Remarks on statistical mechanics of discrete and continuous media with application to the magnetohydrodynamic dynamo

In this paper commemorating the 60th birthday of David Montgomery, issues tantalizing to me that evolved from my collaborations with him are highlighted: sustainment of the magnetohydrodynamic dynamo, relationships between discrete and continuous models of media, and closures for nonlinear theories of discrete and continuous media. In particular, it is speculated that a tractable statistical model of a magnetohydrodynamic dynamo may arise from a proper formulation of a solenoidal expansion basis for the magnetic and velocity fields in the context of an appropriate closure, such as the eddy-damped quasinormal Markovian model.