Writing has often been put forth as one indicator of civilization. This correspondence dovetails with the even broader cross-species expectation that the degrees of social complexity and levels of computational communication should closely correlate. Although in a general sense across human cooperative arrangements, a basic relationship between these variables undoubtedly exists, more detailed and fine-grained analyses indicate important axes of variability. Here, our focus is on prehispanic Mesoamerica and the means of computation and communication employed over more than three millennia (ca. 1500 BCE–1520 CE). We take a multiscalar and diachronic analytical frame, in which we look at 30 central places, six macroregions, and Mesoamerica as whole. By unraveling elements of “social complexity”, and decoupling computation from communication, we illustrate that institutional differences in governance had a marked effect on the specific modes and technologies through which prehispanic Mesoamerican peoples communicated across time and space. Demographic and spatial scale, though relevant, do not alone determine time/space diversity in media of computational communication. This article is part of the theme issue “Evolution of Collective Computational Abilities of (Pre)Historic Societies”.