THE inevitable rational consequences which follow with mathematical certainty when once the existence of space-time as a model of the universe is conceded, are often puzzling to beginners, who feel that these consequences are too paradoxical to be acceptable. Of course, we must distinguish between a paradox of feeling, and a paradox of logic or an inconsistency. Any inconsistencies would be fatal to a rational construction and would denote either errors of reasoning or the presence of some fundamental contradiction in our basic premises. If, therefore, when analysing any given example in Einstein’s theory, we proceed to follow our deductions by adopting successively two different alternatives in our point of view, both of which would be consistent with the premises of the theory, and if we finally compare the results thus obtained and find them to be contradictory, hence inconsistent, the theory of relativity could never survive. However, it is scarcely probable that any such inconsistencies will ever be discovered by the layman, inasmuch as the theory of relativity is the work of mathematicians, for whom, more than for any one else, accurate and consistent reasoning is the indispensable condition of research. On the other hand, though no inconsistencies or paradoxes of logic can exist in Einstein’s theory, this does not mean that the conclusions of relativity may not appear strange and lead to paradoxes of feeling. But once more it is important to differentiate between strangeness or paradoxes of feeling, and inconsistency or paradoxes of reason. [Pg 226] The important point which must be settled, therefore, is whether our habitual notions of time, space and simultaneity are rational necessities, or whether they are merely feasible notions among a number of equally feasible ones. The question we have to decide is analogous to that which Kant proposed to solve when he stated that Euclidean geometry and three-dimensional space were the a priori forms of pure perception. Kant was wrong, as the discovery of non-Euclidean geometries proved without doubt. To-day Einstein has done for space, time and motion what Riemann and Lobatchewski did for the geometry of space alone. He has furnished us with a model just as rational as the model of classical science; and this model has the additional advantage of being in accord with empirical observation to a high order of precision, instead of being a mere approximate construction as was the classical structure. Indirectly, then, Einstein has proved that our innate classical conceptions of space, time, simultaneity and motion were by no means rational necessities.