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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Olcott thinks One is Infinity
Date: Fri, 10 May 2024 18:39:13 -0400
Organization: i2pn2 (i2pn.org)
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On 5/10/24 6:28 PM, olcott wrote:
> On 5/10/2024 4:59 PM, Richard Damon wrote:
>> On 5/10/24 5:43 PM, olcott wrote:
>>> On 5/10/2024 4:19 PM, Richard Damon wrote:
>>>> On 5/10/24 5:11 PM, olcott wrote:
>>>>> On 5/10/2024 3:50 PM, Richard Damon wrote:
>>>>>> On 5/10/24 4:27 PM, olcott wrote:
>>>>>>> On 5/10/2024 3:09 PM, Richard Damon wrote:
>>>>>>>> On 5/10/24 1:49 PM, olcott wrote:
>>>>>>>>> On 5/10/2024 11:12 AM, Richard Damon wrote:
>>>>>>>>>> On 5/10/24 11:50 AM, olcott wrote:
>>>>>>>>>>> On 5/10/2024 9:18 AM, Richard Damon wrote:
>>>>>>>>>>>> On 5/9/24 11:10 PM, olcott wrote:
>>>>>>>>>>>>> On 5/9/2024 9:31 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 5/9/24 11:38 AM, olcott wrote:
>>>>>>>>>>>>>>> On 5/8/2024 8:38 PM, immibis wrote:
>>>>>>>>>>>>>>>> On 8/05/24 21:05, olcott wrote:
>>>>>>>>>>>>>>>>> On 5/8/2024 10:13 AM, Mike Terry wrote:
>>>>>>>>>>>>>>>>>> On 08/05/2024 14:01, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 5/8/2024 3:59 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>> On 2024-05-07 19:05:54 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> On 5/7/2024 1:54 PM, Fred. Zwarts wrote:
>>>>>>>>>>>>>>>>>>>>>> Op 07.mei.2024 om 17:40 schreef olcott:
>>>>>>>>>>>>>>>>>>>>>>> On 5/7/2024 6:18 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 5/7/24 3:30 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-06 18:28:37 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/6/2024 11:19 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-05 17:02:25 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> The x86utm operating system: 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://github.com/plolcott/x86utm enables
>>>>>>>>>>>>>>>>>>>>>>>>>>>> one C function to execute another C function 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> in debug step mode.
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Simulating Termination analyzer H simulates 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> the x86 machine code of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>> input (using libx86emu) in debug step mode 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> until it correctly matches a
>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct non-halting behavior pattern proving 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> that its input will never
>>>>>>>>>>>>>>>>>>>>>>>>>>>> stop running unless aborted.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Can D correctly simulated by H terminate 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> normally?
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 00 int H(ptr x, ptr x)  // ptr is pointer to 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> int function
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 01 int D(ptr x)
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 02 {
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 03   int Halt_Status = H(x, x);
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 04   if (Halt_Status)
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 05     HERE: goto HERE;
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 06   return Halt_Status;
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 07 }
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 08
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 09 int main()
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10 {
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 11   H(D,D);
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 12 }
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Execution Trace*
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Line 11: main() invokes H(D,D);
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> *keeps repeating* (unless aborted)
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Line 03: simulated D(D) invokes simulated 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H(D,D) that simulates D(D)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Simulation invariant*
>>>>>>>>>>>>>>>>>>>>>>>>>>>> D correctly simulated by H cannot possibly 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach past its own line 03.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above execution trace proves that (for 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> every H/D pair of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite set of H/D pairs) each D(D) 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by the H that this D(D)
>>>>>>>>>>>>>>>>>>>>>>>>>>>> calls cannot possibly reach past its own 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> line 03.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> When you say "every H/D pair" you should 
>>>>>>>>>>>>>>>>>>>>>>>>>>> specify which set of pairs
>>>>>>>>>>>>>>>>>>>>>>>>>>> you are talking about. As you don't, your 
>>>>>>>>>>>>>>>>>>>>>>>>>>> words don't mean anything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Every H/D pair in the universe where D(D) is 
>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by the
>>>>>>>>>>>>>>>>>>>>>>>>>> same H(D,D) that D(D) calls. This involves 1 
>>>>>>>>>>>>>>>>>>>>>>>>>> to ∞ steps of D
>>>>>>>>>>>>>>>>>>>>>>>>>> and also includes zero to ∞ recursive 
>>>>>>>>>>>>>>>>>>>>>>>>>> simulations where H
>>>>>>>>>>>>>>>>>>>>>>>>>> H simulates itself simulating D(D).
