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devel / comp.theory / Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

SubjectAuthor
* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ keyolcott
+- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Python
+- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
 `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |+* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Malcolm McLean
    ||`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    || `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Malcolm McLean
    ||  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    ||   +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    ||   |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    ||   | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    ||   |  `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    ||   `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    | +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    | |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    | | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    | |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    | |   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    | |    `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    | |     `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |    `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |     +- Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |     `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |      +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |      |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |      | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |      |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |      |   `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |      `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |       `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |   +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |   |`- Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |+- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Python
    |   |        |    |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |    `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |     `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Jeff Barnett
    |   |        |    |      |`- Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |      |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |      |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      |   +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Jeff Barnett
    |   |        |    |      |   |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      |   | `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |      |   |  `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      |   |   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |      |   |    `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      |   |     `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |      |   |      `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      |   |       +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |      |   |       |`- Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |      |   |       `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |   |        |    |      |   `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |   |        |    |      `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |       `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |        `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |         `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |          +- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |   |        |    |          `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |           `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |            +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |            |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |            | +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Dennis Bush
    |   |        |    |            | |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |            | | +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Python
    |   |        |    |            | | |`* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |            | | | +- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Python
    |   |        |    |            | | | `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |   |        |    |            | | `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |   |        |    |            | +* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse
    |   |        |    |            | |`- Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |            | `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Richard Damon
    |   |        |    |            `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |             +- Refuting the Peter Linz Halting Problem Proof --- Version(10) [Malcolm McLean
    |   |        |    |             `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |              `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |               `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    |                `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   |        |    |                 `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        |    `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
    |   |        `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [André G. Isaak
    |   `* Refuting the Peter Linz Halting Problem Proof --- Version(10) [Andy Walker
    `- Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piecBen Bacarisse

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Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<t2f5e2$75k$1@dont-email.me>

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
Date: Mon, 4 Apr 2022 10:12:49 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Mon, 4 Apr 2022 16:12 UTC

On 2022-04-04 08:05, olcott wrote:
> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>
>>>> It might be time to skip ahead because the next exercise is to do the
>>>> same for P, a TM that decides if a string encodes a prime number.  Can
>>>> you think of how to specify that without giving an algorithm?
>>>>       P.q0 ??? ⊦* P.qy    if ???
>>>>       P.q0 ??? ⊦* P.qn    otherwise.
>>>> (The three ??? won't all be the same things.)  Any idea how to flesh
>>>> this out?  If you can, you will be able to do it for E very easily too.
>>>
>>> P.q0 S ⊦* P.qy    if Is-Prime-Number(S)
>>> P.q0 S ⊦* P.qn    otherwise.
>>
>> That's getting close.  We know, from how the notation works, that S is a
>> string of symbols in the TM's alphabet.  But writing Is-Prime-Number(S)
>> suggests that is not natural language.  That's a very hard route to go
>> down.  I'd have to ask you for the definition of Is-Prime-Number.
>> Defining it symbolically is messy and if the definition is /not/ formal,
>> dressing the definition up with a formal-looking name is just
>> superficial.
>>
>
> It goes through some tedious steps to see if it is a prime number:
>
> A prime number is a natural number greater than 1 that is not a product
> of two smaller natural numbers.

I think you are reading too much into this. All Ben really is asking is
for you to restate your condition in a clear and concise fashion.

Let's say I have some natural number p. If I say that "p is a prime
number" that's 100% clear since the meaning of 'prime number' is well
established.

On the other hand, if I say Is-Prime-Number(p), that's not nearly as
clear. Why? Because one normally introduces a formalism either to convey
some special technical meaning or to avoid some sort of ambiguity which
natural language might create. So the reader is left wondering exactly
which special meaning you might have in mind or which possible ambiguity
you might be trying to avoid. They then end up scouring your answer
trying to find where you've defined 'Is-Prime-Number()' only to come up
empty-handed and uncertain about your meaning.

That's why it is generally *not* a good idea to always introduce things
that look like they might be technical terms or C functions or whatever
but which have not been defined by you. The reader is left wondering
what aspect of your intended meaning they might be missing.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<06WdnbDsFYTbh9b_nZ2dnUU7_8xh4p2d@giganews.com>

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
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<n72dnae_RMuWrdf_nZ2dnUU7_83NnZ2d@giganews.com> <877d85buic.fsf@bsb.me.uk>
<1cudneORZsT2qNf_nZ2dnUU7_8zNnZ2d@giganews.com> <87mth1ae3z.fsf@bsb.me.uk>
<RJCdnVAp-PNjodf_nZ2dnUU7_8zNnZ2d@giganews.com> <877d85adc8.fsf@bsb.me.uk>
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<w_WdndouypjXZtf_nZ2dnUU7_8zNnZ2d@giganews.com> <t2f5e2$75k$1@dont-email.me>
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 by: olcott - Mon, 4 Apr 2022 16:18 UTC

On 4/4/2022 11:12 AM, André G. Isaak wrote:
> On 2022-04-04 08:05, olcott wrote:
>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>
>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>> same for P, a TM that decides if a string encodes a prime number.  Can
>>>>> you think of how to specify that without giving an algorithm?
>>>>>       P.q0 ??? ⊦* P.qy    if ???
>>>>>       P.q0 ??? ⊦* P.qn    otherwise.
>>>>> (The three ??? won't all be the same things.)  Any idea how to flesh
>>>>> this out?  If you can, you will be able to do it for E very easily
>>>>> too.
>>>>
>>>> P.q0 S ⊦* P.qy    if Is-Prime-Number(S)
>>>> P.q0 S ⊦* P.qn    otherwise.
>>>
>>> That's getting close.  We know, from how the notation works, that S is a
>>> string of symbols in the TM's alphabet.  But writing Is-Prime-Number(S)
>>> suggests that is not natural language.  That's a very hard route to go
>>> down.  I'd have to ask you for the definition of Is-Prime-Number.
>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>> dressing the definition up with a formal-looking name is just
>>> superficial.
>>>
>>
>> It goes through some tedious steps to see if it is a prime number:
>>
>> A prime number is a natural number greater than 1 that is not a
>> product of two smaller natural numbers.
>
> I think you are reading too much into this. All Ben really is asking is
> for you to restate your condition in a clear and concise fashion.
>
> Let's say I have some natural number p. If I say that "p is a prime
> number" that's 100% clear since the meaning of 'prime number' is well
> established.
>
> On the other hand, if I say Is-Prime-Number(p), that's not nearly as
> clear. Why? Because one normally introduces a formalism either to convey
> some special technical meaning or to avoid some sort of ambiguity which
> natural language might create. So the reader is left wondering exactly
> which special meaning you might have in mind or which possible ambiguity
> you might be trying to avoid. They then end up scouring your answer
> trying to find where you've defined 'Is-Prime-Number()' only to come up
> empty-handed and uncertain about your meaning.
>
> That's why it is generally *not* a good idea to always introduce things
> that look like they might be technical terms or C functions or whatever
> but which have not been defined by you. The reader is left wondering
> what aspect of your intended meaning they might be missing.
>
> André
>

OK. It looks like we are finally beginning to make progress towards
actual closure.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<87ilro7r87.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=29395&group=comp.theory#29395

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]
Date: Mon, 04 Apr 2022 17:23:04 +0100
Organization: A noiseless patient Spider
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 by: Ben Bacarisse - Mon, 4 Apr 2022 16:23 UTC

olcott <NoOne@NoWhere.com> writes:

> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>
>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>> you think of how to specify that without giving an algorithm?
>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>
>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>> P.q0 S ⊦* P.qn otherwise.
>>>> That's getting close. We know, from how the notation works, that S is a
>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>> suggests that is not natural language. That's a very hard route to go
>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>> dressing the definition up with a formal-looking name is just
>>>> superficial.
>>>
>>> It goes through some tedious steps to see if it is a prime number:
>>>
>>> A prime number is a natural number greater than 1 that is not a
>>> product of two smaller natural numbers.
>> We've hit a bit of a road-block rather sooner that I had expected.
>> First off, there's no need to define what a prime number is. If at some
>> point it turns out that your readers do not know, go ahead and define
>> it, but it's too widely understood by comp.theory readers to bother
>> about.
>> But writing (as I think you are suggesting)
>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>> prime number
>> is not really adequate. There are two 'it'. To what do they refer?
>
> You told me to make sure that I do not provide an algorithm.

Yes, that good. You didn't.

Now, to what do the two 'it's refer?

> This is somewhat algorithmic:

No, no. The non-algorithmic way is best. You should be able to
specific what a computation does even when yo have no idea how to write
the an algorithm to do it. Sometimes there isn't ad algorithm!

>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>> be a prime number.
>> Can you see how you (a) make it shorter, (b) make it clearer?

My reply has three questions in it (depending on how you count) but you
didn't answer any of them. This will only work if you try to answer
these questions. Sometimes the answer will be "I don't know what you
mean", but that's a perfectly good answer.

--
Ben.

