It might appear that solving initial value problems in the past'' is of little interest at an institution dedicated toinventing the future.'' However, this impression is deceiving. It is actually of great interest to know how the present influences the future or whether it impacts the future at all. In this context, backward uniqueness (inverting the future) becomes of paramount significance. As is taught in every beginning course on complex analysis, the modulus of an analytic function on a bounded domain has its maximum on the boundary. The Phragmen-Lindeloef theorem extends this result to unbounded regions, under the assumption of a suitable growth condition at infinity. In this talk, it will be shown how the Phragmen-Lindeloef theorem can be used to prove backward uniqueness for linear partial differential equations. Examples include problems which in a sense are perturbations of cases where backward uniqueness does not hold. In particular, we shall show how backward uniqueness can be obtained for the linearized equations of compressible fluid flow and for the damped wave equation with absorbing boundary conditions.