When causation does not imply correlation:robust violations of the faithfulness axiom

Current methods of detecting causal relationships from data rely on analysing the patterns of correlation among the variables. Given some basic assumptions about how causal relationships constrain these patterns, this allows causal inferences to be made. I demonstrate that one commonly used assumption, called Faithfulness (roughly, where there is causation there must be correlation), is robustly violated for a large class of systems of a type that occurs throughout the life and social sciences: control systems. These systems exhibit correlations indistinguishable from zero between variables that are directly causally connected, and can show very high correlations between variables that have no direct causal connection, only a connection via causal links between uncorrelated variables. Their patterns of correlation are robust, in that they remain unchanged when their parameters are varied. The violation of Faithfulness is fundamental to what a control system does: hold some variable constant despite the disturbing influences on it. No method of causal analysis that requires Faithfulness is applicable to such systems