Ok, so if the causality relation between A,B is not linear, then it will go unnoticed by correlation, i.e., we may have A causing B but Corr(A, B)=0. I am trying to find good examples to illustrate this but not coming up with much. I can think of Hooke's law, where data pairs (x, kx^2) would have zero correlation. Is this an " effective" way of illustrating the point that causation does not imply ( nonzero) correlation? Any other examples?