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Too Much

Little Science, Big Science

by Derek J. De Solla Price
Columbia University Press, $4.50

So far, it has been the humanists and theologians who have been pessimistic: they claim to detect changes in the moral temper, a radical break in history. But the scientists have for the most part remained cheerful. Or if they have been pessimistic, it has not been for science itself, but for the fact that men of affairs have made such poor use of science.

This little book by the Avalon Professor of History of Science at Yale changes all that: science is in crisis too, and many of us will say, thank God, we had suspected as much all along. Professor Price delivered this book in the form of four lectures at Brookhaven National Laboratory. It might well, and not at all sensationally, have been titled, “The Coming Crisis of Science,” and what he means by that is just what Marxist critics used to mean by the Coming Crisis of Capitalism; a crisis in growth, occasioned by internal contradictions. He detects, to begin with, certain peculiarities in the pattern of scientific growth, and argues that science will be unable to continue growing at its present rate. As science in effect approaches the end of the three-hundred-year period in which it has transformed all the conditions of life, certain institutional peculiarities in the operations of science itself are becoming manifest. Professor Price formally remains optimistic: but his optimism is like that of a pagan historian who might have traced the decline of the classical world, only to end by saying: But who knows what wonderful possibilities might succeed it?

Professor Price’s arguments derive entirely from statistical data. He has graphed the broad growth of science, as measured by numbers of scientists, scientific societies, of scientific journals and articles and the incidence of distinguished scientists. And his graphs without forcing the point clearly reveal a number of mathematical characteristics that science shares with other growing institutions. The rate of growth of science since the 1660s, when the appearance of scientific societies, of scientific journals and measurable numbers of scientists permit Dr. Price’s type of analysis, has been exponential. That is to say, the rate of growth is constant, as in the case of compound interest. We are aware of the awful power of steady rates of growth as demonstrated in such stories as that of the man who asked the Shah for only one grain of rice on the first square of the chessboard, provided he double it on the second, and double those on the fourth, and so on. Science, regardless of how it is measured, has grown in this way. Science “doubles” every ten or fifteen years. If we count only really very good scientific work or scientists, it “doubles” every twenty years. (This produces such oddities as the fact that most scientists and most scientific work are recent, and since the “doubling” rate has remained constant, this has been true from the beginning. Clearly, if the mass of science “doubles” every ten or fifteen years, a man who has had a productive life of forty or fifty years, will have lived while nearly all the scientific work ever done has taken place, and will have been contemporary with the great majority of all the scientists who have ever lived.)

This rate of growth has maintained itself for almost three hundred years. The number of trained scientific workers already includes about 2 per cent of the labor force; the amount spent on research and development amounts to the same proportion of the gross national product. If science maintains its current rate of growth, we shall have the absurdity, within a century, that there will be two scientists for every man, woman and child in the country.

Obviously things will change long before that. Professor Price suggests the change has already begun: Our present concern with the recruitment of scientific manpower, the unmanageability of the scientific literature, the size of government research expenditures, reflects not a qualitative change in the nature of science, from small to big, but that the rate of growth has now approached the state which all growth rates eventually reach in a finite world: since the exponential curve cannot shoot upward into infinity, it ultimately reaches a point of inflection at which having risen from the floor, it begins to level off as it approaches the ceiling. This is the so-called S-curve which natural populations, whether fruit-flies in a bottle or human populations without birth control, describe. But at the point of inflection strange things often happen to the S-curve. Instead of leveling off quietly into senescence—in which the numbers of scientists, the amount of scientific activity and expenditures on science no longer increase—the curve may begin to show wild movements up and down, a cybernetic “hunting.” There are good examples from reality—for example, graphs of mineral production begin as exponential curves, and as they approach senescence begin to fluctuate wildly. Or perhaps suddenly all the conditions change, and a new phase of growth, a new curve, begins from a new floor, consisting of the ceiling which defined the previous curve. When this happens the curve is said to “escalate”—which is what happened to the rate at which universities were founded at the end of the Middle Ages.

We must point out that there is nothing really in common between Professor Price and Oswald Spengler: Professor Price comes to his curve not from any general argument about the nature of things but from observing his charts and mathematically analyzing the rates at which we have accumulated tens of thousands of scientific journals and millions of articles and scientists. The argument then proceeds from quite matter-of-fact observations (though at times the mathematics is rather more involved than I have suggested) which demonstrate the impossibility that things can continue as they are.

To add two more points made by Professor Price, though we cannot report some of the underlying mathematical argument: The number of good scientists (and he is very ingenious in deriving from his empirical data a convincing way of determining in a population the number of good scientists) increases more slowly than the number of all scientists. It increases only as the square root of the total number of scientists. It also turns out that the cost of scientific research is also increasing as the square of the number of all scientists. Thus to increase the number of good scientists becomes catastrophically expensive: as a matter of fact, long before we reach the absurd condition in which every man, woman, and child must be a scientist, we reach another and much more immediate absurdity. To triple the number of good scientists would mean increasing our expenditure for scientific research to “more than double our entire Gross National Product.”

Professor Price is more than an empirical mathematician; he is also an exceedingly sharp observer of how science functions in the deepening shadow of the curves. He describes the problems of monitoring scientific literature, and shows how we attempt to cope with them through the rise of “invisible colleges” of affluent, peripatetic scientists, moving to different centers of work and associating in relatively small groups for conferences and the rapid exchange of pre-prints and pre-pre-prints. We find a rapid rise, in all advanced fields, of multiple authorship. We find the decline of the scientific predominance of older nations and the phenomenal rise in the scientific productivity of new ones: they are at the beginning of their exponential rise as they top for the first time the scientific and intellectual resources of their populations. They are not yet laboring with the difficulty of forcing the flattening logistical curve to move up again by heavy infusions of money.

We find, too, perhaps, changes in the character of scientists. Important to national power, they are now not only provided for but competed for—a relatively inflexible and hard-to-increase supply is matched against a rocketing demand; thus the new forms of big organization, as the few good scientists try to distribute themselves more efficiently over more fields of work and among more co-workers. Professor Price ends on an optimistic note: he envisages ever more powerful scientists, with greater knowledge of practical affairs, politics and organizational technique. And as they become more involved in politics, they will, he thinks, in some sense, transform it. But I am not at all sure, nor is he, how we are to get over the hump that he has so convincingly delineated; we must still solve the serious problems of big organizations and communication within them and between them. His description of the crisis is brilliant and original; his hopes concerning how we come out are less convincing.

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