Tag Archives: Galileo

Originally published April 4, 1983






“I HAVE NO great faith,” confessed Adam Smith, “in political arithmetic.” The great Smith’s great modern successor, John Maynard Keynes, allowed himself similar views. After a page of moderately sophisticated mathematics in The General Theory of Employment, Interest, and Money, Keynes wrote: “I do not myself attach much value to manipulations of this kind … they involve just as much tacit assumption to what values are taken as independent … as does ordinary discourse, whilst I doubt if they carry us further than ordinary discourse can.” In a footnote in another part of the work, he remarked: “Those who (rightly) dislike algebra will lose little by omitting the first section of this chapter.” (Lay readers may, in fact, act on this advice throughout his book, for he almost, always follows a possibly forbidding mathematical statement with the same idea expressed in “ordinary discourse.”)

The propensity to quantify, however, is as American as apple pie and cheesecake. We do not hesitate when asked whether we agree that Bo Derek is a 10. With a little rumination, we will rank our worry about unemployment, or how important we think speed on the base paths is to the New York Yankees, on a scale from 1-5. Taking such matters seriously enough to pay attention to them, we were predisposed to be impressed when told a couple of months ago by the National Association of Business Economists that a poll of 230 of its 4,000 members “forecast that the real gross national product will increase only 3.3 per cent over the 12 months of 1983.” Speaking for myself, I will agree that there will be 12 months in 1983 – provided we manage to avoid a nuclear war.

Aside from that, I note that we are here offered an average (or perhaps a mean or even a mode) of 230 more or less educated guesses, more or less inspired by occupational calling to be optimistic. And I observe the words that follow: “Real” doesn’t mean anything empirical you can point to but is a statistical construct; the nominal GNP (on which the “real” is based) is a somewhat different agreed-upon (but still misleading) fiction; the expected increase will probably be measured by comparing a weighted extrapolation from the constructs for December 1983 with a similar extrapolation from those of December 1982.

In short, the apparent authority and precision of that 3.3 per cent forecast are as phony as a 3.3-dollar bill. Yet we view such figures as important, try to develop policies based on them, and will congratulate the forecasters if the result is as close as 2.3 or 4.3 per cent. After all, that would be an error of only $30 billion, give or take a few hundred million. Never mind that you could employ 3 million people with $30 billion.

Although this is pretty mild stuff, anyone coming fresh on a meeting of economists or a reading of their journals is likely to feel he’s stumbled into a nest of mathematicians. It is possible that the proliferation of equations is a by-product of the computer and thus qualifies for inclusion in the GNP. Nevertheless, it is by no means certain that the pyrotechnic display of subscripts and superscripts is (to try to rehabilitate a debased word) relevant. The difficulty is not merely the familiar one of

GIGO, or garbage-in/garbage-out; it is the more fundamental consideration that the basic concepts and problems of economics are simply not mathematical.

The first clear claim that economics is mathematical came in 1871, half way between Adam Smith and the present.

It was made by William Stanley Jevons (a logician and economist much admired by Keynes), who argues that “our science must be mathematical, simply because it deals with quantities. Whenever the things treated are capable of being greater or less, there the laws and relations must be mathematical in nature.” (Jevons’ emphases.)

Jevons anticipated an attack on the ground of GIGO. He countered: “In reality, there is no such thing as an exact science, except in a comparative sense …. Had physicists waited until their data were perfectly precise before they brought in the aid of mathematics, we should have still been in the age of science which terminated in the time of Galileo.” As a debater’s point, this is pretty good.

The question is, are all “sciences” that deal in quantities indeed just mathematical? As a matter of fact, the exceptions to Jevons’ rule are legion, from penology to pharmacology. Criminals are sentenced to prison for a number of days or years, or are required to pay a fine of a number of dollars; but no one supposes that judges do or should turn to mathematicians for advice in imposing sentence. Likewise, it is usual to prescribe 10 grains of aspirin for a headache, but the prescription does not appear in any mathematics text. The extreme example, of course, is baseball; the sport is awash in statistics, yet mathematicians are not especially noted for their skill at playing or managing[1].

