BTW, Geoff - although I join with you in deploring the sartorial sloppiness of the baseball cap, I can't agree with you that it is not "a proper hat"

I should have defined terms a bit better, RC. I think of a hat as having a full brim, whereas a cap has only a bill. So, if one wants to emulate a duck or a platypus, on which a bill belongs, one wears a baseball cap; if one wants to be stylish, however, one wears a properhat!
This distinction exists in other languages as well, so I don't think I'm just talking through my hat.