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- Author or Editor: Roland Wagner-Döbler x
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Abstract
Time-series of collaboration trends indicated through co-authorships are examined from 1800 to presence in mathematics, logic, and physics. In physics, the share of co-authored papers expands in the second half of the19th century, in mathematics in the first decades of the 20th century, in logic in the second half of the 20th century. Subdisciplines of mathematics, of physics, and areas of logic show large differences in their respective propensities to collaborate. None of the existing explanatory approaches meets this heterogeneity; the most salient feature is a propensitiy to collaborate in fields where theoretical and applied research is combined.
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".
Abstract
In this paper we have looked at a new measure of connectedness between research areas, namely, the migration of authors between subfields as seen from their contributions to different areas. Migration may be considered as an embodied knowledge flow that bridges some part of the cognitive gap between fields. Our hypothesis is that the rate of author migration will reflect cognitive similarity or affinity between disciplines. This is graphically shown to be reasonable, but only above certain levels of migration for our data from mathematical reviews spanning 17 years (1959–1975). The inter-related structure of Mathematics is then mapped using migration data in the appropriate range. We find the resulting map to be a good reflection of the disciplinary variation in the field of Mathematics.
Abstract
We show that scientific production can be described by two variables: rate of production (rate of publications) and career duration. For mathematical logicians, we show that the time pattern of production is random and Poisson distributed, contrary to the theory of cumulative advantage. We show that the exponential distribution provides excellent goodness-of-fit to rate of production and a reasonable fit to career duration. The good fits to these distributions can be explained naturally from the statistics of exceedances. Thus, more powerful statistical tests and a better theoretical foundation is obtained for rate of production and career duration than has been the case for Lotka's Law.
Abstract
We show that scientific production can be described by two variables: rate of production (rateof publications) and career duration. For 19th century physicists, we show that the time pattern ofproduction is random and Poisson distributed, contrary to the theory of cumulative advantage. Weshow that the exponential distribution provides excellent goodness-of-fit to rate of production andcareer duration. The good fits to these distributions can be explained naturally from the statisticsof exceedances. Thus, more powerful statistical tests and a better theoretical foundation isobtained for rate of production and career duration than has been the case for Lotka's Law.
Abstract
According to authors like H. E. Stanley and others, growth dynamics of university research displays a quantitative behaviour similar to the growth dynamics of firms acting under competitive pressure. Features of such behaviour are probability distributions of annual growth rates or the standard deviation of growth rates. We show that a similar statistical behaviour can be observed in the growth dynamics of German university enrolments or in the growth dynamics of physics and mathematics, both for the 19th century. Since competitive pressure was generally weak at that time, interpretations of statistical similarities as to pointing to a “firm-like behaviour” are questionable.
Summary
To compare science growth of different countries is both, of theoretical and of pragmatic interest. Using methods for the analysis of complex growth processes introduced by H. E. Stanley and others, we exhibit quantitative features of Chinese science growth from 1986 to 1999 and compare them with corresponding features of western countries. Patterns of growth dynamics of Chinese universities publication output do not differ significantly from those found in the case of western countries. The same is valid for Chinese journals when compared to international journals. In nearly all cases the size distribution of output over universities or journals is near to a lognormal one, the growth rate distribution is Laplace-like, and the standard deviations of the corresponding conditional distributions with regard to size decay according to a power law. This means that regarding some structural-dynamical properties China's recent science system cannot be distinguished from a western one - despite different prehistory and different political and economic environment.
