landijk wrote:So really the point is that the number you compute using Chalnoth's setup might not be the same thing you get if you actually tried to measure the resistance. Now given that we're talking about an infinite grid, perhaps it's silly to worry about this kind of thing. However, a finite grid will behave identically to an infinite grid within the time it takes for current to propagate to the boundary. So if you had an astronomical grid of resistors, maybe you would see some unexpectedly high resistance for a few seconds after you hooked up your multimeter.
Actually, the mere fact that you can take a relatively small finite grid of resistors as a very good approximate solution to the infinite grid indicates that you don't have to wait until the current propagates to infinity before your measurement is accurate: the further the current propagates, the less effect it has.