Re: Another clueless wikipedia article

Simon G Best wrote:
> examachine@xxxxxxxxx wrote:
> >
> > Hmm, Ben seemed to draw the same thing as I did, and he even agreed to
> > that case (saying that physical computers cannot implement countable
> > infinity). That's why I now think it is misleading. It is an ambiguous
> > expression there.
>
> I'm not convinced. He was responding to what you said the article said,
> but what you said the article said was not actually what the article
> said. So, if he's got the impression that the article said that PCs
> aren't Turing Machines, is it because he got that impression from the
> article itself, or because you've given him that impression? (He might
> have just accepted what you incorrectly stated about what the article
> said, with the result that he's got the wrong impression of it as a
> result. I've seen that sort of thing happen before.)
>
> It's also possible that there's also confusion here about what can be
> meant by such expressions as 'PCs aren't Turing Machines'. Is it
> 'Turing Machines' as in the machines themselves? Or is it 'Turing
> Machines' in the sense of the model of computing represented by Turing
> Machines collectively and generally? Sometimes we mean the latter, in
> which case we're not saying that there is no Turing Machine that a PC is
> (or is equivalent to), but that no PC is a Universal Turing Machine (or
> equivalent). I think that's the sense in which Ben means it.
>
> But there's also a red-herring case, as well, which may be relevant.
> Sometimes, people point out that Turing Machines have inexhaustible
> storage space on their tapes, which PCs do not have. Therefore, they
> claim, PCs cannot be Turing Machines (in the sense of the machines
> themselves), no matter what Turing Machine we might be considering. But
> this is confusing what we could call 'implementation details' with the
> computations represented by those machines. For example, consider a
> Turing Machine which immediately halts, no matter what its input is.
> The output will be identical to the input. Such a Turing Machine can be
> implemented on a PC by just immediately echoing everything entered
> through the keyboard (the input) straight to the screen (the output),
> key-press by key-press, in a never-ending loop - the output will be
> identical to the input, no matter how much input there is!

You have my deepest respect. An excellent explanation.

The fact that a turing machine is just a model is often overlooked. In
the article, I tend to think that a clear example of a device that can
be only considered to be a FSM and not a more powerful computer would
be much better. Why, because it automatically avoids such long-winded
thoughts as these. Thus, while the FSM-TM-Desktop PC discussion may be
useful, it would better be moved as additional material. Why skip the
soda vending machine, which is a much more natural example?

By the way, what is such a natural example of PDA?

Regards,

--
Eray

.

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