Abstract: In this talk, we will discuss measurable dynamical systems and what it means to be able to “speed up” one system to “look like” another.  In a 1985 paper of Arnoux, Ornstein, and Weiss, they consider this situation for ergodic Z-actions and show that under certain conditions, one system could be sped up to be isomorphic to another.  We review this result and consider the case for Z^d -actions, resulting in a generalized theorem that is joint work with Dave McClendon.  We also discuss further related results and situations.