The fetishism of mathematics
from David Ruccio
I am tempted, in response to Paul Romer, to paraphrase the Old Moor: “The use of mathematics in economics appears, at first sight, a very trivial thing, and easily understood. Its analysis shows that it is, in reality, a very queer thing, abounding in metaphysical subtleties and theological niceties.”
The last time I had the occasion to comment on Romer’s work was in reaction to the neoclassical colonialism of his proposal for “charter cities” in poor countries. Now, in a desperate bid to save the last vestiges of so-called endogenous growth theory, Romer has gone on the attack against what he calls “mathiness” in contemporary growth theory.
What is mathiness?
The style that I am calling mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.
Clearly, there is a particular notion of science behind this attack, the idea that
Science is a process that does lead to a broadly shared consensus. It is arguably the only social process that does. Consensus forms around theoretical and empirical statements that are true. Tight links between words from natural language and symbols from the formal language of mathematics encourage the use of words that are analytical and precise.
Everything else is non-science, what Romer refers to as “academic politics.”
Those of us who work in and around the discipline of economics have read and heard (and been subject to the bludgeoning in the name of) this old-fashioned positivist philosophy of science before: mathematics is the “hard stuff” that “real scientists” do—and, when they do it correctly, they contribute to “progress” and eventually reach a “broadly shared consensus.”
The implication is that anyone who does not agree with the presumed consensus is engaged in an activity other than science. It is the fetishism of mathematics, which I’ve had the occasion to write out before (in one of my first published articles).
But there’s something else going on here—not just an attack on mathematical “errors” committed in various areas of contemporary growth theory and the defense of a particular notion of science (really, “science is the most important human accomplishment”?). It’s the problem of capital.
As I often explain to students (as I’ve written before), the theory of capital is the most controversial topic in the history of economic thought because the theory of capital is the theory of profits—and therefore an answer to the question, do the capitalists deserve the profits they get?
It’s no surprise, then, that Romer credits the work of Robert Solow and Gary Becker as good examples of mathematical science (having contributed to neoclassical growth theory with notions of physical capital and human capital, respectively) and criticizes Joan Robinson (who troubled the neoclassical economists of her day by asking the key question, “what is capital?”) for engaging in “academic politics.”
In the end, Romer invokes mathematics and science to protect his “factional interest,” one that is committed to explaining economic growth in terms of “the scale effects introduced by nonrival ideas.”
Economists have a collective stake in flushing mathiness out into the open. We will make faster scientific progress if we can continue to rely on the clarity and precision that math brings to our shared vocabulary, and if, in our analysis of data and observations, we keep using and refining the powerful abstractions that mathematical theory highlights—abstractions like physical capital, human capital, and nonrivalry.
That’s what Romer wants us to focus on (problems such as the growth in the market for mobile phones) and not to ask what capital itself is and what role it plays in various forms and stages of capitalist development.
And, it seems, the only way he can attempt to deflect us from those difficult but important questions is by invoking the fetishism of mathematics.