What in the world is a Quaternion and how do I understand IT?
Throw me everything you know about it.
In: Mathematics
To answer it from a less utilitarian perspective, when constructing the numbers in math, the most popular model starts from defining the natural numbers (by constructing a set that adheres to the Peano axioms, but that’s not quite important now), and then doubling up the numbers, so an integer is represented by two naturals, so for example the integer 3 can be thought of as the natural 3 and the natural 0 in pair, where i3 is n3 – n0 in the common sense of subtraction. Any natural pairs where the difference is 3 will represent this integer. The same way we get to the rationals, just with “division”. The reals is a different jump, but after that we can continue doubling up, so we get the complex numbers, and from two complexes you get the quaternions, two quaternions give you octaves and so on.
The trick is, you always have to define how the usual operations, addition and multiplication works on pairs of numbers. It turns out you start to lose properties as you go higher than complex.
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