 When deciding whether a spacetime is singular, therefore, we want a definition that is not restricted to geodesics. We need, however, some way of overcoming the fact that non-singular spacetimes include inextendible paths of finite proper length that are not prima facie pathological (e.g., flat spacetimes with inextendible paths of unbounded total acceleration). The most widely accepted solution to this problem makes use of a slightly different, technically complex notion of length, known as ‘generalized affine length’ (Schmidt  1971).[1]  Unlike proper time, this generalized affine length depends on some arbitrary choices. (Roughly speaking, the length will vary depending on the coordinates one chooses to compute it; see  note 1.)  If the length is infinite for one such choice, however, it will be infinite for all other choices. Thus the question of whether a path has a finite or infinite generalized affine length is a well-defined question, and that is all we will need. 