Re: DDD correctly emulated by H0 --- Ben fails to understand computable functions

On 6/25/24 10:21 AM, olcott wrote:

On 6/25/2024 9:04 AM, Ben Bacarisse wrote:

Alan Mackenzie <acm@muc.de> writes:
>

[ Followup-To: set ]
>
In comp.theory olcott <polcott333@gmail.com> wrote:

On 6/25/2024 4:22 AM, joes wrote:

Am Sat, 22 Jun 2024 13:47:24 -0500 schrieb olcott:

On 6/22/2024 1:39 PM, Fred. Zwarts wrote:

Op 21.jun.2024 om 15:21 schreef olcott:

>

When we stipulate that the only measure of a correct emulation is the
semantics of the x86 programming language then we see that when DDD is
correctly emulated by H0 that its call to H0(DDD) cannot possibly
return.

Yes. Which is wrong, because H0 should terminate.

>
[ .... ]
>

The call from DDD to H0(DDD) when DDD is correctly emulated
by H0 cannot possibly return.

>

Until you acknowledge this is true, this is the
only thing that I am willing to talk to you about.

>
I think you are talking at cross purposes.  Joes's point is that H0
should terminate because it's a decider.  You're saying that when H0 is
"correctly" emulating, it won't terminate.  I don't recall seeing anybody
arguing against that.
>
So you're saying, in effect, H0 is not a decider.  I don't think anybody
else would argue against that, either.

>
He's been making exactly the same nonsense argument for years.  It
became crystal clear a little over three years ago when he made the
mistake of posting the pseudo-code for H -- a step by step simulator
that stopped simulating (famously on line 15) when some pattern was
detected.  He declared false (not halting) to be the correct result for
the halting computation H(H_Hat(), H_Hat()) because of what H(H_Hat(),
H_Hat()) would do "if line 15 were commented out"!
>
PO does occasionally make it clear what the shell game is.
>

 *Ben fails to sufficiently understand Computable Functions*

No, Peter Olcott fails to understand what he is talking about.
There is no requirement that 'Halting' even BE a computable function, and in fact has been proven not to be one.
So, an argument based on it being one, starts off with a LIE.

Computable functions are the formalized analogue of
the intuitive notion of algorithms, in the sense that
a function is computable if there exists an algorithm
that can do the job of the function, i.e.
 *given an input of the function domain*
*it can return the corresponding output*
 https://en.wikipedia.org/wiki/Computable_function