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Labels: tech talks

Labels: tech talks

In seeing that economics is a science of tracing consequences,
we must have become aware that, like logic and mathematics, it is a science of recognizing inevitable implications.

We may illustrate this by an elementary equation in algebra. Suppose we say that if x = 5 then x + y = 12. The "solution" to this equation is that y equals 7; but this is so precisely because the equation tells us in effect that y equals 7. It does not make that assertion directly, but it inevitably implies it.

What is true of this elementary equation is true of the jtnost complicated and abstruse equations encountered in mathematics. The answer already lies in the statement of the problem. It must, it is true, be "worked out." The result, it is true, may sometimes come to the man who works out the equation as a stunning surprise. He may even have a sense of discovering something entirely new—a thrill like that of "some watcher of the skies, when a new planet swims into his ken." His sense of discovery may be justified by the theoretical or practical consequences of his answer. Yet his answer was already contained in the formulation of the problem. It was merely not recognized at once. For mathematics reminds us that inevitable implications are not necessarily obvious implications.

All this is equally true of economics. In this respect economics might be compared also to engineering. When an engineer has a problem, he must first determine all the facts bearing on that problem. If he designs a bridge to span two points, he must first know the exact distance between those two points, their precise topographical nature, the maximum load his bridge will be designed to carry, the tensile and compressive strength of the steel or other material of which the bridge is to be built, and the stresses and strains to which it may be subjected. Much of this factual research has already been done for him by others. His predecessors, also, have already evolved elaborate mathematical equations by which, knowing the strength of his materials and the stresses to which they will be subjected, he can determine the necessary diameter,shape, number and structure of his towers, cables and girders.

In the same way the economist, assigned a practical problem, must know both the essential facts of that problem and the valid deductions to be drawn from those facts. The deductive side of economics is no less important than the factual. One can say of it what Santayana says of logic Cand what could be equally well said of mathematics), that it "traces the radiation of truth," so that "when one term of a logical system is known to describe a fact, the whole system attaching to that term becomes, as it were, incandescent."

Now few people recognize the necessary implications of the economic statements they are constantly making. When they say that the way to eccnomic salvation is to increase "credit," it is just as if they said that the way to economic salvation is to increase debt: these are different names for the same thing seen from opposite sides. When they say that the way to prosperity is to increase farm prices, it is like saying that the way to prosperity is to make food dearer for the city worker. When they say that the way to national wealth is to pay out governmental subsidies, they are in effect saying that the way to national wealth is to increase taxes. When they make it a main objective to increase exports, most of them do not realize that they necessarily make it a main objective ultimately to increase imports. When they say, under nearly all conditions, that the way to recovery is to increase wage rates, they have found only another way of saying that the way to recovery is to increase costs of production.

It does not necessarily follow, because each of these propositions, like a coin, has its reverse side, or because the equivalent proposition, or the other name for the remedy, sounds much less attractive, that the original proposal is under all conditions unsound. There may be times when an increase in debt is a minor consideration as against the gains achieved with the borrowed funds; when a government subsidy is unavoidable to achieve a certain purpose; when a given industry can afford an increase in production costs, and so on. But we ought to make sure in each case that both sides of the coin have been considered, that all the implications of a proposal have been studied. And this is seldom done.

Elisabeth Shue, The Saint (1997)
Apparently, Shue was following Coulomb's little-known second law of physics: When in doubt, always hide secret formulas in your bra. Then make out with Val Kilmer.

"Work smarter, not harder" is a slogan often bandied about by business efficiency task forces. Everyone knows that a modicum of planning and organization can save a lot of wasted effort. Smart managers are constantly looking for ideas that will streamline their operations and improve the productivity of their workforces. Any edge, even one as small as one percent, is worth it.

So how about an idea that increases productivity by a thousand percent?

The "business" of scientific computing saw just such an idea back in 1965, stuffed in a suggestion box known as Mathematics of Computation, a journal published by the American Mathematical Society. In a five-page paper titled "An Algorithm for the Machine Calculation of Complex Fourier Series," James W. Cooley of the IBM T.J. Watson Research Center (now at the University of Rhode Island) and John W. Tukey of Princeton University and AT&T Bell Laboratories laid out a scheme that sped up one of the most common activities in scientific and engineering practice: the computation of Fourier transforms.

Their algorithm, which soon came to be called the fast Fourier transform--FFT for short--is widely credited with making many innovations in modern technology feasible. Its impact extends from biomedical engineering to the design of aerodynamically efficient aircraft. Over the last two and a half decades, Cooley and Tukey's paper has been cited in well over a thousand articles in journals ranging from Geophysics to Applied Spectroscopy. According to Gil Strang of MIT, the FFT is "the most valuable numerical algorithm in our lifetime."

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