Causality in Complex Systems

Systems involving many interacting variables are at the heart of the natural and social sciences. Causal language is pervasive in the analysis of such systems, especially when insight into their behavior is translated into policy decisions. This is exemplified by economics, but to an increasing extent also by biology, due to the advent of sophisticated tools to identify the genetic basis of many diseases. It is argued here that a regularity notion of causality can only be meaningfully defined for systems with linear interactions among their variables. For the vastly more important class of nonlinear systems, no such notion is likely to exist. This thesis is developed with examples of dynamical systems taken mostly from mathematical biology. It is discussed with particlar reference to the problem of causal inference in complex genetic systems, systems for which often only statistical characterizations exist.