  We compare two approaches to Ricci curvature on non-smooth spaces, in the
case of the discrete hypercube $\{0,1\}^N$. While the coarse Ricci curvature of
the first author readily yields a positive value for curvature, the
displacement convexity property of Lott, Sturm and the second author could not
be fully implemented. Yet along the way we get new results of a combinatorial
and probabilistic nature, including a curved Brunn--Minkowski inequality on the
discrete hypercube.
