Blandford & Thorne, Applications of Classical Physics: Taylor & Wheeler, Spacetime Physics: These definitions seem to be based on the notion of a "physical" or "practical" infinitesimal: a quantity too small to be detected. But how can we measure the accuracy of an imaginary detector? Taylor & Wheeler answer this by saying: you decide. In that case, could we not define a (trivial) global Lorentz frame if we specify zero accuracy, and a Lorentz frame of any other size, from infinite down, by an appropriate choice of accuracy? This seems at odds with the connotation of smallness. Blandford & Thorne's clocks and rulers are regarded as in some sense "ideal", yet not ideally accurate. What quality does their idealness consist of if not accuracy? (I take it it's not that they're just a very nice colour and you can check your emails on them.) Is it just that that there's a scale limit on their accuracy, so that, given a finite degree of accuracy of instruments, you can always choose smaller and smaller scales till you find a scale where they detect no curvature--rather than the empty statement that given a degree of curvature, you can always find instruments not accurate enough to detect it! I notice that Blandford and Thorne only specify a spatial accuracy at this stage; is that significant? Besides curvature, could topology limit the size of a Lorentz frame of a given accuracy? The metric tensor field is defined at each point. Its value at each point contains information about curvature. Sometimes the value is derived by an infinitesimal analogue of the Pythagorean formula. If curvature is significant enough that it can't be neglected in such a small region as one point, how can it be neglected in such a large region as a space shuttle? Is it because different degrees of accuracy are being used in these two cases, i.e. this way of talking about the metric tensor field assumes ideal, unlimited accuracy (and if so, how does that mesh with the idea of a differential a linear approximation)?