Hinton - The Fourth Dimension.pdf

112
THE FOURTH DIMENSION
would correspond to a sudden and arbitrary change of a
into b and b into a, so that, to use Kant’s words, it would
be possible to call one thing by one name at one time
and at another time by another name.
In an experience of this kind we have a kind of chaos,
in which no order exists; it is a manifold not subject to
the concepts of reason.
Now is there any process by which order can be introduced
into such a manifold—is there any function of
consciousness in virtue of which an ordered experience
could arise?
In the precise condition in which the posits are, as
described above, it does not seem to be possible. But
if we imagine a duality to exist in the manifold, a
function of consciousness can be easily discovered
which will produce order out of no order.
Let us imagine each posit, then, as having a dual aspect.
Let a be 1a in which the dual aspect is represented by the
combination of symbols. And similarly let b be 2b,
c be 3c, in which 2 and b represent that dual aspects
of b, 3 and c those of c.
Since a can arbitrarily change into b, or into c, and
so on, the particular combinations written above cannot
be kept. We have to assume the equally possible occurrence
of form such as 2a, 2b, and so on; and in order
to get a representation of all these combinations out of
which any set is alternatively possible, we must take
every aspect with every aspect. We must, that is, have
every letter with every number.
Let us now apply the method of space representation.
Notes.—At the beginning of the next chapter the same
structures as those which follow are exhibited in
more detail and a reference to them will remove
any obscurity which may be found in the immediately
following passages. They are there carried