How can one determine the shape of one´s surroundings by listening to ambient signal sources? Traditional remote-sensing ideas place strong requirements on the topology and geometry of the sensorium in order to exploit linearity, often by using integral transform methods. I will explain some recent work that avoids making such assumptions, and instead recovers topological structure first. At the center of the approach is a variant of the Whitney embedding theorem, suitably extended to handle certain kinds of discontinuities inherent in the received signal profile. I will also exhibit some experimental apparatus and associated results that demonstrate the feasibility of this approach in practice.