I have a different concept of the quaternion, as not necessarily involving complex numbers. A quaternion has four independent variables - one scalar and three vectors, which could also be vectors in real space. Hamilton was applying this to electromagnetics, which is where the imaginary numbers come in. But when he wrote about quaternions being a model for space-time (in 1843!), I think he was referring to vectors in real space.

I have a different concept of the quaternion, as not necessarily involving complex numbers. A quaternion has four independent variables - one scalar and three vectors, which could also be vectors in real space. Hamilton was applying this to electromagnetics, which is where the imaginary numbers come in. But when he wrote about quaternions being a model for space-time (in 1843!), I think he was referring to vectors in real space.