Thus it is evident that there are three expressions which may be considered in reference to a knowledge of a block of cubes as almost identical: “Casting out the self”—“Seeing as a higher child”—and thirdly, “Acquiring an intuitive knowledge of four-dimensional space.”
Thus, taking the simplest and most obvious facts—the arrangement of a few cubes—we found that there was a known part and an unknown part; the known part corresponding to our act of putting, the unknown part the cube which, of some size or another, must be taken as given in the external world. Then there was obviously a self-element present in the Up and Down felt as in the cubes. This being removed, Right and Left had also to go. So, to get the knowledge of this simple set of objects clear of self-elements, two universe transforming thoughts have to be used; and when these thoughts are thus incorporated the cubes become different.
It will be obvious to the reader that in these pages I have merely touched the surface of the subject. But the deeper matters which are contained in the knowledge of a block of cubes are difficult to express, and are so mixed up with the practical work, as far as I conceive them at present, that it is best to consider in some detail the applications to the world about us of those truths of which we have already got a clear apprehension from the block of cubes.
Instead, then, of going on, let us conclude the present paper by going back, and taking a simple instance of the general truth that progress in the knowledge of a block of cubes is casting out the self.
Let the reader turn to Diagram I. and make out the shape which the following numbers denote—namely, 1, 4, 5. If the following numbers be said, 18, 27, 26, it will be found that they denote the same shape, but in a different position. Now if the block of cubes be well known, these two sets of names, 1, 4, 5, and 18, 27, 26, ought to convey instantly to the mind the same idea. However quickly they are realized, it ought to be evident that they are the same shape.
And a good deal of the practical work in learning a block of cubes consists in gaining this faculty of immediate apprehension. But when it is gained it is seen to consist much more of getting rid of an imperfection than in being any real advance. For if the two shapes are identical we need not ask ourselves how it is we see them as the same, but we have to ask ourselves what is the reason why we do not recognize their identity; and the answer evidently is that, if we do not recognize their identity, it is due to the particular relationship of each shape to ourselves. One is down on our left hand, another is up on our right, and they are turned relatively to us different ways. Now these differences, which are merely relative to us, we impress upon the shapes, and really feel the shapes to be different. The practice consists in getting rid of the influence of these self-elements, so that two shapes, however complicated, being alike, when their names are said, we feel them to be alike without calculation or reflection. Thus the power of seeing likeness and analogy in this domain is merely another name for the power of casting out the self-elements from our mental presentation of any objects with which we come into contact.
Footnotes
[1]A B C D framework, X and Y two lines interlinked.
[2]See [Appendix].
[3]For details, see [Appendix III.]