- Paperback: 408 pages
- Publisher: Westview Press; New Ed edition (31 Dec 1993)
- Language English
- ISBN-10: 0201406853
- ISBN-13: 978-0201406856
- Product Dimensions: 22.4 x 15.3 x 2.2 cm
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
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Amazon Bestsellers Rank:
578,236 in Books (See Top 100 in Books)
- #2 in Books > Scientific, Technical & Medical > Mathematics > Geometry > Analytic Topology
- #6 in Books > Science & Nature > Mathematics > Geometry & Topology > Analytic Topology
- See Complete Table of Contents
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Customer Reviews
Most Helpful Customer Reviews
Format:Paperback
Controversial in its applications and implications, but perfectly rigorous in its mathematics, this book attempts to advance a "general theory of models". The premise is that a phenomenological approach (one which addresses the observed, rather than the underlying, dynamics of a system) is sufficient to achieve a practical understanding of complex systems. The great advantage would be in biological systems, where the consitituent dynamics are of such complexity that only higher-level processes and behaviour can be observed.
This runs counter to the methodology responsible for most major advances in science, and predates the widespread use of computers which allows much greater insight into the complexities, so the work is perhaps out-of-date in this major respect. Moreover, Thom's thinking runs well beyond what experience has shown the mathematics to be capable of, and I would suggest that the book is largely of historical significance. However, it is a provocative and inspiring text, well worth it if you have the the background.
The mathematics on which this book's argument is based is differential topology, which is typically not encountered until the postgraduate level. While the "Mathematical Summary" is a useful review of what you have to know to begin the book, it is of very limited use in actually learning the mathematics, being at best an aide-memoir. For anyone below postgrad, a better start would be Saunder's "Introduction to Catastrophe Theory".
This runs counter to the methodology responsible for most major advances in science, and predates the widespread use of computers which allows much greater insight into the complexities, so the work is perhaps out-of-date in this major respect. Moreover, Thom's thinking runs well beyond what experience has shown the mathematics to be capable of, and I would suggest that the book is largely of historical significance. However, it is a provocative and inspiring text, well worth it if you have the the background.
The mathematics on which this book's argument is based is differential topology, which is typically not encountered until the postgraduate level. While the "Mathematical Summary" is a useful review of what you have to know to begin the book, it is of very limited use in actually learning the mathematics, being at best an aide-memoir. For anyone below postgrad, a better start would be Saunder's "Introduction to Catastrophe Theory".
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
4 reviews
32 of 32 people found the following review helpful
An Ingenious Classic
15 Nov 2002
Format:Paperback|Amazon Verified Purchase
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:
--------------------------------------------
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
6 of 6 people found the following review helpful
the only thing he left out was black holes
18 Oct 2001
Format:Hardcover
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.
13 of 18 people found the following review helpful
Thom Sctructural Stability and Evolution Explanation
9 Mar 2000
Format:Paperback
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.
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