How many of you like HP41C calculators?

Not quite, unless you define "can be computed" in terms of Turing machines or something provably equivalent to Turing machines, in which case it becomes a tautology. What Turing showed is that certain other, intuitively plausible, models of (discrete) computation are all equivalent to Turing machines in terms of what they can compute. He did not show that there are no other possible models of computation, not even of discrete computation; indeed, without a precise definition of what "computation" means, nobody can. (As I remarked in this connection in a different message, there are operations describable in the language of analysis and calculus that no discrete device, including a Turing machine, can ever carry out, so I suspect it is already false. However, I also suspect this is not often realized, because our notion of what constitutes computation is so bound up with discrete devices.) This statement amounts to stating that nobody will ever develop a notion of computability that includes things TMs cannot compute. While this may be true, it is a prediction, not a statement of current fact. (As I noted above, I suspect it is a statement of current non-fact.) /~\ The ASCII der Mouse \ / Ribbon Campaign X Against HTML mouse(a)rodents.montreal.qc.ca / \ Email! 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B