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
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 by: olcott - Mon, 4 Apr 2022 16:27 UTC

On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>
>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>
>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>> suggests that is not natural language. That's a very hard route to go
>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>> dressing the definition up with a formal-looking name is just
>>>>> superficial.
>>>>
>>>> It goes through some tedious steps to see if it is a prime number:
>>>>
>>>> A prime number is a natural number greater than 1 that is not a
>>>> product of two smaller natural numbers.
>>> We've hit a bit of a road-block rather sooner that I had expected.
>>> First off, there's no need to define what a prime number is. If at some
>>> point it turns out that your readers do not know, go ahead and define
>>> it, but it's too widely understood by comp.theory readers to bother
>>> about.
>>> But writing (as I think you are suggesting)
>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>> prime number
>>> is not really adequate. There are two 'it'. To what do they refer?
>>
>> You told me to make sure that I do not provide an algorithm.
>
> Yes, that good. You didn't.
>
> Now, to what do the two 'it's refer?
>
>> This is somewhat algorithmic:
>
> No, no. The non-algorithmic way is best. You should be able to
> specific what a computation does even when yo have no idea how to write
> the an algorithm to do it. Sometimes there isn't ad algorithm!
>
>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>> be a prime number.
>>> Can you see how you (a) make it shorter, (b) make it clearer?
>
> My reply has three questions in it (depending on how you count) but you
> didn't answer any of them. This will only work if you try to answer
> these questions. Sometimes the answer will be "I don't know what you
> mean", but that's a perfectly good answer.
>

Anything besides the bare function name is somewhat algorithmic so what
you are asking for seems impossible.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<t2f6sn$jp7$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
Date: Mon, 4 Apr 2022 10:37:41 -0600
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 by: André G. Isaak - Mon, 4 Apr 2022 16:37 UTC

On 2022-04-04 10:27, olcott wrote:

> Anything besides the bare function name is somewhat algorithmic so what
> you are asking for seems impossible.

Why do you need a 'bare function name' at all? What's wrong with plain,
ordinary, English expressions like 'p is prime number' as opposed to
undefined 'bare function names' like Is-Prime-Number(p)?

You claimed my earlier post 'made progress', but you don't seem willing
to actually incorporate that into your answer.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<0P2dnWG47MDhvdb_nZ2dnUU7_8xh4p2d@giganews.com>

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 by: olcott - Mon, 4 Apr 2022 16:44 UTC

On 4/4/2022 11:37 AM, André G. Isaak wrote:
> On 2022-04-04 10:27, olcott wrote:
>
>> Anything besides the bare function name is somewhat algorithmic so
>> what you are asking for seems impossible.
>
> Why do you need a 'bare function name' at all? What's wrong with plain,
> ordinary, English expressions like 'p is prime number'

That makes sense.

> as opposed to
> undefined 'bare function names' like Is-Prime-Number(p)?
>
> You claimed my earlier post 'made progress', but you don't seem willing
> to actually incorporate that into your answer.
>
> André
>

My dialogue with you is not the same dialogue as my Dialogue with Ben.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<877d847hkd.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]
Date: Mon, 04 Apr 2022 20:51:46 +0100
Organization: A noiseless patient Spider
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 by: Ben Bacarisse - Mon, 4 Apr 2022 19:51 UTC

olcott <NoOne@NoWhere.com> writes:

> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>
>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>
>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>> dressing the definition up with a formal-looking name is just
>>>>>> superficial.
>>>>>
>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>
>>>>> A prime number is a natural number greater than 1 that is not a
>>>>> product of two smaller natural numbers.
>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>> First off, there's no need to define what a prime number is. If at some
>>>> point it turns out that your readers do not know, go ahead and define
>>>> it, but it's too widely understood by comp.theory readers to bother
>>>> about.
>>>> But writing (as I think you are suggesting)
>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>> prime number
>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>
>>> You told me to make sure that I do not provide an algorithm.
>> Yes, that good. You didn't.
>> Now, to what do the two 'it's refer?

OK, maybe things have gone too far already, but why are you ignoring my
questions? Your phrase used 'it' twice. What did you intend to refer
to by these two pronouns? It was not an idle question. I think when
you answer it, at least one problem will become clear.

>>> This is somewhat algorithmic:
>> No, no. The non-algorithmic way is best. You should be able to
>> specific what a computation does even when yo have no idea how to write
>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>
>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>> be a prime number.
>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>> My reply has three questions in it (depending on how you count) but you
>> didn't answer any of them. This will only work if you try to answer
>> these questions. Sometimes the answer will be "I don't know what you
>> mean", but that's a perfectly good answer.
>
> Anything besides the bare function name is somewhat algorithmic so
> what you are asking for seems impossible.

Here's a supporting exercise. Write down at least half a dozen strings
that might be passed to P. At least one of them should be a string that
P must accept and at least one must be a string the P should reject, but
you should say, for each one, whether P accepts of rejects it.

Be prepared for me to raise questions about what the strings represent.
It's easy to assume conventions from everyday life that should be stated
explicitly. You must have come across this in software: "the manual
said the input should be a number but it went wrong for सहस्र."

Finally, don't fuss about the prime bit. Just use the word prime.
Everyone one knows what it means. The key thing here is to state /what/
must be prime for P to correctly accept a string.

--
Ben.

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<UeadnWsKI5oqzNb_nZ2dnUU7_83NnZ2d@giganews.com>

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 by: olcott - Mon, 4 Apr 2022 20:14 UTC

On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>
>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>
>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>> superficial.
>>>>>>
>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>
>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>> product of two smaller natural numbers.
>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>> First off, there's no need to define what a prime number is. If at some
>>>>> point it turns out that your readers do not know, go ahead and define
>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>> about.
>>>>> But writing (as I think you are suggesting)
>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>> prime number
>>>>> is not really adequate. There are two 'it'. To what do they refer?

The TM determines that S is a prime number.

>>>>
>>>> You told me to make sure that I do not provide an algorithm.
>>> Yes, that good. You didn't.
>>> Now, to what do the two 'it's refer?
>
> OK, maybe things have gone too far already, but why are you ignoring my
> questions? Your phrase used 'it' twice. What did you intend to refer
> to by these two pronouns? It was not an idle question. I think when
> you answer it, at least one problem will become clear.
>

Andre thought that you were simply looking for English:
"p is a prime number"

>>>> This is somewhat algorithmic:
>>> No, no. The non-algorithmic way is best. You should be able to
>>> specific what a computation does even when yo have no idea how to write
>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>
>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>> be a prime number.
>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>> My reply has three questions in it (depending on how you count) but you
>>> didn't answer any of them. This will only work if you try to answer
>>> these questions. Sometimes the answer will be "I don't know what you
>>> mean", but that's a perfectly good answer.
>>
>> Anything besides the bare function name is somewhat algorithmic so
>> what you are asking for seems impossible.
>
> Here's a supporting exercise. Write down at least half a dozen strings
> that might be passed to P. At least one of them should be a string that
> P must accept and at least one must be a string the P should reject, but
> you should say, for each one, whether P accepts of rejects it.
>

(is prime?)
1 yes
2 no
3 yes
4 no
5 yes
6 no

> Be prepared for me to raise questions about what the strings represent.
> It's easy to assume conventions from everyday life that should be stated
> explicitly. You must have come across this in software: "the manual
> said the input should be a number but it went wrong for सहस्र."
>
> Finally, don't fuss about the prime bit. Just use the word prime.
> Everyone one knows what it means. The key thing here is to state /what/
> must be prime for P to correctly accept a string.
>

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<t2fjog$1vec$1@gioia.aioe.org>

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
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 by: Python - Mon, 4 Apr 2022 20:17 UTC

Incredible crank Peter Olcott wrote:
> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>
>>>>>>>>>> It might be time to skip ahead because the next exercise is to
>>>>>>>>>> do the
>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
>>>>>>>>>> number.  Can
>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>          P.q0 ??? ⊦* P.qy    if ???
>>>>>>>>>>          P.q0 ??? ⊦* P.qn    otherwise.
>>>>>>>>>> (The three ??? won't all be the same things.)  Any idea how to
>>>>>>>>>> flesh
>>>>>>>>>> this out?  If you can, you will be able to do it for E very
>>>>>>>>>> easily too.
>>>>>>>>>
>>>>>>>>> P.q0 S ⊦* P.qy    if Is-Prime-Number(S)
>>>>>>>>> P.q0 S ⊦* P.qn    otherwise.
>>>>>>>> That's getting close.  We know, from how the notation works,
>>>>>>>> that S is a
>>>>>>>> string of symbols in the TM's alphabet.  But writing
>>>>>>>> Is-Prime-Number(S)
>>>>>>>> suggests that is not natural language.  That's a very hard route
>>>>>>>> to go
>>>>>>>> down.  I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>> Defining it symbolically is messy and if the definition is /not/
>>>>>>>> formal,
>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>> superficial.
>>>>>>>
>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>
>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>> product of two smaller natural numbers.
>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>> First off, there's no need to define what a prime number is.  If
>>>>>> at some
>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>> about.
>>>>>> But writing (as I think you are suggesting)
>>>>>>      P.q0 S ⊦* P.qy    it goes through some tedious steps to see
>>>>>> if it is a
>>>>>>                        prime number
>>>>>> is not really adequate.  There are two 'it'.  To what do they refer?
>
> The TM determines that S is a prime number.
>
>>>>>
>>>>> You told me to make sure that I do not provide an algorithm.
>>>> Yes, that good.  You didn't.
>>>> Now, to what do the two 'it's refer?
>>
>> OK, maybe things have gone too far already, but why are you ignoring my
>> questions?  Your phrase used 'it' twice.  What did you intend to refer
>> to by these two pronouns?  It was not an idle question.  I think when
>> you answer it, at least one problem will become clear.
>>
>
> Andre thought that you were simply looking for English:
> "p is a prime number"
>
>>>>> This is somewhat algorithmic:
>>>> No, no.  The non-algorithmic way is best.  You should be able to
>>>> specific what a computation does even when yo have no idea how to write
>>>> the an algorithm to do it.  Sometimes there isn't ad algorithm!
>>>>
>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
>>>>>> there to
>>>>>> be a prime number.
>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>> My reply has three questions in it (depending on how you count) but you
>>>> didn't answer any of them.  This will only work if you try to answer
>>>> these questions.  Sometimes the answer will be "I don't know what you
>>>> mean", but that's a perfectly good answer.
>>>
>>> Anything besides the bare function name is somewhat algorithmic so
>>> what you are asking for seems impossible.
>>
>> Here's a supporting exercise.  Write down at least half a dozen strings
>> that might be passed to P.  At least one of them should be a string that
>> P must accept and at least one must be a string the P should reject, but
>> you should say, for each one, whether P accepts of rejects it.
>>
>
>
> (is prime?)
> 1 yes
> 2 no
> 3 yes
> 4 no
> 5 yes
> 6 no

Can I bring popcorn?

