The fourth dimension

112 THE FOURTH DIMENSION

would correspond to a sudden and arbitrary change of a into 6 and 6 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 @ be la in which the dual aspect is represented by the combination of symbols. And similarly let 6b be 26, ce be 3c, in which 2 and 6 represent the dual aspects of 6, 3 and ¢ those of ec.

Since @ can arbitrarily change into }, or into ¢, 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 those 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 represention.

Note.—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 remoye any obscurity which may be found in the immediately following passages. They are there carried