In order to apply the ideas of vector spaces to functions, the text I have (Wavelets for Computer Graphics: Theory and Applications by Stollnitz, DeRose and Salesin) conveniently says
Since addition and scalar multiplication of functions are well defined, we can then think of each constant function over the interval $[0,1)$ as a vector, and we'll let $V^0$ denote the vector space of all such functions.
Ok, so I've heard this notion before, and it kind of makes sense. You want to apply the rules of vector spaces (and define things like inner product) for functions, so you go and say "a function is a vector."
But how does this mesh with the traditional physics definition of vector? A vector must have a magnitude and direction. What's going on here between algebra and physics?