To get an insight into the discussion by Einstein which is about to follow, we must first dispose of a certain arbitrariness of language, lying in the customary indiscriminate use of the terms, infinite, immeasurable, and unbounded. Suppose we have a globe about one foot in diameter, the surface of which is inhabited by extremely small, ultramicroscopic creatures that can move about freely and can think. The surface of the sphere constitutes the world of the micro-men, and he has a very good reason for considering it infinite, for, however far and in whatever direction he may move, he never encounters a boundary. But we, who live in our space, look on to this spherical surface, and recognize that his judgment is erroneous. To us his spherical world seems decidedly finite and quite measurable, although it has no determinable beginning and no end, and thus must appear unbounded to the micro-man. In fact, we ourselves may regard it as boundless, if we can succeed in forming an abstraction that leaves out of account its limitations in our own space. Now, it might occur to a particularly intelligent micro-being to undertake a voyage for the purpose of making measurements. He carefully marks his point of departure, walks Straight ahead in a certain direction, describing a circle on his sphere--a circle which he will necessarily regard as a straight line. He continues ever onwards in the firm conviction that he is getting farther and farther away from his starting-point. Suddenly, he discovers that he has reached it again. He discovers, by the mark he made, that he has not been describing a straight line, but a line that merges into itself. The micro-professor would be compelled to declare: Our world, the only one known to me, is not infinite, although in a certain sense boundless. Moreover, it is not immeasurable, since it can be measured in at least one direction by the number of steps I have walked. From this we may infer that our former geometrical view was either wrong or incomplete, and that, in order to understand our world properly, we must build up a new geometry. We may assume that the majority of the remaining micro-inhabitants would at first protest strongly against this decision. The idea that a line, which appears to them to be pointing always in the same direction, is curved, seems to them inconceivable and absurd. They would only gradually overcome their scruples of thought by getting an insight into a newly developed geometry that makes clear to them for the first time the conception of a sphere.