Hinton - The Fourth Dimension.pdf

APPENDIX I: THE MODELS 235
would be the appearance of the cube when it had almost
completely gone through. This set of nine will be the
same as the first set of nine.
Now we have in the plane three sets of nine slabs
each, which represent three sections of the twenty-seven
block.
They are put alongside one another. We see that it
does not matter in what order the three sets of nine are put.
As the cube passes through the plane they represent appearances
which follow the one after the other. If they
were what they represented, they could not exist in the
same plane together.
This is a rather important point, namely, to notice that
they should not co-exist on the plane, and that the order
in which they are placed is indifferent. When we
represent a four-dimensional body our solid cubes are to
us in the same position that the slabs are to the plane
being. You should also notice that each of these slabs
represents only the very thinnest slice of a cube. The
set of nine slabs first set up represents the side surface of
the block. It is, as it were, a kind of tray—a beginning
from which the solid cube goes off. The slabs as we use
them have thickness, but this thickness is a necessity of
construction. They are to be thought of as merely of the
thickness of a line.
If now the block of cubes passed through the plane
at the rate of an inch a minute the appearance to a plane
being would be represented by:—
1. The first set of nine slabs lasting for one minute.
2. The second set of nine slabs lasting for one minute.
3. The third set of nine slabs lasting for one minute.
Now the appearances which the cubes would present
to the plane being in other positions can be shown by
means of these slabs. The use of such slabs would be
the means by which a plane being could acquire a