In the growing field of tabletop computing research, there has been an understandable focus on interactive aspects of tabletop use, in terms of technology, design, and behavioural analysis. In this paper, I highlight the importance of considering also non-interactive aspects of tabletop computing and the mutually dependent relationship between interactive and non-interactive. We illustrate aspects of this relationship using findings from a deployment of an interactive tabletop in a public setting. The findings highlight how consequences of interaction can impact on non-interactive behaviours and intentions and how non-interactive actions can constrain interactive behaviours on the tabletop. In doing this we aim to raise more awareness of the relationship between interactivity and non-interactivity within tabletop computing research.