Customer Reviews (3)

An Ingenious Classic
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

the only thing he left out was black holes
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 Sctructural Stabilityand Evolution Explanation
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 helpof the catastrophe theory. ... Read more

Customer Reviews (1)

Highly speculative
The title of this book obviously has its origins in "semiotics", a school of philosophy and linguistics of French origin, and the author, being French himself, is clearly influenced by this school (although in this book no admission to this is made). He does however discuss why he chose the name "semiophysics": namely to seek out "significant forms", and to build a "general theory of intelligibility". The author attempts to show in the book that there are only certain elements of reality that really make sense and only these can be used as a basis for a meaningful linguistic description. Thus one must find "stable elements" or "salient forms" which the author contends have the shape of balls, and interact like living beings. Mathematically speaking, the "balls" are bounded closed sets of maximum dimension (three in this case). There are then "pregnances" which propagate from one salient form to another. The form can then change its state, and can re-emit the pregnance, the latter of which may or may not be changed in the process. The author endeavors to combine this approach with what he had discovered in the works of Aristotle.

Those readers who know of the author's work in mathematics, particularly in differential topology, may perhaps be surprised by the content of this book. There are some interesting concepts elucidated in it, but as a whole the wording and argumentation are rather difficult to follow. Catastrophe theory, a theory developed by the author in the 1960s, is used here in an attempted justification of the Aristotelian notion of "continuity". Thus the book could be viewed as an interpretation of Aristotle from the viewpoint of catastrophe theory. The concept of continuity is primordial for the author, for he believes that discontinuity, which is modeled by the formalism of catastrophe theory, requires continuity for its definition. Most interestingly though, the author holds that all epistemology must be "genetic", for it must, in his words, take into account the the effect of evolutionary alterations that humans have been subjected to for many millenia. But he still presupposes, and says so explicitly, the Euclidean nature of space-time, asserting that the discovery of non-Euclidean geometry and general relativity are irrelevant to the problems which he is going to discuss. These discoveries, he says, belong to the "ontological region", and lie outside the cognitive activity of ancient man. The goal of the book is to take concepts from the "exact" sciences, such as the notion of a field in physics, phase transitions (implying discontinuities), and the notion of individuality. These notions are then extended to abstract spaces of a semantic character (this move clearly overlapping what is done in semiotics). Chapter 8 of the book, entitled "Aristotelian Perspectives in Language Theory" is another example of the influence of semiotics on the author's project.

There are some discussions in the book that reflect the time of publication. For instance, the author speaks of the replacing of a point by a small oscillator that duplicates itself, and remarks that this concept may be useful from a quantum mechanical standpoint. But string theories were definitely around at the time of publication, and the replacing of point particles by strings that oscillate, and are created and destroyed, is an example of what the author is asserting (but does not elaborate on in any detail). Also, the catastrophe theory of the author was supposed to model the (discontinuous) processes of cell division, or "morphogenesis". He remarks, interestingly, that "not much is known about the internal structure of the cytoplasm", and so "any attempt at symbolizing cellular dynamics can only be speculation". But since the time of publication of this book, the mathematical modeling of cellular dynamics has really taken off, and there is now a large group of researchers that are attempting to create a comprehensive mathematical model of the cell. Most of these developments do not involve catastrophe theory, no doubt because of its qualitative emphasis.

Thus as a whole the book is highly speculative and pre-scientific. It might be difficult to appreciate by the general scientific crowd, for one must have a background in both catastrophe theory and Aristotelian philosophy in order to follow it. My opinion is that the current emphasis on quantitative mathematical modeling in all of the areas that the author discusses will continue to be the dominant one as we move further into the 21st century. All of this effort requires meticulous validation and experimentation, especially in the medical and biological areas. The truth of these efforts will thus be defined by the success they have on human health, and, with the exception of problems in medical ethics, "philosophical foundations" will take a back seat. Science does not need such a foundation. ... Read more

Book Description
This digital document, covering the life and work of Rene Frederic Thom, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 2048 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author

Book Description
In this unique critical volume, the authors turn the semiotic spotlight on an obscure area of art: the drawings and notations choreographers use to think about the human body in motion. ... Read more