That is why we do not trouble to give physical significance to our co-ordinates from the start. Formerly, the co-ordinates used in physics were supposed to be carefully measured distances; now we realize that this care at the start is thrown away. It is at a later stage that care is required. Our co-ordinates now are hardly more than a systematic way of cataloguing events. But mathematics provides, in the method of tensors, such an immensely powerful technique that we can use co-ordinates assigned in this apparently careless way just as effectively as if we had applied the whole apparatus of minutely accurate measurement in arriving at them. The advantage of being haphazard at the start is that we avoid making surreptitious physical assumptions, which we can hardly help making, if we suppose that our co-ordinates have initially some particular physical significance. We assume that, if two events are close together (but not necessarily otherwise), there is an interval between them which can be calculated from the differences between their co-ordinates by some such formula as we considered in the preceding chapter. That is to say, we take the squares and products of the differences of co-ordinates, we multiply them by suitable amounts (which in general will vary from place to place), and we add the results together. The sum obtained is the square of the interval. We do not assume in advance that we know the amounts by which the squares and products must be multiplied; this is going to be discovered by observing physical phenomena. We know, however, certain things. We know that the old Newtonian physics is very nearly accurate when our co-ordinates have been chosen in a certain way. We know that the special theory of relativity is still more nearly accurate for suitable co-ordinates. From such facts we can infer certain things about our new co-ordinates, which, in a logical deduction, appear as postulates of the new theory. As such postulates we take: 1. That every body travels in a geodesic in space-time, except in so far as electromagnetic forces act upon it. 2. That a light ray travels so that the interval between two parts of it is zero. 3. That at a great distance from gravitating matter, we can transform our co-ordinates by mathematical manipulation so that the interval shall be what it is in the special theory of relativity; and that this is approximately true wherever gravitation is not very powerful. Each of these postulates requires some explanation.