Course median spaces, defined by Bowditch, generalize several notions of nonpositive curvature in geometric group theory. Notably, hyperbolic groups and CAT(0) cube complexes are coarse median. We prove a metric obstruction to being coarse median and give some applications to higher rank lattices and tubular groups. In particular, we show that a tubular group is quasi-isometric to a CAT(0) cube complex only if it is cocompactly cubulated. Zoom link https://wwu.zoom.us/j/65491213372 with password the name of the mathematician who solved Hilbert's 3rd problem (4 letters, lowercase).