I'm having a cold and my brain is only operating at half speed right now, so maybe I'm just confused. But I always thought that variables lived either in scalar or list context. Are there such beasts as numerical and string contexts as well?

Indeed in Perl 5 (and earlier), as opposed to Perl 6, there is no precise notion of numerical or string contexts. However those terms are sometimes loosely used to indicate "used as a number" and "used as a string respectively": in some cases, but by no means in all of them, there's an actual difference.