Hinton - The Fourth Dimension.pdf

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REMARKS ON THE FIGURES 191
The cube with the yellow, red, blue axes is shown in
Yellow
3
3
2
1
Red
x
Blue Null
Fig. 113.
fig. 113. If the red line is
moved equally in the yellow and
in the blue directions by four
equal motions of 1⁄4 inch each,
it takes the positions 11, 22, 33,
and ends as a red line.
Now the whole of this red,
yellow, blue, or brown cube appears
as a series of faces on the
successive sections of the tesseract
starting from the ochre
cube and letting the blue axis
run in the fourth dimension. Hence the plane traced out
by the red line appears as a series of lines in the
successive sections, in our ordinary way of representing
the tesseract; these lines are in different places in each
successive section.
r
2
1
Yellow x
Null White
1
0
1 2 3
2
b0 b1 b2 b3 b4
Fig. 114.
Thus drawing our initial cube and the successive
sections, calling them b0, b1, b2, b3, b4, fig. 115, we have
the red line subject to this movement appearing in the
positions indicated.
We will now investigate what positions in the tesseract
another line in the pink face assumes when it is moved in
a similar manner.
Take a sections of the original cube containing a vertical
line 4, in the pink plane, fig. 115. We have, in the
section, the yellow direction, but not the blue.
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4
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