On Thu, 31 Jul 2008 09:24:30 -0700, Darren New wrote:

> Jim Henderson wrote:
>> Absence of evidence is not evidence of absence. ;-)
> 
> Sure it is. It's not proof of absence, of course, but it's stronger
> evidence than not.
> 
> http://www.overcomingbias.com/2007/08/absence-of-evid.html
> 
>> But now here, in the 21st century, we've finally exhausted the base of
>> knowledge?  I don't think that's the case.
> 
> The problem is that you're confusing math with physics. In math, yes, we
> have exhausted the base of knowledge of the halting problem. The halting
> problem goes like this:
> 
> Assume A.  Assume B.   Assume C.  Therefore D.
> 
> You're arguing "maybe assumption B is counterfactual."  That doesn't
> disprove the halting problem. It doesn't mean you can solve the halting
> problem. It merely means the halting problem doesn't apply to your
> current situation.
> 
> Indeed, one of the assumptions required for the halting problem to hold
> (namely, unbounded storage) is *known* to be impossible to realize in
> this universe (or at least normally assumed to be impossible even by
> people who understand the halting problem). That *still* doesn't mean
> the halting problem is "solved".
> 
> Math isn't physics.

Now my brain hurts. ;-)

Jim

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