Hardy conjectured that the error term arising from approximating the number of lattice points lying in a radius-R disc by its area is O(R^{1/2+o(1)}). One source of support for this conjecture is a folklore heuristic that uses i.i.d. random variables to model the lattice points lying near the boundary and square-root cancellation of sums of these random variables. In this talk I will examine this heuristic and discuss how lattice points near the circle interact with one another. This is joint work with Igor Wigman.