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.
