Self-organization of scientific specialization and diversification: A quantitative case study

Social Studies of Science

Volumn 27, Issue 1, 1997, Pages 147-170

  Wagner Döbler, Roland ^a,b  

^a UNIVERSITY OF MUNICH   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031532296     PISSN: 03063127     EISSN: None     Source Type: Journal    
DOI: 10.1177/030631297027001009     Document Type: Article

References (38)

1. See Jarmo Pulkkinen, The Threat of Logical Mathematism: A Study on the Critique of Mathematical Logic in Germany at the Turn of the 20th Century (Frankfurt a.M.: Lang, 1994). That mélange never disappeared completely, but it changed its geographical centres and its political affinities, inter alia.
2. All global descriptions are from: Roland Wagner-Döbler and Jan Berg, Mathematische Logik von 1847 bis zur Gegenwart, Eine bibliometrische Untersuchung (Berlin & New York: de Gruyter, 1993).
3. Gert H. Müller, in collaboration with Wolfgang Lenski (ed.), Ω-Bibliography of Mathematical Logic, Vols 1-6 (Berlin, Heidelberg & New York: Springer, 1987).
4. Alonzo Church, 'A Bibliography of Symbolic Logic', The Journal of Symbolic Logic, Vol. 1 (1936), 121-216; 'Additions and Corrections', ibid., Vol. 3 (1938), 178-92. For a quantitative comparison with the Ω-Bibliography, see Wagner-Döbler & Berg, op. cit. note 2, 60-63.
5. Alonzo Church, 'A Bibliography of Symbolic Logic', The Journal of Symbolic Logic, Vol. 1 (1936), 121-216; 'Additions and Corrections', ibid., Vol. 3 (1938), 178-92. For a quantitative comparison with the Ω-Bibliography, see Wagner-Döbler & Berg, op. cit. note 2, 60-63.
6. Wagner-Döbler & Berg, op. cit. note 2.
7. In ibid., 116, a number of documentary categories were not excluded, and only the first classification codes of an entry were considered.
8. Nicholas Rescher, Cognitive Systematisation (Oxford: Blackwell, 1979), 190. Rescher is one of the few philosophers of science dealing with specialization, classification, and taxonomy of science.
9. Wagner-Döbler & Berg, op. cit. note 2, 60ff.
10. Ibid., 118-19.
11. This phenomenon has also been observed in biology: Petr B. Shelishch, 'A Quantitative Study of Biologists in the 18th and 19th Centuries', Scientometrics, Vol. 4 (1982), 317-29.
12. Wagner-Döbler & Berg, op. cit. note 2, 65ff.
13. These reductions in the radius of attention to other areas may be the main mechanism by which scientists come to cope with the 'information explosion', as Bar-Hillel observed many years ago: see Yehoshua Bar-Hillel, 'Is Information Retrieval Approaching a Crisis?', American Documentation, Vol. 14 (1963), 95-98.
14. Other modes of calculation would not touch this outcome. For example, I considered all authors and all (not only the first one) of the publications' classification codes for the periods 1926-35 (1), 1951-60 (2), and 1976-85 (3), with the following results, corresponding with the data exhibited in Figure 54 in Wagner-Döbler & Berg, op. cit. note 2: (1) 70 areas/212 authors = 0.330; (2) 106 areas/931 authors = 0.114; (3) 113 areas/7094 authors = 0.016.
15. In his bibliography: see Church, op. cit. note 4;
16. Wagner-Döbler & Berg, op. cit. note 2.
17. Ibid., 82.
18. Y. Here f(x) denotes the number of people with at least x contributions. With concern to firm sizes, see Yuji Ijiri and Herbert A. Simon, 'Interpretations of Departures from the Pareto Curve Firm-Size Distributions', Journal of Political Economy, Vol. 82 (1974), 315-31.
19. The same is valid for Lotka distributions of publication output: see Roland Wagner-Döbler and Jan Berg, 'The Dependence of Lotka's Law on the Selection of Time Periods in the Development of Scientific Areas and Authors', Journal of Documentation, Vol. 51 (1995), 28-43.
20. Roland Wagner-Döbler and Jan Berg, 'Nineteenth-Century Mathematics in the Mirror of Its Literature: A Quantitative Approach', Historia Mathematica, Vol. 23 (1996, 288-318). Because here the publications are indexed only with one classification code, the conformity with Lotka's law is far better.
