The Ergodic Theory Carnival
The Birkhoff ergodic theorem, proved by George David Birkhoff in 1931, allows us to investigate the long-term behavior of certain dynamical systems. In this article, we explain what it means for a function to be ergodic, and we present Birkhoff's theorem. We construct models of activities typically found at carnivals and compare and contrast them by analyzing their ergodic theory properties. We use these carnival models to show how Birkhoff's ergodic theorem can be used to help a photographer set up her equipment to take pictures of all children on a carousel and to aid a magician in finding a lost jewel in a sticky mess of taffy.