Abstract

Structures of scientific activity and the exponential growth (as a function of time) of modern science. Scientific research may have an additive, multiplicative or exponential character. ‚Additive’︁ signifies that single facts are gathered; ‚multiplicative’︁ signifies that out of several facts, a regularity or formula is recognized: single facts are thereby multiplied into many. ‚Exponential’︁ signifies that every finding serves as a springboard for further findings, which in turn serve as springboards for others as well. This exponential character, however, does not necessarily have as a consequence an exponential growth of knowledge as a function of time.The slogan of the doubling of knowledge every 15 years is not universally valid: since the 16th century knowledge of plant species has doubled every 60 years; for animal species during the two centuries before ca. 1930, the doubling period is 21–22 years. For comets, the doubling periods are considerably longer and for chemical elements, the increase is only linear (one new element every 2 1/2 years). Science as a whole is composed of many such smaller fields. The specification of the speed (or better the acceleration) of its growth depends on which ‚degree of importance’︁ of knowledge is measured. If one takes only very important (e.g. University Textbook) knowledge as a standard, the doubling period is just short of a century. Of course, this does not alter the correctness of the observation that modern science has grown exponentially. If, however, one wishes to speak of a ‚law’︁, it is necessary to formulate one.