  A basic problem in dynamics is to identify systems with positive entropy,
i.e., systems which are "chaotic." While there is a vast collection of results
addressing this issue in topological dynamics, the phenomenon of positive
entropy remains by and large a mystery within the broader noncommutative domain
of C*-algebraic dynamics. To shed some light on the noncommutative situation we
propose a geometric perspective inspired by work of Glasner and Weiss on
topological entropy. This is a written version of the author's talk at the
Winter 2002 Meeting of the Canadian Mathematical Society in Ottawa, Ontario.
