Suppose that X is a projective variety and that L is a line bundle on X. It is sometimes useful to fix an ample line bundle A and study the space of sections H^0(X,mL+A) as a function of the integer m. One might ask how the dimension of the space of sections grows with m: is the growth rate roughly polynomial, as would be the case without the extra twist by A? I will explain an example in which the growth rate is very far from being polynomial, based on the dynamics of birational automorphisms of a certain CY3.