[155] The whole science of geometry may be said to owe its being to the exorbitant interest which the human mind takes in _lines_. We cut space up in every direction in order to manufacture them. [156] Kant was, I believe, the first to call attention to this last order of facts. After pointing out that two opposite spherical triangles, two gloves of a pair, two spirals wound in contrary directions, have identical inward determinations, that is, have their parts defined with relation _to each other_ by the same law, and so must be _conceived_ as identical, he showed that the impossibility of their mutual superposition obliges us to assign to each figure of a symmetrical pair a peculiar difference of its own which can only consist in an _outward_ determination or relation of its parts, no longer to each other, but to the whole of an objectively outlying space with its points of the compass given absolutely. This in_con_ceivable difference is perceived only "through the relation to right and left, which is a matter of immediate intuition." In these last words (_welches unmittelbar auf Anschauung geht_--Prolegomena, § 12) Kant expresses all that we have meant by speaking of up and down, right and left, as _sensations_. He is wrong, however, in invoking relation to extrinsic total space as essential to the existence of these contrasts in figures. Relation to our own body is enough. [157] In the eyes of many it will have seemed strange to call a relation a mere line, and a line a mere sensation. We may easily learn a great deal _about_ any relation, say that between two points: we may divide the line which joins these, and distinguish it, and classify it, and find out _its_ relations by drawing or representing new lines, and so on. But all this further industry has naught to do with our _acquaintance_ with the relation itself, in its first intention. So cognized, the relation _is_ the line and nothing more. It would indeed be fair to call it something less; and in fact it is easy to understand how most of us come to feel as if the line were a much grosser thing than the relation. The line is broad or narrow, blue or red, made by this object or by that alternately, in the course of our experience; it is therefore independent of any one of these accidents; and so, from viewing it as no one of _such_ sensible qualities, we may end by thinking of it as something which cannot be defined except as the negation of all sensible quality whatever, and which needs to be put _into_ the sensations by a mysterious act of 'relating thought.'