  We show that at the level of linear response the low frequency limit of a
strongly coupled field theory at finite temperature is determined by the
horizon geometry of its gravity dual, i.e. by the "membrane paradigm" fluid of
classical black hole mechanics. Thus generic boundary theory transport
coefficients can be expressed in terms of geometric quantities evaluated at the
horizon. When applied to the stress tensor this gives a simple, general proof
of the universality of the shear viscosity in terms of the universality of
gravitational couplings, and when applied to a conserved current it gives a new
general formula for the conductivity. Away from the low frequency limit the
behavior of the boundary theory fluid is no longer fully captured by the
horizon fluid even within the derivative expansion; instead we find a
nontrivial evolution from the horizon to the boundary. We derive flow equations
governing this evolution and apply them to the simple examples of charge and
momentum diffusion.
