From V.I. Arnold “Catastrophe Theory” (1986), after E.C. Zeeman.


We shall characterize a creative personality (e.g. a scientist) by three parameters, called 'technical proficiency', 'enthusiasm', and 'achievement'. Clearly these parameters are interrelated. This gives rise to a surface in three-dimensional space with coordinates (T, E, A). Let us project this surface onto the (T, E) plane along the A axis. For a generic surface the singularities are folds and cusps (by Whitney's theorem). It is claimed that a cusp situated as indicated in Fig. 6 satisfactorily describes the observed phenomena.



In fact, let us see how under these assumptions the achievement of a scientist will change in dependence on his technical proficiency and enthusiasm. If enthusiasm is not great, then achievement grows monotonically and fairly slowly with technical proficiency. If enthusiasm is sufficiently great, then qualitatively different phenomena begin to occur. In this case with increasing technical proficiency achievement can increase by a jump (such a jump occurs for instance at point 2 in Fig. 6 as enthusiasm and technical proficiency change along curve 1). The domain of high achievement at which we then arrive is indicated in Fig. 6 by the word 'geniuses'.


On the other hand a growth of enthusiasm not supported by a corresponding growth in technical proficiency leads to a catastrophe (at the point 4 of curve 3 in Fig. 6) where achievement falls by a jump and we drop to the domain denoted in Fig. 6 by the word 'maniacs'. It is instructive that the jumps from the state of genius to that of maniac and back take place along different lines, so that for sufficiently great enthusiasm a genius and maniac can possess identical enthusiasm and technical proficiency, differing only in achievement (and previous history).