  Bizon and Rostworowski have recently suggested that anti-de Sitter spacetime
might be nonlinearly unstable to transfering energy to smaller and smaller
scales and eventually forming a small black hole. We consider pure gravity with
a negative cosmological constant and find strong support for this idea. While
one can start with a single linearized mode and add higher order corrections to
construct a nonlinear geon, this is not possible starting with a linear
combination of two or more modes. One is forced to add higher frequency modes
with growing amplitude. The implications of this turbulent instability for the
dual field theory are discussed.
