The classical and extensively-studied Fr & eacute;chet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a "flipped" Fr & eacute;chet measure defined by a sup min - the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of "social distance" between two curves (or general domains), where agents traverse curves while trying to stay as far apart as possible. We first study the flipped Fr & eacute;chet measure between two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms. We then consider this measure on polygons, where it denotes the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon. We investigate several variants of the problem in this setting, for some of which we provide linear-time algorithms. We draw connections between our proposed flipped Fr & eacute;chet measure and existing related work in computational geometry, hoping that our new measure may spawn investigations akin to those performed for the Fr & eacute;chet distance, and into further interesting problems that arise.