 (Two points here. First, recall that a ‘dilatation’ is a scale transformation. Second, in what follows we will refer to the group which consists of the union of translations, rotations and dilatations as the ‘similarity group’.) If these Machian theorists are able to formulate a dynamics on shape space (i.e., a dynamics which identifies the curves in shape space which represent nomologically possible worlds), then that dynamics will, in light of the above reduction, not bring with it a meaningful notion of absolute position, or absolute velocity, or absolute scales. Barbour and collaborators take such a dynamics to realize Mach-heavy: the undetectable spacetime structure associated with such quantities has been expunged. Below, we will see how this can be done in the concrete contexts of Newtonian particle dynamics and general relativity.