I will discuss two connections between quantitative operator K-theory and scalar curvature, arising from recent work with Zhizhang Xie and Guoliang Yu. The first comes from the observation that, on a manifold with uniformly positive scalar curvature, the “propagation” at which the index of an elliptic operator vanishes is inversely related to the lower bound of scalar curvature; this leads to a refinement of the well-known obstruction of Rosenberg to positive scalar curvature on closed spin manifolds in the form of the higher index. The second is an approach to Gromov’s band width conjecture using quantitative techniques in K-theory.