Hinton - The Fourth Dimension.pdf

196
or.
THE FOURTH DIMENSION
Now let the ochre cube turn out and the brown cube
gr.
pur.
B
Null r.
Red
x
Yellow
Null b. Blue Null
Fig. 120.
come in. The dotted lines
show the position the ochre
cube has left (fig. 120).
Here we see three out
of the four points through
which the cutting space
passes, null r., null y., and
null b. The plane they
determine lies in the cutting space, and this plane
cuts out of the brown cube a triangle with orange,
purple and green sides, and null points. The orange line
of this figure is the same as the orange line in
the last figure.
Now let the light purple cube swing into our space,
towards us, fig. 121.
The cutting space which passes through the four points,
r.
Null r.
pur.
l. bl.
P.
x White Null wh.
Null
Blue
Null b.
Fig. 121.
null r., y., wh., b., passes through
the null r., wh., b., and therefore
the plane these determine
lies in the cutting space.
This triangle lies before us.
It has a light purple interior
and pink, light blue, and
purple edges with null points.
This, since it is all of the
plane that is common to it, and this bounding of the
tesseract, gives us one of the bounding faces of our
sectional figure. The pink line in it is the same as the
pink line we found in the first figure—that of the ochre
cube.
Finally, let the tesseract swing around the light yellow
plane, so that the light green cube comes into our space.
It will point downwards.
The three points, n. y., n. wh., n. b., are in the cutting