by Daniel Bell
My definition is narrower, however, than Machlup’s own comprehensive classification, which argues in The Production and Distribution of Knowledge in the United States that “an objective interpretation according to what is known will be less satisfactory than a subjective interpretation according to the meaning which the knower attaches to the known, that is who knows and why and what for.” 6 Using then “the subjective meaning of the known to the knower as the criterion,” Machlup distinguishes five types of knowledge:
1. Practical knowledge: useful in a man’s work, his decisions, and actions; can be subdivided, according to his activities into: (a) Professional knowledge; (b) Business knowledge; (c) Workman’s knowledge; (d) Political knowledge; (e) Household knowledge; (f) Other practical knowledge.
2. Intellectual knowledge: Satisfying a man’s intellectual curiosity, regarded as part of liberal education, humanistic and scientific learning, general culture; acquired as a rule in active concentration with an appreciation of the existence of open problems and cultural values.
3. Small-talk and pastime knowledge: Satisfying the non-intellectual curiosity or his desire for light entertainment and emotional stimulation, including local gossip, news of crimes and accidents, light novels, stories, jokes, games, etc.; acquired as a rule in passive relaxation from “serious” pursuits; apt to dull his sensitiveness.
4. Spiritual knowledge: related to his religious knowledge of God and of the ways to the salvation of the soul.
5. Unwanted knowledge: outside his interests, usually accidentally acquired, aimlessly retained.7
Robert Lane, who has put forth the idea of “a knowledge society,” seeks to establish an epistemological foundation for his conception. Like Machlup, Lane includes both the “known” and the “state of knowing,” but he also seeks to emphasize the increased self-consciousness about society which such knowledge provides. Lane writes:
As a first approximation to a definition, the knowledgeable society is one in which, more than in other societies, its members: (a) inquire into the basis of their beliefs about man, nature and society; (b) are guided (perhaps unconsciously) by objective standards of veridical truth, and, at upper levels of education, follow scientific rules of evidence and inference in inquiry; (c) devote considerable resources to this inquiry and thus have a large store of knowledge; (d) collect, organize and interpret their knowledge in a constant effort to extract meaning from it for the purposes at hand; (e) employ this knowledge to illuminate (and perhaps modify) their values and goals as well as to advance them. Just as the “democratic” society has a foundation in governmental and interpersonal relations, and the “affluent society” a foundation in economics, so the knowledgeable society has its roots in epistemology and the logic of inquiry.8
Definitions of this kind are neither right nor wrong; they are, rather, boundaries of usage. An effort to deal with comprehensive societal change would need to take these definitions into account. For the purposes of social policy, however—the need to determine the allocation of societal resources for some specified purpose of social utility—I would propose a restricted definition: Knowledge is that which is objectively known, an intellectual property, attached to a name or a group of names and certified by copyright or some other form of social recognition (e.g. publication). This knowledge is paid for—in the time spent in writing and research; in the monetary compensation by the communication and educational media. It is subject to a judgment by the market, by administrative or political decisions of superiors, or by peers as to the worth of the result, and as to its claim on social resources, where such claims are made. In this sense, knowledge is part of the social overhead investment of society; it is a coherent statement, presented in a book, article, or even a computer program, written down or recorded at some point for transmission, and subject to some rough count. Such a utilitarian definition, needless to say, shuns the relevant questions of a “sociology of knowledge”: the social setting of ideas, their interconnections, their relation to some structural foundation, and the like. Any evaluation of the specific character of particular sets of knowledge would, of course, have to take up such questions; these, however, are outside my purview here.9
THE MEASUREMENT OF KNOWLEDGE
