Hinton - The Fourth Dimension.pdf

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Orange
THE FOURTH DIMENSION
Here (fig. 125) we have the null r., y., b. points, and of
Green
Purple
Null r.
Red
x
Yellow
Null b. Blue Null
Fig. 125.
the sectional space all we
see is the plane through these
three points in it.
In this figure we can draw
the parallels to the red and
yellow axes and see that, if
they started at a point half
way along the blue axis, they
would each be cut at a point so as to be half of their
previous length.
Swinging the tesseract into our space about the pink
face of the ochre cube we likewise find that the parallel
to the white axis is cut at half its length by the sectional
space.
Hence in a section made when the tesseract had passed
half across our space the parallels to the red, white, yellow
Brown
Light green
Light purple
bl.
Green
Blue L. blue bl.
Section b2 interior Light brown
Fig. 126.
axes, which are now in our
space, are cut by the section
space, each of them half way
along, and for this stage of
the traversing motion we
should have fig. 126. The
section made of this cube by
the plane in which the sectional
space cuts it, is an
equilateral triangle with purple, l. blue, green points,
and l. purple, brown, l. green lines.
Thus the original ochre triangle, with null points and
pink, orange, light yellow lines, would be succeeded by a
triangle coloured in manner just described.
This triangle would initially be only a very little smaller
than the original triangle, it would gradually diminish,
until it ended in a point, a null point. Each of its
edges would be of the same length. Thus the successive