Classical mechanics, like geometry, can yield surprising results in a non‐Euclidean space. One such result, recently discussed in the journalScienceby MIT planetary scientist Jack Wisdom, concerns the motion of a composite object as it undergoes a cyclic series of changes in body shape. Consider, for example, a person making the precise, regular motions of an Olympic swimmer. In empty Euclidean (flat) space, the swimmer's center of mass wouldn't move; water in the pool, of course, provides the external reaction force that propels real swimmers. The curved‐space surprise is that a swimmer executing an appropriate cycle of internal changes can move, even without external forces.