 Worlds differ in the distributions of these traits, and a natural, albeit simple, suggestion is to measure the likeness between two worlds by the number of agreements on traits. This is tantamount to taking distance to be measured by the size of the symmetric difference of generating states – the so-called city-block measure. As is well known, this will generate a genuine metric, in particular satisfying the triangular inequality. If \(w_1\) is the actual world this immediately induces a system of nested spheres, but one in which the spheres come with numbers attached: