An interesting article is "The Origins of the Turing Thesis Myth", which explains why it's a myth that a Turing machine can do anything a computer can.
The quick summary is that Turing machines can compute any algorithmic function. However,real computers do more than computing functions, and today's applications cannot be modeled by Turing Machines.
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 :)
Eh, but the problem is the assumption that the world itself cannot be modelled as part of the tape that the Turing Machine eats.
From a quick glance through the paper and the LtU comments it seems that its point is that interactive I/O cannot be modelled by the Turing Machine.
But as I've learned in Haskell, I/O can itself be mathematically treated, specifically by monads: the world-before-i/o-event is the monad that is input to a function, and the world-after-i/o-event is the monad you return. And I'm pretty sure that monads themselves can be modeled by TM: they can be represented by a part of the tape that the TM gets to and modifies, just like any function-to-TM mapping.
The problem is that the paper uses words like 'model' and 'function-based' rather vaguely. You can model I/O with a TM, but you can't actually do it, which is what they're getting at.
