Patterns of Scientific Productivity and Social Change: A Discussion of Lotka's Law and Bibliometric Symmetry

Abstract

This paper examines the application of symmetry principles to bibliometric laws, using Lotka's law for illustration. A general model describing scientific productivity is defined and modified to be consistent with a generalized form of Lotka's law; the model in this form is shown to be stable with regard to at least two forms of social change. Then the consequences of invariance under change of time span are investigated, and it is shown that the function occurring in Lotka's law, with an arbitrary exponent, is essentially the only one with desireable properties that is consistent with the symmetry constraint.