Hinton - The Fourth Dimension.pdf

3
APPLICATION TO KANT’S THEORY OF EXPERIENCE 113
on to a greater multiplicity of dimensions, and the
significance of the process here briefly explained
becomes more apparent.
Take three mutually rectangular axes in space 1, 2, 3
c
b a
a
b
c
a b c
1 2
Fig. 59.
(fig. 59), and on each mark three points,
the common meeting point being the
first on each axis. Then by means of
these three points on each axis, we
define 27 positions, 27 points in a
cubical cluster, shown in fig. 60, the
same method of co-ordination being
used as has been described before.
Each of these positions can be named by means of the
axes and the points combined.
Thus, for instance, the one marked by an asterisk can
3
1 2
Fig. 60.
be called 1c, 2b, 3c, because it is
opposite to c on 1, to b on 2, to
c on 3.
Let us now treat of the states of
consciousness corresponding to these
positions. Each point represents a
composite of posits, and the manifold
of consciousness corresponding
to them is of a certain complexity.
Suppose now the constituents, the points on the axes,
to interchange arbitrarily, any one to become any other,
and also the axes 1, 2 and 3, to interchange amongst
themselves, any one to become any other, and to be subject
to no system or law, that is to say, that order does
not exist, and that the points which run abc on each axis
may run bac, and so on.
Then any one of the states of consciousness represented
by the points in the cluster can become any other. We
have a representation of a random consciousness of a
certain degree of complexity.