catastrophe type model

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“It is an intriguing thought that the same mathematics may underlie not only the way the genetic code causes the embryo to unfold but also the way the printed word causes our imaginations to unfold.”

                                                 — E.C. Zeeman, “Catastrophe Theory”,
                                                     Scientific American (April 1976), page 83

©2013 By Bob Litton

Most of us Earthlings consider “catastrophe” a synonym for “disaster”. Not so do the mathematicians, in whose abstract realm a catastrophe is just a way of describing an abrupt change in the world of things and events. For, they say, discontinuous or divergent events are simply another aspect of continuous and stable events.

The way these theories manage to come about is apropos. The system for describing continuous phenomena mathematically — called “differential calculus” — was invented concurrently by an Englishman and a German in the 17th century. It took a Frenchman, René Thom, to come up with a way of describing divergences in 1968. The suitableness arises out of the common notion that the British and the Germans are staid, while the French are spontaneous. The general tendency of differential calculus was to lob off imaginative bypaths, to make the universe into a safely circumscribed, predictable clock.

And yet, catastrophe theory is, in a fundamental sense, as deterministic as differential calculus. Using it, one supposedly could predict the moment a dog will bite (by measuring the space between his lips) or when he will tuck in his tail and run (by measuring the angle between his ears and skull). In another and just as basic sense, however, catastrophe theory does relate positively to the imagination: It not only serves practical ends when it is applied through continually multiplying ramifications to diverse aspects of Nature and human society, but it also may serve as a model to explain, as catastrophist E.C. Zeeman says in the article cited in the epigraph above, how our imagination itself works. Let us speculate as to what implications catastrophe theory might have for at least two of the humanities: dramatic criticism and ethics.

Thom devised seven basic mathematical formulas with accompanying diagrams —some quite visually pleasing* — to explain his theory; and he gave them colorful names such as “butterfly” and “swallowtail” due to their resemblance to natural phenomena . Thom’s “laws” have supposedly become diffused throughout educated society by now; at least, that would seem to be the case, since a term, “tipping point”, an essential element in the catastrophe theory, has appeared in news reports on a variety of subjects during the past decade. Most of those reports have concerned the weather and economic predictions, but I would not be surprised to see the theory affect dramatic criticism; for, one of the basic facts of psychological catastrophes is that a person cannot be neutralized by two contrary emotions of equal intensity. “…(T)wo controlling factors are then in direct conflict,” says Zeeman. “Simple models that cannot accommodate discontinuity might predict that the two stimuli would cancel each other, leading again to neutral behavior. That prediction merely reveals the shortcomings of such simplistic models, since neutrality is in fact the least likely behavior.”[1] It is conceivable then that a theater critic of the catastrophe school could chop Hamlet all to pieces.

Interpretations of Hamlet the character are multiple (e.g., straight forward: his search for certainty before committing a distasteful act; influence of the Reformation: contemporary debate about the existence of Purgatory; Freudian: Oedipus-Complex; Mirror: other characters’ interpretations of Hamlet’s motives and actions as concentrated on their selves, and the audience’s interpretations). Heretofore, the variety of the interpretations has been held up as a sign of the superiority of Shakespeare’s psychological perspicacity. The “straight forward” interpretation — the one most generally adopted — maintains that the prince represents the ineffective intellectual (of reason divided against its self). Perhaps because of Shakespeare’s literary stature, the nearly flawless classical structure of this play, and the poetic quality of the lines the playwright puts into Hamlet’s mouth, such inaction has been considered a weakness in the character and not of the characterization. But what if someone eventually analyzes Hamlet the character through the lens of catastrophe theory and discovers that the prince is really just a poked bag full of contrary ideas and not of contrary emotions.

What would be necessary to accomplish this, of course, would be measurable parameters, something that could be graphed so that, say, a “butterfly” or a “swallowtail” catastrophe would develop. Each stage in Hamlet’s psychological development would have to be given some numerical value. However, it should not be more difficult to “measure” Hamlet’s speeches than it was to measure the lip-span of an enraged dog. Something of the sort has already been done with self-pity, which Zeeman declares can be measured directly. Self-pity, he says,

is a defensive attitude commonly adopted by children, and it often seems that sympathy is powerless to alleviate it. A sarcastic remark, on the other hand, may provoke a sudden loss of temper and, by releasing tension, may open a pathway back to a less emotional state. It is unfortunate that sarcasm should succeed where sympathy fails, but the cause of that irony is apparent in the model. The sarcasm brings an increase in frustration, and as a result the point representing mood travels across the behavior surface as far as the fold curve; having reached the extremity of the bottom sheet, it is forced to make a catastrophic jump to the top sheet, and self-pity is transformed into anger.[2]

Once the parameters as scales have been worked out, the catastrophic analysis should be applicable to the protagonist in any play, at least in any play purporting to fit the mold of a play having a protagonist who undergoes some sort of “recognition of self” event. If the protagonist does not measure up to the criteria (i.e., if his change is not adequately justified by the cumulative causes) then he might be declared an “incomplete protagonist”; and the play, a “flop”.

