  Several recent developments point to the fact that rational maps from
n-punctured spheres to the null cone of D dimensional momentum space provide a
natural language for describing the scattering of massless particles in D
dimensions. In this note we identify and study equations relating the kinematic
invariants and the puncture locations, which we call the scattering equations.
We provide an inductive algorithm in the number of particles for their
solutions and prove a remarkable property which we call KLT Orthogonality. In a
nutshell, KLT orthogonality means that "Parke-Taylor" vectors constructed from
the solutions to the scattering equations are mutually orthogonal with respect
to the Kawai-Lewellen-Tye (KLT) bilinear form. We end with comments on possible
connections to gauge theory and gravity amplitudes in any dimension and to the
high-energy limit of string theory amplitudes.
