Nature 269, 759 - 763 (27 October 1977); doi:10.1038/269759a0

Claims and accomplishments of applied catastrophe theory

Raphael S. Zahler^* & Hector J. Sussmann^†

^*104 Hubinger Street, New Haven, Connecticut 06511.
^†Department of Mathematics, Butgers College, Hill Centre for the Mathematical Sciences, Busch Campus, New Brunswich—New Jersey 08903.

Several representative attempts to apply catastrophe theory to biological and social science problems turn out on close analysis to be characterised by incorrect reasoning, far-fetched assumptions, erroneous consequences, and exaggerated claims. Catastrophe theory seems to have made no significant contributions to biology and the social sciences, and to have no advantage over other better-established mathematical tools which have been used to better effect.

References

1.	Stewart, I. N. in Encyclopedia Britannica Book of the Year (Encyclopedia Britannica, New York, 1977).
2.	Sussman, H. J. & Zahler, R. S. Synthese (in the press).
3.	Kozak, J. J. & Benham, C. J. Proc. natn. Acad. Sci., U.S.A. 71, 1977 (1974).
4.	Zeeman, E. C. Sci. Amer. 234, 65 (1976).
5.	Zeeman, E. C., in Lectures on Mathematics in the Life Sciences 7, 69 (1974).
6.	Zeeman, E. C. in Towards A Theoretical Biology 4, 8 (Edinburgh University Press, Edinburgh, 1972).
7.	Kline, M. Mathematics in Western Culture (Oxford University Press, New York, 1974).
8.	Jones, D. D. The Application of Catastrophe Theory to Ecological Systems (International Institute for Applied Systems Analysis, Schloss Laxenburg, Austria, 1975).
9.	Hodgkin, A. L. & Huxley, A. F. J. Physiol., Lond. 117, 500 (1952).
10.	Crelin, E. S. J. exp. Zool. 120, 547 (1952).
11.	Elsdale, T., Pearson, M. & Whitehead, M., J. Embryol. exp. Morph. 35, 625 (1976).
12.	Woodcock, A. E. R. Ann. N. Y. Acad. Sci. 231, 60 (1974).
13.	Dodson, M. M. Math. Biosci. 28, 243 (1976).
14.	Isnard, C. A., Zeeman, E. C., in Use of Models in The Social Sciences (Tavistock, London, 1974).
15.	Blainey, G. The Causes of War (Macmillan, New York, 1973).
16.	Kolata, G. Science 196, 287 (1977).
17.	Zeeman, E. C., et al. Br. J. math. stat. Psych. 29, 73 (1976).