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> "In the universe" is not a set. In typical set 
>>>>>>>>>>>>>>>>>>>>>>>>> theories like ZFC there
>>>>>>>>>>>>>>>>>>>>>>>>> is no universal set.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> This template defines an infinite set of finite 
>>>>>>>>>>>>>>>>>>>>>>> string H/D pairs where each D(D) that is 
>>>>>>>>>>>>>>>>>>>>>>> simulated by H(D,D) also calls this same H(D,D).
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> These H/D pairs can be enumerated by the one to ∞ 
>>>>>>>>>>>>>>>>>>>>>>> simulated steps of D and involve zero to ∞ 
>>>>>>>>>>>>>>>>>>>>>>> recursive simulations of H simulating itself 
>>>>>>>>>>>>>>>>>>>>>>> simulating D(D). Every time Lines 1,2,3 are 
>>>>>>>>>>>>>>>>>>>>>>> simulated again defines
>>>>>>>>>>>>>>>>>>>>>>> one more level of recursive simulation.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> 1st element of H/D pairs 1 step  of D  is 
>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>> 2nd element of H/D pairs 2 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>> 3rd element of H/D pairs 3 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> 4th element of H/D pairs 4 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>> this begins the first recursive simulation at 
>>>>>>>>>>>>>>>>>>>>>>> line 01
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> 5th element of H/D pairs 5 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>> simulated by
>>>>>>>>>>>>>>>>>>>>>>> next step of the first recursive simulation at 
>>>>>>>>>>>>>>>>>>>>>>> line 02
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> 6th element of H/D pairs 6 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>> simulated by
>>>>>>>>>>>>>>>>>>>>>>> last step of the first recursive simulation at 
>>>>>>>>>>>>>>>>>>>>>>> line 03
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> 7th element of H/D pairs 7 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>> this begins the second recursive simulation at 
>>>>>>>>>>>>>>>>>>>>>>> line 01
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Is this the definition of the infinite set of H? 
>>>>>>>>>>>>>>>>>>>>>> We can think of many more simulations that only 
>>>>>>>>>>>>>>>>>>>>>> these.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> This template defines an infinite set of finite 
>>>>>>>>>>>>>>>>>>>>> string H/D pairs where
>>>>>>>>>>>>>>>>>>>>> each D(D) that is simulated by H(D,D) also calls 
>>>>>>>>>>>>>>>>>>>>> this same H(D,D).
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> No-one can possibly show one element of this set 
>>>>>>>>>>>>>>>>>>>>> where D(D) reaches
>>>>>>>>>>>>>>>>>>>>> past its own line 03.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> If H is a decider of any kind then the D build from 
>>>>>>>>>>>>>>>>>>>> it reaches its line
>>>>>>>>>>>>>>>>>>>> 4 as numberd above. Whether the simulation of D by H 
>>>>>>>>>>>>>>>>>>>> reaches that line
>>>>>>>>>>>>>>>>>>>> is another question.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> *My fully operational code proves otherwise*
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> I seems like you guys don't have a clue about how 
>>>>>>>>>>>>>>>>>>> infinite
>>>>>>>>>>>>>>>>>>> recursion works. You can run the code and see that I 
>>>>>>>>>>>>>>>>>>> am correct.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> I have one concrete instance as fully operational code.
>>>>>>>>>>>>>>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c
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