 Now, in trivial examples of spacetimes with missing points such as the one offered before, flat spacetime with a closed set in the shape of Ingrid Bergman excised from it, one does not need any technical machinery to add the missing points back in. One can do it by hand. Many spacetimes with incomplete paths, however, do not allow missing points to be attached in any obvious way by hand, as that example does. For this program to be viable, which is to say, in order to give substance to the idea that there really are points that in some sense ought to have been included in the spacetime in the first place, we require a physically natural completion procedure that can be applied to incomplete paths in arbitrary spacetimes. There are several proposals for such a construction (Hawking 1966c, Geroch 1968a, Schmidt  1971).[3] 