Hinton - The Fourth Dimension.pdf

REMARKS ON THE FIGURES 183
that is represented in the sections b1, b2, b3; in fig. 107
the red and white axes are in our space, the blue out of
it; in the other case, the red and blue are in our space,
the white out of it. It is evident that the face pink y.,
opposite the pink face in fig. 107, makes a cube shown
in squares in b1, b2, b3 on the opposite side to the light
purple squares. Also the light yellow face at the base
of the cube b0, makes a light green cube, shown as a series
of base squares.
The same light green cube can be found in fig. 108.
The base square in wh0, is a green square, for it is enclosed
by blue and yellow axes. From it goes a cube in the
white direction, this is then a light green cube and the
same as the one just mentioned as existing in the sections
b0, b1, b2, b3, b4.
The case is, however, a little different with the brown
cube. This cube we have altogether in space in the
section wh0, fig. 108, while it exists as a series of squares,
the left-hand ones, in the sections b0, b1, b2, b3, b4. The
brown cube exists as a solid in our space, as shown in
fig. 108. In the mode of representation of the tesseract
exhibited in fig. 107, the same brown cube appears as a
succession of squares. That is, as the tesseract moves
across space, the brown cube would actually be to us a
square—it would be merely the lasting boundary of another
solid. It would have no thickness at all, only extension
in two dimensions, and its duration would show its solidity
in three dimensions.
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