Abstract: Realistic computer graphics will change the way people think and communicate. Achieving deeper success as a ubiquitous medium will require a more resonant understanding of visual modelling that must embrace mathematical, philosophical, cultural, perceptual and social aspects. With an interleaved understanding, people will be able to create visual ontologies that better align to their expressive needs. In turn, this will naturally lead to ubiquitous supporting technologies. First we need good visual models. A model induces an ontology of things that inevitably omits aspects of the phenomenon, whether desired or not. Thus modelling a model's incompleteness is crucial, for it allows us to account for artifacts, errors, and ontological surprises such as the "uncanny valley." Over the years, my choice of tools to model models has been mathematics. In this paper, I will speak to how little progress we have made and how much broader our investigation must be.