"Matt Calabrese" <rivorus@gmail.com> wrote
My argument is that what you call numeric types aren't always simply numeric types. Division of similar quantities result in a quantity with an empty classification but which has unique units, such as with radians. Completely separately, I do see an orthogonal problem. How should we handle multiplication of two quantities of empty classification. For instance, degrees * degrees should result in degrees^2, just like meters * meters results in meters^2. This concept does make sense, however, squaring a quantity which has an empty classification would result in another quantity having an empty classification (0^2 equals 0). So, we run into the odd case that degrees and degrees^2 have the same classification.
FWIW angle * angle is known as a 'solid angle". steradian is a solid angle unit. regards Andy Little