Invisible wrote:
>>> Unless quantum computing ever works some day, and it turns out to 
>>> have _fundamentally_ different capabilities, the halting problem will 
>>> never be solved.
>>
>> Quantum computing (today) doesn't even solve NP problems in P time, 
>> let alone non-computable problems. :-)
> 
> But you get what I'm saying. Maybe there is some fundamentally new 
> system that changes the rules, so to speak.

That still won't solve the halting problem, because the halting problem 
isn't defined in terms of this fundamentally new system.

It's like saying "integers are not closed under division", and then 
saying "but we've discovered rationals!"   Integers *still* aren't 
closed under division, even if you invent rationals.

> Even if such a system were to exist, you would still have a new, 
> generalised Halting Problem, and you're back to square one.

That's rather harder to say, really, since we by definition have no idea 
what a program in this entirely new paradigm would look like. But I 
suspect you're correct.

-- 
Darren New / San Diego, CA, USA (PST)

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