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<QIadnYCjduZ6y9b_nZ2dnUU7_81g4p2d@giganews.com>

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 by: olcott - Mon, 4 Apr 2022 20:36 UTC

On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>
>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>
>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>> superficial.
>>>>>>
>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>
>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>> product of two smaller natural numbers.
>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>> First off, there's no need to define what a prime number is. If at some
>>>>> point it turns out that your readers do not know, go ahead and define
>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>> about.
>>>>> But writing (as I think you are suggesting)
>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>> prime number
>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>
>>>> You told me to make sure that I do not provide an algorithm.
>>> Yes, that good. You didn't.
>>> Now, to what do the two 'it's refer?
>
> OK, maybe things have gone too far already, but why are you ignoring my
> questions? Your phrase used 'it' twice. What did you intend to refer
> to by these two pronouns? It was not an idle question. I think when
> you answer it, at least one problem will become clear.
>
>>>> This is somewhat algorithmic:
>>> No, no. The non-algorithmic way is best. You should be able to
>>> specific what a computation does even when yo have no idea how to write
>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>
>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>> be a prime number.
>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>> My reply has three questions in it (depending on how you count) but you
>>> didn't answer any of them. This will only work if you try to answer
>>> these questions. Sometimes the answer will be "I don't know what you
>>> mean", but that's a perfectly good answer.
>>
>> Anything besides the bare function name is somewhat algorithmic so
>> what you are asking for seems impossible.
>
> Here's a supporting exercise. Write down at least half a dozen strings
> that might be passed to P. At least one of them should be a string that
> P must accept and at least one must be a string the P should reject, but
> you should say, for each one, whether P accepts of rejects it.
>
> Be prepared for me to raise questions about what the strings represent.
> It's easy to assume conventions from everyday life that should be stated
> explicitly. You must have come across this in software: "the manual
> said the input should be a number but it went wrong for सहस्र."
>
> Finally, don't fuss about the prime bit. Just use the word prime.
> Everyone one knows what it means. The key thing here is to state /what/
> must be prime for P to correctly accept a string.
>

I am estimating that we will finally achieve closure on this.
Creating a common language between us will achieve the basis for mutual
understanding.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Mon, 4 Apr 2022 20:47 UTC

On 4/4/2022 3:36 PM, olcott wrote:
> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>
>>>>>>>>>> It might be time to skip ahead because the next exercise is to
>>>>>>>>>> do the
>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
>>>>>>>>>> number.  Can
>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>          P.q0 ??? ⊦* P.qy    if ???
>>>>>>>>>>          P.q0 ??? ⊦* P.qn    otherwise.
>>>>>>>>>> (The three ??? won't all be the same things.)  Any idea how to
>>>>>>>>>> flesh
>>>>>>>>>> this out?  If you can, you will be able to do it for E very
>>>>>>>>>> easily too.
>>>>>>>>>
>>>>>>>>> P.q0 S ⊦* P.qy    if Is-Prime-Number(S)
>>>>>>>>> P.q0 S ⊦* P.qn    otherwise.
>>>>>>>> That's getting close.  We know, from how the notation works,
>>>>>>>> that S is a
>>>>>>>> string of symbols in the TM's alphabet.  But writing
>>>>>>>> Is-Prime-Number(S)
>>>>>>>> suggests that is not natural language.  That's a very hard route
>>>>>>>> to go
>>>>>>>> down.  I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>> Defining it symbolically is messy and if the definition is /not/
>>>>>>>> formal,
>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>> superficial.
>>>>>>>
>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>
>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>> product of two smaller natural numbers.
>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>> First off, there's no need to define what a prime number is.  If
>>>>>> at some
>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>> about.
>>>>>> But writing (as I think you are suggesting)
>>>>>>      P.q0 S ⊦* P.qy    it goes through some tedious steps to see
>>>>>> if it is a
>>>>>>                        prime number
>>>>>> is not really adequate.  There are two 'it'.  To what do they refer?
>>>>>
>>>>> You told me to make sure that I do not provide an algorithm.
>>>> Yes, that good.  You didn't.
>>>> Now, to what do the two 'it's refer?
>>
>> OK, maybe things have gone too far already, but why are you ignoring my
>> questions?  Your phrase used 'it' twice.  What did you intend to refer
>> to by these two pronouns?  It was not an idle question.  I think when
>> you answer it, at least one problem will become clear.
>>
>>>>> This is somewhat algorithmic:
>>>> No, no.  The non-algorithmic way is best.  You should be able to
>>>> specific what a computation does even when yo have no idea how to write
>>>> the an algorithm to do it.  Sometimes there isn't ad algorithm!
>>>>
>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
>>>>>> there to
>>>>>> be a prime number.
>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>> My reply has three questions in it (depending on how you count) but you
>>>> didn't answer any of them.  This will only work if you try to answer
>>>> these questions.  Sometimes the answer will be "I don't know what you
>>>> mean", but that's a perfectly good answer.
>>>
>>> Anything besides the bare function name is somewhat algorithmic so
>>> what you are asking for seems impossible.
>>
>> Here's a supporting exercise.  Write down at least half a dozen strings
>> that might be passed to P.  At least one of them should be a string that
>> P must accept and at least one must be a string the P should reject, but
>> you should say, for each one, whether P accepts of rejects it.
>>
>> Be prepared for me to raise questions about what the strings represent.
>> It's easy to assume conventions from everyday life that should be stated
>> explicitly.  You must have come across this in software: "the manual
>> said the input should be a number but it went wrong for सहस्र."
>>
>> Finally, don't fuss about the prime bit.  Just use the word prime.
>> Everyone one knows what it means.  The key thing here is to state /what/
>> must be prime for P to correctly accept a string.
>>
>
> I am estimating that we will finally achieve closure on this.
> Creating a common language between us will achieve the basis for mutual
> understanding.
>

The process that we are doing looks like it will be effective on the
basis of eliminating all hidden assumptions.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<1995ece1-8094-442d-b82d-a0a2563653f2n@googlegroups.com>

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
From: wyni...@gmail.com (wij)
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 by: wij - Mon, 4 Apr 2022 22:23 UTC

On Tuesday, 5 April 2022 at 04:47:42 UTC+8, olcott wrote:
> On 4/4/2022 3:36 PM, olcott wrote:
> > On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
> >> olcott <No...@NoWhere.com> writes:
> >>
> >>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
> >>>> olcott <No...@NoWhere.com> writes:
> >>>>
> >>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
> >>>>>> olcott <No...@NoWhere.com> writes:
> >>>>>>
> >>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
> >>>>>>>> olcott <No...@NoWhere.com> writes:
> >>>>>>>>
> >>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
> >>>>>>>>
> >>>>>>>>>> It might be time to skip ahead because the next exercise is to
> >>>>>>>>>> do the
> >>>>>>>>>> same for P, a TM that decides if a string encodes a prime
> >>>>>>>>>> number. Can
> >>>>>>>>>> you think of how to specify that without giving an algorithm?
> >>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
> >>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
> >>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to
> >>>>>>>>>> flesh
> >>>>>>>>>> this out? If you can, you will be able to do it for E very
> >>>>>>>>>> easily too.
> >>>>>>>>>
> >>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
> >>>>>>>>> P.q0 S ⊦* P.qn otherwise.
> >>>>>>>> That's getting close. We know, from how the notation works,
> >>>>>>>> that S is a
> >>>>>>>> string of symbols in the TM's alphabet. But writing
> >>>>>>>> Is-Prime-Number(S)
> >>>>>>>> suggests that is not natural language. That's a very hard route
> >>>>>>>> to go
> >>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number..
> >>>>>>>> Defining it symbolically is messy and if the definition is /not/
> >>>>>>>> formal,
> >>>>>>>> dressing the definition up with a formal-looking name is just
> >>>>>>>> superficial.
> >>>>>>>
> >>>>>>> It goes through some tedious steps to see if it is a prime number:
> >>>>>>>
> >>>>>>> A prime number is a natural number greater than 1 that is not a
> >>>>>>> product of two smaller natural numbers.
> >>>>>> We've hit a bit of a road-block rather sooner that I had expected.
> >>>>>> First off, there's no need to define what a prime number is. If
> >>>>>> at some
> >>>>>> point it turns out that your readers do not know, go ahead and define
> >>>>>> it, but it's too widely understood by comp.theory readers to bother
> >>>>>> about.
> >>>>>> But writing (as I think you are suggesting)
> >>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see
> >>>>>> if it is a
> >>>>>> prime number
> >>>>>> is not really adequate. There are two 'it'. To what do they refer?
> >>>>>
> >>>>> You told me to make sure that I do not provide an algorithm.
> >>>> Yes, that good. You didn't.
> >>>> Now, to what do the two 'it's refer?
> >>
> >> OK, maybe things have gone too far already, but why are you ignoring my
> >> questions? Your phrase used 'it' twice. What did you intend to refer
> >> to by these two pronouns? It was not an idle question. I think when
> >> you answer it, at least one problem will become clear.
> >>
> >>>>> This is somewhat algorithmic:
> >>>> No, no. The non-algorithmic way is best. You should be able to
> >>>> specific what a computation does even when yo have no idea how to write
> >>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
> >>>>
> >>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
> >>>>>> there to
> >>>>>> be a prime number.
> >>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
> >>>> My reply has three questions in it (depending on how you count) but you
> >>>> didn't answer any of them. This will only work if you try to answer
> >>>> these questions. Sometimes the answer will be "I don't know what you
> >>>> mean", but that's a perfectly good answer.
> >>>
> >>> Anything besides the bare function name is somewhat algorithmic so
> >>> what you are asking for seems impossible.
> >>
> >> Here's a supporting exercise. Write down at least half a dozen strings
> >> that might be passed to P. At least one of them should be a string that
> >> P must accept and at least one must be a string the P should reject, but
> >> you should say, for each one, whether P accepts of rejects it.
> >>
> >> Be prepared for me to raise questions about what the strings represent..
> >> It's easy to assume conventions from everyday life that should be stated
> >> explicitly. You must have come across this in software: "the manual
> >> said the input should be a number but it went wrong for सहस्र."
> >>
> >> Finally, don't fuss about the prime bit. Just use the word prime.
> >> Everyone one knows what it means. The key thing here is to state /what/
> >> must be prime for P to correctly accept a string.
> >>
> >
> > I am estimating that we will finally achieve closure on this.
> > Creating a common language between us will achieve the basis for mutual
> > understanding.
> >
> The process that we are doing looks like it will be effective on the
> basis of eliminating all hidden assumptions.
> --
> Copyright 2022 Pete Olcott
>
> "Talent hits a target no one else can hit;
> Genius hits a target no one else can see."
> Arthur Schopenhauer

