  A simple model for viscous liquid dynamics is introduced. Consider the
surface of the union of hyper-spheres centered at random positions inside a
hypercube with periodic boundary conditions. It is argued and demonstrated by
numerical simulations that at high dimensions geodetic flows on this surface is
a good model for viscous liquid dynamics. It is shown that this simple model
exhibits viscous dynamics for densities above the percolation threshold in $8$,
$12$ and $16$ dimensions. Thus the slowing down of the dynamics, measured by
the mean-squared displacement, extends to several orders of magnitude similarly
to what is observed in other models for viscous dynamics. Furthermore, the
shape of the mean-squared displacement is to a very good approximation the same
as for the standard model in simulations of viscous liquids: the Kob-Andersen
binary Lennard Jones mixture.
