IS Chemical Information Growing Exponentially?
Laurence E. Strong and 0. Theodor Benfey Earlham College Richmond, Indiana
In an earlier article1 the authors stated that the amount of chemical information was doublimg every thirteen years. It is the purpose of this note to summarize data bearing on this point. Chemical Abstracls
Table 1 gives the number of lines in the decennial subject indexes of Chemical Abstracts since 1907. It was felt that the subject indexes represented the best measure of chemical information available. In order to find a relation between total chemical information and time, it was necessary to estimate an initial value for the lines of Chemical Abstracts equivalent to all chemical information prior to 1907. Mere extrapolation backwards of the curves did not seem justified, since the geometric increase in information might be a phenomenon of the twentieth century. An estimate of the relation of total information prior to 1909 and information published from 191&1919 was obtained from Beilstein's "Handhuch der Organischen Chemie." The main work covering literature up to 1909 is approximately twice as large as the supplement for 191&1919. Assuming that Beilstein really does abstract all of organic chemistry prior to 1909 and that a similar relation holds for the whole of chemistry, and given that the number of lines in the decennial subject index to Chemical Abstracts for 1907-16 is 3.6 X lo6, we took the cumulative total for 1906 to be equivalent to 8 X lo5. If the order of magnitude is reliable, then the exact value is not particularly important in the cumulative totals. Table 2 gives the cumulative totals including this base figure. The data are plotted in Figure 1. The Table 1 .
Lines in Decennial Subject Indexes of Chemical Abstracts Lines
Cumulative total
5.6 - 0 1906 Figure 1.
'46 DECENNIAL INDEX YEARS
Chemical Abstmetr cumdorive lines in indexer.
open circles are for the logarithm of the total lines while the filled circles are for the arithmetic totals. From the logarithmic plot it appears that during the past half century the amount of chemical information has approximately doubled each thirteen years.% Of course the sobering implication of this is that in the period from now until 1973 an amount of chemical information will be published equal in magnitude to all that has been published in the past. Other Growth Potterns in Science
'Estimate based on annual indexes, corrected for a 17% reduction in number of lines when annual indexes are oombined into decennial indexes.
Table 2. Year
Cumulative Subject Index Lines in Chemical Abstracts Lines
Year
Lines
L. E., AND BENFEY,0.T.,J. CHEM.EDUC.,35, 164 STRONG, (1958).
A similar rate of growth to the one just mentioned is that reported for the Library of the London Chemical Society. When the library was founded in 1841, a single bookstack sufficed. In 1900 the library contained 10,000 volumesand in 1918 its holdings amounted to 25,000.' Other aspects of science in addition to chemistry show somewhat simiiar expansion patterns. In Figure 2 are plotted two different indexes of this growth. The left band lime describes the increase in number of names published in successive volumes of "American Men of This estimate is also supported by the fact that the second suadement (1920-29) ta Beilstein is ao~roximatelvtwice as large a6 the &t (191619). Proc. Chem. Soc., 226 (1957). "on.,
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Volume 37, Number I , January 1960
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college and university libraries started in this country, they have, on the average, doubled in size every sixteen years.'
Figure 2.
Growth in some aspects of science.
Science" during the past fifty years.' The right hand line shows total expenditures for research and development made in the United States during various years since 1920,"ach set of data conforms reasonably to a straight line when plotted semi-logarithmically. For names listed in "American Men of Science" the best straight line has a slope corresponding to doubling each twelve years while for research and development expenditures the line has a slope corresponding to doubling each six years. That research and development money increases so much more rapidly than publication is probably not surprising since a large fraction of the money in recent years goes into military work where publication and similar public activity are greatly curtailed. Thus in 1957-58 it is estimated that over 55% of total expenditure was for military purposes. Parabolic or Exponential?
It may be that the phenomenon under discussion is not even limited to science. Fremont Rider, after an exhaustive study of the growth of American college and university libraries, finds that, on the average their holdmgs double every sixteen years: To be sure the tahles cited carry the story back only to 1831; but every scrap of statistical evidence that we can gather shows that as far back as we can reach, the story is exactly the same. It seem8, as stated, to be a mathematical fact that, ever since
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CATFIELL, J., AND J. McK., editors, "American Men of Science," Science Press, Lanoaster, Pa., 5th ed., 1933, p. vii; 6th ed., 1938, p. viii; 7th ed., 1944, p. v; 8th ed., 1949, p. i; 9th ed., 1955, Vol. I, p. i; Vol. 111,p. i; publisher's announcement of the 10th edition, 1959. The ninth and tenth editions include a fuller coverage of the social sciences. Chem. Eng. News, 36, 63-9 (1958). R I D E R ,F., "The Scholar and the Future of the Research Library," Hadham Press, New York, 1944, p. 8.
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Journol o f Chemicol Education
Our calculations lead us to believe that the growth of chemical information is more rapid than the rate suggested recently by Crane.? Crane predicts, on the basis of the number of abstracts published in Chemical Abstraets during the last ten years, that the number of abstracts published per year will increase linearly during the next years. This implies a quadratic or parabolic growth curve for the total number of abstracts whereas a doubling of information implies a logarithmic growth curve. While over a short period of a few years, the difference between the two functions is small, in a period of ten years or more the difference rapidly becomes quite large. Of course an exponential function implies that cumulative knowledge approaches infinity as a limit, an event which is certainly to be avoided if a t all possible. While it seems clear that the accumulation of chemical information in the past has approximated an exponential curve there is no theory for this relation. Consequently one cannot make a prediction about the future with any great confidence. The implication of an exponential increase is most distressing since it implies a staggering amount of publication for the not very distant future. How can even a modest fraction of this be assimilated? A few years ago, Alan Gregg published a provocative article on the population problem."e suggested that the expansion of the human population of the earth has certain similarities to the growth of a cancerous tumor in a living organism. At worst this is no more than an interesting analogy hut Gregg points out, "To say that the world has cancer, and that the cancer cell is man, has neither experimental proof nor the validation of predictive accuracy; but I see no reason that instantly forbids such speculation." Probably we should hope that the exponential relation presented here and the parabolic relation suggested by Crane are both wide of the mark. It would be comforting to know that we are dealing with an Sshaped growth curve which leads to an essentially constant annual publication rate. Lacking this comfortable assurance perhaps we need to explore the possibility that chemistry is iu danger of growing in a cancerous and indigestible way.
' CR~NE,E. J., Proe. Chem. Sac., 334 (1957). GREW,A,, Science, 121, 681 (1955).
