Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
familiarity with out cube. Turn the catalogue cube (or
imagine the coloured figure turned) so that the red line
runs up, the yellow line out to the right, and the white
line towards you. Then turn the block of cubes to
occupy a similar position.
The block has now a different wall in contact with
the plane. Its appearance to a plane being will not be
the same as before. He has, however, enough slabs to
represent this new set of appearances. But he must
remodel his former arrangement of them.
He must take a null, a red, and a null slab from the
first of his sets of slabs, then a white, a pink, and a white
from the second, and then a null, a red, and a null from
the third set of slabs.
He takes the first column from the first set, the first
column from the second set, and the first column from
the third set.
To represent the half-way-through appearance, which
is as if a very thin slice were cut out half way through the
block, he must take the second column of each of his
sets of slabs, and to represent the final appearance, the
third column of each set.
Now turn the catalogue cube back to the normal
position, and also the block of cubes.
There is another turning—a turning about the yellow
line, in which the white axis comes below the support.
You cannot break through the surface of the table, so
you must imagine the old support to be raised. Then
the top of the block of cubes in its new position is at the
level at which the base of it was before.
Now representing the appearance on the plane, we must
draw a horizontal line to represent the old base. The
line should be drawn three inches high on the cardboard.
Below this the representative slabs can be arranged.
It is easy to see what they are. The old arrangements