No use. Even all the people you find agree with you is still useless. To claim
you solved the HP problem, you have to show ALL your H first. People cannot
judge or teach 'claims'. But your P already showed wrong, no need to publish H.

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<xvGdnTDk_8tm7Nb_nZ2dnUU7_8zNnZ2d@giganews.com>

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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Mon, 4 Apr 2022 22:32 UTC

On 4/4/2022 5:23 PM, wij wrote:
> On Tuesday, 5 April 2022 at 04:47:42 UTC+8, olcott wrote:
>> On 4/4/2022 3:36 PM, olcott wrote:
>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>> olcott <No...@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>>
>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>
>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to
>>>>>>>>>>>> do the
>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
>>>>>>>>>>>> number. Can
>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to
>>>>>>>>>>>> flesh
>>>>>>>>>>>> this out? If you can, you will be able to do it for E very
>>>>>>>>>>>> easily too.
>>>>>>>>>>>
>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>> That's getting close. We know, from how the notation works,
>>>>>>>>>> that S is a
>>>>>>>>>> string of symbols in the TM's alphabet. But writing
>>>>>>>>>> Is-Prime-Number(S)
>>>>>>>>>> suggests that is not natural language. That's a very hard route
>>>>>>>>>> to go
>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/
>>>>>>>>>> formal,
>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>> superficial.
>>>>>>>>>
>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>
>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>> product of two smaller natural numbers.
>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>> First off, there's no need to define what a prime number is. If
>>>>>>>> at some
>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>> about.
>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see
>>>>>>>> if it is a
>>>>>>>> prime number
>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>>>>
>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>> Yes, that good. You didn't.
>>>>>> Now, to what do the two 'it's refer?
>>>>
>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>> to by these two pronouns? It was not an idle question. I think when
>>>> you answer it, at least one problem will become clear.
>>>>
>>>>>>> This is somewhat algorithmic:
>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>
>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
>>>>>>>> there to
>>>>>>>> be a prime number.
>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>> mean", but that's a perfectly good answer.
>>>>>
>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>> what you are asking for seems impossible.
>>>>
>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>> that might be passed to P. At least one of them should be a string that
>>>> P must accept and at least one must be a string the P should reject, but
>>>> you should say, for each one, whether P accepts of rejects it.
>>>>
>>>> Be prepared for me to raise questions about what the strings represent.
>>>> It's easy to assume conventions from everyday life that should be stated
>>>> explicitly. You must have come across this in software: "the manual
>>>> said the input should be a number but it went wrong for सहस्र."
>>>>
>>>> Finally, don't fuss about the prime bit. Just use the word prime.
>>>> Everyone one knows what it means. The key thing here is to state /what/
>>>> must be prime for P to correctly accept a string.
>>>>
>>>
>>> I am estimating that we will finally achieve closure on this.
>>> Creating a common language between us will achieve the basis for mutual
>>> understanding.
>>>
>> The process that we are doing looks like it will be effective on the
>> basis of eliminating all hidden assumptions.
>> --
>> Copyright 2022 Pete Olcott
>>
>> "Talent hits a target no one else can hit;
>> Genius hits a target no one else can see."
>> Arthur Schopenhauer
>
> No use. Even all the people you find agree with you is still useless. To claim
> you solved the HP problem, you have to show ALL your H first. People cannot
> judge or teach 'claims'. But your P already showed wrong, no need to publish H.

My analysis is based on this model: If "an X is a Y" and Z says that "an
X is a Y" then anything in the universe that disagrees is necessarily
incorrect.

"an X is a Y" =
The input to embedded_H specifies a non-halting sequence of
configurations. (input is non-halting)

Z says that "an X is a Y" =
embedded_H rejects its input.

If you can think of a case where
"an X is a Y" is simultaneously true and false then you have a rebuttal,
otherwise not so much.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
From: wyni...@gmail.com (wij)
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 by: wij - Mon, 4 Apr 2022 22:41 UTC

On Tuesday, 5 April 2022 at 06:32:34 UTC+8, olcott wrote:
> On 4/4/2022 5:23 PM, wij wrote:
> > On Tuesday, 5 April 2022 at 04:47:42 UTC+8, olcott wrote:
> >> On 4/4/2022 3:36 PM, olcott wrote:
> >>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
> >>>> olcott <No...@NoWhere.com> writes:
> >>>>
> >>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
> >>>>>> olcott <No...@NoWhere.com> writes:
> >>>>>>
> >>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
> >>>>>>>> olcott <No...@NoWhere.com> writes:
> >>>>>>>>
> >>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
> >>>>>>>>>> olcott <No...@NoWhere.com> writes:
> >>>>>>>>>>
> >>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
> >>>>>>>>>>
> >>>>>>>>>>>> It might be time to skip ahead because the next exercise is to
> >>>>>>>>>>>> do the
> >>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
> >>>>>>>>>>>> number. Can
> >>>>>>>>>>>> you think of how to specify that without giving an algorithm?
> >>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
> >>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
> >>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to
> >>>>>>>>>>>> flesh
> >>>>>>>>>>>> this out? If you can, you will be able to do it for E very
> >>>>>>>>>>>> easily too.
> >>>>>>>>>>>
> >>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
> >>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
> >>>>>>>>>> That's getting close. We know, from how the notation works,
> >>>>>>>>>> that S is a
> >>>>>>>>>> string of symbols in the TM's alphabet. But writing
> >>>>>>>>>> Is-Prime-Number(S)
> >>>>>>>>>> suggests that is not natural language. That's a very hard route
> >>>>>>>>>> to go
> >>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
> >>>>>>>>>> Defining it symbolically is messy and if the definition is /not/
> >>>>>>>>>> formal,
> >>>>>>>>>> dressing the definition up with a formal-looking name is just
> >>>>>>>>>> superficial.
> >>>>>>>>>
> >>>>>>>>> It goes through some tedious steps to see if it is a prime number:
> >>>>>>>>>
> >>>>>>>>> A prime number is a natural number greater than 1 that is not a
> >>>>>>>>> product of two smaller natural numbers.
> >>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
> >>>>>>>> First off, there's no need to define what a prime number is. If
> >>>>>>>> at some
> >>>>>>>> point it turns out that your readers do not know, go ahead and define
> >>>>>>>> it, but it's too widely understood by comp.theory readers to bother
> >>>>>>>> about.
> >>>>>>>> But writing (as I think you are suggesting)
> >>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see
> >>>>>>>> if it is a
> >>>>>>>> prime number
> >>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
> >>>>>>>
> >>>>>>> You told me to make sure that I do not provide an algorithm.
> >>>>>> Yes, that good. You didn't.
> >>>>>> Now, to what do the two 'it's refer?
> >>>>
> >>>> OK, maybe things have gone too far already, but why are you ignoring my
> >>>> questions? Your phrase used 'it' twice. What did you intend to refer
> >>>> to by these two pronouns? It was not an idle question. I think when
> >>>> you answer it, at least one problem will become clear.
> >>>>
> >>>>>>> This is somewhat algorithmic:
> >>>>>> No, no. The non-algorithmic way is best. You should be able to
> >>>>>> specific what a computation does even when yo have no idea how to write
> >>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
> >>>>>>
> >>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
> >>>>>>>> there to
> >>>>>>>> be a prime number.
> >>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
> >>>>>> My reply has three questions in it (depending on how you count) but you
> >>>>>> didn't answer any of them. This will only work if you try to answer
> >>>>>> these questions. Sometimes the answer will be "I don't know what you
> >>>>>> mean", but that's a perfectly good answer.
> >>>>>
> >>>>> Anything besides the bare function name is somewhat algorithmic so
> >>>>> what you are asking for seems impossible.
> >>>>
> >>>> Here's a supporting exercise. Write down at least half a dozen strings
> >>>> that might be passed to P. At least one of them should be a string that
> >>>> P must accept and at least one must be a string the P should reject, but
> >>>> you should say, for each one, whether P accepts of rejects it.
> >>>>
> >>>> Be prepared for me to raise questions about what the strings represent.
> >>>> It's easy to assume conventions from everyday life that should be stated
> >>>> explicitly. You must have come across this in software: "the manual
> >>>> said the input should be a number but it went wrong for सहस्र."
> >>>>
> >>>> Finally, don't fuss about the prime bit. Just use the word prime.
> >>>> Everyone one knows what it means. The key thing here is to state /what/
> >>>> must be prime for P to correctly accept a string.
> >>>>
> >>>
> >>> I am estimating that we will finally achieve closure on this.
> >>> Creating a common language between us will achieve the basis for mutual
> >>> understanding.
> >>>
> >> The process that we are doing looks like it will be effective on the
> >> basis of eliminating all hidden assumptions.
> >> --
> >> Copyright 2022 Pete Olcott
> >>
> >> "Talent hits a target no one else can hit;
> >> Genius hits a target no one else can see."
> >> Arthur Schopenhauer
> >
> > No use. Even all the people you find agree with you is still useless. To claim
> > you solved the HP problem, you have to show ALL your H first. People cannot
> > judge or teach 'claims'. But your P already showed wrong, no need to publish H.
> My analysis is based on this model: If "an X is a Y" and Z says that "an
> X is a Y" then anything in the universe that disagrees is necessarily
> incorrect.
>
> "an X is a Y" =
> The input to embedded_H specifies a non-halting sequence of
> configurations. (input is non-halting)
>
> Z says that "an X is a Y" =
> embedded_H rejects its input.
>
> If you can think of a case where
> "an X is a Y" is simultaneously true and false then you have a rebuttal,
> otherwise not so much.
> --
> Copyright 2022 Pete Olcott
>
> "Talent hits a target no one else can hit;
> Genius hits a target no one else can see."
> Arthur Schopenhauer


