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Rescher's Principle of Decreasing Marginal Returns of Scientific Research

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Abstract

In his book "Scientific Progress", Rescher (1978, German ed. 1982, French ed. 1993)developed a principle of decreasing marginal returns of scientific research, which is based, interalia, on a law of logarithmic returns and on Lotka's law in a certain interpretation. In the presentpaper, the historical precursors and the meaning of the principle are sketched out. It is reported onsome empirical case studies concerning the principle spread over the literature. New bibliometricdata are used about 19th-century mathematics and physics. They confirm Rescher's principleapart from the early phases of the disciplines, where a square root law seems to be moreapplicable. The implication of the principle that the returns of different quality levels grow theslower, the higher the level, is valid. However, the time-derivative ratio between (logarithmized)investment in terms of manpower and returns in terms of first-rate contributors seems not to belinear, but rather to fluctuate vividly, pointing to the cyclical nature of scientific progress. Withregard to Rescher's principle, in the light of bibliometric indicators no difference occurs betweena natural science like physics and a formal science like mathematics. From mathematical progressof the 19th century, constant or increasing returns in the form of new formulas, theorems andaxioms are observed, which leads to a complementary interpretation of the principle of decreasingmarginal returns as a principle of scientific "mass production".

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References

  1. N. Rescher, Scientific Progress, Pittsburgh Univ. Pr., Pittsburgh, Pa., 1978. German ed.: Wissenschaft-licher Fortschritt, de Gruyter, Berlin, 1982. French ed.: Le Progrès Scientifique, Presses Universitaires France, Paris, 1993.

    Google Scholar 

  2. C. S. Peirce, Economy of research. In: Peirce: Collected Papers, Vol. 7, Harvard Univ. Pr., Cambridge, 1958, 76-83. Later reflections, 84–88. First 1879 and 1902.

    Google Scholar 

  3. S. Toulmin, The intellectual authority and the social context of the scientific enterprise: Holton, Rescher and Lakatos, Minerva, 18 (1980), 652-667.

    Google Scholar 

  4. K. E. Boulding, Review of N. Rescher: Scientific Progress, International Journal of General Systems, 6 (1980), 173-174.

    Google Scholar 

  5. L. Vaizey, Review of N. Rescher: Scientific Progress, Journal of Economic Literature, 17 (1979), 1070-1071.

    Google Scholar 

  6. A. Schubert, Review of N. Rescher: Scientific Progress, Scientometrics, 5 (1983), 135-136.

    Google Scholar 

  7. N. Rescher, Cognitive Economy: The Economic Dimension of the Theory of Knowledge, Univ. of Pittsburgh Pr., Pittsburgh, 1989.

    Google Scholar 

  8. J. Wolf, Die Volkswirtschaft der Gegenwart und Zukunft, Deichert, Leipzig, 1912.

    Google Scholar 

  9. S. S. Kuznets, Secular Movements in Production and Prices, Riverside Pr., Boston, 1930, Repr. Kelley, New York, 1967.

    Google Scholar 

  10. E. W. Hulme, Statistical Bibliography in Relation to the Growth of Modern Civilization, printed by Butler & Tanner, London, 1923.

    Google Scholar 

  11. O. Giarini, H. LoubergÉ, The Diminishing Returns of Technology, Pergamon Pr., Oxford, 1978.

    Google Scholar 

  12. G. Silverberg, L. Soete, Introduction, in: The Economics of Growth and Technical Change, Aldershot 1994, 1-5; p. 2.

  13. I. Niiniluoto, Scientific progress, Synthese, 45 (1980), 427-462.

    Google Scholar 

  14. Another possibility to model different “quality-levels” is to construct different levels as roots of the total output in the form of Q γ, with γ= 0.5 as square root law. This is mathematically not equivalent with the first-rate standard. formula Fδlog Q (cf. Rescher,1, p. 102 and A. Schubert6).

  15. R. Wagner-DÖbler, Publikationsverhalten gestern und heute: 15000 Autoren einer mathematischen Spezialdisziplin auf dem Prüfstand, In: W. Neubauer, K.-H. Meier (Eds), Technik und Information, Dt. Dokumentartag 1992, DGD, Frankfurt a.M., 1993, with further references.

    Google Scholar 

  16. W. Goffman, K. S. Warren, Scientific Information Systems and the Prinicple of Selectivity, Praeger, New York, 1980; pp. 134-136.

