On Tue, 29 Jul 2008 11:42:47 -0700, Darren New wrote:

> Jim Henderson wrote:
>> This is the problem, though:  The assumption is that computing will
>> always use a Turing model, like I said.
> 
> No, computing doesn't today using a Turing model, and the Halting
> problem applies to many more computing models than the Turing model.
> 
> The Halting problem isn't solvable. If you come up with a new computing
> model that "solves" it, what you're solving isn't the halting problem
> any more.
> 
> It's like arguing "Maybe 2+2 will equal 6 some day, if 2 turns into 3."
> But if 2 turns into 3, you're not longer adding 2+2.
> 
> The halting problem is a precisely defined mathematical construct. Maybe
>   newer computing models might conceivably obsolete the implications of
> the halting problem, but they won't actually negate its proof. (In the
> same sense, that computers are far faster may obsolete the problems
> caused by some algorithms taking O(N^3) instructions, but that doesn't
> make the algorithm take fewer instructions.)

Well, like I said, perhaps I chose a bad example - I should stick to 
things I know, maybe.  :-)

Jim

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