Extending special relativity via the perplex numbers

In analogy to the complex numbers z=x+iy, where the ‘‘imaginary’’ i is such that i2=−1, a system of perplex numbers z=x+hy is introduced, where the ‘‘hallucinatory’’ h is such that ‖h‖=−1. This system, invented by four freshmen at St. Olaf College, appears to have relevance in physics. In particular, it provides a natural way to extend the usual formalism of special relativity to the case ‖v‖>c. This is done by means of a velocity parameter φ, such that v=c tanh φ, where tanh is an extension of the ordinary hyperbolic tangent function. The fact that this extension has two different angles φ for each velocity v accounts for the different approaches in the literature to superluminal phenomena.