On growth, ageing, and fractal differentiation of science

On the basis of the measured time-dependent distribution of references in recent scientific publications, we formulate a novel model on the ageing of recent scientific literature. The framework of this model is given by a basic set of mathematical expressions that allows us to understand and describe large-scale growth and ageing processes in science over a long period of time. In addition, a further and striking consequence results in a self- consistent way from our model. After the Scientific Revolution in 16th century Europe, the `Scientific Evolution' begins, and the driving processes growth and ageing unavoidably lead - just as in our biological evolution - to a fractal differentiation of science. A fractal structure means a system build up with subsystems characterised by a power-law size distribution. Such a distribution implies that there is no preference of size or scale. Often this phenomenon is regarded as a fingerprint of self-organisation. These findings are in agreement with earlier empirical findings concerning the clustering of scientific literature. Our observations reinforce the idea of science as a complex, largely self-organising 'cognitive eco-system'. They also refute Kuhn's paradigm model of scientific development.