to
. From a purely mathematical angle, such an assumption is by no means absurd; and it is this generalisation of the possible behaviour of our conceptual measuring rods which was studied by Weyl. It must be borne in mind, however, that for the present we are not discussing the problem of real space; we are not arguing about the actual behaviour of our rigid measuring rods as defined by practical congruence. We are merely speculating, as mathematicians, on a logical extension of geometry.
Let us therefore review our premises. We assume that two unit rods which coincide at a point
cease to coincide when brought together at another point
, after having followed different paths of transfer from