Home > The Economics Profession > The fetishism of mathematics

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.

  1. May 19, 2015 at 6:27 pm

    I totally agree with you, David (and desagree with Lars). Solow’s growth theory, and Romer “endogeneous growth model” enters in the same category of “mathiness” (that is, ideology disguised in mathematics”) that Lucas’s, Prescott’s, etc. models.

  2. May 19, 2015 at 11:08 pm

    Profit (not mathematics) is the key
    Comment on ‘The fetishism of mathematics’

    You nearly hit the jackpot of theoretical economics.

    You write: “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 …. It’s the problem of capital. As I often explain to students …, 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?” (See intro)

    The question whether capitalists “deserve” the profits they get is, clearly, a normative question. It leads straight away to moralizing. Everybody likes moralizing but let us resist the temptation to go further in this direction here.

    The first question to ask is rather: What exactly is profit and how is it determined for the economy as a whole? One should think that economists have found an answer in the last 200 years to this all important question. Did they?

    “Rather surprisingly, therefore, the nature of profits remains something of a mystery in contemporary economics; indeed, in the realm of “advanced” theory — namely the perfectly competitive general equilibrium models — profits have disappeared altogether. This is clearly an unsatisfactory situation. It is, first of all, illogical at best to argue both that profits are the mainspring of the capitalist system and that they do not exist. And second, the disappearance of profits from theory has not been accompanied by a similar phenomenon in the real world, where, in fact, profits (and losses) live on. Surely the task of theory is to account for this appearance, not ignore it.” (Obrinsky, 1981, p. 491), see also (Desai, 2008)

    It is also a curious observation that profit does not appear once in the JEL Classification Code of economic subjects.

    This is the fact of the matter: Neither Classicals, nor Walrasians, nor Marshallians, nor Marxians, nor Keynesians, nor Institutionialists, nor Monetary Economists, nor Austrians, nor Sraffaians, nor Evolutionists, nor Game theorists, nor EconoPhysicists, nor RBCers, nor New Keynesians, nor New Classicals ever came to grips with profit. Hence, they fail to capture the essence of the market economy.

    There is only one bright spot in the utter scientific darkness. The exception is Constructive Heterodoxy (2015).

    Egmont Kakarot-Handtke

    References
    Desai, M. (2008). Profit and Profit Theory. In S. N. Durlauf, and L. E. Blume (Eds.), The New Palgrave Dictionary of Economics Online, pages 1–11. Palgrave Macmillan, 2nd edition. URL http://www.dictionaryofeconomics.com/article?id=pde2008_P000213.
    Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: Profit. SSRN Working Paper Series, 2575110: 1–18. URL
    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2575110.
    Obrinsky, M. (1981). The Profit Prophets. Journal of Post Keynesian Economics,
    3(4): 491–502. URL http://www.jstor.org/stable/4537615.

  3. Eubulides
    May 20, 2015 at 3:25 am

    I wonder if Romer has ever read Ian Steedman’s take down of his mathiness?

  4. Larry Motuz
    May 23, 2015 at 4:52 am

    Three observations:

    1. Rationality requires providential forethought about what the consequences of consumption are for different consumers. This requires looking at and measuring the very different instrumental benefits that goods provide in their different uses. This also means that different budget allocations themselves change in response to nominal price changes.It also means that those with fixed means may have great meeting basic needs out of the mutable portions of their budget allocations.

    2. Consumption is the sue of a good for a defined purpose. Some of the time, that defined purpose, may be simply be ‘making money by producing widgets” as firms do. At other times, it means getting nutrients vital to life from food. Benefits from different uses have different units of account. With foods, those are energy units, vitamins, minerals, etc. The human consumer and the firm, though distinct, are both users of goods to obtain specific benefits.

    3. Income inequality matters … for people with higher means are able to afford a diversity of goods unavailable to those with lower means. Thus, the income distribution itself can be used to construct aggregate estimates of ‘supply’ and ‘demand’ and how these are affected by the distribution of income. Clearly, this raise the task of setting macro-economic theorizing on .
    the micro-foundations.

    4. Utility for a consumer can be positive or negative. Negative utility occurs when what is realized is less than what is required. For human beings, if one needs 2500 calories daily but achieve only 1600, then {1600 – 2500}/2500, then the negative utility index is -.36 for that person. Over a day that doesn’t matter. Over a year, it certainly does!

    Anyone interested in exploring the above with me should write me at larry[dot]motuz at gmail[dot] com.

  5. Larry Motuz
    May 23, 2015 at 4:54 am

    Typos: Four Observations

    The line “It also means that those with fixed means may have great meeting basic needs is ‘missing the word difficulties after ‘great’. Indeed, it may be impossible.

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