…and in turn “geometric algebra” is the physicist’s name for a subset of the even more general mathematicians Clifford algebra (which of course is a subspace of the tensor algebra over the underlying vector space…)
As a programmer / physicist, the analogy I use is that if I had to represent an 8-dimensional parameter as an array, I would write:
double foo[8];
complex foo[4];
When you consider problems in real geometry, this is plausible. But on the other hand, not all mathematics is real geometry. For some applications in mathematics, the complex-geometric perspective is more natural.
P.S. Of course p-adic (and in particular 2-adic) geometry is even cooler than anything real or complex ... ;-)
If mathematicians designed computer software, their data structures would look like:
struct Person {
char name;
complex name_height;
}No it's not. This is such a typical and braindead HN take.
I claimed the exact opposite: whether real or complex numbers as basic objects are more natural depends on the problem that you consider.