Science Since Babylon Enlarged Edition



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it, p. lxxi. This last is especially remarkable for the fact that it shows the full time-scale, beginning with a slow exponential growth (about forty years for a doubling) and then changing to the modern normal rate (about fifteen years to double) just at the time of the first astronomical periodical publications in the early nineteenth century. For chemical papers see the analysis by Laurence E. Strong and O. Theodor Benfey, "Is Chemical Information Growing Exponen-

  1. of such a statistical investigation of numbers of scientific papers, there is next presented a curve showing the numbers of papers recorded by Physics A bstracts since it came into being in igoo. In the earliest decade, this journal’s main function was to record electrical engineering papers, and not before World War I did it find it useful to list the physics section separately; we therefore ignore the mixed data before 1918.

  2. It is, however, quite remarkable that from igi8 to the present day the total number of physics papers recorded in the abstracts—clearly a rather complete and significant selection—has followed an exponential growth curve to an order of accuracy which does not fluctuate by more than about 1 per cent of the total. There are now about 180,000 physics papers recorded in these volumes, and the number has steadily doubled at a rate even faster than once every fifteen years. In this curve, one particular side effect is worth noting. The data show that during World War II, in the period 1938-48, the production of physics papers was reduced to reach a minimum of very nearly one-third of what it normally would have been. In the whole decade including the war, some 60,000 instead of 120,000 papers came out.

  3. Two diametrically opposed conjectures have been made with respect to the effect of the war upon science. The one school would argue that the enormous stimulation of giant projects like that of the atomic bomb helped science in a way that no peacetime activities could have afforded. The tially?” in Journal of Chemical Education, 57 (i960), p. 29. Since my first publication on this subject (in Archives Internationales d’Histoire des Sciences, No. 14, 1951, pp. 85-93) extended and republished in a more popular form in Discovery (June, 1956), pp. 240-3, there have come to my notice about thirty such analyses, all with similar results. 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.

  4. Thousands of “Physics Abstracts" since 1900



  6. Total number of Physics Abstracts published since January 1, igoo. The full curve gives the total, and the broken curve represents the exponential approximation. Parallel curves are drawn to enable the effect of the wars to be illustrated.

  7. Other school says that the mobilization of men and money for purpose of war effort rather than for scientific advance was a diversion, an actual retardation instead of an acceleration of science. The graph shows immediately that neither of these things happened—or, rather, if they did, they balanced each other so effectively that no resultant effect is to be found. Once science had recovered from the war, the curve settled down to exactly the same slope and rate of progress that it had before. It had neither a greater nor a

  8. less initial slope; it is exactly as if the war loss had not occurred. The present curve runs accurately parallel to its projected prewar course.

  9. Returning to the main investigation, we can note that once again the accuracy of exponential growth is most surprising, especially because of the large factor involved, and also because its regularity is so much greater than one normally finds in the world of statistics. I might add that exactly the same sort of result occurs if one takes the head- count for scientific books or for abstracts of chemical, biological, or mathematical papers.^ It may also be found in the bibliographies which exist for particular specialties within any of these domains. One may, in fact, with a suitably documented topic, perform such a mathematical analysis and thereby demonstrate very clearly the successive phases: first, precursors; then, a steady state of exponential growth; next, a decline to linear growth, when no new manpower is entering the field; and finally, the collapse of the field, when only a few occasional papers are produced, or an alternative revival, should it suddenly take on a new' lease of life, through a redefinition of its content and mode of operation.

  10. The figures for book publication and the size of libraries are the subjects of many investigations, several of them instigated by worried librarians charged with the management of their monster. Perhaps the best selection of data is in F. Rider, The Scholar and the Future of the Research Library (New York, 1944). Roughly speaking, both the world population of book titles and the sizes of all the great libraries double in about twenty years (estimates usually range from seventeen to twenty-three years). If we allow that in some five hundred years of book production there must have been some twenty-five doubling periods, this will give about 2^ — 30,000,000 lx)oks alive today, a figure conforming well with normal estimates. In the Third Annual Report of the Council on Library Resources (period ending June 30, 1959), where such data are presented, I find a wistful comment that deserves repetition: "The world’s population is laid to rest each geti- eration; the world’s books have a way of lingering on.” Such is the stuff of cumulative growth, the distinction of scholarship in general, but of science in particular.

  11. N

  12. Science Since Babylon N



  1. Total number of papers published in the field of mathematical theory of determinants and matrices, plotted exponentially (left) and linearly (right). There are three stages in the growth, the first an irregular period of precursors and a slightly premature beginning, from 1740 to about 1800. The next stage is one of pure exponential growth from 1800 to about 1880 and the last is a period of linear growth extending from 1880 to the present. In the exponential portion there is a doubling every twelve- years. In the linear portion the growth maintains its value at 1880, i.e., about thirty-five papers per year, or roughly one dozen full-time workers in the field.

  2. So far we only have the very crudest measure of the size of science; there has been no discussion of the relation between the number of papers and the number and quality of the scientists working and the research they produce. It is relatively easy to establish a relationship between scientists and their papers. For example, one can readily take an index volume for several years of publication in a particular journal or over a whole field and count the number of men who published but one paper, those with two, three, and so on. This has been done many times, and for my

  3. present purpose, it will suffice to cite Lotka’s Law of Productivity, ® which states that the number of authors publishing just N papers is proportional to i/N^. Thus, if you have a certain chance of producing one paper during your lifetime, you have one-quarter that chance of producing two, one-ninth for three, one-hundredth for ten, and so on.

  4. Again, this is a reasonably expected mathematical law, but it is surprising to see that it seems to be followed to much greater accuracy than one might predict. Once more, it is surprising to find that this seems to be a universal law. Thus, it is obeyed equally well by data taken from the first few volumes of the seventeenth-century Philosophical Transactions and by those from a recent volume of Chemical Abstracts. The distribution of productivity among scientists has not changed much over the whole three hundred years for which papers have been produced.

  5. As a result of the constancy of this law, it is possible to say that over the years there have been about three papers for every author. If we care to define a scientist as a man who writes at least one scientific paper in his lifetime, then the number of scientists is always approximately one-third of the number of published papers. Actually, the mathematics of this computation is not quite trivial; it is necessary to make a somewhat arbitrary assumption about the maximum number of papers that could be written by any man

  6. 5. Lotka’s Law was first published in "The Frequency Distribution of

  7. Scientific Productivity,” Journal of the Washington Academy of Sciences, j6 (1926), 317. It is commented upon as an example of an almost universal distribution law in George K.. Zipf, Human Behavior and the Principle of Least Effort (Cambridge, Mass., 1949), pp. 514-^6 (some of the theory and examples are not entirely trustworthy). An independent and more mathematical formulation in terms of skew distribution functions and their theory may be found in Herbert A. Simon, Models of Man, Social and Rational (New York, 1957), pp. 160-1, where further source materials are cited.

  8. in one lifetime.® Happily, the agreement with statistical data is so good that assumptions do not appear to be very critical.

  9. Having established this, we may transfer all our remarks about the growth of scientific literature into equivalent remarks about the manpower involved. Hence, during the last three hundred years, the size of the labor force of science has grown from the first few to the order of hundreds of thousands. Now this is something so familiar, it seems, from discussion of the explosion of the w'orld population, and from the well-known troubles of libraries, which seem to be doubling in size every few decades that it may look as if we are merely making new soup with old bones.

  10. To state it a little more dramatically, however, we may remark that at any time there co-exist in the scientific population scientists produced over, let us say, the last forty years. Thus, at any one time, about three doubling periods’ worth of scientists are alive. Hence, some 8o to go per cent of all scientists that have ever been, are alive now. We might miss Newton and Aristotle, but happily most of the contributors are with us still!

  11. It must be recognized that the growth of science is something very much more active, much vaster in its problems, than any other sort of growth happening in the world today. For one thing, it has been going on for a longer time and more steadily than most other things. More important, it is growing much more rapidly than anything else. All other

  12. 6. So far as I know, the record for meaningful scientific publications in huge quantities is held by William Thompson, Lord Kelvin. From about 1840 to 1870 he produced about 8.5 papers per year, thereafter until his retirement some 15.0 per year (for a period of about thirty years), then about 5.0 per year until his death in 1907; in all a total of about 660 papers in one lifetime, a working average of one fine paper per month, year in and year out. Almost every one of these could be viewed as a major scientific contribution. See Postscript, p. 195.

  13. things in population, economics, nonscientific culture, are growing so as to double in roughly every human generation of say thirty to fifty years. Science in America is growing so as to double in only ten years—it multiplies by eight in each successive doubling of all nonscientific things in our civilization. If you care to regard it this way, the density of science in our culture is quadrupling during each generation.

  14. Alternatively, one can say that science has been growing so rapidly that all else, by comparison, has been almost stationary. The exponential growth has been effective largely in increasing the involvement of our culture with science, rather than in contributing to any general increase in the size of both culture and science. The past three centuries have brought science from a one-in-a-million activity to a point at which the expenditure of several per cent of all our national productivity and available manpower is entailed by the general fields of science and its closely associated applications.

  15. An excellent example of such concentration is the electrical engineering industry, the technology of which is more implicitly scientific than any other. Published manpower figures show the usual exponential increase, acting as if it started with a single man ca. 1750 (the time of Franklin’s experiments on lightning) and doubling until there were two hundred thousand people employed in 1925 and an even million by 1955. At this rate, the whole working population should be employed in this one field as early as

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