On 28 Apr 1998 15:52:50 -0500, rickert at cs.niu.edu (Neil Rickert)
wrote:
>No, I disagree. In fact this was the sort of thing that the
>disagreement between Bill Modlin and me was about. We can say that
>something is a computation without having to map it into the action
>of a formal Turing machine. From my perspective, the Turing theory
>is that of an idealized mathematical model of computation. It is not
>a constraint on any actual computation, that it is required to
>conform to the idealized model. We generally don't expect our
>idealized models to exactly correspond to reality. Rather, the
>expectation is that the model fits well enough to be useful for
>theoretical analysis.
I disagree, in turn. It is only insofar as a PC or whatever conforms
to the Turing model that it can be said to execute algorithms. That
is what it *means* to be Turing equivalent: the TM defines the
effective procedure. When your PC departs from the TM spec in this
respect, it is *broken*. TM *is* an idealization when it comes to
infinite tape, perhaps. But insofar as performing syntactic
operations on symbols is concerned, as soon as your CPU ceases to be
TM fastidious, you'll need a trip to the shop. That it fit the model
is critical for its practical utility; forget theoretical analysis.
--
Jer
"If you meet the buddha, kill the buddha."
Lin-chi (dead)
