Catastrophe theory is difficult to understand if one wants to go beyond the surface, to the mathematical roots. Most biologists do not have the necessary mathematical knowledge for this, and they are not likely ever to obtain it. Therefore it is advisable to start from the visual, geometrical or topological side in order to get some hunch of the contents of the whole approach - look at fig. 6 in "The shift of SW Scanian Sand Martins (Riparia riparia) from colonies to roosts in late summer"! (New reading suggestion added from October 2003: http://perso.wanadoo.fr/l.d.v.dujardin/ct, "An introduction to Catastrophe Theory for experimentalists" by Lucien Dujardin, Laboratory of Parasitology, University of Lille). There are essentially two reactions to the Sand Martin model, either: "This is nonsense", or: "There is something here" - this seems to be a promising description of a natural phenomenon, namely the 50 % or 75 % or 90 % or 99 % synchronization that we observe in e.g. breeding, moult and migration among birds. Systemic behaviour is all-pervading in a group of living creatures, and this omnipresent systemic behaviour is bound to put the agenda also for e.g. the "selection" of individuals - because the system level with its potential catastrophes (outbursts, simultaneous action, leaps in levels, cuts; all kinds of instant, sudden change) is the primary, superior level, the level constraining other levels. In the "nonsense" case there is no motive for intensified study (so: log out), in the "something" case the vague feeling could start a deepening of interest and eventually a theoretical breakthrough (so: stay with the site). I will try two parallel approaches to accommodate different needs: on one side a strict presentation of the theory in mathematical language - on the other a presentation where I try to tell what the whole thing is about in plain language.
Catastrophe theory obviously describes events, that are described by no other theory, on the other hand it has been blamed for giving poor prediction outside the realm of mechanical "catastrophe machines". That should not bother us: with, say, two state variables and three parameters, prediction is under all circumstances very difficult, and the strength of catastrophe theory is to let us see the alternatives and the connection between alternatives/alternative states. It is by no means indeterministic, but the "divergence" feature (slight differences in path produce large differences in state) puts it somewhere half-way between strict, Newtonian determinacy and the indeterminacy of chaotic systems. Still, prediction should be possible and is possible, but it takes some mathematical training and some afterthought; this has never been done in connection with catastrophe theory by ecologically minded biologists. (Although there is a sort of affinity between catastrophe theory and biological systems: the latter are incessantly perturbed, and still retain a high degree of stability. So, the "floating" character of the underlying structure of state equations need not be the result of a formal exercise in the biological case; it is a built-in feature that thrusts itself upon the researcher).
In the past there have been many attempts to advance a theoretical biology (e.g. May's "Theoretical Ecology" where chaos theory is introduced as the additional extra, the key to theoretical flight), but each time the project has fallen short of its objective because the Darwinist backbone of biology (a skeleton in the cupboard, shrewdly avoided by the theoretical physicist May and some of his co-authors, embraced by others) has been left untouched.1 Biology remains a dogmatically empiricist science, where theory is relevant only at a low, very technical level. And this state is made permanent by the people sitting on the vicarages: it takes no more than a literary effort to dress anything between heaven and earth in Darwinist rubbish. Today's dominant generation of biologists is part of the problem, and there may follow other problem generations until the situation becomes intolerable. Right now, biology seems to be an eternal expansion of Brehm's Tierleben, from version 8.4.2 to version 220.127.116.11 to version 18.104.22.168.0... - in a sense it has become anecdotic, adding nothing but amendments to the old stock. In contrast I maintain, that any serious dedication to biology must take mathematics as its point of departure; it is not until the student masters e.g. qualitative dynamics (implying a radical shift of focus from individuals to collectives, not the usual, superficial shift) that he (read: she/her/herself where relevant) should be free to devote himself to his/her favourite topic: lice and fleas of the Brown Rat (or the white wing-patches of the Pied Flycatcher). But it takes more than that to change biology: a fighting heart, the prevailing paradigm must be openly attacked. This is what will build the road to a theoretical biology: profound knowledge of applied mathematics, relentless attack on Darwinism, good empirical material that can nourish an adequate theory and be nourished by it.
1. In passing May himself dismisses the catastrophe theory with the following words: "Second, some of the above remarks can be recast, post hoc, in the language of catastrophe theory. I doubt that much is gained thereby." (p. 103, 2nd ed.) He is slightly authoritarian, has a tendency to resort to authority where reason fails, I can feel it throughout his writings - but who hasn't in this sphere? /CP/
This is going to be like walking a tightrope, so I need comments and reactions, in order to find my balance. Any comment is welcome, to e-mail adress: http://cp.hollviken'at'swipnet.se., or post adress: Christer Persson, Ljungsätersvägen 43, S 23641 Höllviken, Sweden.