We assume that there is an “interval” between two events, in the sense explained in Chapter VII, but we no longer assume that we can unambiguously compare the length of an interval in one region with the length of an interval in another. It is assumed by Weyl, who introduced this limitation, that we can compare a number of small intervals which all start from the same point; also that, in a very small journey, our measuring rod will not alter its length much, so that there will only be a small error if we compare lengths in neighboring places by the usual methods. Weyl found that, by diminishing our assumptions as to interval in this way, it was possible to bring electromagnetism and gravitation into one system. The mathematics of Weyl’s theory is complicated, and I shall not attempt to explain it. For the present, I am concerned with a different consequence of his theory. If lengths in different regions cannot be compared directly, there is an element of convention in the indirect comparisons which we actually make. This element will be at first unrecognized, but will be such as to simplify to the utmost the expression of the laws of nature. In particular, conditions of symmetry may be entirely created by conventions as to measurement, and there is no reason to suppose that they represent any property of the real world. The law of gravitation itself, according to Eddington, may be regarded as expressing conventions of measurement. “The conventions of measurement,” he says, “introduce an isotropy[13] and homogeneity into measured space which need not originally have any counterpart in the relation-structure which is being surveyed. This isotropy and homogeneity is exactly expressed by Einstein’s law of gravitation.”[14] [13] “Isotropy” means being similar in all directions—_e.g._, that a foot rule is as long when it points north as when it points east. [14] _Mathematical Theory of Relativity_, p. 238. The limitations of knowledge introduced by the selectiveness of our perceptual apparatus may be illustrated by the indestructibility of matter. This has been gradually discovered by experiment, and seemed a well-founded empirical law of nature. Now it turns out that, from our original space-time continuum, we can construct a mathematical expression which will have properties causing it to appear indestructible. The statement that matter is indestructible then ceases to be a proposition of physics, and becomes instead a proposition of linguistics and psychology. As a proposition of linguistics: “Matter” is the name of the mathematical expression in question. As a proposition of psychology: Our senses are such that we notice what is roughly the mathematical expression in question, and we are led nearer and nearer to it as we refine upon our crude perceptions by scientific observation. This is much less than physicists used to think they knew about matter.