society. First of all, I invite you to follow the link above and come back to read the rest of my thoughts.
Wilczek has published a book recently, A Beautiful Question: Finding Nature’s Deep Design (Google Play link, Amazon link). I have not read it to the end yet, but I hope I will over the winter break. His discussion in the Aeon post immediately made me think about the art of mathematics and how it motivates me (and many others) to do economic theory and guides our attempts to do it.
Empires built on math
In my early years studying for my doctorate, I thought of math as a collection of empire-building tools for empires of the mind (castles in the sky might be another apt name). Economic theory, heavily math-laden, becomes in this view a galaxy far, far away where each theorist builds an empire (or at least a few starships) to impose order on the universe. Once you have laid down your assumptions, you then have a solid foundation for building and you are the emperor of your theoretical creations, as long as you can write down your mathematical arguments correctly.
This view is not far from Asimov’s galactic empire fiction. Indeed, Asimov himself thought that some sort of social physics exists, and if we can discover its laws, we could predict the unfolding of societies over vast, even galactic, scales. For economics, this perspective explains at least some of the psychological attraction theorists feel towards their castles in the sky. This attraction is particularly prominent for me when I am working on general equilibrium theory, which most of the profession has left behind.
Ethereal but irrelevant?
Good question! Let me first tell a story about logic and the demise of the Hilbert program in mathematics. Then I will talk about the fragmentation of economic theory, this one brought about by the confrontation of the theory with empirical tests, such as they are (famously much harder in the social sciences than in physics).
Hilbert was a prominent German mathematician. His famous and eponymous program was an attempt to make all mathematics utterly rigorous by putting it on a formal basis and to prove within that framework that mathematics is consistent. (Perhaps the best way to understand “formalization” in this sense, besides the obvious which is that it should be totally understandable to a computer, is by thinking about something von Neumann said: “Young man, in mathematics you don’t understand things. You just get used to them.” —source)
Hilbert’s program came undone when Kurt Gödel came up with his stunning, deep, and worldview shattering (for mathematicians) Incompleteness Theorems. The gist of these theorems is that if you build all of mathematics on a finite list of axioms, then you cannot prove by using this list of axioms all true theorems of mathematics and you cannot prove that the mathematics you have founded on these axioms is consistent (contains no contradictions).
Coming as it did in 1930, this devastating development seems to be a symptom of the fragmentation of European culture, which was soon to produce a horrible war. But what does it have to do with economic theory? Well, it tells us that the theoretical castles are indeed based on air, not stone foundations.
What’s worse, that’s not all that ails theoretical empire-building in economics. While there are plenty of valid criticisms to aim at empirical research in economics, its basic import is that grand, unified economic theories perform badly. This has led to the growth of “behavioral economics”. (Once again, let me point out how silly this name is: isn’t all economics behavioral? — I prefer psychological economics). However mainstream this field has become, it does have a shattering impact on beautiful theory-building that aims at wide applicability.
We contain multitudes and that can be beautiful too!
Well, it was good enough for Walt Whitman. How about we apply it to the entire society, whose functioning is the domain of study of economic theory, broadly conceived? Does the fragmentation I just talked about make further theory development ugly?
Many social scientists have written on this issue. To me, it seems that a fragmented field of theories can still be an object of beauty in the mind of the theorist. Think of it as a kaleidoscope (a word that literally means “a device for showing beauty”). This is how I attempt to keep my motivation up when I am struggling with long, messy arguments trying to prove something in complicated mathematical models of society that invariably leave my head spinning after only a couple of hours of effort.
Another good thing to say about the fragmented collection of models that constitutes modern economic theory is that it has produced some quite literally life-saving innovations (kidney exchanges, which came from a deeply mathematical field of economic theory called mechanism design theory). A good and easily readable account is Al Roth’s recent book Who Gets What — and Why.
Some others to read on related matters
In conclusion, here are some thoughtful works to read carefully that I constantly feel guilty for not having time to read carefully enough.
Dani Rodrik has a recently published book in which he “argues that economics can be a powerful tool that improves the world―but only when economists abandon universal theories and focus on getting the context right”, as the book description on Amazon states. Another book I have started — so I really should wrap this post up now and get back to reading, even without having convinced myself that this gigantic post is as well written as possible! Of course it’s not. But I move on anyway. Ars Longa, Vita Brevis. Or, in the original language of Hippocrates, taken from the last link:
Ὁ βίος βραχύς, ἡ δὲ τέχνη μακρή, ὁ δὲ καιρὸς ὀξύς, ἡ δὲ πεῖρα σφαλερή, ἡ δὲ κρίσις χαλεπή. In English: Life is short, and art long, opportunity fleeting, experience perilous, and decision difficult.