Hinton - The Fourth Dimension.pdf

THE EVIDENCES FOR A FOURTH DIMENSION 79
no such thing as a bending over in four dimensions of
any object of a size which we can observe. The region
of the extremely minute is the one, then, which we
shall have to investigate. We must look for some
phenomenon which, occasioning movements of the kind
we know, still is itself inexplicable as any form of motion
which we know.
Now in the theories of the actions of the moisture
particles of bodies on one another, and in the motions of
the ether, mathematicians have tacitly assumed that the
mechanical principles are the same as those which prevail
in the case of bodies which can be observed, it has been
assumed without proof that the conception of motion being
three-dimensional, holds beyond the region from observations
in which it was formed.
Hence it is not from any phenomena explained by
mathematics that we can derive a proof of four dimensions.
Every phenomenon that has been explained is explained
as three-dimensional. And, moreover, since in the region
of the very minute we do not find rigid bodies acting
on each other at a distance, but elastic substances and
continuous fluids such as ether, we shall have a double
task.
We must form the conceptions of the possible movements
of elastic and liquid four-dimensional matter, before
we can begin to observe. Let us, therefore, take the fourdimensional
rotation about a plane, and enquire what it
becomes in the case of extensible fluid substances. If
four-dimensional movements exist, this kind of rotation
must exist, and the finer portions of matter must exhibit
it.
Consider for a moment a rod of flexible and extensible
material. It can turn about an axis, even if not straight;
a ring of india rubber can turn inside out.
What would this be in the case of four dimensions?