  The gravitational N-body problem, for $N>2$, is the oldest unsolved problem
in mathematical physics. Some of the most ideal examples that can be found in
nature are globular star clusters, with $N \sim 10^6$. In this overview, I
discuss six types of fundamental sources of unpredictability, each of which
poses a different challenge to attempts to determine the long-term behavior of
these systems, governed by a peculiar type of thermodynamics.
