  A gravity-driven inflation is shown to arise from a simple higher dimensional
universe. In vacuum, the shear of $n>1$ contracting dimensions is able to
inflate the remaining three spatial dimensions. Said another way, the expansion
of the 3-volume is accelerated by the contraction of the $n$-volume. Upon
dimensional reduction, the theory is equivalent to a four dimensional cosmology
with a dynamical Planck mass. A connection can therefore be made to recent
examples of inflation powered by a dilaton kinetic energy. Unfortunately, the
graceful exit problem encountered in dilaton cosmologies will haunt this
cosmology as well.
