  Suppose $G$ is a simple group. For any nontrivial elements $g$ and $h$, $g$
can be written as a finite product of conjugates of $h$ or the inverse of $h$.
G is called uniformly simple if the length of such an expression is uniformly
bounded. We show that the infinite alternating group is non-uniformly simple
and evaluate how the length of such an expression is unbounded.
