by Daniel Bell
The difficulty with Ridenour’s proposed “law of social change” is that such curves are plotted only for single variables and presume a saturation. But what may be true of beanstalks, or yeast, or fruit flies, or similar organisms whose logistic growths have been neatly plotted in fixed ecological environments may not hold for social situations where decisions may be postponed (as in the case of births) or where substitutions are possible (as in the case of bus or subway transit for passenger cars), so that the growths do not develop in some fixed, “immanent” way. It is for this reason that the use of logistic curves may be deceptive.
Yet one advantage of this technique remains: by the use of mathematical language, one can often discern identical underlying structures in highly diverse phenomena. One may not think of people marrying and having children as the same kind of phenomenon as replacing capital equipment in a plant, but Richard Stone, the Cambridge, England economist, finds an exact mathematical analogy between the two. Stone discerns an equally striking analogy between epidemics in a population and the demand for education.23 In charting the demand for education, the simple extrapolation of past trends is clearly unacceptable, for as we have seen, at some point there is a “system break,” and a jump in the trend. (If one had projected the demand for American universities on the basis of the trends in the 1950 decade, one would have assumed that only by 1975 would 40 percent of the age eighteen to twenty-two cohort be in college; actually that figure was reached in 1965.) Stone suggests that higher education can be regarded as an “epidemic process.” “At each stage, the number who catch the infection and decide to go to a university depends partly on the numbers who have gone and so are available to be infected.” In time, the “contagion” spreads until everyone susceptible to it is infected. The pattern is definable by a differential equation whose product, again, is the -shaped or logistic curve.
To the extent that one can use logistic-curve analysis, even as baselines rather than for actual forecasts, a number of difficult problems present themselves, for at crucial points in the trajectory of the -curve, “critical magnitudes” are reached and the logistic curve “reacts” to the approaching ceiling conditions in different ways. Pearl and Ridenour posited a simple saturation and a levelling off. In Science Since Babylon, Derek Price seemed to accept the same simplistic view:
It is a property of the symmetrical sigmoid curve that its transition from small values to saturated ones is accomplished during the central portion in a period of time corresponding to only the middle five or six doubling periods (more exactly 5.8), independent of the exact size of the ceiling involved. ... For science in the United States, the accurate growth figures show that only about thirty years must elapse between the period when some few percent of difficulty is felt and the time when that trouble has become so acute that it cannot possibly be satisfied. ... We are already, roughly speaking, about halfway up the manpower ceiling.24
Two years later, however, Price had begun to change his mind. It seems that the knowledge curves were not simple -shaped or logistic curves. Under the influence of the writings of Gerald Holton, the Harvard physicist, Price sought to identify more differentiated modes of change. In rather exuberantly hypostasized language, Price now wrote:
... growths that have long been exponential seem not to relish the idea of being flattened. Before they reach a mid-point they begin to twist and turn, and, like impish spirits, change their shapes and definitions so as not to be exterminated against that terrible ceiling. Or, in less anthropomorphic terms, the cybernetic phenomenon of hunting sets in and the curve begins to oscillate wildly. The newly felt constriction produces restorative reaction, but the restored growth first wildly overshoots the mark and then plunges to greater depths than before. If the reaction is successful, its value usually seems to lie in so transforming what is being measured that it takes a new lease on life and rises with a new vigor until, at last, it must meet its doom.
One therefore finds two variants of the traditional logistic curve that are more frequent than the plain -shaped curve. In both cases the variant sets in some time during the inflection, presumably at a time when the privations of the loss of exponential growth become unbearable. If a slight change of definition of the thing that is being measured can be so allowed as to count a new phenomenon on equal terms with the old, the new logistic curve rises phoenixlike on the ashes of the old, a phenomenon first adequately recognized by Holton and felicitously called by him “escalation.” Alternatively, if the changed conditions do not admit a new exponential growth, there will be violent fluctuations persisting until the statistic becomes so ill-defined as to be uncountable, or in some cases the fluctuations decline logarithmically to a stable maximum. At times death may even follow this attainment of maturity, so that instead of a stable maximum there is a slow decline back to zero, or a sudden change of definition making it impossible to measure the index and terminating the curve abruptly in midair.25
So much, then, for the symmetry of the sigmoid curve! Price proposes: “Now that we know something about the pathological afterlife of a logistic curve, and that such things occur in practice in several branches of science and technology, let us reopen the question of the growth curve of science as a whole.”26 What Price finally discovers is that after the “breakdown” of the exponential growth of knowledge, the curve (after tightening its sinews for a jump!) may move “either toward escalation or toward violent fluctuation.” But in which direction we do not know. So where are we then? The idea of “escalation,” or the renewal of an upward curve, may have some meaning where there is a deterministic path, following some physical laws, and in this sense it has found a place in technological forecasting, where it appears under the rubric of “envelope curve” forecasting. But to talk of “violent fluctuations” provides little help in charting measurable changes, for such fluctuations have no determinate pattern.
