<p>It is a central task for theories of representation to give a principled account of the distinction between representational and non-representational systems. In this paper, I begin by arguing that this plausibly involves giving an account that accurately reflects differences in the explanatory practice of the sciences. I then show that one of the most sophisticated and empirically well-informed attempts to give such an account faces a fundamental problem, the problem of adjacent cases, and I suggest that we have reason to suspect that this problem generalizes to other traditional accounts. Finally, I sketch a radically gradualist alternative that solves the problem in a simple and elegant way and provides a plausible view of the transition from mere sensitivity to genuine representation.</p>