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You think one imaginary number is crazy? Just wait till you learn about quaternions. One real number and 3 imaginary numbers forming a four dimensional coordinate system. It's the basis for quantum mechanics and most video game engines. Who thinks of this shit?
Quaternions? Basis of quantum mechanics? Pretty sure that's not right at all. A lot of games use them for rotations in place of rotation matrices though I suppose.
Iirc, using quaternions for rotations let's you avoid "gimbal locking".
Quaternions are not the basis for quantum mechanics. Biquaternions have some applications in quantum field theory, but there are many areas of quantum mechanics where there's no need or space for anything above complex.
Oops my bad, it's been a while. I thought the Hamiltonian used quaternions, but I guess that's just complex numbers.
The Hamiltonian using Hamilton's numbers? Now I think about it it is a bit silly that two entirely separate yet highly propinquitous concepts have such similar names. Physics really went downhill once humans started writing it down.
The general concept is called Spinors, Quaternions are just one representation. Here's a great video on them. In physics they're using them because they're necessary (video explains), in computer graphics we're using them because they're algorithmically convenient, very cheap to compute and ignore that whole half-spin thing. It's one of those instances where it's cheaper to compute useless information and then throw it away as opposed to avoiding to compute it.
They're also absolutely impossible to deal with when authoring stuff, as in rotating things in Blender, it's just a representation on the backend. Quaternions would avoid gimbal lock but when authoring you really rather deal with that than a 4-dimensional hypersphere.
We owe "quatties" to hamilton, but there is a generalization of the process in case you're curious: https://en.wikipedia.org/wiki/Cayley–Dickson_construction