Hinton - The Fourth Dimension.pdf

114
THE FOURTH DIMENSION
Now let us examine carefully one particular case of
arbitrary interchange of the points, a, b, c; as one such
case, carefully considered, makes the whole clear.
Consider the points named in the figure 1c, 2a, 3c;
1c, 2c, 3a; 1a, 2c, 3c, and
1c2a3c 1a2c3c
1c2c3a
Fig. 61.
examine the effect on them
when a change of order takes
place. Let us suppose, for
instance, that a changes into b,
and let us call the two sets of
points we get, the one before
and the one after, their change
conjugates.
Before the change 1c 2a 3c 1c 2c 3a 1a 2c 3c
After the change 1c 2b 3c 1c 2c 3b 1b 2c 3c} Conjugates
The points surrounded by rings represent the
conjugate points.
It is evident that as consciousness, represented first by
the first set of points and afterwards by the second set of
points, would have nothing in common in its two phases.
It would not be capable of giving an account of itself.
There would be no identity.
If, however, we can find any set of points in the
cubical cluster, which, when any arbitrary change takes
place in the points on the axes, or in the axes themselves,
repeats itself, is reproduced, then a consciousness represented
by those points would have a permanence. It
would have a principle of identity. Despite the no law,
no order, of the ultimate constituents, it would have
an order, it would form a system, the conditions of a
personal identity would be fulfilled.
The question comes to this, then. Can we find a
system of points which is self-conjugate, which is such
that when any point on the axes becomes another other, or