Predictions from the Law. I suppose that it is at first rather staggering to find a law supposed to control the movements of stars and planets turned into a law finicking with the behaviour of measuring rods. But there is no prediction made by the law of gravitation in which the behaviour of measuring appliances does not play an essential part. A typical prediction from the law is that on a certain date 384,400,000 metre rods laid end to end would stretch from the earth to the moon. We may use more circumlocutory language, but that is what is meant. The fact that in testing the prediction we shall trust to indirect evidence, not carrying out the whole operation literally, is not relevant; the prophecy is made in good faith and not with the intention of taking advantage of our remissness in checking it. We have condemned the law of gravitation as a put-up job. You will want to know how after such a discreditable exposure it can still claim to predict eclipses and other events which come off. A famous philosopher has said— “The stars are not pulled this way and that by mechanical forces; theirs is a free motion. They go on their way, as the ancients said, like the blessed gods.”[24] This sounds particularly foolish even for a philosopher; but I believe that there is a sense in which it is true. [Pg 148] We have already had three versions of what the earth is trying to do when it describes its elliptic orbit around the sun. (1) It is trying to go in a straight line but it is roughly pulled away by a tug emanating from the sun. (2) It is taking the longest possible route through the curved space-time around the sun. (3) It is accommodating its track so as to avoid causing any illegal kind of curvature in the empty space around it. We now add a fourth version. (4) The earth goes anyhow it likes. It is not a long step from the third version to the fourth now that we have seen that the mathematical picture of empty space containing “illegal” curvature is a sheer impossibility in a world surveyed from within. For if illegal curvature is a sheer impossibility the earth will not have to take any special precautions to avoid causing it, and can do anything it likes. And yet the non-occurrence of this impossible curvature is the law (of gravitation) by which we calculate the track of the earth! The key to the paradox is that we ourselves, our conventions, the kind of thing that attracts our interest, are much more concerned than we realise in any account we give of how the objects of the physical world are behaving. And so an object which, viewed through our frame of conventions, may seem to be behaving in a very special and remarkable way may, viewed according to another set of conventions, be doing nothing to excite particular comment. This will be clearer if we consider a practical illustration, and at the same time defend version (4). [Pg 149]