Now, neither Adam Smith nor John Maynard Keynes would deny that twice two dollars is four dollars, or that 3.3 per cent of $3 trillion is $99 billion. Quite the contrary, they would insist on such relations. But in the passage referred to at the start of this essay, Smith was objecting to the Corn Laws, and he would have done so no matter what proportion of wheat was imported. The reasons for his objections had nothing to do with the mathematics involved, which only demonstrated the relative seriousness of the situation.

The attraction of mathematics for economists is no doubt enhanced (as Jevons suggests) by the hope that somehow they will discover something similar to Newton’s inverse-square law. Mankind would be forever in their debt.

At first glance, Newton’s problem and the econometricians’ do seem similar. Both are confronted by a world of infinite detail and variety, and both are sustained by the hope that, somewhere in the blooming, buzzing confusion, orderly and reliable laws may be discovered. Actually, Newton experienced the order and reliability every moment of his life and could not – literally – have taken a step otherwise. The notorious apple neither flew away erratically nor disintegrated in midair; it fell solidly, as anyone would expect. An orange would have done the same. What did they have in common?

One essential insight had been provided by Galileo. He was not the first to disprove Aristotle by dropping (perhaps from the Tower of Pisa) objects of different weights. But he did, with his experiments rolling brass balls down an inclined plane, confirm that the velocity of a falling object depended not at all on whether it was, as he said in II Saggiatore, “white or red, bitter or sweet, sounding or mute, of a pleasant or unpleasant odor.” Thus it was possible to disregard the sense qualities of objects and concentrate on distance and time.

THE WORLD of physics is a world of abstractions discovered by men, but it does not depend on men for its operation. It is in this sense value free. Distance and clock time are not values; it makes no sense to approve, or disapprove of them; Margaret Fuller could not refuse to accept the universe. It is a fact that the chemical bond works in the way Linus Pauling discovered, and neither Linus Pauling nor anyone else can change this.

No value appears in the full physical description of an object. A full physical description defines an object that obeys physical laws, not an economic object obeying economic laws, whatever they may be. A full physical description of the piece of green-backed paper in my pocket does not reveal what makes it money or what money does. Any good that I buy with my money will obey physical laws, but that is not what will make it a good. Every service that is performed must rely on physical law, but that does not explain what is economic about it. Every object is a physical object, and any object may come to be an economic object, but only some objects are actually economic objects. Whether or not a particular object becomes an economic object depends upon what human beings do with it. [editor’s emphasis].

Money, goods and services are human values. Economic production and consumption are human activities. The consumption of food is essential to life, but that fact is in biology and says nothing about the price of apples. You may be convinced that apples are physiologically better for you than acorns indeed one must insist that some foods are physiologically more efficacious than others – and your conviction may affect the price you are willing to pay, but it is only the price that is an economic concern.

As distance and clock time are fundamental physical concepts, money, goods and services are fundamental economic concepts. Each list can be extended, but one distinction will always separate them: The former are value free, while the latter are value bound. If it made a difference what Linus Pauling felt about electrons, physics would collapse. If it didn’t make a difference how much money Linus Pauling (or someone) would pay for an electron microscope, either the microscope would not be an economic good, or economics would collapse.

Economics is not value free, and no amount of abstraction can make it value free. The econometricians’ search for equations that will explain the economy is forever doomed to frustration. It is often said that their models don’t work because, on the one hand, the variables are too many and, on the other, the statistical data are too sparse. But the physical world is as various as the economic world (they are both infinite) and Newton had fewer data and less powerful means of calculation than are at the disposal of Jan Tinbergen and his econometrician followers. The difference is fundamental, and the failure to understand it reduces much of modern economics to a game that unfortunately has serious consequences.

The New Leader

[1] Editor’s note – this may have been a good point when written but not so strong in the years since baseball began paying attention to Bill James



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