Looking at the light brown region we see that it increases in four ways. Hence, the tesseracts of which it is composed increase in number in each of four dimensions, and the shape they form does not remain thin in any of the four dimensions. Consequently this region becomes the solid content of the block of tesseracts, itself; it is the real four-dimensional solid. All the other regions are then boundaries of this light brown region. If we suppose the process of increasing the number of tesseracts and diminishing their size carried on indefinitely, then the light brown coloured tesseracts become the whole interior mass, the three-coloured tesseracts become three-dimensional boundaries, thin in one dimension, and form the ochre, the brown, the light purple, the light green. The two-coloured tesseracts become two-dimensional boundaries, thin in two dimensions, _e.g._, the pink, the green, the purple, the orange, the light blue, the light yellow. The one-coloured tesseracts become bounding lines, thin in three dimensions, and the null points become bounding corners, thin in four dimensions. From these thin real boundaries we can pass in thought to the abstractions—points, lines, faces, solids—bounding the four-dimensional solid, which in this case is light brown coloured, and under this supposition the light brown coloured region is the only real one, is the only one which is not an abstraction. It should be observed that, in taking a square as the representation of a cube on a plane, we only represent one face, or the section between two faces. The squares, as drawn by a plane being, are not the cubes themselves, but represent the faces or the sections of a cube. Thus in the plane being’s diagram a cube of twenty-seven cubes “null” represents a cube, but is really, in the normal position, the orange square of a null cube, and may be called null, orange square. A plane being would save himself confusion if he named his representative squares, not by using the names of the cubes simply, but by adding to the names of the cubes a word to show what part of a cube his representative square was. Thus a cube null standing against his plane touches it by null orange face, passing through his plane it has in the plane a square as trace, which is null white section, if we use the phrase white section to mean a section drawn perpendicular to the white line. In the same way the cubes which we take as representative of the tesseract are not the tesseract itself, but definite faces or sections of it. In the preceding figures we should say then, not null, but “null tesseract ochre cube,” because the cube we actually have is the one determined by the three axes, white, red, yellow. There is another way in which we can regard the colour nomenclature of the boundaries of a tesseract. Consider a null point to move tracing out a white line one inch in length, and terminating in a null point, see fig. 103 or in the coloured plate.