0. Soc-like Models

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. It is a capital mistake to theorize before one has data. Is it SOC or not? asked Hendrik Jeldtoft Jensen in the final chapter of his book Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. Let us quote the beginning of that chapter that is still unanswered: Ever since the term " self-organized criticality " was introduced by Bak, Tang, and Wiesenfeld (BTW) in their 1987 paper for Physical Review Letters, the concept has been surrounded by a hectic air of controversy. There are a number of reasons for this. One reason is the bold and optimistic claims that were made. The attitude was that here finally is a line of thinking that will allow us to bring the statistical physics of Boltzmann and Gibbs in touch with the exciting real world of nonequilibrium physics, and that SOC is powerful enough to explain everything from mountain formation to stock-market variation. Super-general theories always meet a certain amount of skepticism from expert scientists working in the specific fields. It is difficult to draw a precise line between the general and the specific. It might not appear likely to the geologist that the many specific details or earthquakes can be understood in terms of a simple numerical cellular automaton. The biologist working on the immensely complicated interconnected web of evolving species might not find it anything but a bad joke to represent evolution in terms of a string of random numbers with nearest neighbor interaction only. So what then is SOC good for? Let us consider some important questions. (1) Can we identify SOC as well-defined distinct phenomenon different from any other category or behavior? (2) Can we identify a certain construction that can be called a theory of self-organized critical systems? (3) Has SOC taught us anything about the world that we did not know prior to BTW's seminal 1987 paper? (4) Is there any predictive power in SOC – that is, can we state the necessary and sufficient conditions a system must fulfill in order