John A. De Goes wrote:
On Feb 13, 2009, at 2:11 PM, Jonathan Cast wrote:
The compiler should fail when you tell it two mutually contradictory things, and only when you tell it two mutually contradictory things.
By definition, it's not a contradiction when the symbol is unambiguously typeable. Do you think math textbooks are filled with contradictions when they give '+' a different meaning for vectors than matrices or real numbers???
Yes. Yes, I do. It is precisely this abuse of notation which makes, for instance, statistics textbooks impossible to read (without already knowing the material). Scalars, vectors, and matrices are fundamentally different here and the operations on them should be unambiguous, regardless of context. When reading a machine learning algorithm it should *never* be a question whether something is scalar or not. Ambiguity is a bug. Replacing one kind for another is almost always wrong. For another example, consider matrices vs their transposes. Many folks can't be bothered to type a single character to clarify when things should be transposed before multiplying. No matter how quickly someone can test the equation to verify it, leaving that information off makes the equation simply wrong. And it's not as if square matrices aren't ubiquitous. -- Live well, ~wren