  We argue that Poisson statistics in logarithmic time provides an idealized
description of non-equilibrium configurational rearrangements in aging glassy
systems. The description puts stringent requirements on the geometry of the
metastable attractors visited at age $t_w$. Analytical implications for the
residence time distributions as a function of $t_w$ and the correlation
functions are derived. These are verified by extensive numerical studies of
short range Ising spin glasses.
