Hinton - The Fourth Dimension.pdf

CHAPTER XII
THE SIMPLEST FOUR-DIMENSIONAL SOLID
A PLANE being, in learning to apprehend solid existence,
must first of all realise that there is a sense of direction
altogether wanting to him. That which we call right
and left does not exist in his perception. He must
assume a movement in a direction, and a distinction of
positive and negative in that direction, which has no
reality corresponding to it in the movements he can
make. This direction, this new dimension, he can only
make sensible to himself by bringing in time, and supposing
that changes, which take place in time, are due to
objects of a definite configuration in three dimensions
passing transverse to his plane, and the different sections
of it being apprehended as changes of one and the same
plane figure.
He must also acquire a distinct notion about his
plane world, he must no longer believe that it is the all
of space, but that space extends on both side of it. In
order, then, to prevent his moving off in this unknown
direction, he must assume a sheet, an extended solid sheet,
in two dimensions, against which, in contact with which,
all his movements take place.
When we come to think of a four-dimensional solid,
what are the corresponding assumptions which we must
make?
We must suppose a sense which we have not, a sense
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