The torus and the disk

This paper is a survey of a coherent program of mathematics spanning 28 years. It begins with questions concerning classification and structure in ergodic theory and abstract dynamical systems and describes the author's involvement with toral automorphisms, topological entropy, iteration of maps on the interval, symbolic dynamics, and ultimate engineering applications. It serves as a case study of how unplanned-for practical applications can result from the pursuit of mathematics for its own sake.