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This question currently has three votes to close. While it seems rather vague and "stone-soupy", I seem to remember hearing that there is something to be said in this direction, via Clifford algebras and higher-dimensional versions of Cauchy-Riemann.
So for me, this doesn't automatically fall into the class of questions which do not admit good answers, although I admit that as phrased it could easily invite a bunch of not very good ones...
As you can see, I pointed it to a page that was identical to the first question. Unfortunately, this doesn't cover the second, "why not quaternions" question.
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