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. Transcriber’s Notes --Retained publication information from the printed edition: this eBook is public-domain in the country of publication. --Silently corrected a few palpable typos; left intentionally nonstandard usage unchanged. --In the text versions only, text in italics is delimited by _underscores_. --In the text versions only, superscript text is preceded by ^caret. --In the text versions only, subscript text is preceded by _underscore. End of Project Gutenberg's Scientific Romances (First Series), by C. H. Hinton