John Wiley & Sons
October 17, 1979
Connectivity, complexity, catastrophe: these are loaded words in the system theory lexicon. At one level the words connote an intuitively satisfying characterization of important aspects of processes that pervade modern life. How often does one see descriptions such as “a tightly connected system,” “a large, complex system,” “a catastrophic outcome,” and so on? Upon more careful examination, though, the “three C’s” appear as the smile of the Cheshire cat rather than as a useful characterization of system-theoretic properties. The problem is one of translation of intuition into operational terms. Until the words are given a definite operational meaning within the context of a given mathematical model of a particular problem, they mean whatever one wants them to mean, a normal situation in philosophy but one with obvious defects as a model for policy making or control.
In the pages that follow, we attempt a somewhat eclectic overview of some of the recent work aimed at mathematically coming to grips with connectivity, complexity, and catastrophe (CCC). In some sense, this book can be regarded as an extended outline, as the goal has been more to range over a wide variety of approaches to CCC, rather than to provide in-depth coverage of a few particular approaches. Since there is by no means consensus about how the basic concept should actually be viewed, we feel that our approach is at least defensible. Nonetheless, many readers may wish for more details. For this reason, we have attempted to provide a balanced reading list at the end of each chapter for those who wish to dig deeper. Consequently, the book should be regarded as a high-altitude flight over some of the mountaintops of the system theory world, not paying too much attention to the fine points found only in the valleys. It is to be hoped that this approach will make the basic ideas accessible to a wider range of readers than would a purely technical treatment devoted to detailed excursions down into the valleys. For the same reason, we have also provided numerous applications of the CCC ideas from a wide variety of fields. At worst, these applications should assist the reader by providing motivation for some of the more esoteric mathematics. At best, some of the applications may justify the entire book; the reader himself must be the final judge.