In article <6i7h70$gij at ux.cs.niu.edu>, Neil Rickert <rickert at cs.niu.edu> wrote:
>andersw+ at pitt.edu (Anders N Weinstein) writes:
>There are things that are being done by the computer on my desk that
>I could not map into a Turing machine.
>>I'm not talking 'analog'. My concern is with interaction. A Turing
>machine is not interactive. A person is, and the computer on my desk
>is.
Formal models of computation treat *interaction* in terms of
symbols getting written onto the tape memory. This seems a
pretty good model of how the operating system code views a device.
There are control registers and concurrency and interupt handling to be
taken into account of too. But I don't see how the general functioning
is outside the domain of a formal model that includes such symbolic
events.
>> But it has to be something to which the
>>theory of computation applies, doesn't it?
>>I don't see why. The computer sends out a signal on one of its
>output channels. This causes something to happen in the world.
>Whatever happens then results in further input to the computer. In
Right. An input/output machine deposits a symbol on a special square on
its tape (a device's "control register"). Some time later symbols wind
up somewhere else on the tape (a data buffer). If I wanted to model the
asynchronous interrupts, that would complicate things but it seems
do-able (for stored-instruction register machines, the program counter
gets spontaneously changed and a bit else). In effect the machine has
coopted the world. But the world is no part of its symbolic program,
the world only makes a difference to that in so far as it deposits
symbols on the tape.
>effect the computer has coopted the world as part of the mechanism it
>uses in its procedures. If the computer on my desk is sufficiently
>interactive, then you might not be able to apply the theory of
>computation unless you can formalize the entire universe as a Turing
>machine.
That is not obvious to me, since we don't have to model the external
interactions in order to define the internal program, i.e. what it
does conditional on such and such symbols winding up on its tape as input.
[More another time]