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Mon, 4 Apr 2022 22:53 UTC

On 4/4/2022 5:41 PM, wij wrote:
> On Tuesday, 5 April 2022 at 06:32:34 UTC+8, olcott wrote:
>> On 4/4/2022 5:23 PM, wij wrote:
>>> On Tuesday, 5 April 2022 at 04:47:42 UTC+8, olcott wrote:
>>>> On 4/4/2022 3:36 PM, olcott wrote:
>>>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>>
>>>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to
>>>>>>>>>>>>>> do the
>>>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
>>>>>>>>>>>>>> number. Can
>>>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to
>>>>>>>>>>>>>> flesh
>>>>>>>>>>>>>> this out? If you can, you will be able to do it for E very
>>>>>>>>>>>>>> easily too.
>>>>>>>>>>>>>
>>>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>>>> That's getting close. We know, from how the notation works,
>>>>>>>>>>>> that S is a
>>>>>>>>>>>> string of symbols in the TM's alphabet. But writing
>>>>>>>>>>>> Is-Prime-Number(S)
>>>>>>>>>>>> suggests that is not natural language. That's a very hard route
>>>>>>>>>>>> to go
>>>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/
>>>>>>>>>>>> formal,
>>>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>>>> superficial.
>>>>>>>>>>>
>>>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>>>
>>>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>>>> product of two smaller natural numbers.
>>>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>>>> First off, there's no need to define what a prime number is. If
>>>>>>>>>> at some
>>>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>>>> about.
>>>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see
>>>>>>>>>> if it is a
>>>>>>>>>> prime number
>>>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>>>>>>
>>>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>>>> Yes, that good. You didn't.
>>>>>>>> Now, to what do the two 'it's refer?
>>>>>>
>>>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>>>> to by these two pronouns? It was not an idle question. I think when
>>>>>> you answer it, at least one problem will become clear.
>>>>>>
>>>>>>>>> This is somewhat algorithmic:
>>>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>>>
>>>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
>>>>>>>>>> there to
>>>>>>>>>> be a prime number.
>>>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>>>> mean", but that's a perfectly good answer.
>>>>>>>
>>>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>>>> what you are asking for seems impossible.
>>>>>>
>>>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>>>> that might be passed to P. At least one of them should be a string that
>>>>>> P must accept and at least one must be a string the P should reject, but
>>>>>> you should say, for each one, whether P accepts of rejects it.
>>>>>>
>>>>>> Be prepared for me to raise questions about what the strings represent.
>>>>>> It's easy to assume conventions from everyday life that should be stated
>>>>>> explicitly. You must have come across this in software: "the manual
>>>>>> said the input should be a number but it went wrong for सहस्र."
>>>>>>
>>>>>> Finally, don't fuss about the prime bit. Just use the word prime.
>>>>>> Everyone one knows what it means. The key thing here is to state /what/
>>>>>> must be prime for P to correctly accept a string.
>>>>>>
>>>>>
>>>>> I am estimating that we will finally achieve closure on this.
>>>>> Creating a common language between us will achieve the basis for mutual
>>>>> understanding.
>>>>>
>>>> The process that we are doing looks like it will be effective on the
>>>> basis of eliminating all hidden assumptions.
>>>> --
>>>> Copyright 2022 Pete Olcott
>>>>
>>>> "Talent hits a target no one else can hit;
>>>> Genius hits a target no one else can see."
>>>> Arthur Schopenhauer
>>>
>>> No use. Even all the people you find agree with you is still useless. To claim
>>> you solved the HP problem, you have to show ALL your H first. People cannot
>>> judge or teach 'claims'. But your P already showed wrong, no need to publish H.
>> My analysis is based on this model: If "an X is a Y" and Z says that "an
>> X is a Y" then anything in the universe that disagrees is necessarily
>> incorrect.
>>
>> "an X is a Y" =
>> The input to embedded_H specifies a non-halting sequence of
>> configurations. (input is non-halting)
>>
>> Z says that "an X is a Y" =
>> embedded_H rejects its input.
>>
>> If you can think of a case where
>> "an X is a Y" is simultaneously true and false then you have a rebuttal,
>> otherwise not so much.
>> --
>> Copyright 2022 Pete Olcott
>>
>> "Talent hits a target no one else can hit;
>> Genius hits a target no one else can see."
>> Arthur Schopenhauer
>
> You simply do not have H. What you say? If you say yes, then show it to prove.


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 4 Apr 2022 23:09 UTC

On 4/4/22 6:32 PM, olcott wrote:
> On 4/4/2022 5:23 PM, wij wrote:
>> On Tuesday, 5 April 2022 at 04:47:42 UTC+8, olcott wrote:
>>> On 4/4/2022 3:36 PM, olcott wrote:
>>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>>> olcott <No...@NoWhere.com> writes:
>>>>>
>>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>>>
>>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>>
>>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to
>>>>>>>>>>>>> do the
>>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
>>>>>>>>>>>>> number.  Can
>>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>>>           P.q0 ??? ⊦* P.qy    if ???
>>>>>>>>>>>>>           P.q0 ??? ⊦* P.qn    otherwise.
>>>>>>>>>>>>> (The three ??? won't all be the same things.)  Any idea how to
>>>>>>>>>>>>> flesh
>>>>>>>>>>>>> this out?  If you can, you will be able to do it for E very
>>>>>>>>>>>>> easily too.
>>>>>>>>>>>>
>>>>>>>>>>>> P.q0 S ⊦* P.qy    if Is-Prime-Number(S)
>>>>>>>>>>>> P.q0 S ⊦* P.qn    otherwise.
>>>>>>>>>>> That's getting close.  We know, from how the notation works,
>>>>>>>>>>> that S is a
>>>>>>>>>>> string of symbols in the TM's alphabet.  But writing
>>>>>>>>>>> Is-Prime-Number(S)
>>>>>>>>>>> suggests that is not natural language.  That's a very hard route
>>>>>>>>>>> to go
>>>>>>>>>>> down.  I'd have to ask you for the definition of
>>>>>>>>>>> Is-Prime-Number.
>>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/
>>>>>>>>>>> formal,
>>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>>> superficial.
>>>>>>>>>>
>>>>>>>>>> It goes through some tedious steps to see if it is a prime
>>>>>>>>>> number:
>>>>>>>>>>
>>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>>> product of two smaller natural numbers.
>>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>>> First off, there's no need to define what a prime number is.  If
>>>>>>>>> at some
>>>>>>>>> point it turns out that your readers do not know, go ahead and
>>>>>>>>> define
>>>>>>>>> it, but it's too widely understood by comp.theory readers to
>>>>>>>>> bother
>>>>>>>>> about.
>>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>>>       P.q0 S ⊦* P.qy    it goes through some tedious steps to see
>>>>>>>>> if it is a
>>>>>>>>>                         prime number
>>>>>>>>> is not really adequate.  There are two 'it'.  To what do they
>>>>>>>>> refer?
>>>>>>>>
>>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>>> Yes, that good.  You didn't.
>>>>>>> Now, to what do the two 'it's refer?
>>>>>
>>>>> OK, maybe things have gone too far already, but why are you
>>>>> ignoring my
>>>>> questions?  Your phrase used 'it' twice.  What did you intend to refer
>>>>> to by these two pronouns?  It was not an idle question.  I think when
>>>>> you answer it, at least one problem will become clear.
>>>>>
>>>>>>>> This is somewhat algorithmic:
>>>>>>> No, no.  The non-algorithmic way is best.  You should be able to
>>>>>>> specific what a computation does even when yo have no idea how to
>>>>>>> write
>>>>>>> the an algorithm to do it.  Sometimes there isn't ad algorithm!
>>>>>>>
>>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
>>>>>>>>> there to
>>>>>>>>> be a prime number.
>>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>>> My reply has three questions in it (depending on how you count)
>>>>>>> but you
>>>>>>> didn't answer any of them.  This will only work if you try to answer
>>>>>>> these questions.  Sometimes the answer will be "I don't know what
>>>>>>> you
>>>>>>> mean", but that's a perfectly good answer.
>>>>>>
>>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>>> what you are asking for seems impossible.
>>>>>
>>>>> Here's a supporting exercise.  Write down at least half a dozen
>>>>> strings
>>>>> that might be passed to P.  At least one of them should be a string
>>>>> that
>>>>> P must accept and at least one must be a string the P should
>>>>> reject, but
>>>>> you should say, for each one, whether P accepts of rejects it.
>>>>>
>>>>> Be prepared for me to raise questions about what the strings
>>>>> represent.
>>>>> It's easy to assume conventions from everyday life that should be
>>>>> stated
>>>>> explicitly.  You must have come across this in software: "the manual
>>>>> said the input should be a number but it went wrong for सहस्र."
>>>>>
>>>>> Finally, don't fuss about the prime bit.  Just use the word prime.
>>>>> Everyone one knows what it means.  The key thing here is to state
>>>>> /what/
>>>>> must be prime for P to correctly accept a string.
>>>>>
>>>>
>>>> I am estimating that we will finally achieve closure on this.
>>>> Creating a common language between us will achieve the basis for mutual
>>>> understanding.
>>>>
>>> The process that we are doing looks like it will be effective on the
>>> basis of eliminating all hidden assumptions.
>>> --
>>> Copyright 2022 Pete Olcott
>>>
>>> "Talent hits a target no one else can hit;
>>> Genius hits a target no one else can see."
>>> Arthur Schopenhauer
>>
>> No use. Even all the people you find agree with you is still useless.
>> To claim
>> you solved the HP problem, you have to show ALL your H first. People
>> cannot
>> judge or teach 'claims'. But your P already showed wrong, no need to
>> publish H.
>
>
> My analysis is based on this model: If "an X is a Y" and Z says that "an
> X is a Y" then anything in the universe that disagrees is necessarily
> incorrect.

