This paper considers the implications of big data practices for theories about the surveilled subject who, analysed from afar, is still gazed upon, although not directly watched as with previous surveillance systems. We propose this surveilled subject be viewed through a lens of proximity rather than interactivity, to highlight the normative issues arising within digitally mediated relationships. We interpret the ontological proximity between subjects, data flows and big data surveillance through Merleau-Ponty's ideas combined with Levinas' approach to ethical proximity and Coeckelberg's work on proximity in the digital age. This leads us to highlight how competing normativities, and normative dilemmas in these proximal spaces, manipulate the surveilled subject's embodied practices to lead the embodied individual towards experiencing them in a local sense. We explore when and how the subject notices these big data practices and then interprets them through translating their experiences into courses of action, inaction or acquiescence.