Veit Elser <ve10@cornell.edu> wrote:
Keith F. Lynch <kfl@KeithLynch.net> wrote:
The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped.
I?m curious, what?s the *first* thing?
As I had posted just two hours earlier, in the same thread, "Everyone's first thought when they learn about i is to ask what it *is*. To which I can answer that at least I know its last digit, which is 3. :-)" Students get useful answers when they ask what pi and e are, so why not ask what i is? Instead of being given digits, they're told how to use it. And after they use it for a while, they realize they now know what it is. (Except that half of them are actually using -i. :-) )
It?s actually very cool that the Galois automorphism i <-> -i is co-opted by physics in the time-reversal transformation. The real numbers turned out to be incomplete in a very real sense!
Think quaternions, not complex numbers. Three interchangeable and symmetrical dimensions, plus one very different dimension with a direction built in.