Patterns of growth. In recent years we have become accustomed to the statement that the “amount” of knowledge is increasing at an exponential rate. The first rough count—the first flag of warning on the growth of knowledge as a coming storage and retrieval problem—came in 1944, when Fremont Rider, the Wesleyan University librarian, calculated that American research libraries were, on the average, doubling in size every sixteen years. Taking ten representative colleges, Rider showed that between 1831 (when each college had on the average about 7,000 books in its library) and 1938, their holdings had doubled every twenty-two years; taking comparable growth figures of larger American universities from 1831, the doubling rate was about sixteen years.10 Rider chose Yale as an example of what the problem would be like in the future:
It appears that, along in the early part of the eighteenth century, the Yale library possessed somewhere around 1,000 volumes. If it had continued from this start to double every sixteen years it should, in 1938, have grown to about 2,600,000 volumes. In 1938, it actually did have 2,748,000 volumes, i.e. an amazingly close correspondence with the “standard” rate of growth. ... It takes but a few moments’ computation to work out that the Yale University library in 1849 occupied approximately 1¼ miles of shelving, and that its card catalog—if it then had a card catalog—would have occupied approximately 160 card drawers. In 1938 its 2,748,000 volumes occupied perhaps eighty miles of shelving, and its card catalog of all sorts in all locations must have occupied a total of somewhere around ten thousand drawers. To service this library required in 1938 a staff of over two hundred persons, of whom probably half were catalogers.11
Rider speculated—whimsically, it seemed at the time—what would happen if the Yale Library continued to grow “at a rate no greater than the most conservative rate” at which library holdings have been growing. In the year 2040, he estimated the Yale Library would have
approximately 200,000,000 volumes, which will occupy over 6,000 miles of shelves. Its card catalog file—if it then has a card catalog—will consist of nearly three-quarters of a million catalog drawers, which will of themselves occupy not less than eight acres of floor space. New material will be coming in at the rate of 12,000,000 volumes a year; and the cataloging of this new material will require a cataloging staff of over six thousand persons.12
Rider’s findings on the growth of American research libraries were generalized by Derek Price to include almost the entire range of scientific knowledge. In Science Since Babylon, the first of his book publications to deal with this problem,13 Price sought to chart the growth of the scientific journal and the learned paper as the two major indicators of knowledge. The scientific journal and the learned paper were innovations of the scientific revolution of the late seventeenth century. They allowed for the relatively rapid communication of new ideas to the growing circle of persons interested in science. The earliest surviving journal was the Philosophical Transactions of the Royal Society of London, first published in 1665, followed by some three or four similar journals published by other national academies in Europe. Thereafter, the number of journals increased, reaching a total of about one hundred by the beginning of the nineteenth century, one thousand by mid-century, and some ten thousand by 1900. Price concluded:
If we make ... a count extending in time range from 1665 to the present day, it is immediately obvious that the enormous increase in the population of scientific periodicals has proceeded from unity to the order of a hundred thousand with an extraordinary regularity seldom seen in any man-made or natural statistic. It is apparent to a high order of accuracy, that the number has increased by a factor of ten during every half-century starting from a state in 1750 when there were about ten scientific journals in the world.14
In s
ubsequent publications, Price has defended the counting of papers as a relevant indicator of scientific knowledge. In an essay published in 1965, he wrote:
To the scientist himself, the publication represents some mysteriously powerful, eternal, and open archive of the Literature into which he is reading his findings. Only in very rare and special instances does one have to consider pure scientific work in which there is no end product of literature. These would include pathological cases such as that of Henry Cavendish, who researched diligently but did not publish the bulk of his findings, which were therefore lost for a century until they were disinterred by Clerk Maxwell only a few years after the valuable results had been discovered independently by others. Is unpublished work like this, or work that is suppressed and unpublished because it is a national secret, a contribution to science? I find, in general, that it is fair enough to say it is not. Science is not science that communication lacks! ...