21. With respect to the frequency distribution of scientific output in terms of publications see R. Wagner-Döbler, 'Where has the Cumulative Advantage Gone? Some Observations about the Frequency Distributions of Scientific Productivity, of Duration of Scientific Participation, and of Speed of Publication', Scientometrics, Vol. 32 (1995), 123-32.
22. Wagner-Döbler & Berg, op. cit. note 2, 131. The result did not change when I then computed the distribution for a decade, namely 1961-70.
23. Wagner-Döbler & Berg, op. cit. note 2.
24. Ibid., 66.
25. For an early attempt to explore this topic, see Michael Mulkay, 'Conceptual Displacement and Migration in Science: A Preparatory Paper', Science Studies, Vol. 4 (1974), 205-34.
26. For an institutional level of analysis see: Arie van Heeringen and Pieter A. Dijkwel, 'The Relationship between Age, Mobility, and Scientific Productivity, Part 1: Effect of Mobility on Productivity', Scientometrics, Vol. 11 (1987), 267-80. Productivity (not in terms of papers, but in terms of citations) tended to increase if institutional mobility was connected with the move from one area to another. Without this, it did not increase. Nothing can be said so far about the causal relation between cognitive mobility and productivity.
27. Michael Hallet, 'Towards a Theory of Mathematical Research Programmes', British Journal for the Philosophy of Science, Vol. 30 (1979), 1-25 and 135-59.
28. Wagner-Döbler & Berg, op. cit. note 2, 83-84.
29. 'Nicholas Bourbaki' is a pseudonym for a distinguished group of (mostly anonymous and mostly French) mathematicians. Under that pseudonym, mathematical monographs appear continuously which are written by members of the group and passed jointly by the whole group. The composition of the group changes by means of informal mechanisms. See Jean A. Dieudonné, 'The Work of Nicolas Bourbaki', The American Mathematical Monthly, Vol. 77 (1970), 134-45.
30. Three authors had only a full fifth period; three had only the fourth completely; two authors had only the third period completely. Twice an author's last period comprised four years only.
31. I computed the average distance of a distance matrix considering only the differences between the twenty-one logicians with respect to the sheer number of their contributions. The average distance is 64.29 (s.d. 46.63).
32. Mark S. Granovetter, 'The Strength of Weak Ties', American Journal of Sociology, Vol. 78 (1973), 1360-80.
33. This working definition is widespread. See, for example, contributions in Milan Zeleny (ed.), Autopoiesis, Dissipative Structures, and Spontaneous Social Orders (Boulder, CO: Westview Press, 1980).
34. Herbert A. Simon, The Science of the Artificial (Cambridge, MA: The MIT Press, 1969), 84-118. See also: Dieter Germert, 'The Formation of Hierarchical Structure as a Key to Self-Organization', in G.J. Dalemoort (ed.), The Paradigm of Self-Organization. (New York: Gordon & Breach, 1989) 60-72.
35. Herbert A. Simon, The Science of the Artificial (Cambridge, MA: The MIT Press, 1969), 84-118. See also: Dieter Germert, 'The Formation of Hierarchical Structure as a Key to Self-Organization', in G.J. Dalemoort (ed.), The Paradigm of Self-Organization. (New York: Gordon & Breach, 1989) 60-72.
36. A.F.J. van Raan, 'Fractal Dimension of Co-Citations', Nature, Vol. 347 (18 October 1990), 626. George Zipf found similar distributions in linguistics, economics, biology, and other fields: see G.K. Zipf, Human Behavior and the Principle of Least Effort (New York & London: Hafner, 1949; repr. 1965).
37. A.F.J. van Raan, 'Fractal Dimension of Co-Citations', Nature, Vol. 347 (18 October 1990), 626. George Zipf found similar distributions in linguistics, economics, biology, and other fields: see G.K. Zipf, Human Behavior and the Principle of Least Effort (New York & London: Hafner, 1949; repr. 1965).
38. See Zipf, op. cit. note 32.