Such speculations would not have bothered anybody twenty years ago, for then the physicist did not have to handle any cases of such high speeds. But when radium was discovered it was found that this metal was continuously throwing off particles of negative electricity with approximately the speed of light. Now if these electrons are not matter they are at any rate the material of which matter is made. They can be detected and counted and tracked and deflected and speeded and weighed. They are very real things, perhaps the ultimate reality of all things, yet their extreme velocity carries them out of Newton’s world and into Einstein’s. INTRODUCING THE FOURTH DIMENSION Now Einstein’s world, as I said before, differs from the world in which we are accustomed to live in many particulars. It has four dimensions instead of three. One of these dimensions may be time. Time, too, must be relative, not absolute. This is even harder to imagine than the relativity of space. As some schoolboy said: “If there were no matter in the universe the law of gravitation would fall to the ground.” Quite so. WHAT IS MEANT BY DIMENSIONS No dimensions: A mathematical point. Has position but no size. Represented by a dot. Like this . One dimension: Has length but no breadth. Made by moving a point along straight in any direction. Represented by a line. Like this ---- Two dimensions: A plane surface like this page. Has length and breadth but no thickness. Made by moving a line in a direction perpendicular to its length (that is, into the second dimension). Represented by two straight lines of indefinite length perpendicular to each other. The lines are called axes and are labeled _x_ and _y_. The point where they meet, the origin, is marked O. Like this [Illustration] Three dimensions: A solid like a cube. Has length, breadth and thickness. Made by moving a plane in a direction perpendicular to the other two (that is, into the third dimension). Cannot be pictured on paper, but is indicated by three axes, _x_, _y_, and _z_, of which _x_ and _y_ are on the plane of the page and _z_ is supposed to be stuck up at right-angles to the other two. Stick a pin into the paper at the point O and you will have the third or _z_ axis. Like this [Illustration] Four dimensions: Has length, breadth, thickness and extension into a fourth dimension, say time. Made by moving a cube in a direction perpendicular to the other three (that is, into the fourth dimension). Cannot be pictured on paper, but may be indicated by four axes, _x_, _y_, _z_ and _t_ (or _u_), each at right-angles to the other three. Like this [Illustration] More dimensions: