Re: The proof that I was referring to is on the website

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/15/04 

Date: Sun, 15 Aug 2004 03:58:46 GMT

"The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote in message news:ia12v1-q8o.ln1@lexi2.athghost7038suus.net...
> In sci.logic, Peter Olcott
> <olcott@worldnet.att.net>
> wrote
> on Fri, 13 Aug 2004 23:28:31 GMT
> <z8cTc.205642$OB3.109982@bgtnsc05-news.ops.worldnet.att.net>:
> >
> > "The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote in message
news:mdmtu1-0rk.ln1@lexi2.athghost7038suus.net...
> >> In sci.logic, Peter Olcott
> >> <olcott@worldnet.att.net>
> >> wrote
> >> on Thu, 12 Aug 2004 12:15:22 GMT
> >> <ubJSc.200491$OB3.149139@bgtnsc05-news.ops.worldnet.att.net>:
> >> > If you make you point much more succinctly I will respond to it.
> >>
> >> You want succinct? Try this.
> >>
> >> Given any machine type Mx with side effect x, I can construct an
> >> isomorphic standard Turing machine M(x). If you have a
> >> WillHaltx, I can construct a WillHalt(x). Since WillHalt(x)
> >> is impossible, WillHaltx is also impossible.
> >>
> >> I can't make it much more succinct than that. :-P
> >>
> >> [rest snipped for succinctness]
> >>
> >> --
> >> #191, ewill3@earthlink.net
> >> It's still legal to go .sigless.
> >
> > It look like you just claimed that you can prove that
> > no TM ever can do anything correctly. If I derive
> > a TM that adds together two integers, you can make
> > a machine that fails to add together two integers, thus
> > proving that no machine can correctly add two integers.
> >
> > That's what it looks like you just said.
> > I suspect that you need to look into the difficulty
> > or proving a negative. For many things this is
> > completely impossible. To prove that no TM
> > can possibly solve the Halting Problem is a form
> > of proving a negative.
> >
>
> But that's exactly what Turing proved, by constructing
> a LoopIfHalts given a machine implementing WillHalt that
> can't be evaluated by (that particular variant of) WillHalt.

Yet with my new whiz bang updated version of WillHalt, now
LoopIfHalts and every other TM in the universal set of TMs
can be correctly evaluated. www.halting-problem.com

> As for adding 2 integers, a Turing machine might have some
> difficulties with that; the simplest method I can think of
> would involve rewriting the input as the machine adds, so
> as to allow it to keep track. There are also issues on
> computing the output length properly.
>
> It looks doable but rather complicated, and not all that
> germane to the halting problem.
>
> You are on the hook for producing a working WillHalts. I'll
> accept a working WillHalts that works for *most* machines,
> at this point. Obviously LoopIfHalts is a lost cause.
>
> (Of course, one can cheat and simply run the test machine
> for, say, 1 million cycles; if it halts sometime within
> those cycles, yes, it halts, and if it doesn't halt within
> those cycles, indicate "I've no clue". A bit silly,
> but workable from an engineering standpoint. One can also
> include heuristics for some of the more common engineering
> errors.)
>
> --
> #191, ewill3@earthlink.net
> It's still legal to go .sigless.

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