Einstein’s and De Sitter’s hypotheses do not exhaust the possibilities of a finite world: they are merely the two simplest forms of such a world. There are arguments against each, and it hardly seems probable that either is quite true. But it does seem probable that something more or less analogous is true. If the universe is finite, it is theoretically conceivable that there should be a complete inventory of it. We may be coming to the end of what physics can do in the way of stretching the imagination and systematizing the world. The period since Galileo has been essentially the period of physics, as the age of the Greeks was the period of geometry. It may be that physics will lose its attractions through success: if the fundamental laws of physics come to be fully known, adventurous and inquiring intellects will turn to other fields. This may alter profoundly the whole texture of human life, since our present absorption in machinery and industrialism is the reflection in the practical world of the theorist’s interest in physical laws. But such speculations are even more rash than those of De Sitter, and I do not wish to lay any stress upon them. CHAPTER XII: CONVENTIONS AND NATURAL LAWS One of the most difficult matters in all controversy is to distinguish disputes about words from disputes about facts: it ought not to be difficult, but in practice it is. This is quite as true in physics as in other subjects. In the seventeenth century there was a terrific debate as to what “force” is; to us now, it was obviously a debate as to how the word “force” should be defined, but at the time it was thought to be much more. One of the purposes of the method of tensors, which is employed in the mathematics of relativity, is to eliminate what is purely verbal (in an extended sense) in physical laws. It is of course obvious that what depends on the choice of co-ordinates is “verbal” in the sense concerned. A man punting walks along the boat, but keeps a constant position with reference to the river bed so long as he does not pick up his pole. The Lilliputians might debate endlessly whether he is walking or standing still: the debate would be as to words, not as to facts. If we choose co-ordinates fixed relatively to the boat, he is walking; if we choose co-ordinates fixed relatively to the river bed, he is standing still. We want to express physical laws in such a way that it shall be obvious when we are expressing the same law by reference to two different systems of co-ordinates, so that we shall not be misled into supposing we have different laws when we only have one law in different words. This is accomplished by the method of tensors. Some laws which seem plausible in one language cannot be translated into another; these are impossible as laws of nature. The laws that can be translated into _any_ co-ordinate language have certain characteristics: this is a substantial help in looking for such laws of nature as the theory of