Quaternions are numbers like the real numbers: they can be added, subtracted, multiplied, and divided. There is something odd about them, hinted at by the Latin. Quaternions are composed of four numbers that work together as one. They were discovered by several people back in the eighteen hundreds. Some enthusiasts thought quaternions would be able to express everything that could happen in our three dimensions of space and one for time because quaternions naturally had that form too. Math accidents do not happen − they revel deep things about how Nature works.
Unfortunately, the big fans of quaternion mathematics claimed far more than they would deliver. Useful ideas born from initial quaternion work − for example the notion of scalars, vectors, div, grad, and curl − were stripped out of their initial context, and made more "general". I use the quotes because from my viewpoint, there is nothing more general than a number that can be added, subtracted, multiplied, and divided. I am trying to continue the project of applying four−dimen- sional quaternions to the four−dimensional spacetime we live in.