Six-Dimensional Lorentz Category

Joachim Lambek had a longstanding interest in the use of quaternions as a tool for explaining fundamental aspects of special relativity, dating from his days as a doctoral student to the end of his career. It is known (since the beginning of the twentieth century) that many areas of theoretical physics may be represented by quaternions with complex coefficients (so called “biquaternions”). This posthumous chapter illustrates how time may (or even should) be represented by three dimensions, so that space–time is represented by a six-dimensional Lorentz category (three space coordinates and three temporal coordinates).