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.
Fig. 62.
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 when any axis becomes any other, such a set is transformed into itself, its identity is not submerged, but rises superior to the chaos of its constituents?
Such a set can be found. Consider the set represented in [fig. 62], and written down in the first of the two lines—
| Self- conjugate | { | 1a 2b 3c | 1b 2a 3c | 1c 2a 3b | 1c 2b 3a | 1b 2c 3a | 1a 2c 3b |
| 1c 2b 3a | 1b 2c 3a | 1a 2c 3b | 1a 2b 3c | 1b 2a 3c | 1c 2a 3b |
If now a change into c and c into a, we get the set in the second line, which has the same members as are in the upper line. Looking at the diagram we see that it would correspond simply to the turning of the figures as a whole.[2] Any arbitrary change of the points on the axes, or of the axes themselves, reproduces the same set.
[2] These figures are described more fully, and extended, in the next chapter.
Thus, a function, by which a random, an unordered, consciousness could give an ordered and systematic one, can be represented. It is noteworthy that it is a system of selection. If out of all the alternative forms that only is attended to which is self-conjugate, an ordered consciousness is formed. A selection gives a feature of permanence.