Hinton - The Fourth Dimension.pdf

100
THE FOURTH DIMENSION
premiss, mood E, the next to the mood I, and the last
to mood O.
The cube we see is as it were merely a tray against
which the four-dimensional figure rests. Its section at
any stage is a cube. But a transition in this direction
being transverse to the whole of our space is represented
by no space motion. We can exhibit successive stages of
the result of transference of the cube in that direction,
but cannot exhibit the product of a transference, however
small, in that direction.
minor
(1)
O
I
E
A A E I O
major
O
I
E
A
(2)
A E I O
O
I
E
A
Fig. 56.
(3)
A E I O
O
I
E
A
(4)
A E I O
To return to the original method of representing our
variables, consider fig. 56. These four cubes represent
four sections of the figure derived from the first of them
by moving it in the fourth dimension. The first por-
tion of the motion, which begins with 1, traces out a
more than solid body, which is all in the first figure.
The beginning of this body is shown in 1. The next
portion of the motion traces out a more than solid body,
all of which is in the second figure; the beginning of
this body is shown in 2; 3 and 4 follow on in
like manner. Here, then, in one four-dimensional figure we
have all the combinations of the four variables, major
premiss, minor premiss, figure, conclusion, represented,
each variable going through its four varieties. The disconnected
cubes drawn are our representation in space by
means of disconnected sections of this higher body.