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

This set of studies investigates the nature and magnitude of the redistribution of income throughout the world. Each of the distinguished authors addresses questions as complex as how governmental social policies effected the redistribution of income and what were the consequences.

Mitchell O. Locks, The Influence of Pattern-Bargaining on Manufacturing Wages in the Cleveland, Ohio, Labor Market, 1945-1950, The Review of Economics and Statistics, Vol. 37, No. 1 (Feb., 1955), pp. 70-76

IT is today rather generally accepted that the gloomy future which Malthus predicted as a result of the application of an increasing population to a fixed quantity of resources can be warded off by increases in the quantity of capital and improvements in the techniques of production. This will undoubtedly be true for a century or so; but it cannot be true for periods which are, after all, fairly short in terms of human history. Specifically, at the present time world population is probably increasing at an annual rate of about one and one-half per cent, which means that population is doubling every fifty years. If this rate of increase were to be maintained until 4250 A.D., the population of the world would weigh six sextillion, six hundred quintillion short tons, which is also the estimated weight of the world. Given the law of conservation of matter, it follows that there is nothing that science will be able to do even in an atomic age to increase output sufficiently to maintain the present rate of population growth until 4250 A.D.; sometime well before that date the increase must come to an end. Note that only the timing depends on the one and one-half per cent rate of population increase that has been used. If the correct rate were three per cent, only half the time would be required; if it were 34 per cent, twice as much time would be needed. It follows that if the time period is long enough, diminishing returns are always with us despite improvements in techniques and increases in capital.

HOW stable are consumer expectations? In view of the growing awareness of a relationship between expectations and consumer buying, and the concomitant rising popularity of intentions surveys and attitudinal surveys as indicators of consumer purchases, this question assumes a new importance. To what extent, for example, can attitudes and expectations ascertained at one moment of time be extrapolated six months or a year in advance, as is implicitly done when information of this type is used either alone or in conjunction with other material to predict the future course of expenditures? ' Basic to the use of attitude and expectations data in explaining and predicting human behavior and basic to the design of surveys for obtaining such data is the question of the length of time these data retain their validity. Some light is thrown on this question by data collected during an experimental monthly consumer panel operation conducted by the writer with the aid of the Bureau of Economic and Business Research of the University of Illinois. The results of an analysis of these data as they relate to this question are presented here.