  Stabilization, by deformation, of the Poincar\'{e}-Heisenberg algebra
requires both the introduction of a fundamental lentgh and the noncommutativity
of translations which is associated to the gravitational field. The
noncommutative geometry structure that follows from the deformed algebra is
studied both for the non-commutative tangent space and the full space with
gravity. The contact points of this approach with the work of David Finkelstein
are emphasized.
