On a symmetrical analysis of conical order and its relation to time-space theory

In a paper “On the Connexion of a Certain Identity with the Extension of Conical Order ton Dimensions,” which appeared in the ‘Proceedings of the Cambridge Philosophical Society for July, 1928, I remarked that it was “interesting to note that Conical Order, although it might be used to construct geometries ofn dimensions, will givenn — 1 of these dimensions of one character and only one of the other.” This is illustrated in Time-Space Theory where the square to the distance between two Time-Space points (x 1 ,y 1 ,z 1 ,t 1 ), (x 2 ,y 2 ,z 2 ,t 2 ) is (x 1 -x 2 )2 + (y 1 -y 2 )2 + (z 1 -z 2 )2 + (t 1 -t 2 )2 it they lie in what I have called a separation line; while, if they lie in what I have called an inertia line, the square of the distance between is (t 1 -t 2 )2 - (x 1 -x 2 )2 - (y 1 -y 2 )2 - (z 1 -z 2 )2 . If the Time-Space points lie in an optical line this expression is zero. It is however, misleading in this case to say that the distance is zero.