Re: Can you find anything wrong with this solution to the Halting Problem?

From: Jón Fairbairn (jon.fairbairn_at_cl.cam.ac.uk)
Date: 07/14/04 

Date: 14 Jul 2004 11:25:18 +0100

"Peter Olcott" <olcott@att.net> writes:

> I wrote:
> > Of course it is! If a well understood theorem says P, and
> > someone comes along and says ¬P, the theorem is already a
> > refutation of ¬P, so there's no work to do.
>
> And of course every theorem is created only by infallible
> people that never make any mistakes, thus (as you are
> directly implying) no theorem has ever once been found
> to be incorrect in the entire history of mankind.

Wrong. As I pointed out, Turing's proof is simple and has
been checked many times and has counterparts in all other
models of computation. Other proofs may be mistaken, but
this one is simple enough to survive mechanical checking.

> Sorry for the sarcastic rant but I have seen your form
> of reply far too many times.

That's hardly surprising.

[pointless wittering snipped]

> Do you ever admit defeat when you are totally 100% correct?

I never say I'm 100% correct.

Now it's my turn to be sarcastic. I meet someone in the
street who says: "Spires of gold! Castles in the air! Silver
palaces! This way" and I have some time, so I follow him to
see what he's on about. We go north and take the first
turning to the east. I'm willing to consider the possibility
that he might have something, so I continue to follow.

Then we take the first turning to the south and I ask "Are
you sure this is the quickest way to get there?" to which he
replies "Spires of gold! Castles in the air! Silver palaces!
Just keep going!" So I follow him along the street to the
next junction, where he turns west. "But we are heading back
to where we started" I complain. "Spires of gold! Castles in
the air! Exfoliating porrige" he replies. I wonder if he may
be a foreign gentleman for whom English is not his first
language, so I try a few phrases in other tongues, to no
avail.

Now we are right back where we started and I say so. "Spires
of gold! Castles in the air! Silver palaces! I can prove
it!" he exclaims. I smile and nod and wave goodbye, for he
has proved something, but it's nothing to do with fabulous
architecture. 

-- 
Jón Fairbairn                                 Jon.Fairbairn@cl.cam.ac.uk

Relevant Pages