Page:Mind (Old Series) Volume 12.djvu/27

14 PKOF. W. JAMES : denied to it all sensational content whatever. But just as, in the field of quantity, the relation between two numbers is another number, so in the field of space the relations are facts of the same' order with the facts they relate. If these latter be patches in the circle of vision, the former are certain other patches between them. When, we speak of the relation of direction of two points towards each other, we mean simply the sensation of the line that joins the two points together. The line is the relation ; feel it and you feel the relation, see it and you see the relation ; nor can you in any conceivable way think the latter except by imagining the former (however vaguely), or describe or indicate the one except by pointing to the other. And the moment you have imagined or pointed out the line, the relation stands before you, or your interlo- cutor, in all its completeness, with nothing further to be done. Just so the relation of direction between two lines is identical with the peculiar sensation of shape of the space enclosed between them. This is commonly called an angular relation. If these relations are sensations, no less so are the rela- tions of position. The relation of position between the top and bottom points of a vertical line is that line, and nothing else. The relations of position between a point and a horizontal line below it are potentially numerous. There is one more important than the rest, called its dis- tance. This is the sensation, ideal or actual, of a perpen- dicular drawn from the point to the line. 1 Two lines, one from each extremity of the horizontal to the point, give us a peculiar sensation of triangularity. This feeling may be said to constitute the locus of all the relations of position of the elements in question. Rightness and leftness, upness and downness, are again pure sensations differing specifically from each other, and generically from everything else. If we take a cube and label one side top, another bottom, a third front, and a fourth hack, there remains no form of words by which we can describe to another person which of the remain- ing sides is right and which left. We can only point and say here is right and there is left, just as we should say this is red and that blue, without being able to give an idea of them in words. Of two points seen beside each other at all, one is always affected by one of these feelings, and the other by the opposite ; the same is true of the extremities of any line. 2 1 The whole science of geometry may be said to owe its being to the exorbitant interest the human mind takes in lines. We cut space up in every direction in order to manufacture them. 2 Kant was, I believe, the first to call attention to this order of facts. Cp. Prolegomena, 12.