 The assumption “that bodies exist independently of place” is valid if and only if the properties of bodies remain invariant when moved. That is, if a body changes place, that is a movement, and if the body continues to have the same properties in any different place, then its properties are invariant under transformation. Riemann goes on to say that, without this assumption, the units of comparison that are the basis for astronomical and other measurements — rays of light as the shortest path between two points, rigid bodies like meter sticks as the basis of distance measurement — no longer have the invariant properties on which one can base valid measurements. 