And this is what comes of trying to be flippant around people who know more than I do :)
That's a very interesting paper. I hadn't really thought about the theoretical ramifications of everything we let computers do these days... On the "I agree" front, there really isn't much to say.
Though I'm not convinced that it's strictly untrue that "all computable problems are function-based." For instance, take the robotic car: you could, for instance, model that as sequence of functions being called with new inputs, where each call represented the motion of that car over one "tick," which could be as short or as long as you like. And if there's a hole in that argument (which there may well be), then if worst comes to worse, we can use quantum mechanics to model the section of the universe with the computer running the program and obtain a mathematical description that way :)