Unless Z also says that an A is a B when it isn't. That is the failicy
of proving by example.


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]
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 by: Ben Bacarisse - Mon, 4 Apr 2022 23:14 UTC

olcott <NoOne@NoWhere.com> writes:

> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>
>>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>>
>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>> superficial.
>>>>>>>
>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>
>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>> product of two smaller natural numbers.
>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>> First off, there's no need to define what a prime number is. If at some
>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>> about.
>>>>>> But writing (as I think you are suggesting)
>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>>> prime number
>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>
> The TM determines that S is a prime number.

Saying "P" rather than "the TM" is simpler. The first 'it' refers to
P. The second 'it' refers to the string S. But being prime is a
property of numbers not strings.

>>>>>
>>>>> You told me to make sure that I do not provide an algorithm.
>>>> Yes, that good. You didn't.
>>>> Now, to what do the two 'it's refer?
>>
>> OK, maybe things have gone too far already, but why are you ignoring my
>> questions? Your phrase used 'it' twice. What did you intend to refer
>> to by these two pronouns? It was not an idle question. I think when
>> you answer it, at least one problem will become clear.
>
> Andre thought that you were simply looking for English:
> "p is a prime number"

I didn't read that sub-thread.

>>>>> This is somewhat algorithmic:
>>>> No, no. The non-algorithmic way is best. You should be able to
>>>> specific what a computation does even when yo have no idea how to write
>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>
>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>>> be a prime number.
>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>> My reply has three questions in it (depending on how you count) but you
>>>> didn't answer any of them. This will only work if you try to answer
>>>> these questions. Sometimes the answer will be "I don't know what you
>>>> mean", but that's a perfectly good answer.
>>>
>>> Anything besides the bare function name is somewhat algorithmic so
>>> what you are asking for seems impossible.
>> Here's a supporting exercise. Write down at least half a dozen strings
>> that might be passed to P. At least one of them should be a string that
>> P must accept and at least one must be a string the P should reject, but
>> you should say, for each one, whether P accepts of rejects it.
>
> (is prime?)
> 1 yes
> 2 no

2 is prime, 1 is not. I'll assume this is a typo.

> 3 yes
> 4 no
> 5 yes
> 6 no

>> Be prepared for me to raise questions about what the strings
>> represent.

So what about the following strings:

0x11
IX
nineteen
1001
सहस्र

?

>> It's easy to assume conventions from everyday life that should be stated
>> explicitly. You must have come across this in software: "the manual
>> said the input should be a number but it went wrong for सहस्र."
>> Finally, don't fuss about the prime bit. Just use the word prime.
>> Everyone one knows what it means. The key thing here is to state /what/
>> must be prime for P to correctly accept a string.

You will need to find a way to describe what symbols can be in the
string and what the resulting strings mean.

Since this is taking way longer than I had thought, you can just ask me
how I'd do it and you can see if you agree or not.

--
Ben.

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Mon, 4 Apr 2022 23:29 UTC

On 4/4/2022 6:14 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>
>>>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>>>
>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>> superficial.
>>>>>>>>
>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>
>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>> product of two smaller natural numbers.
>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>> First off, there's no need to define what a prime number is. If at some
>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>> about.
>>>>>>> But writing (as I think you are suggesting)
>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>>>> prime number
>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>
>> The TM determines that S is a prime number.
>
> Saying "P" rather than "the TM" is simpler. The first 'it' refers to
> P. The second 'it' refers to the string S. But being prime is a
> property of numbers not strings.
>
>>>>>>
>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>> Yes, that good. You didn't.
>>>>> Now, to what do the two 'it's refer?
>>>
>>> OK, maybe things have gone too far already, but why are you ignoring my
>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>> to by these two pronouns? It was not an idle question. I think when
>>> you answer it, at least one problem will become clear.
>>
>> Andre thought that you were simply looking for English:
>> "p is a prime number"
>
> I didn't read that sub-thread.
>
>>>>>> This is somewhat algorithmic:
>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>> specific what a computation does even when yo have no idea how to write
>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>
>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>>>> be a prime number.
>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>> My reply has three questions in it (depending on how you count) but you
>>>>> didn't answer any of them. This will only work if you try to answer
>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>> mean", but that's a perfectly good answer.
>>>>
>>>> Anything besides the bare function name is somewhat algorithmic so
>>>> what you are asking for seems impossible.
>>> Here's a supporting exercise. Write down at least half a dozen strings
>>> that might be passed to P. At least one of them should be a string that
>>> P must accept and at least one must be a string the P should reject, but
>>> you should say, for each one, whether P accepts of rejects it.
>>
>> (is prime?)
>> 1 yes
>> 2 no
>
> 2 is prime, 1 is not. I'll assume this is a typo.
>
>> 3 yes
>> 4 no
>> 5 yes
>> 6 no
>
>>> Be prepared for me to raise questions about what the strings
>>> represent.
>
> So what about the following strings:
>
> 0x11
> IX
> nineteen
> 1001
> सहस्र
>
> ?

I would simply make tape elements UTF-32.

>
>>> It's easy to assume conventions from everyday life that should be stated
>>> explicitly. You must have come across this in software: "the manual
>>> said the input should be a number but it went wrong for सहस्र."
>>> Finally, don't fuss about the prime bit. Just use the word prime.
>>> Everyone one knows what it means. The key thing here is to state /what/
>>> must be prime for P to correctly accept a string.
>
> You will need to find a way to describe what symbols can be in the
> string and what the resulting strings mean.
>

The algorithm already does that.
The ultimate semantics of the data is the algorithm.

> Since this is taking way longer than I had thought, you can just ask me
> how I'd do it and you can see if you agree or not.
>

Anything that you think is best.
I think that we are finally on a path of full mutual dialogue.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<87lewk5otp.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=29414&group=comp.theory#29414

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]
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 by: Ben Bacarisse - Tue, 5 Apr 2022 00:57 UTC

olcott <NoOne@NoWhere.com> writes:

> On 4/4/2022 6:14 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>
>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>
>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>>>>
>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>> superficial.
>>>>>>>>>
>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>
>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>> product of two smaller natural numbers.
>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>> First off, there's no need to define what a prime number is. If at some
>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>> about.
>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>>>>> prime number
>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>
>>> The TM determines that S is a prime number.
>> Saying "P" rather than "the TM" is simpler. The first 'it' refers to
>> P. The second 'it' refers to the string S. But being prime is a
>> property of numbers not strings.
>>
>>>>>>>
>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>> Yes, that good. You didn't.
>>>>>> Now, to what do the two 'it's refer?
>>>>
>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>> to by these two pronouns? It was not an idle question. I think when
>>>> you answer it, at least one problem will become clear.
>>>
>>> Andre thought that you were simply looking for English:
>>> "p is a prime number"
>> I didn't read that sub-thread.
>>
>>>>>>> This is somewhat algorithmic:
>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>
>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>>>>> be a prime number.
>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>> mean", but that's a perfectly good answer.
>>>>>
>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>> what you are asking for seems impossible.
>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>> that might be passed to P. At least one of them should be a string that
>>>> P must accept and at least one must be a string the P should reject, but
>>>> you should say, for each one, whether P accepts of rejects it.
>>>
>>> (is prime?)
>>> 1 yes
>>> 2 no
>> 2 is prime, 1 is not. I'll assume this is a typo.
>>
>>> 3 yes
>>> 4 no
>>> 5 yes
>>> 6 no
>>
>>>> Be prepared for me to raise questions about what the strings
>>>> represent.
>> So what about the following strings:
>> 0x11
>> IX
>> nineteen
>> 1001
>> सहस्र
>> ?