Our definition holds, then, that science is that which is published in scientific journals, papers, reports and books. In short it is that which is embodied in the Literature. Conveniently enough, this Literature is far easier to define, delimit and count than anything else one might deal with. Because of its central function for scientists, it has been subjected to centuries of systematization by indexes, classifications, journals of abstracts and retrieval systems. ... All such literature can be, and in very many cases has actually been counted, classified, and followed through the years as a time series. The chief component of the Research Literature, for example, can be defined as the papers published in the scientific serials included in the World List of Scientific Periodicals—a familiar tool of all reference librarians.15
By 1830, when it became obvious, with about three hundred journals being published in the world, that the cultivated man of science could no longer keep abreast of new knowledge, a new device appeared, the abstract journal, which summarized each article so that the interested individual could then decide which article to consult in full. But, as Price points out, the number of abstract journals has also increased, following the same trajectory, multiplying by a factor of ten every half-century. Thus, by 1950 the number of abstract journals had attained a “critical magnitude” of about three hundred.
Out of these figures, Price has sought to draw a “law of exponential increase.” He considers that the most remarkable conclusion is that the number of new journals has grown exponentially rather than linearly. “The constant involved is actually about fifteen years for a doubling, corresponding to a power of ten in fifty years and a factor of a thousand in a century and a half. ...”
If this is true, it is remarkable that not only do we find such a rapid growth but that the particular curve should be exponential, the mathematical consequence of having a quantity that increases in such a way that the bigger it is the faster it grows. “Why should it be,” asks Price, “that journals appear to breed more journals at a rate proportional to their population at any one time instead of at any particular constant rate?” It must follow, he says, “that there is something about scientific discoveries or the papers by which they are published that makes them act in this way. It seems as if each advance generates a new series of advances at a reasonably constant birth rate, so that the number of births is strictly proportional to the size of the population of discoveries at any given time.” 16
This “law of exponential increase,” which applies to the number of scientific journals, is also “obeyed,” Price argues, by the actual number of scientific papers in those journals. Taking the papers recorded in the Physics Abstracts from 1918 to the present day, the total number, he claims, has followed an exponential growth curve, the accuracy of which does not vary by more than I percent of the total. At the beginning of the 1960s, there were about 180,000 physics papers recorded in those volumes, and the number has steadily doubled at a rate even faster than once every fifteen years. On the basis of about thirty such analyses since 1951, Price concludes that “it seems beyond reasonable doubt that the literature in any normal, growing field of science increases exponentially, with a doubling in an interval ranging from about ten to about fifteen years.” 17
A later study of mathematical publications by Kenneth O. May 18confirms the general pattern sketched by Price for physics, but finds that “the rate of growth for mathematics is only half that found by Price.” The doubling intervals cited by Price “correspond to an annual increase of from about 7 to 5 percent, whereas we have found for mathematics, an annual increase of about 2.5 percent and doubling about every 28 years.”
The difference arises from the choice of a starting point. As May points out: “Before jumping to the conclusion that mathematics has a different growth rare than other sciences, note that although Price speaks of ‘the literature’ as though he were referring to the total literature his data are actually for the literature in each field after a certain time, in each case the beginning of an abstracting service: 1900 for physics, 1908 for chemistry, 1927 for biology, and 1940 for mathematics.”
Professor May, in his inquiry, went back to 1868, to the Jahrbuch über die Fortschritte der Mathematik, tracing the growth through 1940 and from 1941 to 1965 in the Mathematical Reviews. He also points out that in mathematics, by successively ignoring the literature prior to 1900, 1920, and 1940, one could achieve a series of growth curves similar to Price’s higher findings. “It appears likely,” May concludes, “that if Price and others took into account the literature prior to their statistical series, they would obtain substantially lower growth rates. This analysis supports the conjecture that the over-all total scientific literature has been accumulating at a rate of about 2.5 percent per year, doubling about four times a century.”
