Hinton - The Fourth Dimension.pdf

98
THE FOURTH DIMENSION
our space. It can only be represented by a device analogous
to that by which the plane being represents a cube.
He represents the cube shown above, by taking four
square sections and placing them arbitrarily at convenient
distances the one from the other.
So we must represent this higher solid by four cubes:
each cube represents only the beginning of the corresponding
higher volume.
It is sufficient for us, then, if we draw four cubes, the
first representing that region in which the figure is of the
first kind, the second that region in which the figure is
of the second kind, and so on. These cubes are the
beginnings merely of the respective regions—they are
the trays, as it were, against which the real solids must
be conceived as resting, from which they start. The first
one, as it is the beginning of the region of the first figure,
is characterised by the order of the terms in the premisses
being that of the first figure. The second similarly has
the terms of the premisses in the order of the second
figure, and so on.
These cubes are shown below.
For the sake of showing the properties of the method
of representation, not for the logical problem, I will make
a digression. I will represent in space the moods of the
minor and of the conclusion and the different figures,
keeping the major always in mood A. Here we have
three variables in different stages, the minor, the conclusion,
and the figure. Let the square of the left-hand
side of the original cube be imagined to be standing by
itself, without the solid part of the cube, represented by
(2) fig. 55. The A, E, I , O, which run away represent the
moods of the minor, the A, E, I, O, which run up represent
the moods of the conclusion. The whole square, since it
is the beginning of the region in the major premiss, mood
A, is to be considered as in major premiss, mood A.