True, that is what's happening. The cool thing is that dimensional (in J terms, it's 'rank') overloading is inherent to the language.

Most operators have implicit dimensional looping or respond different to differently ranked inputs.

Take for example integers (i.):

       i.3
    0 1 2
       i.3 3
    0 1 2
    3 4 5
    6 7 8

(That's kind of a dumb example, but I think it at least hints at the expressive power of rank.)