Fig. 99.
A plane being’s representation of a block of eight cubes by two sets of four squares.
Hence, as the plane being must represent the solid regions, he would come to by going right, as four squares lying in some position in his plane, arbitrarily chosen, side by side with his original four squares, so we must represent those eight four-dimensional regions, which we should come to by going in the fourth dimension from each of our eight cubes, by eight cubes placed in some arbitrary position relative to our first eight cubes.
Fig. 100.
Our representation of a block of sixteen tesseracts by two blocks of eight cubes.[3]
[3] The eight cubes used here in 2 can be found in the second of the model blocks. They can be taken out and used.
Hence, of the two sets of eight cubes, each one will serve us as a representation of one of the sixteen tesseracts which form one single block in four-dimensional space. Each cube, as we have it, is a tray, as it were, against which the real four-dimensional figure rests—just as each of the squares which the plane being has is a tray, so to speak, against which the cube it represents could rest.
If we suppose the cubes to be one inch each way, then the original eight cubes will give eight tesseracts of the same colours, or the cubes, extending each one inch in the fourth dimension.
But after these there come, going on in the fourth dimension, eight other bodies, eight other tesseracts. These must be there, if we suppose the four-dimensional body we make up to have two divisions, one inch each in each of four directions.
The colour we choose to designate the transference to this second region in the fourth dimension is blue. Thus, starting from the null cube and going in the fourth dimension, we first go through one inch of the null tesseract, then we come to a blue cube, which is the beginning of a blue tesseract. This blue tesseract stretches one inch farther on in the fourth dimension.