Posts Tagged ‘mathematics’

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Every time there’s a controversy in economics, the problem of mathematics seems to be at the center of the discussion. That’s because, in economics, discussing the role of mathematics is inextricably related to issues of science, epistemology, and methodology, which are themselves rarely discussed but are implicit in pretty much all of these discussions.

In short, we’re never very far from physics-envy.

That’s certainly the starting point of Noah Smith, who compares the mathematics of physics (the supposed “language of nature”) with that of macroeconomics (in which it serves to “signal intelligence”). And then, of course, Paul Krugman rides to the rescue, arguing that mathematical models, when “used properly,. . .help you think clearly, in a way that unaided words can’t.”

Uh, OK. “Used properly” is the operative clause there. The real question is, what is the proper use of mathematics in economics? And, what is the proper way of thinking about the proper use of mathematics? That’s where all the issues of science, epistemology, and methodology come to the fore.

As it turns out, one of the first articles I ever published, “The Merchant of Venice, or Marxism in the Mathematical Mode,” was on that very subject. I had mostly ignored mathematics during my undergraduate years but then, in graduate school and especially when I began to conduct the research for my dissertation (on mathematical planning models), I realized I wanted both to learn the econmath and to learn how to think about the econmath. Ironically, I ended up teaching “Mathematics for Economists” to first-year doctoral students for over a decade (it was basically a course in linear algebra and multivariate calculus, in which students also had to write a paper on the history and/or methodology of the mathematization of economics).

The argument I made in my dissertation and later in the “Merchant of Venice” article was that economists (mainstream economists especially, but also not a small number of heterodox economists, including Marxists) treated mathematics as a special language or code. They considered it special either in the sense that it was the language of nature (and therefore overprivileged) or a neutral medium for thinking and expressing ideas (and therefore underprivileged). Either way, it was considered special.

My alternative view was that mathematics was just one language among many, and therefore one set of metaphors among many. And like all metaphors, it served at one and the same time to enable and disable particular kinds of ideas. Therefore, we need to both write mathematical models and to erase them in order to produce new ideas.*

But that’s not how most economists think about mathematical models. And when they do think and write about them, they tend to invoke one or another argument for mathematics as a special code. They also tend to forget about all the other uses of mathematics in economics—not only as a signalling device but as a hammer to bludgeon all other approaches out of existence.

It’s the tool that is often used, in economics, to separate science from non-science—which, of course, if you say it quickly, becomes nonsense.

*That argument, concerning the not-so-special status of mathematics, so incensed one of my colleagues he attempted to derail my tenure case. Fortunately, another of my colleagues forced him to back down and I ended up receiving a unanimous recommendation.

Whose dream?

Posted: 14 February 2012 in Uncategorized
Tags: , ,

Many years ago, I was invited to give a talk, “Whose Dream? The Role of Mathematics in Radical Economics,” at American University.*

I was reminded of that event on reading Ian Stewart’s essay on the Black-Scholes equation and the financial crash.

Black-Scholes underpinned massive economic growth. By 2007, the international financial system was trading derivatives valued at one quadrillion dollars per year. This is 10 times the total worth, adjusted for inflation, of all products made by the world’s manufacturing industries over the last century. The downside was the invention of ever-more complex financial instruments whose value and risk were increasingly opaque. So companies hired mathematically talented analysts to develop similar formulas, telling them how much those new instruments were worth and how risky they were. Then, disastrously, they forgot to ask how reliable the answers would be if market conditions changed.

And that’s exactly what happened years earlier with Long-Term Capital Management. The board of directors of LTCM included Myron Scholes and Robert C. Merton, who shared the 1997 Nobel Prize in Economics for a “new method to determine the value of derivatives.” Their dream of conquering uncertainty, and of making tons of money in the process, is told in the Trillion Dollar Bet.

 

* This was before we used the internet to arrange such seminars. So, the title of my talk, conveyed by telephone, appeared on posters all over campus as “Who’s Dream?” Needless to say, the participants in the seminar wanted to know what Dr. Who had to do with economics.

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Many economists are obsessed with mathematics. That’s especially true among neoclassical economists but not unknown, as I have discovered, among Marxian and other heterodox economists.

Clearly, Krugman’s critique of mathematical elegance has struck a chord:

As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.

The latest to have his feathers ruffled and to proclaim that mathematics is the special code of economics is Gregory Mankiw:

mathematics is, fundamentally, the language of logic. Modern research into Keynes’s theories—I have conducted such research myself—tries to put his ideas into mathematical form precisely to figure out whether they logically cohere. It turns out that the task is not easy.

No, mathematics is one among many languages, one set of metaphors among others. But for economists like Mankiw, mathematics has a unique, special status in the way economic analysis is carried out. It’s the blunt weapon used to question the validity of Keynes’s theory and to bludgeon other not-necessarily-mathematical approaches to economics.

That’s what I argued in “The Merchant of Venice, or Marxism in the Mathematical Mode,” an essay published in 1988 (during the period when I taught graduate Mathematical Methods for Economics). When mathematics is assumed to be the special code of economics, it is either underprivileged or overprivileged. Underprivileged, if it is seen to be a neutral medium, and thus does not affect the results of economic analysis. It is the “language of logic,” which all economists should be forced to use. Overpriviledged, if it is taken to be the language of the book of nature, which means that only using mathematical formalisms and models provides access to reality.

Underprivileged or overprivileged, empiricism or rationalism—in both cases, mathematics becomes a special code.

The goal of questioning the fetishism of mathematics is, of course, not to argue against the use of mathematical forms of discourse but to recognize that, like all sets of metaphors, mathematics enlightens and obscures, it needs to be written down and erased, at the same time.

Treviso

And it all began with the Treviso Arithmetic, the earliest known printed mathematics book in the West, an anonymous textbook in commercial arithmetic written in vernacular Venetian and published in Treviso, Italy in 1478.