Re: How the requirements that Professor Sipser agreed to are exactly met --- WDH

Keith Thompson <Keith.S.Thompson+u@gmail.com> writes:

olcott <polcott333@gmail.com> writes:

On 5/14/2025 3:51 PM, dbush wrote:

On 5/14/2025 11:45 AM, olcott wrote:

On 5/14/2025 6:20 AM, Richard Damon wrote:

>
And since the DD that HHH is simulating WILL HALT when fully
simulated (an action that HHH doesn't do)

>
*NOT IN THE ACTUAL SPEC*
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its
     input D until H correctly determines that its simulated D
     would never stop running unless aborted then
>

That Sipser didn't agree what you think the above means:
 

>
If that was actually true then you could provide an
alternative meaning for the exact words stated above.
>
I keep challenging you to provide this alternative
meaning and you dodge because you know that you are
lying about there being any alternative meaning
FOR THE EXACT WORDS LISTED ABOVE.

>
No alternative meaning is needed, just a correct interpretation of the
words (which appear to be incomplete).
>
The quoted sentence is cut off, something that I suspect you didn't
notice.  Here's the full quotation from a previous article:
>

<Sipser approved abstract>
MIT Professor Michael Sipser has agreed that the following verbatim
paragraph is correct (he has not agreed to anything else in this
paper):
>
If simulating halt decider H correctly simulates its input D until H
correctly determines that its simulated D would never stop running
unless aborted then H can abort its simulation of D and correctly
report that D specifies a non-halting sequence of configurations.
</Sipser approved abstract>

>
**If** H correctly simulates its input in the manner you claim,
**then** H can correctly report the halting status of D.  (That's a
paraphrase that probably doesn't capture the full meaning; the full
**quotation is above.)
>
To put it another way, If H correctly simulated its input in
the manner you claim, then H could correctly report the halting
status of D.
>
I'm not surprised that Sipser would agree to that.  The problem is
that it's a conditional statement whose premise is impossible.
>
If an equilateral triangle had four sides, then each of its four
vertices would be 90 degrees.  That doesn't actually mean that
there exists an equilateral triangle with four 90-degree vertices,
and in fact no such triangle exists.  Similarly, *if* a general
halt decider existed, then there are a lot of things we could say
about it -- but no general halt decider can exist.

It's certainly true that it can be taken to be a purely hypothetical
remark, but I suspect PO played a more subtle trick on the professor.
Nothing in the quote that PO presented states that D is special in any
particular way.  If D is simply "its input" then the statement is simply
true of some inputs to H: those that can be determined to be non-halting
can be reported as such.  There will be many such inputs if the
simulator is clever at detecting certain patterns.

But D and H are the names that Sipser uses in his book in his HP proof.
Was it made clear that D is not just the name of the input (as the first
few words of the quote might suggest) but is in fact one very specific
input constructed from H itself?  I don't know, and I doubt we ever
will.  If that was made clear, then PO should be saying that Sipser
agreed to more than just the quoted words and in that case I'd wager his
agreement was based on the hypothetical nature of the quote.

I'm not quite 100% confident in my reasoning here.  I invite any
actual experts in computational theory (not you, PO) to criticize
what I've written.

I am no expert, though I did teach this material in a CS degree course
for many years.

Richard (H) has reminded us about avoiding straw man arguments and to
instead address the strongest, clearest version of the point of view we
reject.  PO is playing with this idea by constructing straw men to be
agreed with!.  He spent years honing a sentence to express his position
until is was vague enough that someone important would agree with it.

PO should, however, have asked Sipser to agree with an honest and clear
statement of his (incorrect) views:

(a) That false (non-halting) is the correct result for some inputs that
represent halting computations.

(b) This is because, in the special case of a putative halt decider that
uses simulation, it is correct to report on what /would/ happen were the
simulation /not/ aborted.

(c) In the specific case where D is constructed from a simulating H in
the manner typically found in Halting Theorem proofs, H would then be
able to correctly report a result because H can detect that D halts only
because H has to stop simulating to report at all.

No one would agree to any of this, so PO must hide these points in some
sort of waffle or other.  As I say, it took years to move from being
relatively clear to being vague enough to trick the professor.  All of
(a), (b) and (c) can be found, in varying degrees of clarity, in PO's
posts of the last 20 years.

--
Ben.