You commented on only one of these.

> I would simply make tape elements UTF-32.

(1) UTF-32 (both of them!) are transfer encodings and TMs work on
abstract symbols. The encoding of the symbols is immaterial.

(2) You could define the tape alphabet to includes all Unicode symbols
but there is no point. You need no more the one symbol to represent any
number, so that would be adding unnecessary complexity.

Aside: TMs are often specified to operate on numbers in unary notation
because it is so simple. One is represented with a single symbol (any
symbol can be chosen) "X". Two by two of them "XX", three by three of
them "XXX" and so on.

>>>> It's easy to assume conventions from everyday life that should be stated
>>>> explicitly. You must have come across this in software: "the manual
>>>> said the input should be a number but it went wrong for सहस्र."
>>>> Finally, don't fuss about the prime bit. Just use the word prime.
>>>> Everyone one knows what it means. The key thing here is to state /what/
>>>> must be prime for P to correctly accept a string.
>> You will need to find a way to describe what symbols can be in the
>> string and what the resulting strings mean.
>>
>
> The algorithm already does that.
> The ultimate semantics of the data is the algorithm.

(1) How will you specify what's needed in those cases where you don't
know an algorithm to solve the problem?

(2) Algorithms are usually many orders of magnitude more complex than
specifications.

(3) Have you never specified the expected behaviour of function or
subroutine before? I thought your background was in software
engineering. A function is rarely specified by giving the algorithm.
Look up and standard C function and you'll find something like this:

NAME
sqrt, sqrtf, sqrtl - square root function

SYNOPSIS
#include <math.h>

double sqrt(double x);
float sqrtf(float x);
long double sqrtl(long double x);

DESCRIPTION
These functions return the nonnegative square root of x.

No algorithm in sight.

>> Since this is taking way longer than I had thought, you can just ask me
>> how I'd do it and you can see if you agree or not.
>
> Anything that you think is best.


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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 by: olcott - Tue, 5 Apr 2022 01:27 UTC

On 4/4/2022 7:57 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/4/2022 6:14 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>
>>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>>
>>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>>>>>
>>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>>> superficial.
>>>>>>>>>>
>>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>>
>>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>>> product of two smaller natural numbers.
>>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>>> First off, there's no need to define what a prime number is. If at some
>>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>>> about.
>>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>>>>>> prime number
>>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>
>>>> The TM determines that S is a prime number.
>>> Saying "P" rather than "the TM" is simpler. The first 'it' refers to
>>> P. The second 'it' refers to the string S. But being prime is a
>>> property of numbers not strings.
>>>
>>>>>>>>
>>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>>> Yes, that good. You didn't.
>>>>>>> Now, to what do the two 'it's refer?
>>>>>
>>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>>> to by these two pronouns? It was not an idle question. I think when
>>>>> you answer it, at least one problem will become clear.
>>>>
>>>> Andre thought that you were simply looking for English:
>>>> "p is a prime number"
>>> I didn't read that sub-thread.
>>>
>>>>>>>> This is somewhat algorithmic:
>>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>>
>>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>>>>>> be a prime number.
>>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>>> mean", but that's a perfectly good answer.
>>>>>>
>>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>>> what you are asking for seems impossible.
>>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>>> that might be passed to P. At least one of them should be a string that
>>>>> P must accept and at least one must be a string the P should reject, but
>>>>> you should say, for each one, whether P accepts of rejects it.
>>>>
>>>> (is prime?)
>>>> 1 yes
>>>> 2 no
>>> 2 is prime, 1 is not. I'll assume this is a typo.
>>>
>>>> 3 yes
>>>> 4 no
>>>> 5 yes
>>>> 6 no
>>>
>>>>> Be prepared for me to raise questions about what the strings
>>>>> represent.
>>> So what about the following strings:
>>> 0x11
>>> IX
>>> nineteen
>>> 1001
>>> सहस्र
>>> ?
>
> You commented on only one of these.
>
>> I would simply make tape elements UTF-32.
>
> (1) UTF-32 (both of them!) are transfer encodings and TMs work on
> abstract symbols. The encoding of the symbols is immaterial.
>
> (2) You could define the tape alphabet to includes all Unicode symbols
> but there is no point. You need no more the one symbol to represent any
> number, so that would be adding unnecessary complexity.
>

Less than two seems too counter-intuitive, thus cumbersome.
Complexity is not the size of the encoding it is the mental effort
required to achieve complete understanding.

> Aside: TMs are often specified to operate on numbers in unary notation
> because it is so simple.

The notation is simple making the algorithm more complex.

> One is represented with a single symbol (any
> symbol can be chosen) "X". Two by two of them "XX", three by three of
> them "XXX" and so on.
>

I looked that up recently.
End of string then needs to be two blanks not just one.

>>>>> It's easy to assume conventions from everyday life that should be stated
>>>>> explicitly. You must have come across this in software: "the manual
>>>>> said the input should be a number but it went wrong for सहस्र."
>>>>> Finally, don't fuss about the prime bit. Just use the word prime.
>>>>> Everyone one knows what it means. The key thing here is to state /what/
>>>>> must be prime for P to correctly accept a string.
>>> You will need to find a way to describe what symbols can be in the
>>> string and what the resulting strings mean.
>>>
>>
>> The algorithm already does that.
>> The ultimate semantics of the data is the algorithm.
>
> (1) How will you specify what's needed in those cases where you don't
> know an algorithm to solve the problem?
>


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<874k3761bq.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]
Date: Tue, 05 Apr 2022 15:40:09 +0100
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 by: Ben Bacarisse - Tue, 5 Apr 2022 14:40 UTC

olcott <NoOne@NoWhere.com> writes:

> On 4/4/2022 7:57 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 4/4/2022 6:14 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>
>>>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>>>>>>
>>>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>>>> superficial.
>>>>>>>>>>>
>>>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>>>
>>>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>>>> product of two smaller natural numbers.
>>>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>>>> First off, there's no need to define what a prime number is. If at some
>>>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>>>> about.
>>>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>>>>>>> prime number
>>>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>>
>>>>> The TM determines that S is a prime number.
>>>> Saying "P" rather than "the TM" is simpler. The first 'it' refers to
>>>> P. The second 'it' refers to the string S. But being prime is a
>>>> property of numbers not strings.
>>>>
>>>>>>>>>
>>>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>>>> Yes, that good. You didn't.
>>>>>>>> Now, to what do the two 'it's refer?
>>>>>>
>>>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>>>> to by these two pronouns? It was not an idle question. I think when
>>>>>> you answer it, at least one problem will become clear.
>>>>>
>>>>> Andre thought that you were simply looking for English:
>>>>> "p is a prime number"
>>>> I didn't read that sub-thread.
>>>>
>>>>>>>>> This is somewhat algorithmic:
>>>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>>>
>>>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>>>>>>> be a prime number.
>>>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>>>> mean", but that's a perfectly good answer.
>>>>>>>
>>>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>>>> what you are asking for seems impossible.
>>>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>>>> that might be passed to P. At least one of them should be a string that
>>>>>> P must accept and at least one must be a string the P should reject, but
>>>>>> you should say, for each one, whether P accepts of rejects it.
>>>>>
>>>>> (is prime?)
>>>>> 1 yes
>>>>> 2 no
>>>> 2 is prime, 1 is not. I'll assume this is a typo.
>>>>
>>>>> 3 yes
>>>>> 4 no
>>>>> 5 yes
>>>>> 6 no
>>>>
>>>>>> Be prepared for me to raise questions about what the strings
>>>>>> represent.
>>>> So what about the following strings:
>>>> 0x11
>>>> IX
>>>> nineteen
>>>> 1001
>>>> सहस्र
>>>> ?
>> You commented on only one of these.
>>
>>> I would simply make tape elements UTF-32.
>> (1) UTF-32 (both of them!) are transfer encodings and TMs work on
>> abstract symbols. The encoding of the symbols is immaterial.
>> (2) You could define the tape alphabet to includes all Unicode symbols
>> but there is no point. You need no more the one symbol to represent any
>> number, so that would be adding unnecessary complexity.
>
> Less than two seems too counter-intuitive, thus cumbersome.

But this is just because you have not yet written a TM. For many tasks,
unary makes the TM much simpler -- by an order of magnitude in many cases.

> Complexity is not the size of the encoding it is the mental effort
> required to achieve complete understanding.

For numerical problems there is less mental effort involved with unary.
That's why tally sticks can be found dating from the Palaeolithic.

>> Aside: TMs are often specified to operate on numbers in unary notation
>> because it is so simple.
>
> The notation is simple making the algorithm more complex.

No. This exercise will help you see why that is not true:

Write a TM that adds two numbers. The input will be strings of the
form {n}+{m} where {x} is the unary representation of x. The TM
should halt with only {n+m} on the tape.


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

<t2hsgu$mmd$1@gioia.aioe.org>

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From: anw...@cuboid.co.uk (Andy Walker)
Newsgroups: comp.theory
Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
key missing piece in dialogue ]
Date: Tue, 5 Apr 2022 17:59:10 +0100
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 by: Andy Walker - Tue, 5 Apr 2022 16:59 UTC

On 04/04/2022 14:28, Ben Bacarisse wrote:
[I wrote:]
>> The reasons why it's not possible to write a halt decider show
>> up perfectly well if you try to do so in K&R C for a PDP 11 [64K bytes
>> code, same for date, 2.4M discs, ...]. They're not things that can
>> only be done with supercomputers with hundreds of processors, etc.
>> These interminable threads get hung up on the behaviour of programs of
>> less than a page of code.
> Now here there is technical wrinkle. One can, probably, prove that
> halting of bounded-resource computations can't be solved by certain
> similarly bounded-resource machines. But who'd want to do the maths to
> prove that? And if the decider has unbounded resources, then halting of
> bounded-resource computations /is/ decidable -- trivially so.

