This latitude in interpretation is a characteristic of mathematical physics. What we know is certain very abstract logical relations, which we express in mathematical formulæ; we know also that, at certain points, we arrive at results which are capable of being tested experimentally. Take, for example, the eclipse observations by which Einstein’s theory as to the bending of light was established. The actual observation consisted in the careful measurement of certain distances on certain photographic plates. The formulæ which were to be verified were concerned with the course of light in passing near the sun. Although the part of these formulæ which gives the observed result must always be interpreted in the same way, the other part of them may be capable of a great variety of interpretations. The formulæ giving the motions of the planets are almost exactly the same in Einstein’s theory as in Newton’s, but the meaning of the formulæ is quite different. It may be said generally that, in the mathematical treatment of nature, we can be far more certain that our formulæ are approximately correct than we can be as to the correctness of this or that interpretation of them. And so in the case with which this chapter is concerned: the question as to the nature of an electron or a proton is by no means answered when we know all that mathematical physics has to say as to the laws of its motion and the laws of its interaction with the environment. A definite and conclusive answer to our question is not possible just because a variety of answers are compatible with the truth of mathematical physics. Nevertheless some answers are preferable to others, because some have a greater probability in their favor. We have been seeking, in this chapter, to define matter so that there _must_ be such a thing if the formulæ of physics are true. If we had made our definition such as to secure that a particle of matter should be what one thinks of as substantial, a hard, definite lump, we should not have been _sure_ that any such thing exists. That is why our definition, though it may seem complicated, is preferable from the point of view of logical economy and scientific caution. CHAPTER XV: PHILOSOPHICAL CONSEQUENCES