Re: Can returning a value change the value itself (in the Halting Problem)

From: peter_douglass (baisly_at_gis.net)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 20:17:55 GMT

"Marc Goodman" <marc.goodman@comcast.net> wrote in message
news:ayMWc.52350$Fg5.18521@attbi_s53...

> peter_douglass wrote:
> > "Marc Goodman" <marc.goodman@comcast.net> wrote in message
> > news:RzLWc.51965$Fg5.43982@attbi_s53...

> >>peter_douglass wrote:

> >>>Could you explain what you mean by a TM with access to its
> >>>own state transition table? What does access mean?

> >>You'd have to ask Peter exactly what he means, it's his
> >>extension.

> > But I'm asking you what you mean.

> I know you are. But since I'm only claiming
> that it has yet to be established that it is possible
> to locally modify "such a machine," whatever that means,
> in such a way as to not change its returned results,
> the burden of proof is on the people making those claims,
> not on me. I'm claiming it hasn't been adequately proven
> yet and it would seem that they would have to be able
> to prove it for _all_ such definitions if they were going
> to make that argument.

If you were only claiming that

a) the burden of proof lies on those making a claim, and
b) the burden of proof in a particular argument has not been met

then I should not bother to ask you what you mean.
But, as it happens, you also claim:

<< if you supply a TM with an extension that allows it
<< to introspect, then you are no longer guaranteed that
<< the "code" of the TM has locality. >>

and

<< even making a "trivial" change to such a TM [a TM with
<< access to its own state transition table that can calculate
<< the check sum of its own state transition table] can cause
<< the result produced by such a TM to change >>

These appears to me to be a very definite claim, and therefore
I feel entitled to ask you what you mean by "a TM with access
to its own state transition table" or "a TM with an extension that
allows it to introspect".

I understand that you raised these claims to rebut claims made
by others. The claims made by others may be wrong, and you
may be in the right "overall". But right now, I'm interested in
the specific claims that you have made, and what they mean.

> > How can you draw this or any other conclusion about
> > TMs supplied with a particular extension if you do not
> > know what it means to have that extension?

> I'm deliberately _not drawing a conclusion_. I'm arguing
> against people who _are drawing a conclusion_.

Let's look at the sentence you wrote, to which I asked
how can you draw this or any other conclusion.

<< I'm just arguing that if you supply a TM with
<< an extension that allows it to introspect, then you are no
<< longer guaranteed that the "code" of the TM has locality.

Is the part "if you supply...then you are no longer..."
not a "conclusion"? Would it make a difference if I called
it an assertion rather than a conclusion?

It seems to me you are making assertions about
TMs with access to their own transition tables, and
TMs with an extension that allows introspection.

Could you please explain what those terms mean
in the assertions you have made.

> The conclusion
> that they are drawing is that a machine that introspects
> can always be locally modified, etc, etc, read the above.

> >>So, making the claim that a TM with such an extension can
> >>be trivially modified to return its results without
> >>changing the results it is computing is far from obvious.

> > Since I don't know what it means to be a TM with such an
> > extension, I can't rationally say one way or the other.

> Great! We're in total agreement. You can help me argue
> against the people who think they've proven etc. etc. etc.

You say: "X is far from obvious".
I say: "I don't know what you mean".
You say: "Great! We're in total agreement"

Perhaps I can help you argue against the people who
think they have proven etc. etc. etc.
Perhaps I can do this by showing the flaws in their
reasoning. Perhaps I can also help you in your efforts
by motivating you to tighten up your presentation.

--PeterD

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