  We show that the cosmological large number coincidence can be interpreted as
giving the filling factor in a Landau problem. The analogy with the Landau
problem leads naturally to the noncommutativity of the gravitational and matter
degrees of freedom. We present a toy model that supports this view. We discuss
some of the physical consequences this noncommutativity implies, like a
different insight into the semiclassical approximation of quantum gravity and a
different tackling of the cosmological constant problem.
