p-adic string theories provide lattice discretization to the ordinary string worldsheet

A class of models called p-adic strings is useful in understanding the tachyonic instability of string theory. These are found to be empirically related to the ordinary strings in the p -> 1 limit. We propose that these models provide discretization for the string worldsheet and argue that the limit is naturally thought of as a continuum limit in the sense of the renormalization group.