THUS far we have discussed more especially that abstraction from the space of experience which we called mathematical space; we have seen it to be entirely amorphous. In the present chapter we shall have to consider the space of experience and determine to what extent it differs from conceptual mathematical space. An important difference as regards the problem of motion has already been noted, for we remember that in physical space, motion often manifests itself as absolute. For the present, however, we shall confine our attention to the problem of congruence. Mathematical space is amorphous; it possesses no intrinsic metrics, and our choice of standards of measurement is largely arbitrary. As a result, absolute shape, size and straightness are meaningless concepts. But in physical space, it is a matter of common knowledge that men have no difficulty in agreeing at least approximately on the sameness of two shapes or of two sizes. They agree that a stone remains undeformed when displaced, hence declare the stone to be rigid, whereas they recognise that an object behaving like a worm is of the squirming variety. So here there appears to exist an important difference between mathematical space, where no particular definition of congruence is suggested, and physical space, where a definite type seems to impose itself naturally and is accepted unanimously. After all, there is nothing very mysterious about this unanimous agreement; for had men refused to be guided in their definition of congruence by their sense of sight, they would have been led into all manner of difficulties. They would have had to assume that a stone carried in their hands, though appearing unchanged visually, was yet squirming, and, vice versa, that bodies which appeared to squirm were yet rigid. The difficulties in reaching some common understanding of measurement would thus have been hopelessly great. In fact, the definition of congruence, which we have mentioned, imposes itself so irresistibly that it is only since the discovery of non-Euclidean geometry that its absolute validity has been refuted.