in reply to use strict won't require explicit name for all variables?
I suspect that it's because $a and $b are, in some places, variables with a "special" meaning to Perl. I'm thinking particularly of sort, which uses $a and $b to stand for the values being compared. If I change the script to use, say $x and $y, I get a strict error, as I'd expect.
This would make $a and $b a bit like the punctuation variables. $_, for example, doesn't need to be explicitly scoped before you use it, which is partly why it's useful as a shortcut.