The Review of Economics and Statistics Vol. 37 No. 2 1955
More on the Misuse of Mathematics in Economics: A Rejoinder
Abstract
A YEAR ago and for another audience, my ET friend David Novick wrote a short piece on the misuse of mathematics in which piece has rather unexpectedly been made the center of controversy.1 Under the circumstances, a rejoinder, and perhaps a more specific restatement of some of Novick's criticisms, is in order. As I share many of his misgivings regarding some economics, 2 and because, as colleagues, we could readily confer on this rejoinder, the following comments can be considered a joint expression of our views. Because some have incorrectly inferred that Novick is opposed to any use of mathematics in the following list of more specific complaints, together with some examples from a recent work of Samuelson, is offered. i. A few writers make a travesty of mathematics by using its notation, but neglecting its operations. Instead of using the powerful techniques of mathematics to make implicit relations explicit, they merely paraphrase with symbols, and sometimes with their own peculiar and unexplained notation, ideas that could readily be stated also in prose. A very few may use mathematics as a form of lifemanship in the best Stephen Potter manner. It is probable, though, that most of these writers have no wish to win arguments through intimidating unintelligibility.3 However, the result is that many able economists, especially the older and more experienced ones, cannot comment on some published ideas because they cannot read them. Not only do many competent economists thus become frustrated, but the constructive criticisms they might make are unnecessarily precluded. This is unhealthy and wasteful.4 2. Economic life is so rich in detail that only a few of its features can ever be described in a set of equations. Hence all the rest necessarily becomes lost from any succeeding analysis if it is limited to mathematical operations. Such caricatures of economic behavior can lead to logically correct conclusions granted the assumptions, the form of the equations, and the input magnitudes if there be any and yet the results may really be useless. This spinning of theories, with little reference to the real world, can retard progress within economics and bring the profession into disrepute among those who must apply economic theories to problem areas. 3. The widespread use of mathematics has often tended to transfer attention and inquiry from the substance of economic life to the formal properties of some of the mathematical expressions used to describe it. Part of Keynes's contribution was to suggest, from his knowledge of the environment, that aggregate income was somehow related to intended savings and intended investment, and that the equilibrium income would equate them. The repeated enunciation of this idea by others, in the form of graphs and equations, has mesmerized some economists into forgetting that many of the Keynesian functions may not exist precisely.5 What are now really needed are empirical investigations to determine the existence and nature of, say, consumption and investment as functions of income. Somewhat analogously a few economists have become so hypnotized by the delightful fluctuations that can be generated by some dynamic equations, chosen supposedly to simulate business cycles, that they forget that the validity of these models remains unknown, and, in fact, may not even be susceptible to test. For example, do all firms, if one can sensibly think of so general a class, really adjust their cyclical inventory position in some unique mechanical fashion? Certainly we need models but surely the cost need not be learning much less about economic behavior. 'This REVIEW, XXXVI (November 1954). 2 Especially the high deductive and exclusive use of algebraic symbols, in extremely abstract models, without ref erence to data and with little thought to the real world. 3 The atheist Diderot is supposed to have been routed in confusion from Catherine the Great's court when confronted by an equation that, Euler told him, demonstrated the existence of God. 'I am indebted, though, to Samuelson for the pains he has taken subsequently to explain his ideas in a language I can better understand. 'In the sense that observed behavior, among classes, times, and countries, indicate no central tendencies.
- DOI
- 10.2307/1925744
- Volume
- 37
- Issue
- 2
- Pages
- 131
- Sources
- openalex crossref