The fourth dimension

114 THE FOURTH DIMENSION

Now let us examine carefully one particular case of arbitrary interchange of the points, a, b,¢; as one such ease, carefully considered, makes the whole clear.

Consider the points named in the figure le, 2a, 3c; le, 2c, 3a; la, 2c, 3c, and examine the effect on them when a change of order takes place. Let us suppose, for instance, that a changes into }, and let us call the two sets of

te2asc la2c3e

Ie2c3a points we get, the one before Fig. 61, and the one after, their change conjugates.

Before the change le 2a3e le 2c 3a 1a 2c 3c

After the change I1c2b3c 1c2c3b 16 2¢ 30 } 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, the no order, of the ultimate constituents, it would have an order, it would form a system, the condition 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 posit on the axes becomes any other, or