Re: Hypothetical possibilities --- Complete Proof

On 8/2/2024 7:19 PM, Mike Terry wrote:

On 02/08/2024 23:42, Ben Bacarisse wrote:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

Of course these traces don't support PO's overall case he is claiming,
because the (various) logs show that DDD halts, and that HHH(DDD)
reports
DDD as non-halting, exactly as Linz/Sipser argue. Er, that's about it!

PO certainly used to claim that false (non-halting) is the correct
result "even though DDD halts" (I've edited the quote to reflect a name
change).  Unless he's changed this position, the traces do support his
claim that what everyone else calls the wrong answer is actually the
right one.

So, in your opinion, what do you believe is PO's criterion for "correct
result", exactly?  It would be handy if you can give a proper
mathematical definition so nobody will have any doubt what it is. Hey, I
know you're more than capable of getting a definition right, so let's
have that definition!

Definition:  A TM P given input I is said to "halt" iff ?????
              or whatever...

I think this is a rather hopeless venture without formally defining the
representation of a TM. For example: In some formulations, there are
specific states defined as "halting states" and the machine only halts
if either the start state is a halt state or there is a transition to a
halt state within the execution trace; In another formulation, machines
halt if there is a transition to an undefined state. Note a few things:
1) the if's above are really iff's, 2) these and many other definitions
all have equivalent computing prowess, 3) Some formulations define
results by what is left on the tape (or other storage device) while
others add the actual halting state to determine the results.

In a conversation about such topics, gentlemen of good faith and
reasonable knowledge can simple ignore these differences and not go off
the rails. This is not true when the pied piper is ignorant,
disillusional, and masturbating while simultaneously spinning a hula
hoop around his neck.

It's easy enough to say "PO has his own criterion for halting, which is
materially different from the HP condition, and so we all agree PO is
correct by his own criterion, but that does not say anything about the
HP theorem because it is different from the HP definition".

But is that /really/ something PO agrees with?  I don't think so
somehow, because I'm pretty sure PO believes his claim "refutes" the HP
result.  He wouldn't say that if he freely acknowleded that he had
invented a completely different definition for halting.  Also, for what
you're saying to be the right way of looking at things, PO would have to
admit that the HP proof with its standard definition of halting is
valid, and that there is nothing wrong with the Linz proof, other than
it not applying to his own favourite PO-halting definition.

I.e. I think your way of looking at it is a bit "too easy" - but I'd be
happy to be convinced! Personally I suspect PO has no such "new and
different definition" and that anything along those lines PO is thinking
of will be quite incoherent.  No doubt you could make some definition
that is at least coherent but we have to ask ourselves - is that
definition /really/ what PO is thinking???

Nowadays, I think PO's position is more that:
-  yes, DDD() halts when run directly
-  but DDD() when it runs inside HHH simulator /really/ does not halt,
in some kind of
    sense that it /really/ has infinite recursion which would never end
    however far it was simulated (because it "exhibits" infinite
recursion in some way)
-  and yes, DDD() /does/ halt when simulated within UTM(DDD),
-  but the behaviour of DDD depends on who is simulating it.  It
terminates when
    UTM simulates it, but doesn't terminate when HHH simulates it, due
to some
    kind of pathelogical relationship specifically with HHH.  This
difference in
    simulation is /more/ than one simulator aborting earlier than the
other...--

Jeff Barnett