CHAPTER III
THE WORLD OF FOUR DIMENSIONS
The distinction between horizontal and vertical is not an illusion; and the man who thinks it can be disregarded is likely to come to an untimely end. Yet we cannot arrive at a comprehensive view of nature unless we combine horizontal and vertical dimensions into a three-dimensional space. By doing this we obtain a better idea of what the distinction of horizontal and vertical really is in those cases where it is relevant, e.g. the phenomena of motion of a projectile. We recognise also that vertical is not a universally differentiated direction in space, as the flat-earth philosophers might have imagined.
Similarly by combining the time-ordering and space-ordering of the events of nature into a single order of four dimensions, we shall not only obtain greater simplicity for the phenomena in which the separation of time and space is irrelevant, but we shall understand better the nature of the differentiation when it is relevant.
A point in this space-time, that is to say a given instant at a given place, is called an "event." An event in its customary meaning would be the physical happening which occurs at and identifies a particular place and time. However, we shall use the word in both senses, because it is scarcely possible to think of a point in space-time without imagining some identifying occurrence.
In the ordinary geometry of two or three dimensions, the distance between two points is something which can be measured, usually with a rigid scale; it is supposed to be the same for all observers, and there is no need to specify horizontal and vertical directions or a particular system of coordinates. In four-dimensional space-time there is likewise a certain extension or
