We shall characterize a creative personality (e.g., a scientist) by three parameters, called "technical proficiency," "enthusiasm," and "achievement." Clearly these parameters are related. 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.
This is the figure:
The "catastrophe" is when you follow line 3. Let me return to quoting Arnold:
A growth of enthusiasm not supported by a corresponding growth in technical proficiency leads to a catastrophe (at point 4 of curve 3) where achievement falls by a jump and we refer to the domain denoted in Fig. 6 by the term "maniacs." It is instructive that the jumps from the state of genius to that of maniac 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).
The deficiencies of this model and many similar speculations in catastrophe theory are too obvious to discuss in detail. I remark only that articles in catastrophe theory are distinguished by a sharp and catastrophic lowering of the level of demands of rigor and also of novelty of published results.
Taken seriously, the catastrophe theory of the '70s and '80s was very much in the same vein as the more recent extravagances of physicists that xkcd was mocking the other day. (Although it did lead to some very beautiful results on swimming-pool patterns.) Fig. 6, however, is an awfully useful caricature of intellectual development, and various things in life keep reminding me of it.