Customer Reviews

Structural Stability and Morphogenesis

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Rene Thom was the primary force behind the creation of Catastrophe Theory, and this is the book that brought his ideas forth. (This is actually the English translation of his original French edition.)

Thom uses topology as his primary mathematical tool for describing and investigating catastrophes and stabilities. As such, this is primarily a qualitative, not a quantitative, approach. The advantage of this is that it allows Thom to spend a great deal of time discussing general characteristics without getting bogged down in formulae or proofs. Indeed, the book is largely text, interspersed with graphs and only the occasional polynomial or differential equations.

And Thom is very insightful when discussing those general characteristics. Along the way he comments on everything from embryology to societal structures as viewed from the perspective of catastrophe theory. Much of the value of the book is buried not in the technical results as it is in his understated comments and speculations regarding the myriad of applications he investigates. Alot of careful and deep thought is present, and there is a significant amount of pregnant wisdom inside.

I originally came to read Thom via the profound books of theoretical biologist Robert Rosen. As someone not conversant in topology or catastrophe theory, I can say that there were some parts that were a technical struggle, but the content is well worth the effort. Someone versed in the math of dynamical systems and topology would be the more typical target audience.

But I stress again that the technical value is equalled or surpassed by the insights Thom brings to understanding physical systems of many types.

Since there are no publishers notes here on Amazon, I will list the table of contents for you:
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Introduction
Form and Structural Stability
Structural Stability in Mathematics
Kinematic of Forms; Catastrophes
Elementary Catastrophes on R4 Associated with Conflicts of Regimes
General Morphology
The Dynamic of Forms
Biology and Topology
Local Models in Embryology
Global Models for a Living Being (Metazoa)
Models in Ultrastructure
The Basic Problems of Biology
From Animal to Man: Thought and Language

I would say his book is very visionary and inspiring of thought. You need some mathematical maturity to understand some of his notation, but there isn't a lot of it. It's more of a science book than a math book in my opinion. His pictures of examples of all of the kinds of the 7 catastrophes were very insightful. This caused me to think of examples on my own.

Thom stablished the foundantions of a new and powefull tool of exploring the non linear behaviour of the physics and byological phenomena. It's impossible to understand the universe and the life evolution whithout help of the catastrophe theory.

René Thom (1923-2002) was one of the greatest mathematicians of the XXth century. He had broad interests outside mathematics as well and thought that his work in topology could be used to bring light into other subjects, particularly biology. His catastrophe theory was hotly debated during the seventies, both loved and hated, and was finally almost forgotten as the lights of fame spotted on chaos theory. Catastrophe theory is a mathematical formalism to explain sudden changes of continuous functions. As such, René Thom's mathematics is as good as it always was. Whether or not it can be useful to explain facts of the real world may be debatable, but Thom has undoubtedly succeeded in bringing advanced mathematical methods in the natural sciences, particularly biology. This book is a gem, the treasure output of an insightful mind. A true source of mathematical and scientific inspiration. A note of warning though: you will need heavy mathematical background to understand this book, and you will have to go through other books on catastrophe theory and topology in order to get the grasp of what is in here.