We present a new formulation of string and particle amplitudes that "emerges" from a simple one-dimensional model. Using a new way to parametrise Teichmuller space, we will see how to find formulas for amplitudes at all orders, including non-planar contributions. The relationship between strings and particles is manifest in this formulation, and the formulas also allow us to study amplitudes with large numbers of particles. The talk will in part cover results from arXiv:2309.15913, "All Loop Scattering as a Counting Problem."