Re: Indirect Reference Changes the Behavior of DDD() relative to DDD emulated by HHH

Op 04.sep.2024 om 14:37 schreef olcott:

On 9/4/2024 3:19 AM, joes wrote:

Am Mon, 02 Sep 2024 08:42:56 -0500 schrieb olcott:

On 9/1/2024 5:48 AM, Fred. Zwarts wrote:

Op 31.aug.2024 om 18:15 schreef olcott:

On 8/31/2024 10:47 AM, Fred. Zwarts wrote:

Op 31.aug.2024 om 17:22 schreef olcott:

On 8/31/2024 10:15 AM, Fred. Zwarts wrote:

Op 31.aug.2024 om 14:50 schreef olcott:

On 8/30/2024 8:31 AM, Mikko wrote:

On 2024-08-29 14:04:05 +0000, olcott said:

On 8/29/2024 3:00 AM, Mikko wrote:

On 2024-08-28 11:46:58 +0000, olcott said:

On 8/28/2024 2:33 AM, Mikko wrote:

On 2024-08-27 13:04:26 +0000, olcott said:

On 8/27/2024 12:45 AM, joes wrote:

Am Mon, 26 Aug 2024 18:03:41 -0500 schrieb olcott:

On 8/26/2024 7:42 AM, Ben Bacarisse wrote:

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

On 23/08/2024 22:07, Ben Bacarisse wrote:

>

We don't really know what context Sipser was given.  I
got in touch at the time so I do know he had enough
context to know that PO's ideas were "wacky" and that
had agreed to what he considered a "minor remark".
Since PO considers his words finely crafted and key to
his so-called work I think it's clear that Sipser did
not take the "minor remark" he agreed to to mean what
PO takes it to mean! My own take if that he (Sipser)
read it as a general remark about how to determine some
cases, i.e. that D names an input that H can partially
simulate to determine it's halting or otherwise.  We
all know or could construct some such cases.

Exactly my reading.  It makes Sipser's agreement
natural, because it is both correct [with sensible
interpretation of terms], and moreover describes an
obvious strategy that a partial decider might use that
can decide halting for some specific cases.  No need for
Sipser to be deceptive or misleading here, when the
truth suffices. (In particular no need to employ
"tricksy" vacuous truth get out clauses just to get PO
off his back as some have suggested.)

Yes, and it fits with his thinking it a "trivial remark".

>

That aside, it's such an odd way to present an argument:
"I managed to trick X into saying 'yes' to something
vague".  In any reasonable collegiate exchange you'd go
back and check: "So even when D is constructed from H, H
can return based on what /would/ happen if H did not stop
simulating so that H(D,D) == false is correct even though
D(D)
halts?".  Just imagine what Sipser would say to that!

Is this an accurate phrasing, pete?

Deciders never compute the mapping of the computation that
they themselves are contained within.

Why not? A decider always either accepts or rejects its
input.

The computation that they themselves are contained within
cannot possibly be an input.

What would prevent that if the input language permits
computations?

When a TM takes its own machine description as input this is not
always that same behavior as the direct execution of the
machine. It is not the same because it is one level of indirect
reference away.

Now you contradict what you said above. You said that deciders
never conpute the mapping of the computation they themselves are
contained within.

Although deciders cannot possibly see their own behavior other
people can see this behavior.
>

Now you are saying that they do in a way that might not be as
expected.

If is a verified fact that DDD has different behavior before it is
aborted in the same way that people are hungry before they eat.

No, the behaviour specified by the finite string does not change
when a simulator decides to do the simulation only halfway. It is
just an incorrect simulation.
>

than the behavior of DDD after it has been aborted, people are not
hungry after they eat.

If two people are hungry and one of them eats, the other one is
still hungry and needs to eat. It is stupid to say that they are no
longer hungry because they have eaten.
Similarly the simulating HHH is not longer hungry, but the
simulated HHH still is hungry and has not yet eaten.

>

The direct execution of DDD includes the behavior of the emulated
DDD after it has been aborted.

And the simulator should also simulate until it sees the behaviour
of after the simulated HHH has aborted its simulator.

People that are not as stupid can see that HHH cannot wait for itself
to abort its own simulation.

And people (except the stupid ones) can see that, because HHH cannot
wait for itself,

Because this would require it to wait forever,
thus HHH knows that to meet its own requirement to halt it must abort
its simulation.

 

And because HHH is simulating itself, the simulated HHH also aborts.
>

 It can not possibly do this. The outermost directly executed
HHH always sees the abort criteria before the next inner
HHH sees it.
 The abort criteria is that HHH sees the DDD has been
emulated twice in sequence.
 When the outer HHH sees that itself and its emulated HHH
has emulated DDD once the emulated HHH only sees that itself
has emulated DDD once.
 

Indeed. A very good explanation. That is what I told you many times. The outer HHH fails to see that the inner HHH would abort as well, because the outer HHH stops one cycle too soon.
If the outer HHH would be changed to do three cycles, it will give the correct answer for the inner HHH that still does two cycles.
But then we can make another DDD with this new HHH and again it would abort one cycle too soon and fail to see that the inner HHH will also abort and halt.
If the outer HHH is programmed to do N cycles and the inner HHH is programmed to do M cycle before the abort, then we see that N must be greater than M for a correct simulation.
This proves that HHH cannot possibly correctly simulate *itself*.
It will always miss the end of the halting program.