The rise and fall of catastrophe theory applications in economics: was the baby thrown out with the bathwater?

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THE RISE AND FALL OF CATASTROPHE THEORY APPLICATIONS IN ECONOMICS: WAS THE BABY THROWN OUT WITH THE BATHWATER?

J. Barkley Rosser, Jr.1


September, 2004

Introduction


The science writer, John Horgan (1995, 1997), has ridiculed what he labels “chaoplexology,” a combination of chaos theory and complexity theory. A central charge against this alleged monstrosity is that it, or more precisely its two component parts separately, are (or were) fads, intellectual bubbles of little consequence. They would soon disappear and deservedly so, once scholars and intellects realized what worthless dross they truly were (or are). As the culminating centerpiece of his argument, Horgan introduced the label, “the four C’s,” which consist of cybernetics, catastrophe theory, chaos theory, and complexity theory.2 More particularly, Horgan singled out catastrophe theory as the supreme example of an intellectual fad to which he compared chaos and complexity theory. This comparison was supposed to constitute the definitive proof of his argument, its pièce de résistance, the point that would send any right-minded or sensible individual running for their intellectual respectability while screaming in horror at the very idea of taking either chaos theory or complexity theory even remotely seriously. Clearly, Horgan considered catastrophe theory to be such an utterly worthless intellectual stock that the very mention of it in conjunction with another idea would trigger an immediate and relentless crash of the other idea’s value in the intellectual bourse once and for all. Such is the current status of catastrophe theory as perceived by many observers of the intellectual scene.

That this is indeed its widely perceived status (or lack thereof) was recently reinforced after the death of its publicly identified founder, the French mathematician René Thom. Obituaries and other reports in media outlets discussed how he had been somewhat depressed and withdrawn in his latter years because of the decline in status of his most famous intellectual progeny. Such reports would not be made if there were nothing to them. Although as we shall see, many of the crucial ideas of catastrophe theory were invented/discovered well before he began to study them, he was the person who first proposed its use as a form of applied topology (Thom, 1969) and was as responsible for the original publicity that generated the reputed fad or intellectual bubble, the other principal figure being the Warwick mathematician, E. Christopher Zeeman (1977), who was responsible for coining the term “catastrophe theory.”

That this is supposedly the status of catastrophe theory more generally means that it is not surprising that this is also largely its status in economics as well. It is a discounted idea or approach or method or theory that no ambitious junior scholar in her right mind would evenly remotely dare to refer to in a paper except either in ridicule or in a remote footnote with little further discussion. Within the last decade hardly any paper in a “leading” journal in economics has appeared that had any reference to “catastrophe theory” in it all in any context, however obscure or remote.3 Whether catastrophe theory was actually a loveable baby or merely a bucket of worthless bathwater, it has most definitely been thrown out by economists, as it has been by scholars from many other disciplines as well. The case would seem to be closed. Indeed the widespread nature of its rejection would seem to be the final proof that it was really just bathwater after all and that Horgan was fully justified to hold it up as the prime example of a ridiculous and ultimately worthless intellectual fad.

This paper will suggest that this viewpoint may need some reconsideration. The reference to “the baby being thrown out with the bathwater” was first applied to the question of catastrophe theory during a debate over its use more than two decades ago by Oliva and Capdeville (1980) in the journal Behavioral Science. This suggests that indeed there was some bathwater that needed to be thrown out, but that catastrophe theory itself was not that bathwater, that it was in fact an at least not totally unloveable baby that deserved to be preserved and raised in a proper household. The position ultimately taken in this paper will partly agree with this perspective. Sins of intellectual hype and exaggeration were committed as were inappropriate applications of the theory. It is not as general in application as its original proponents claimed, and most certainly it is not a general intellectual panacea. There was a fad and an intellectual bubble, and it was perfectly reasonable that there should have been a discounting and a downgrading to some extent. However, it would appear that this has been overdone, that the intellectual marketplace has inefficiently overshot on the downside. A rather telling sign of this is that probably the field in which the attitude towards catastrophe theory did not fall so low, partly because it did not rise so high in the first place, is mathematics. It is indeed time that non-mathematicians became cognizant of this fact and reevaluated the former fad in order to move it to a more proper valuation. This includes in economics as well, where the baby should be brought back in from the outside to be given a proper high chair, if not the highest one in the house.

This paper will proceed by first reviewing the mathematical origins and background of catastrophe theory. Then it will review the details of some of its applications in economics. This will be followed by an examination of the controversy and debate regarding the use of catastrophe theory, with a special focus on discussion of the Zeeman (1974) model of financial market dynamics. Finally, we shall note some alternative approaches that are being used now in order to model the phenomenon of dynamic discontinuity in economics. Although catastrophe theory may deserve to have its own high chair in the house once again, there are some other babies that deserve at least as high a high chair as it does.



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