    Google Scholar 

  17. R. Wagner-DÖbler, Wachstumszyklen technisch-wissenschaftlicher Kreativität, Eine quantitative Studie unter besonderer Beachtung der Mathematik, Campus-Verl., Frankfurt/M., 1997.

    Google Scholar 

  18. S. Cole, Making Science, Harvard Univ. Pr., Cambridge, 1992; Ch. 7.

    Google Scholar 

  19. H. W. Holub, G. Tappeiner, V. Eberharter, The Iron Law of Important Articles, Southern Economic Journal, 58 (1991), 317-328.

    Google Scholar 

  20. R. M. Gascoigne, A Historical Catalogue of Scientists and Scientific Books, From the Earlist Times to the Close of the Nineteenth Century, Garland, New York, 1984.

    Google Scholar 

  21. According to an extensive bibliometric study of 19th-century physics based on the physics index (including mechanics) of the Catalogue of Scientific Papers: R. Wagner-DÖbler, J. Berg, 19th-century physics, A quantitative outline, Scientometrics, 46 (1999), 213-285. As the title of the source says, only contributions to journals are considered. The number of authors who produced only in the form of monographs should be of no statistical significance; Ref. 22.

    Google Scholar 

  22. R. Wagner-DÖbler, J. Berg, Nineteenth-century mathematics in the mirror of its literature. A quantitative approach, Historia Mathematica, 23 (1996), 288-318.

    Google Scholar 

  23. R. Wagner-DÖbler, Alter und intellektuelle Produktivität: Das Beispiel von Mathematikern, Logikern und Schachmeistern, Zeitschrift für Gerontopsychologie und-psychiatrie, 9 (1996), 277-290.

    Google Scholar 

  24. K. O. May, Growth and quality of the mathematical literature, Isis, 59 (1968), 363-371.

    Google Scholar 

  25. R. Wagner-DÖbler, J. Berg, Mathematische Logik von 1847 bis zur Gegenwart, Eine bibliometrische Untersuchung, de Gruyter, Berlin, 1993.

    Google Scholar 

  26. Rescher (Ref. 1, p. 102; 2.2860.50 = 48 < 90 < 2.2860.75 = 331).

  27. B. Glass, Milestones and rates of grwoth in the development of biology, The Quarterly Review of Biology, 54 (1979) March, 31-53.

  28. F. Stuhlhofer, Does the rate of growth of our knowledge depend on the quality-level considered?, Czechoslovak Journal of Physics B, 36 (1986), 154-156.

    Google Scholar 

  29. G. S. Carr, Formulas and Theorems in Pure Mathematics, 2nd ed., Chelsea, New York, N.Y., 1970. First published in 1886 under the title: CARR, A Synopsis of Elementary Results in Pure Mathematics.

    Google Scholar 

  30. J. Schummer, Scientometric studies on chemistry I: The exponential growth of chemical substances, Scientometrics, 39 (1997), 107-123.

    Google Scholar 

  31. M. L. Pao, An empiricial examination of Lotka's law, Journal of the American Society for Information Science, 37 (1986), 26-33.

    Google Scholar 

  32. J. Berg, R. Wagner-DÖbler, A multidimensional analysis of scientific dynamics, Part 1, Case studies of mathematical logic in the 20th century, Scientometrics, 35 (1996), 321-346.

    Google Scholar 

  33. There is nothing miraculous in the existence of cycles in science and technology. A miracle would be the regular occurrence of cycles of a fixed length of, e.g., 50 years, the so-called Kondratiev cycles; but the observable cycles are not as regular.

  34. J. Horgan, The End of Science. Facing the Limits of Knowledge in the Twilight of the Scientific Age, Addison-Wesley, Reading, Mass., 1996. German ed.: Horgan: An den Grenzen des Wissens. Siegeszug und Dilemma der Naturwissenschaften, Luchterhand, München 1997. About Rescher see German ed., pp. 53ff. Cf. the debate between Horgan and Paul Hoffman in Time, April 10, 2000, pp. 74.75 (.Will there be anything left to discover?.).

    Google Scholar 

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Wagner-Döbler, R. Rescher's Principle of Decreasing Marginal Returns of Scientific Research. Scientometrics 50, 419–436 (2001). https://doi.org/10.1023/A:1010506730809

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