We find, in sum, that the “gross” measures of scientific knowledge, plotted as growth curves, are, so far at least, of little help, other than as metaphors, or as a means of alerting us generally to the problems we may have to face in the future because of such growths. To plan for social policy on the basis of such plotted curves would be highly misleading. To deal with such questions, we have to turn to less “exact” but sociologically more meaningful observations on the patterns of the development of knowledge.
THE DIFFERENTIATION OF KNOWLEDGE
The idea of exponentiality, the idea that scientific knowledge accumulates “linearly ” in some compound fashion, has obscured the fact that the more typical, and important, pattern is the development of “branching,” or the creation of new and numerous subdivisions or specialties within fields, rather than just growth.
Contrary to the nineteenth-century image of science as a bounded or exhaustible field of knowledge whose dimensions would eventually be fully explored, we now assume an openness to knowledge which is marked by variegated forms of differentiation. Each advance opens up, sometimes rapidly, sometimes slowly, new fields which, in turn, sprout their own branches. Thus, to take the illustration cited by Gerald Holton, the field of “shock waves” initiated in 1848 by the British mathematician and physicist G. C. Stokes and the astronomer J. Challis, with their theoretical equations of motion in gases, led not only to significant contributions in mathematics and physics along this general line (by Mach, and later by von Neumann and Bethe, among others), but to the branching off of shock tube, aerodynamics, detonations, and magnetohydrodynamics, as four distinct fields. The last field, developed in 1942 by Alfven, plays a fundamental part in both basic and applied fusion research.27
Sometimes a stasis is reached and it seems that a field has been explored as far as possible, then some new discoveries suddenly create a series of new “spurts.” In 1895, Röntgen seemed to have exhausted all the major aspects of x-rays, but in 1912 the discovery of x-ray diffraction in crystals by von Laue, Friedrich, and Knipping transformed two separate fields, that of x-rays and crystall
ography. Similarly the discovery in 1934 of artificial radioactivity by the Joliot-Curies created a qualitative change which gave rise, in one branching point to the work of Hahn and Strassman, which Lise Meitner successfully interpreted as the splitting of the uranium atom, and in another branch to Enrico Fermi s work on the increased radioactivity of metals bombarded with slow neutrons, work which led directly to controlled atomic fission and the bomb.
Much of the phenomenon of branching derives not simply from the “immanent” logic of intellectual development, but from the social organization of science itself. In the nineteenth century, science was a small but worthy profession for individuals in its own right. But in the twentieth century, the way in which scientists have come to organize and coordinate their individual research “into a fast-growing commonwealth of learning,” as Holton puts it, has spurred individuals to develop their own work, subsequently, with their own teams. Holton illustrates this phenomenon with a drawing of a “tree” and its “branches,” which traces, among other things, the work of Nobel laureate I. I. Rabi. In 1929, at Columbia, Rabi made a “breakthrough” in pure physics—sending molecular beams through a magnetic field—which gave rise to branching in several different directions, in optics, solid state masers, atomic structures, and a half-dozen other fields. Rabi not only developed the original molecular beam techniques—the trunk of the tree—but he also stimulated a group of productive associates and students to originate new questions, to move into neighboring parts of the same field, and to provoke a rapid branching into several new areas, some of which then developed branches of their own.28
One can find some indicators of the extraordinary proliferation of fields in the breakdown of specializations listed in the National Register of Scientific and Technical Personnel, a government-sponsored inventory of all persons with competence in scientific work. (The National Register is a cooperative undertaking of the National Science Foundation with the major professional scientific societies in the country.) The Register began shortly after World War II, with about 54 specializations in the sciences; 20 years later there were over 900 distinct scientific and technical specializations listed. To a considerable extent, the proliferation of fields arises out of a system of re-classifications, as more and more fine distinctions are made; but in many instances, the increase is due to the creation of new specializations and branchings. In physics, for example, the 1954 roster listed 10 distinct subfields with 74 specializations; in 1968, there were 12 fields with 154 specializations. In 1954, for example, Theoretical Physics (Quantum) was listed as a distinct field, with subspecializations headed as nuclear, atomic, solids, field; in 1968 the field was no longer listed as such and a more differentiated classification had appeared. In 1954, however, solid-state physics was broken down into 8 subspecializations; in 1968 there were 27 subspecializations under the solid-state classification, a proliferation which was the consequence of the additional “branching” of the field.
None of the scientific societies which are responsible for the maintenance of the rosters have made any studies seeking to chart the growth of their subjects either on the basis of the reclassification or addition of fields. A consistent monitoring of each field might reveal some useful and significant indicators of the rates of change in the development of fields of knowledge.