Many people — of the anti-behaviorist sort — would hate to see such a development, for the same approach could be applied to living beings. In fact, this is already being done in England, where doctors have used catastrophe theory in conjunction with trance therapy to cure girls of anorexia nervosa. It is one thing, of course, to say that a certain behavior has had sufficient precedent cause and quite another thing to create behavior because one knows what will be sufficient cause. The latter action is what essentially terrifies the anti-behaviorists, although they waste no time in transferring their distaste to the former.

The problem is at least as old as Socrates, who advised “know thyself”, and his fellow Athenians, who killed him because self-knowledge was exactly what they did not want. In the ethical sense, however, the unpleasant prospect is not that individuals might be manipulated by some scientist who knows how to “cue” them through catastrophic determinants, but rather that proof irrefutable might evolve out of such research that individuals have no free will — not any more than has a beaker of mercury.

Now, let us lower the level of our discussion from the abstract to the concrete and the particular, where I, at least, feel more comfortable. Take the instance of a young man in the military during the early 1960s — at the height of the Cold War: the Cuban missile crisis. This young man, who had previously accepted the world pretty much as he found it, began to read philosophy books for lack of anything better to do on a small island. Because of his reading, he started to question the beliefs he had taken for granted. Particularly, he began to see his country’s role in the world in a different, less idealistic light. All of a sudden he came to consider that the world might come to an end — and he with it — without his ever having had a chance to do something creative. He felt a strong impulsion to act; but he could not determine the right, the highest mode, of action.

It was not only that the problems were multifarious and overwhelming, but also that he did not feel secure about the sincerity of his own motives. He wondered how he could be certain he was not simply reacting to his environment, which was rather desolate and lonely, after all. He had had no problem joining the service; he felt that the four years he had signed up for was a small price to pay for all the past and potential opportunities he did and would enjoy. Nor did he feel strong animus against any of the other servicemen, not even those who outranked him, not any more anyway that he had felt toward civilians; they were serving their country as well as he, only with what he conceived to be a blindered dedication.

He wanted to be truer to himself than that: if only he could determine what his true self was. What if he committed some irreversible act on the basis of a strong but transitory faith and on the morrow became convinced that he had acted selfishly and foolishly? The poor fellow got so strung out that he began to analyze the motives behind his own thoughts.  He constructed little schematic problems for himself to solve, hoping in that way to abstract the issue to such a point that he could logically answer it in only one way.

For instance, he considered the possibility of a man who regularly craves candy bars discovering one day that he is a diabetic. The imaginary man tries to quit eating candy bars, and as long as he is active doing something else he does not even think about them. Occasionally, however, when he is alone and a candy bar is within easy reach, he is strongly tempted to eat it. The instant he thinks about how the candy bar would taste, that can be the only image occupying his mind. When he thinks about the diabetes, on the other hand, then that disease is the only subject uppermost in his mind. He knows, however, that he will have to act, for he cannot sit there forever, mentally hopping back and forth between desire and fear.

Therefore, the young man wondered, how can we say this fellow had any choice, since in the one second in which he has to act there can be only one thought in his mind? It seems simply fortuitous which thought happens to be there when he makes his move; and yet, whichever one it is, is the one that will “dictate” his choice. What “mechanism” is it that causes one thought to displace the other? Where does that displaced thought “go”? And what is the engine of the final, over-riding impulse that propels action?

The result was a nervous breakdown.

This seems to me to be at least partly how catastrophe theory relates to our artistic and ethical lives.


*(The reader can find more detailed information and illustrations on the seven elemental catastrophe graph forms on the Internet if he/she wishes to delve that deeply into the subject.  My purpose in this essay is not to discuss the mathematical aspects of catastrophe theory, but to explore the theory’s potential applications to dramatic plots and to ethical quandaries.)

[1]E.C. Zeeman, “Catastrophe Theory”, Scientific American (April 1976), page 65.
[2]Ibid., page 69.


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