Hinton - The Fourth Dimension.pdf

REMARKS ON THE FIGURES 197
space, and the triangle they determine is common to
the tesseract and the cutting
space. Hence this
boundary is a triangle having
a light yellow line,
Null y.
Yellow
Gr.
x
Null
Blue
l. y.
White
P.
Null b.
Fig. 122.
l. bl.
Null wh.
which is the same as the
light yellow line of the first
figure, a light blue line and
a green line.
We have now traced the
cutting space between every
set of three that can be
made out of the four points
in which it cuts the tesseract, and have got four faces
which all join on to each other by lines.
The triangles are shown in fig. 123 as they join on to
n.b. pur. n.r. pur. n.b.
br. l.pur.
och.
n.y. l.y
l. gr.
n.wh.
or.
gr. gr.
p.
n.b.
Fig. 123.
l. bl. l. bl.
the triangle in the ochre cube. But
they join on each to the other in an
exactly similar manner; their edges
are all identical two and two. They
form a closed figure, a tetrahedron,
enclosing a light brown portion which
is the portion of the cutting space
which lies inside the tesseract.
We cannot expect to see this light brown portion, any
more than a plane being could expect to see the inside
of a cube if an angle of it were pushed through his
plane. All he can do is to come upon the boundaries
of it in a different way to that in which he would if it
passed straight through his plane.
Thus in this solid section; the whole interior lies perfectly
open in the fourth dimension. Go round it as
we may we are simply looking at the boundaries of the
tesseract which penetrates through our solid sheet. If
the tesseract were not to pass across so far, the triangle