You have a brain. I have a brain. But are they similar? Geometrically, I mean. One approach to this question is to ask how hard it would be to transform your brain into mine. Reframed again, we could look at mappings from your brain to mine, ask which one is easiest, and declare the difficulty of this mapping to be the difference between our brains. But there are two immediate questions… “What is a map between brains?” and “What makes a brain map easy?” These have reasonable answers when we assume that brains are Riemannian manifolds. But the thing is, we don’t understand the shapes of brains—or of much else, for that matter—by staring at metrics. We more often understand shapes by collecting point cloud samplings and staring at the clouds. Come, and I will ramble to you about methods for constructing easy (read “harmonic”) maps between manifolds known only by clouds.