We saw that a geodesic on a surface is the shortest line that can be drawn on the surface from one point to another; for example, on the earth the geodesics are great circles. When we come to space-time, the mathematics is the same, but the verbal explanations have to be rather different. In the general theory of relativity, it is only neighboring events that have a definite interval, independently of the route by which we travel from one to the other. The interval between distant events depends upon the route pursued, and has to be calculated by dividing the route into a number of little bits and adding up the intervals for the various little bits. If the interval is space-like, a body cannot travel from one event to the other; therefore when we are considering the way bodies move, we are confined to time-like intervals. The interval between neighboring events, when it is time-like, will appear as the time between them for an observer who travels from the one event to the other. And so the whole interval between two events will be judged by a person who travels from one to the other to be what his clocks show to be the time that he has taken on the journey. For some routes this time will be longer, for others shorter; the more slowly the man travels, the longer he will think he has been on the journey. This must not be taken as a platitude. I am not saying that if you travel from London to Edinburgh you will take longer if you travel more slowly. I am saying something much more odd. I am saying that if you leave London at 10 A.M. and arrive in Edinburgh at 6.30 P.M. Greenwich time, the more slowly you travel the longer you will take—if the time is judged by your watch. This is a very different statement. From the point of view of a person on the earth, your journey takes eight and a half hours. But if you had been a ray of light traveling round the solar system, starting from London at 10 A.M., reflected from Jupiter to Saturn, and so on, until at last you were reflected back to Edinburgh and arrived there at 6.30 P.M., you would judge that the journey had taken you exactly no time. And if you had gone by any circuitous route, which enabled you to arrive in time by traveling fast, the longer your route the less time you would judge that you had taken; the diminution of time would be continual as your speed approached that of light. Now I say that when a body travels, if it is left to itself, it chooses the route which makes the time between two stages of the journey as long as possible; if it had traveled from one event to another by any other route, the time, as measured by its own clocks, would have been shorter. This is a way of saying that bodies left to themselves do their journeys as slowly as they can; it is a sort of law of cosmic laziness. Its mathematical expression is that they travel in geodesics, in which the total interval between any two events on the journey is _greater_ than by any alternative route.