Hinton - The Fourth Dimension.pdf

THE SIMPLEST FOUR-DIMENSIONAL SOLID 163
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. They
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 further on in the fourth dimension.
Thus, beyond each of the eight tesseracts, which are of
the same colour as the cubes which are their bases, lie
eight tesseracts whose colours are derived from the colours
of the first eight by adding blue. Thus—
Null gives blue
Yellow ,, green
Red ,, purple
Orange ,, brown
White ,, light blue
Pink ,, light purple
Light yellow ,, light green
Ochre ,, light brown
The addition to blue of yellow gives green—this is a