Re: Another clueless wikipedia article

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!