From now on, the real extension of the world has a fourfold order, and the geometry of relativity is necessarily four-dimensional. What we call the space of our Galilean frame at an instant, is but a cross-section of this four-dimensional space-time world; and what we call the time of our frame lies along a perpendicular to this section. As we pass from one Galilean frame to another, we change our space and we change our time. Our new instantaneous space, though still a three-dimensional cross-section of the four-dimensional space-time world, is tilted with respect to our former cross-section; and the same tilting ensues for the perpendicular direction called time. In fact, the situation presents a striking analogy with the various directions of the verticals to the earth’s surface. They, also, manifest different directions because the various two-dimensional portions of the earth’s surface are variously tilted in three-dimensional space. The great change in our understanding of the spatio-temporal background, the great difference between space-time and the separate space and time of classical science, resides, therefore, in this tilting process which accompanies a change of relative motion. In order to make these points clearer, let us understand that when we speak of the instantaneous spaces of two observers in relative motion as being tilted one with respect to the other, hence as lying outside of each other (except for their common two-dimensional cross-section), we do not mean that the space of one is some incomprehensible entity in the opinion of the other. The tilted instantaneous spaces will enter into our perception, but not as spaces alone: they will appear as a succession of two-dimensional surfaces moving with uniform speed.