Hinton - The Fourth Dimension.pdf

THE USE OF FOUR DIMENSIONS IN THOUGHT 89
it is worth our while to bring into the full light of our attention
our habitual assumptions and processes. It often
happens that we find there are two of them which have
a bearing on each other, without this dragging into
the light, we should have allowed to remain without
mutual influence.
There is a fact which it concerns us to take into account
in discussing the theory of the poiograph.
With respect to our knowledge of the world we are
far from that condition which Laplace imagined when he
asserted that an all-knowing mind could determine the
future condition of every object, if he knew the co-ordinates
of its particles in space, and their velocity at any
particular moment.
On the contrary, in the presence of any natural object,
we have a great complexity of conditions before us,
which we cannot reduce to position in space and date
in time.
There is mass, attraction apparently spontaneous, electrical
and magnetic properties which must be superadded
to spatial configuration. To cut the list short we must
say that practically the phenomena of the world present
us problems involving many variables, which we must
take as independent.
From this it follows that in making poiographs we
must be prepared to use space of more than three dimensions.
If the symmetry and completeness of our representation
is to be of use to us we must be prepared to
appreciate and criticise figures of a complexity greater
than those in three dimensions. It is impossible to give
an example of such a poiograph which will not be merely
trivial, without going into details of some kind irrelevant
to our subject. I prefer to introduce the irrelevant details
rather than treat this part of the subject perfunctorily.
To take an instance of a poiograph which does not lead