Hinton - The Fourth Dimension.pdf

186
THE FOURTH DIMENSION
in y1 when we go on in the yellow direction. Thus, the
first section, y1, will begin from an ochre face with light
yellow and orange lines. The colour of the axis which
lies in space towards us in blue, hence the regions of this
section-cube are determined in nomenclature, they will be
found in full in fig. 105.
There remains only one figure to be drawn, and that is
the one in which the red axis is replaced by the blue.
Here, as before, if the red axis goes out into the positive
sense of the fourth dimension, the blue line must come
into our space in the negative sense of the direction which
the red line has left. Accordingly, the first cube will
come in beneath the position of our ochre cube, the one
we have been in the habit of starting with.
x
r0 r1 r2 r3 r4
Fig. 110.
To show these figures we must suppose the ochre cube
to be on a moveable stand. When the red line swings out
into the unknown dimension, and the blue line comes in
downwards, a cube appears below the place occupied by
the ochre cube. The dotted cube shows where the ochre
cube was. That cube has gone and a different cube runs
downwards from its base. This cube has white, yellow,
and blue axes. Its top is a light yellow square, and hence
its interior is light yellow + blue or light green. Its front
face is formed by the white line moving along the blue
axis, and is therefore light blue, the left-hand side is
formed by the yellow line moving along the blue axis,
and therefore green.