It is often stated that ancient architectural monuments such as the Pantheon were constructed as models of the Cosmos. An integral part of that interpretation is the notion that the architectural form of the dome represents the heavens. Ancient cultures created two kinds of models for the universe: analogue models represent their objects through physical resemblance; digital models represent their objects as functions of time. While the idea of roundness appears to be one of the primordial distinctions made with regards to the heavens, round buildings present particular problems that the architect has to solve before he is able to construct a round building as a cosmic model. This paper traces ideas of roundness and the notion of heavenly events as a function of time in ancient culture. It examines the nature of circular and spherical forms as structure. Finally, this information is applied to an analysis of the Pantheon in order to reveal its triumph over of structural problems as well as its function as both an analogue and a digital model.