It is obvious that, if there is a four-dimensional space, matter in three dimensions only is a mere abstraction; all material objects must then have a slight four-dimensional thickness. In this case the above statement will undergo modification. The material cube which is used as the model of the boundary of a tesseract will have a slight thickness in the fourth dimension, and when the cube is presented to us in another aspect, it would not be a mere surface. But it is most convenient to regard the cubes we use as having no extension at all in the fourth dimension. This consideration serves to bring out a point alluded to before, that, if there is a fourth dimension, our conception of a solid is the conception of a mere abstraction, and our talking about real three-dimensional objects would seem to a four-dimensional being as incorrect as a two-dimensional being’s telling about real squares, real triangles, etc., would seem to us. The consideration of the two views of the brown cube shows that any section of a cube can be looked at by a presentation of the cube in a different position in four-dimensional space. The brown faces in _b__{1}, _b__{2}, _b__{3}, are the very same brown sections that would be obtained by cutting the brown cube, _wh__{0}, across at the right distances along the blue line, as shown in fig. 108. But as these sections are placed in the brown cube, _wh__{0}, they come behind one another in the blue direction. Now, in the sections _wh__{1}, _wh__{2}, _wh__{3}, we are looking at these sections from the white direction—the blue direction does not exist in these figures. So we see them in a direction at right angles to that in which they occur behind one another in _wh__{0}. There are intermediate views, which would come in the rotation of a tesseract. These brown squares can be looked at from directions intermediate between the white and blue axes. It must be remembered that the fourth dimension is perpendicular equally to all three space axes. Hence we must take the combinations of the blue axis, with each two of our three axes, white, red, yellow, in turn.