IRC highlights!

Quarternions are sort of an extended imaginary part to the imaginaries; so if you think of the imaginary line as being at right angles to the real number line, the domain of quarternions is at right angles to BOTH of them. In fact, there are even more lines at right angles to all three! Thus Fogel is talking about how the domain of quarternions has its own algebra existing in dimensions above that of the real numbers

i think i'm wrong

also fogel is a mathematician