Hinton - The Fourth Dimension.pdf

CHAPTER III
THE SIGNIFICANCE OF A FOUR-
DIMENSIONAL EXISTENCE
HAVING now obtained the conception of a four-dimensional
space, and having formed the analogy which, without
any further geometric difficulties, enables us to enquire
into its properties, I will refer the reader, whose interest
is principally in the mechanical aspect, to Chapters VI.
and VII. In the present chapter I will deal with the
general significance of the enquiry, and in the next
with the historical origin of the idea.
First, with regard to the question of whether there
is any evidence that we are really in four-dimensional
space, I will go back to the analogy of the plane world.
A being in a plane world could not have any experience
of three-dimensional shapes, but he could have
an experience of three-dimensional movements.
We have seen that his matter must be supposed to
have an extension, though a very small one, in the third
dimension. And thus, in the small particles of his
matter, three-dimensional movements may well be conceived
to take place. Of these movements he would only
perceive the resultants. Since all movements of an
observable size in the plane world are two-dimensional,
he would only perceive the resultants in two dimensions
of the small three-dimensional movements. Thus, there
would be phenomena which he could not explain by his
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