Noah Stein wrote:
Although I obviously disagree with the first part, I agree with the second, with some reservations. Radian is the perfect example of a situation where there is a clear semantic "dimension" even though there is no unit dimension. In this case, tracking that semantic dimension would be just as helpful as tracking regular unit dimensions. And if I'm doing something in radians, I'd like it to be restricted to those computations that are semantically correct. That's impossible, because it's possible to get a correct radian value by simplification of expressions. For example:
1/2*pi = -i * ln(i) (that's the value of arcsine(1) ). It's not possible to derive the "meaning" of the left part of this equation from meanings of the right part. Situation like this very often occur when you work with complex equations. -- With respect, Alex Besogonov(cyberax@elewise.com)