Wednesday, February 21, 2018

Chaos and catastrophes

Michael Crichton's novel Jurassic Park is an allegation against the unreasonable use of science. In the words of Dr. Ian Malcolm, one of the characters in the book:
Scientists are actually preoccupied with accomplishment. So they are focused on whether they can do something. They never stop to ask if they should do something. They conveniently define such considerations as pointless. If they don't do it, someone else will. Discovery, they believe, is inevitable. So they just try to do it first. That's the ga me in science. Even pure scientific discovery is an aggressive, penetrative act... Discovery is always a rape of the natural world. Always.
This problem arises especially in the scientific field that serves as the basis for Crichton's novel, genetic engineering, which poses many important ethical problems. There are many things that we can already do, or are close to achieving, but should they be done? I will mention a few:

         Human cloning.
     Obtaining hybrids or chimeras between humans and animals. I mentioned this in another post in this blog.
    The resurrection of extinct species. Some experts think that it would be better to use our efforts to conserve existing species; that it is not clear that the extinction won’t happen again; and that the benefits obtained from the conservation of those species are debatable. The problem has been raised recently with regard to the possible recovery of species of frogs that have disappeared in recent decades.
To give strength to his allegation, Crichton introduces alleged scientific arguments through his character (Ian Malcolm), who is supposed to be a mathematician expert in chaos theory. Let us look at some of those arguments:
         [In a complex system,] inevitably, underlying instabilities begin to appear.
         Flaws in the system will now become severe.
         System recovery may prove impossible.
         Increasingly, the mathematics will demand the courage to face its implications.
It is easy to see that, while trying to give scientific basis to his novel, Crichton has confused two different theories:
  1. The theory of chaos. Created by Edward Lorenz in the nineteen fifties, during his studies on meteorological predictions, applies to nonlinear systems where an infinitesimal difference in initial conditions leads to huge differences after a certain time, which can be very long. Lorenz introduced the concept of strange attractors, which have a fractal structure, and the butterfly effect, the fact that very small causes can give rise to enormous effects, which is usually expressed as follows: When a butterfly flaps its wings in Australia, this movement can give place much later to a tornado in the United States. Of course, thus expressed, it is an exaggeration, which was probably suggested by the appearance of the strange attractor that emerges from Lorenz’s meteorological equations (see the attached figure), which bears a certain resemblance to the wings of a butterfly.
    Lorenz attractor
  2. The theory of catastrophes. Created by René Thom in the nineteen sxties, it is applied to non-linear systems where a very small change in the parameters of the system can lead in certain situations to abrupt changes in its behavior. They differ from chaotic systems, which are very sensitive to initial conditions after a sufficiently long time, while catastrophic systems are immediately sensitive to changes in their parameters, in certain circumstances. It is curious that in catastrophic systems we also speak of butterflies and other animals. Thus, the swallowtail catastrophes (see the attached figure) are due to the aspect of the three-dimensional representation of the state surface of the system defined by the equation V=x5+ax3+bx2+cx, while the butterfly catastrophes correspond to the equation V=x6+ax4+bx3+cx2+dx.
    Swallowtail catastrophic system
It is evident that the system in Jurassic Park, which collapses abruptly as a consequence of an apparently small change (the action of a saboteur, who disconnects for a certain time the security systems) is a catastrophic system, not a chaotic system, as the author says many times through his character Ian Malcolm. And the successive iterations in the generation of a fractal curve, which serve as a framework for the different sections of the novel, have no relation at all to what is happening.
Anyway, despite the various additional scientific errors of the book, which are related to genetic engineering and have often been pointed out, the plot is attractive and the novel is easy to read, probably due to the morbid fascination at seeing people persecuted and sometimes devoured by dinosaurs.

The same post in Spanish
Thematic Thread on Mathematics: Previous Next
Manuel Alfonseca

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