Now the cool part is that H², C⁴ and R⁸ are all secretly the same 8-dimensional real vector space equipped with various amounts of extra structure - i.e. the structure of a 4-dimensional complex vector space, or a 2-dimensional quaternionic vector space. And you'll probably be more bored than shocked when I tell you that this 8-dimensional real vector space is yearning to become the OCTONIONS.