We present a part of an ongoing effort that attempts to understand why solutions to many stochastic PDEs are intermittent. In particular, we show that there is a strong sense in which large families of SPDEs with intermittent solutions are extremely "excitable." More significantly, we show that this highly nonlinear level of noise excitation is, in a sense dichotomous: "Semidiscrete" equations are nearly always far less excitable than "continuous" equations. The reason for this dichotomy is also identified, and somewhat surprisingly has to do with the structure theory of certain topological groups. This is based on on-going work with Kunwoo Kim.