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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: =?utf-8?Q?Re:_Analysis_of_Flibble=E2=80=99s_Latest:_Detecting_vs._Simulating_Infinite_Recursion_ZFC?=
Date: Sun, 25 May 2025 13:11:28 +0300
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On 2025-05-24 16:13:12 +0000, olcott said:

> On 5/24/2025 10:12 AM, dbush wrote:
>> On 5/24/2025 11:04 AM, olcott wrote:
>>> On 5/23/2025 8:09 PM, dbush wrote:
>>>> On 5/23/2025 9:07 PM, olcott wrote:
>>>>> On 5/23/2025 7:57 PM, dbush wrote:
>>>>>> On 5/23/2025 8:54 PM, olcott wrote:
>>>>>>> On 5/23/2025 7:44 PM, dbush wrote:
>>>>>>>> On 5/23/2025 8:08 PM, Mike Terry wrote:
>>>>>>>>> I suppose Ben quoted PO saying this, because PO /uses/ it to justify 
>>>>>>>>> that a particular /halting/ computation will never halt, PO's HHH 
>>>>>>>>> simulates DDD (which halts) but before DDD halts it spots a pattern in 
>>>>>>>>> the simulation, and announces non-halting. "Eh?" I hear you say! PO 
>>>>>>>>> claims HHH has "correctly determined that DDD would never halt" and so 
>>>>>>>>> is correct to decide non- halting.  His "proof" that it is right to 
>>>>>>>>> decide non-halting is his "when-so- ever.." quote, which broadly 
>>>>>>>>> matches the Sipser quote.
>>>>>>>>> 
>>>>>>>>> So the problem is not so much the "when-so-ever.." words themselves [or 
>>>>>>>>> the words of Sipser's quote], but understanding how PO is so thoroughly 
>>>>>>>>> misinterpreting/misapplying them.  How can PO believe HHH has 
>>>>>>>>> "correctly determined the DDD will never halt" when DDD demonstrably 
>>>>>>>>> halts?
>>>>>>>> 
>>>>>>>> PO is working in a different model than the rest of us, though he 
>>>>>>>> doesn't seem to understand that.
>>>>>>>> 
>>>>>>>> To him, when function H is deciding on something, the implementation of 
>>>>>>>> H is allowed to vary.  This results in functions that call H to vary as 
>>>>>>>> a result.  To him, "DDD" is the same computation *regardless of the 
>>>>>>>> implementation of HHH*, in cases where HHH is simulating DDD.
>>>>>>>> 
>>>>>>>> This is essentially the mapping he's operating with:
>>>>>>>> 
>>>>>>>> -----------------
>>>>>>>> For a function X with input Y and a function H which simulates X:
>>>>>>>> POH(H,X,Y)==1 if and only if there exists an implementation of H that 
>>>>>>>> can simulate X(Y) to completion
>>>>>>>> POH(H,X,Y)==0 if and only if there does not exist an implementation of 
>>>>>>>> H that can simulate X(Y) to completion
>>>>>>>> ----------------
>>>>>>>> 
>>>>>>>> And a "decider" in his case maps the following subset:
>>>>>>>> 
>>>>>>>> ----------------
>>>>>>>> Hx is a PO-halt decider if and only if Hx(X,Y) == POH(Hx,X,Y)
>>>>>>>> ----------------
>>>>>>>> 
>>>>>>>> So given his rules, HHH1(DDD) is deciding on a algorithm while HHH(DDD) 
>>>>>>>> is deciding on a C function whose subfunctions vary.
>>>>>>>> 
>>>>>>>> This of course has nothing to do with the halting problem but he 
>>>>>>>> doesn't get this.  After having spent 22 years on this, he'll come up 
>>>>>>>> with any crazy justification to avoid admitting to himself that he 
>>>>>>>> misunderstood the problem all this time.  He once said (and I don't 
>>>>>>>> recall the exact wording) that "the directly executed D doesn't halt 
>>>>>>>> even though it appears to".
>>>>>>> 
>>>>>>> The problem is that people here are too stupid
>>>>>>> to notice that HHH cannot report on the behavior
>>>>>>> of its caller.
>>>>>>> 
>>>>>>> int min()
>>>>>>> {
>>>>>>>    DD(); // HHH cannot report on the behavior of its caller.
>>>>>>> }
>>>>>>> 
>>>>>> 
>>>>>> What about this?
>>>>>> 
>>>>> 
>>>>> If you can't stay exactly on topic I am going to ignore
>>>>> everything that you say.
>>>>> 
>>>>> HHH cannot report on the behavior of its caller AKA the
>>>>> direct execution of DD().
>>>>> 
>>>> 
>>>> 
>>>> In other words, you again agree with Linz and others that no H exists 
>>>> that can perform the following mapping:
>>>> 
>>>> 
>>>> Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
>>>> described as <X> with input Y:
>>>> 
>>>> A solution to the halting problem is an algorithm H that computes the 
>>>> following mapping:
>>>> 
>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
>>>> 
>>> 
>>> int main()
>>> {
>>>    DD(); // The HHH called by DD cannot report on the behavior
>>> }       // of its caller. Is this OVER-YOUR-HEAD ?
>>> 
>> 
>> 
>> Which means that no HHH exists that meets the below requirements, as 
>> Linz and others proved and as you have *explicitly* agreed is correct:
> 
> You are a damned liar when you say that I said
> that HHH must report on the behavior of its caller.

It is a sin to lie about another persons words.

> No HHH can report on the behavior of its caller
> for the same reason that no function can report
> on the value of the square-root of a dead cat.

False. The reason is not the same. No function can report on the value of
the square root of a dead cat because a desd cat has no square root. But
eevery caller of HHH has some behaviour that includes calling HHH.

-- 
Mikko