Structural Stability And Morphogenesis PDF

Special Preface

It is now some fifteen years since Structural Stability and Morphogenesis was first published in the French edition. The purely mathematical theory of singularities of smooth maps has developed tremendously in that time, especially after the work of V. I. Arnold and his school. However, the main interest of this book lies not in its mathematics, but in the methodological perspective opened up by Catastrophe Theory models.

Of course the book enjoyed no small success around 1973-74 when the work of C. Zeeman and his Warwick school brought Catastrophe Theory to the wider public. Undoubtedly it had some influence in re-directing the attention of physicists from the Quantum World to Classical Dynamics and our usual "macroscopic" Physical World. This trend is remarkable owing to the present emphasis on Chaos and Turbulence Theories. But it seems fair to say that many of the teachings of Structural Stability and Morphogenesis are still awaiting full recognition and possible applications. The hopes raised by C. Zeeman's models in the "soft" sciences dwindled somewhat after the great controversy of the years 1975-76. It became clear that Catastrophe Theory formalism is not able, in general, to predict phenomena, at least in the usual sense of quantitative modeling. But the possibility remains of a qualitative understanding, a fast interpretation of many dynamical situations involving opposite trends.

The views developed in this book about possible applications in many domains, especially in Biology, still await workers to develop them and to confront them with the "hard" facts of experimentation. In that respect, I very much hope that reprinting in the Addison-Wesley Advanced Book Classics series does not mean the book is now no more than a museum curiosity. Like D' Arcy Thompson's book On Growth and Form, itstill contains many ideas that may burgeon in the mind of a curious and intellectually active reader. I sincerely hope that will happen.

Author: Rene Thom