Limits of growth. Any growth which is exponential must at some point level off, or we would reach a point of absurdity. Published figures on the electrical industry, for example, show that if we start with a single man, circa 1750—the time of Franklin’s experiments with lightning—the exponential increase would bring us to two hundred thousand persons employed in 1925, an even million by 1955 and at that rate, the entire working population would be employed in this one field by 1990.19 At some point, necessarily, there is a saturation and levelling-off. In the measurement of the growth of knowledge, as in other fields which have shown similar patterns, the questions revolve around the definition of that saturated state and the estimation of its arrival date.
The exponential pattern which has been described, the approach to some ceiling, is a sigmoid or-shaped curve in which the rate below and above its middle is often quite symmetrical. Because this is so, it lends itself easily to prediction, since one assumes that the rate above the mid-point will match that below and then level off. It is, in fact, the beauty of this curve that has seduced many statisticians into believing almost that it is the “philosopher’s stone” for the charting of human behavior.
The phenomenon of saturation, as applied to a general law of human population, was first proposed in the 1830s by the statistician Adolphe Quetelet, the formulator of social physics, in his reflections on Malthus. A typical population grows slowly from an asymptotic minimum, multiplies quickly, and draws slowly to an ill-defined asymptotic maximum, the curve passing through a point of inflection to become -shaped. In 1838, a mathematical colleague of Quetelet’s, P. F. Verhulst, sought to give a mathematical shape to the same general conclusions, to find a “fonction retardatrice” which would turn the Malthusian curve of geometrical progression into the -shaped or, as he called it, the logistic curve, which would constitute the true “law of population,” and indicate the limit above which the population was not likely to grow.20
Verhulst was making a number of assumptions: that the rate of increase could not be constant; that the rate must be some function, a linear one, of the population for the time being; and that once the rate begins to fall, or saturation sets in, it will fall more as the population begins to grow. Thus the growth factor and the retardation factor are p
roportional to one another so that, because of the “symmetry” of the curve, one can project or forecast the future.21
In 1924, the mathematical biologist Raymond Pearl came across Verhulst’s papers and formulated the Verhulst-Pearl law. In seeking to draw an -shaped population growth curve, Pearl stated that the rate of growth will depend upon the population at the time, and on “the still unutilized reserves of population-support” existing in the available land. Pearl had earlier formulated equations to describe the population growth of fruit flies in a closed environment, and in 1925 on the basis of similar equations, he predicted an American population in 1950 of 148.7 million and in 1960 of 159.2 million. The 1950 prediction came within 3 million persons of the actual count, but the 1960 prediction was already off by more than 25 million. Pearl’s estimate of an upper limit of 197 million in the population of the United States has already been surpassed within this decade, and the population seems to be heading toward the 275 million mark by the year 2000.
The key problem in the use of -curve analysis is that it works only within some “closed system,” based either on fixed resources or physical laws or some concept of an absolute. In other words, the ‘ceiling conditions” force the levelling off of the curve. We do not have a “closed system” in human populations, or society, thus there is always a risk in using such curves for purposes of prediction. Yet there is some value in considering such a model as a “baseline” or fiction against which to test a social reality. The late Louis Ridenour, the former chief scientist of the air force, who was the first person to comment on the Fremont Rider data (in a 1951 paper printed in Bibliography in an Age of Science), pointed out that the phenomenon of the doubling rates of university libraries could be found as well in the assets of life insurance companies, the number of long-distance telephone messages and radio-telephone conversations, the time for circumnavigating the globe, the gross weight of aircraft in common use, airline-passenger miles flown, passenger-car registrations, and so forth. Ridenour, assuming the exponential law to be empirically established, argued, in fact, that there was a “law of social change” paralleling the “autocatalytic processes,” such as chemical reaction or cell growth, which are found in chemistry and biology. In seeking to establish an explanation, Ridenour argued that the rate of public acceptance of a new product or service (such as long-distance telephoning or airline travel) will be proportional to the number of people who are familiar with it through exposure. Since at some point there has to be a saturation, Ridenour, like Verhulst, proposed a differential equation to indicate the rate of slowdown when the curve would begin to reach an absolute upper limit.22
