What did physicists use before the introduction of vectors by Gibbs & Heaviside, was it the exact same as we would use when denoting components with an x or y subscript or something completely crazy? Also, I've read in quite a few places that quaternions are very useful for things like Special Relativity & in particle physics & I've definitely seen them being used quite a lot in Lie Algebra texts as I've browsed through. How hard are they, i.e. what makes them so crazy & what are the prerequisites? The only bad thing I know about them is that it took Maxwell 20 Quaternion equations to convey what Hamilton was able to condense into 4, (or 8 in a sense...).