Yes, but I was thinking of real, skilled, programmers trying to do
the manifestly impossible. I have in mind one of our [successful!] MSc
students who visited two or three years later: "What are you doing?" "Oh,
my boss got fed up with [programs that something-or-other, I forget what],
so he wanted me to write a program that detects [whatever-it-was]." "But
that's not possible, it's a simple reduction from the HP!" "Oh, no, I've
almost done it, just a couple of cases to sort out." A few months later,
he came by again: "Sorted those, but there are a few bugs." "Hm, well,
good luck, but I still think it's impossible." A few months again, and
I got a letter [these were the days before e-mail!] -- "You were right!
It could do the toy examples I gave it, but it got stuck with any real
programs, and I can't make progress, so we've given up."

PO's problems with his "fully coded TMs" aren't caused by his PC
being finite, nor by limitations of C or his OS, nor even [as far as we
know] by bugs in his "emulator", but by his failures to understand what
the HP is really about, and his failures to produce a proper "hatted"
version of his attempts to solve it.

> When trying to get PO to see how to specify a computation, I don't want
> to deal with all the distractions that using some abstract C with no
> pointer limitations will throw up.

Instead, you're having to deal with his apparent [but he may just
be trolling] difficulties in understanding what you want. I wonder how he
would get on with similar exercises in C, where he's not struggling with
the concept of unary [and efficiency] but could simply count and perhaps
analyse characters in the standard input? [FTAOD, "wonder" is something
of an exaggeration.]

--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Balakirev

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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 by: olcott - Tue, 5 Apr 2022 17:07 UTC

On 4/5/2022 9:40 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/4/2022 7:57 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/4/2022 6:14 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>
>>>>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to do the
>>>>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime number. Can
>>>>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to flesh
>>>>>>>>>>>>>>> this out? If you can, you will be able to do it for E very easily too.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>>>>> That's getting close. We know, from how the notation works, that S is a
>>>>>>>>>>>>> string of symbols in the TM's alphabet. But writing Is-Prime-Number(S)
>>>>>>>>>>>>> suggests that is not natural language. That's a very hard route to go
>>>>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/ formal,
>>>>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>>>>> superficial.
>>>>>>>>>>>>
>>>>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>>>>
>>>>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>>>>> product of two smaller natural numbers.
>>>>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>>>>> First off, there's no need to define what a prime number is. If at some
>>>>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>>>>> about.
>>>>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see if it is a
>>>>>>>>>>> prime number
>>>>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>>>
>>>>>> The TM determines that S is a prime number.
>>>>> Saying "P" rather than "the TM" is simpler. The first 'it' refers to
>>>>> P. The second 'it' refers to the string S. But being prime is a
>>>>> property of numbers not strings.
>>>>>
>>>>>>>>>>
>>>>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>>>>> Yes, that good. You didn't.
>>>>>>>>> Now, to what do the two 'it's refer?
>>>>>>>
>>>>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>>>>> to by these two pronouns? It was not an idle question. I think when
>>>>>>> you answer it, at least one problem will become clear.
>>>>>>
>>>>>> Andre thought that you were simply looking for English:
>>>>>> "p is a prime number"
>>>>> I didn't read that sub-thread.
>>>>>
>>>>>>>>>> This is somewhat algorithmic:
>>>>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>>>>
>>>>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing there to
>>>>>>>>>>> be a prime number.
>>>>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>>>>> mean", but that's a perfectly good answer.
>>>>>>>>
>>>>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>>>>> what you are asking for seems impossible.
>>>>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>>>>> that might be passed to P. At least one of them should be a string that
>>>>>>> P must accept and at least one must be a string the P should reject, but
>>>>>>> you should say, for each one, whether P accepts of rejects it.
>>>>>>
>>>>>> (is prime?)
>>>>>> 1 yes
>>>>>> 2 no
>>>>> 2 is prime, 1 is not. I'll assume this is a typo.
>>>>>
>>>>>> 3 yes
>>>>>> 4 no
>>>>>> 5 yes
>>>>>> 6 no
>>>>>
>>>>>>> Be prepared for me to raise questions about what the strings
>>>>>>> represent.
>>>>> So what about the following strings:
>>>>> 0x11
>>>>> IX
>>>>> nineteen
>>>>> 1001
>>>>> सहस्र
>>>>> ?
>>> You commented on only one of these.
>>>
>>>> I would simply make tape elements UTF-32.
>>> (1) UTF-32 (both of them!) are transfer encodings and TMs work on
>>> abstract symbols. The encoding of the symbols is immaterial.
>>> (2) You could define the tape alphabet to includes all Unicode symbols
>>> but there is no point. You need no more the one symbol to represent any
>>> number, so that would be adding unnecessary complexity.
>>
>> Less than two seems too counter-intuitive, thus cumbersome.
>
> But this is just because you have not yet written a TM. For many tasks,
> unary makes the TM much simpler -- by an order of magnitude in many cases.
>

OK.

>> Complexity is not the size of the encoding it is the mental effort
>> required to achieve complete understanding.
>
> For numerical problems there is less mental effort involved with unary.
> That's why tally sticks can be found dating from the Palaeolithic.
>


Click here to read the complete article
Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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 by: olcott - Tue, 5 Apr 2022 17:16 UTC

On 4/5/2022 11:59 AM, Andy Walker wrote:
> On 04/04/2022 14:28, Ben Bacarisse wrote:
> [I wrote:]
>>>     The reasons why it's not possible to write a halt decider show
>>> up perfectly well if you try to do so in K&R C for a PDP 11 [64K bytes
>>> code, same for date, 2.4M discs, ...].  They're not things that can
>>> only be done with supercomputers with hundreds of processors, etc.
>>> These interminable threads get hung up on the behaviour of programs of
>>> less than a page of code.
>> Now here there is technical wrinkle.  One can, probably, prove that
>> halting of bounded-resource computations can't be solved by certain
>> similarly bounded-resource machines.  But who'd want to do the maths to
>> prove that?  And if the decider has unbounded resources, then halting of
>> bounded-resource computations /is/ decidable -- trivially so.
>
>     Yes, but I was thinking of real, skilled, programmers trying to do
> the manifestly impossible.  I have in mind one of our [successful!] MSc
> students who visited two or three years later:  "What are you doing?"  "Oh,
> my boss got fed up with [programs that something-or-other, I forget what],
> so he wanted me to write a program that detects [whatever-it-was]."  "But
> that's not possible, it's a simple reduction from the HP!"  "Oh, no, I've
> almost done it, just a couple of cases to sort out."  A few months later,
> he came by again:  "Sorted those, but there are a few bugs."  "Hm, well,
> good luck, but I still think it's impossible."  A few months again, and
> I got a letter [these were the days before e-mail!] -- "You were right!
> It could do the toy examples I gave it, but it got stuck with any real
> programs, and I can't make progress, so we've given up."
>
>     PO's problems with his "fully coded TMs" aren't caused by his PC
> being finite, nor by limitations of C or his OS, nor even [as far as we
> know] by bugs in his "emulator", but by his failures to understand what
> the HP is really about, and his failures to produce a proper "hatted"
> version of his attempts to solve it.
>

I say the issue is exactly the opposite of this, I am the only one with
a correct understanding of what a halt decider must do.

WE ALL AGREE ON THIS:
A halt decider must compute the mapping from its input finite strings to
its own accept or reject state.

HERE IS WHERE WE DIVERGE:
A halt decider must compute the mapping from its input finite strings to
its own accept or reject state:

On the basis of the actual behavior actually specified by its input.

All of my reviewers (and Linz) always measure a different sequence of
configurations than the one the is actually specified by the actual input.

>> When trying to get PO to see how to specify a computation, I don't want
>> to deal with all the distractions that using some abstract C with no
>> pointer limitations will throw up.
>
>     Instead, you're having to deal with his apparent [but he may just
> be trolling] difficulties in understanding what you want.  I wonder how he
> would get on with similar exercises in C, where he's not struggling with
> the concept of unary [and efficiency] but could simply count and perhaps
> analyse characters in the standard input?  [FTAOD, "wonder" is something
> of an exaggeration.]
>

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [ key missing piece in dialogue ]

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Subject: Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [
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 by: Jeff Barnett - Tue, 5 Apr 2022 18:51 UTC

On 4/5/2022 11:07 AM, olcott wrote:

<SNIP>

> I have been doing this professionally for 30 years.
> I was part of the NPOESS satellite ingest team at our local Air Force
> base. https://en.wikipedia.org/wiki/NPOESS

<SNIP>

Sorry to interrupt your tutoring, but the above is no way to impress
your teacher. Let's look at a few quotes from that article:

1. "The estimated launch date for the first NPOESS satellite, "C1" or
"Charlie 1" was around 2013. Issues with sensor developments were the
primary cited reason for delays and cost-overruns."

That was after you started your internet career. It raises the question
of correlation. Were you trolling while working or ...?

2. "The project had to go through three Nunn-McCurdy reviews,
Congressional hearings that are automatically triggered when a program
goes over budget by more than 25%.[4] Suomi NPP was launched five years
behind schedule, on October 28, 2011."

3. "The White House announced on February 1, 2010, that the NPOESS
satellite partnership was to be dissolved, and that two separate lines
of polar-orbiting satellites to serve military and civilian users would
be pursued instead."

So after this success, did you ever work again?
--
Jeff Barnett

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