Feynman amplitudes constitute a beautiful little island of algebraic geometry surrounded by a sea of physics. Ancient AG's marooned on the island cannot help but feel skeptical about the seaworthness of the transport physics offers from the island to the shores of reality. With the advent of string theory, physicists understand another approach, realizing Feynman amplitudes as suitable limits when the string tension goes to zero. This talk will give an algebra-geometric interpretation of the idea. The Feynman amplitude becomes an integral over the space of nilpotent orbits at a point on the boundary of the moduli space of marked curves. The integrand is a limit of heights of cycles supported on the markings. This is joint work with José Burgos Gil, Omid Amini, and Javier Fresan.