I describe work in progress on using the computer mathematics system, Mathematica, to construct a special "object language" to be used by undergraduate mathematics learners. In this language, graphical objects have a peculiar kind of in-between existence as "visual" data structures that can be manipulated through programs. I attempt to elucidate the nature of this existence, and its possible usefulness for mathematical thinking, and learning, using the example of visualising a four-dimensional "hypercube".