The space of all possible paths through a finite-dimensional configuration space is infinite-dimensional. Nevertheless, paths taken by "real" robotic systems often cluster on a finite-dimensional manifold that is embedded in this infinite-dimensional space and that is governed by a principle of optimality. We take advantage of this property to enable a human user to efficiently specify a desired path for a robot moving through a planar workspace with polygonal obstacles using a sequence of noisy binary inputs, as might be derived from a brain-machine interface. First, we show that the space of all such paths having length that is bounded and locally minimal is homeomorphic to the unit disk. Second, we note that any path mapped to the interior of this disk is a subset of some other path mapped to its boundary. Third, we provide an optimal communication protocol by which the user can, with vanishing error probability, select a point on this boundary. Finally, we validate our approach in preliminary experiments with human subjects.