The Measurement of Technological Change
MODERNITY AND TECHNOLOGICAL CHANGE
The claim of being “new” is the distinctive hallmark of modernity, yet many of these claims represent not so much a specifically new aspect of human experience as a change in scale of the phenomenon. The syncretism of culture was already a distinctive feature of the age of Constantine, with its mingling of the Greek and Asiatic mystery religions. The bifurcation of sensibility is as old, if not older, than Plato’s separation of the rational from the spirited. But the revolutions in transportation and communication which have banded together the world society into one great Oikoumenē (ecumene) have meant the breakdown of older, parochial cultures and the overflowing of all the world’s traditions of art, music, and literature into a new, universal container, accessible to all and obligatory upon all. This very enlargement of horizon, this mingling of the arts, this search for the “new,” whether as a voyage of discovery or as a snobbish effort to differentiate oneself from others, is itself the creation of a new kind of modernity.
At the heart of the issue is the meaning of the idea of culture. When one speaks of a “classical culture” or a “Catholic culture” (almost in the sense of a “bacterial culture”—a breeding of distinctly identifiable strains), one thinks of a long-linked set of beliefs, traditions, rituals, and injunctions which in the course of its history has achieved something of a homogeneous style. But modernity is, distinctively, a break with the past as past, catapulting it into the present. The old concept of culture is based on continuity, the modern on variety; the old value was tradition, the contemporary ideal is syncretism.
In the radical gap between the present and the past, technology has been one of the chief forces in the diremption of social time, for by introducing a new metric and by enlarging our control over nature, technology has transformed social relationships and our ways of looking at the world. To be arbitrary, we can list five ways by which technology wrought these transformations:
1. By producing more goods at less cost, technology has been the chief engine of raising the living standards of the world. The achievement of technology, the late Joseph Schumpeter was fond of saying, was that it brought the price of silk stockings within the reach of every shopgirl, as well as of a queen. But technology has not only been the means of raising levels of living, it has been the chief mechanism of reducing inequality within Western society. In France, writes Jean Fourastié, “the Chief Justice of the Court of Accounts ... earned in 1948 not more than four and a half times as much as his office boy by hour of work, although the difference between these two positions was of the order of 50 to 1 in 1800.” The simple reason for this, as Fourastié points out, is the cheapening of goods and the rise of real wages of the working class in Western life.29
2. Technology has created a new class, hitherto unknown in society, of the engineer and the technician, men who are divorced from the site of work but who constitute a “planning staff” for the operations of the work process.
3. Technology has created a new definition of rationality, a new mode of thought, which emphasizes functional relations and the quantitative. Its criteria of performance are those of efficiency and optimization, that is, a utilization of resources with the least cost and least effort. This new definition of functional rationality has its carryover in new modes of education, in which the quantitative techniques of engineering and economics now jostle the older modes of speculation, tradition, and reason.
4. The revolutions in transportation and communication, as a consequence of technology, have created new economic interdependencies and new social interactions. New networks of social relationships have been formed (pre-eminently the shift from kinship to occupational and professional ties); new densities, physical and social, become the matrix of human action.
5. Esthetic perceptions, particularly of space and time, have been radically altered. The ancients had no concept of “speed” and motion in the way these are perceived today: nor was there a synoptic conception of height—the view from the air—which provides a different standard of assessing a landscape or a cityscape. It is in art, especially in painting, that such a radical change of sensibility has taken place.30
MEASURES OF ECONOMIC CHANGE
It is with the economy that we are first concerned because technology is the foundation of industrial society. Economic innovation and change are directly dependent upon new technology. Yet the awareness of this fact is relatively recent. The founding fathers of contemporary economics were preoccupied with a “dismal science” because of their belief that capital accumulation could not continue indefinitely. These conclusions were based on three assumptions:
the law of diminishing returns; the Malthusian principle, in which an increase in real wages would simply lead to faster population growth and the “dilution” of that increase; and, implicitly, an invariant state of technology. This was the basis of Ricardian economics.31 It was elaborated by John Stuart Mill in the conception of “The Stationary State.”
Even Marx, in this sense a post-Ricardian economist, came to a pessimistic conclusion. Though he was far more sensitive to the revolutionary role of machinery than his contemporaries, Marx felt that the chief consequence of the substitution of machinery for labor would be the centralization of capital, at the expense of other capitalists, the increased exploitation of labor (through longer working days) as more backward capitalists sought to meet competition, and, finally, a set of crises when the system reached a ceiling limit. Arguing from a labor theory of value, Marx felt that the expansion of the “organic composition of capital” could lead only to a decline in the average rate of profit and the continuing impoverishment of labor.
