The fourth dimension

180 THE FOURTH DIMENSION

place. This purple line lasts for a minute—that is, all of a minute, except the moment taken by the crossing our space of the initial and final red line. The purple line having lasted for this period is succeeded by a red line, which lasts for a moment; then this goes and the tesseract has passed across our space. The final red line we call red bl., because it is separated from the initial ted line by a distance along the axis for which we use the colour blue. Thus a line that lasts represents an area duration ; is in this mode of presentation equivalent to a dimension of space. In the same way the white line, during the crossing our space by the tesseract, is succeeded by a light blue line which lasts for the inside of a minute, and as the tesseract leaves our space, having crossed it, the white bl. line appears as the final termination.

Take now the pink face. Moved in the blue direction it traces out a light purple cube. This light purple cube is shown in sections in 0,, b,, 6,, and the farther face of this cube in the blue direction is shown in },a pink face, called pink 6 because it is distant from the pink face we began with in the blue direction. Thus the cube which we colour light purple appears as a lasting square. The square face itself, the pink face, vanishes instantly the tesseract begins to move, but the light purple cube appears as a lasting square. Here also duration is the equivalent of a dimension of space—a lasting square is a cube. It is useful to connect these diagrams with the views given in the coloured plate. »

Take again the orange face, that determined by the red and yellow axes; from it goes a brown cube in the blue direction, for red and yellow and blue are supposed to make brown. This brown cube is shown in three sections in the faces },, b., 6; In b, is the opposite orange face of the brown cube, the face called orange b,

Preeti ser