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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: key error in all the proofs --- Correction of Fred
Date: Fri, 16 Aug 2024 16:04:16 -0400
Organization: i2pn2 (i2pn.org)
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On 8/16/24 3:47 PM, olcott wrote:
> On 8/16/2024 2:23 PM, Richard Damon wrote:
>> On 8/16/24 2:57 PM, olcott wrote:
>>> On 8/16/2024 1:49 PM, Richard Damon wrote:
>>>> On 8/16/24 2:04 PM, olcott wrote:
>>>>> On 8/16/2024 12:54 PM, Richard Damon wrote:
>>>>>> On 8/16/24 1:11 PM, olcott wrote:
>>>>>>> On 8/16/2024 11:47 AM, joes wrote:
>>>>>>>> Am Fri, 16 Aug 2024 10:07:08 -0500 schrieb olcott:
>>>>>>>>> On 8/16/2024 9:59 AM, joes wrote:
>>>>>>>>>> Am Fri, 16 Aug 2024 09:42:13 -0500 schrieb olcott:
>>>>>>>>>>> On 8/16/2024 9:28 AM, Richard Damon wrote:
>>>>>>>>>>>> On 8/16/24 10:09 AM, olcott wrote:
>>>>>>>>>>>>> On 8/16/2024 8:34 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-08-16 12:02:00 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>>>> Unless an unlimited emulation of DDD by HHH can reach the 
>>>>>>>>>>>>> "return"
>>>>>>>>>>>>> instruction of DDD it is construed that this instance of 
>>>>>>>>>>>>> DDD never
>>>>>>>>>>>>> halts.
>>>>>>>>>>>> But that also construes that HHH is a program that DOES an 
>>>>>>>>>>>> unlimited
>>>>>>>>>>>> emulation of DDD, and thus isn't a decider
>>>>>>>>>>> Not at all. never has.
>>>>>>>>>> Yes, because DDD is defined to call its simulator. If you 
>>>>>>>>>> change the
>>>>>>>>>> simulator to abort, you also change the simulated HHH. Nobody 
>>>>>>>>>> cares
>>>>>>>>>> about HHH aborting a pure simulator.
>>>>>>>>
>>>>>>>>>>> HHH must predict what the behavior of an unlimited simulation 
>>>>>>>>>>> would
>>>>>>>>>>> be.
>>>>>>>>>> The HHH that aborts must predict what DDD calling an aborting 
>>>>>>>>>> HHH does
>>>>>>>>> NOT AT ALL, NEVER HAS.
>>>>>>>>> PREDICT WHAT THE BEHAVIOR WOULD BE
>>>>>>>>> IF IT WAS AN UNLIMITED EMULATION
>>>>>>>> Yes, an unlimited simulation of an aborting HHH. 
>>>>>>>
>>>>>>> Prediction of behavior of unlimited emulation
>>>>>>> means prediction of behavior that never aborts.
>>>>>>>
>>>>>>
>>>>>> Right, but the unlimited emulation of the DDD that calls the HHH 
>>>>>> that says non-halting will reach a final state.
>>>>>>
>>>>>
>>>>> I think that you are just twisting my words again.
>>>>>
>>>>> _DDD()
>>>>> [00002172] 55         push ebp      ; housekeeping
>>>>> [00002173] 8bec       mov ebp,esp   ; housekeeping
>>>>> [00002175] 6872210000 push 00002172 ; push DDD
>>>>> [0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
>>>>> [0000217f] 83c404     add esp,+04
>>>>> [00002182] 5d         pop ebp
>>>>> [00002183] c3         ret
>>>>> Size in bytes:(0018) [00002183]
>>>>>
>>>>> The unlimited emulation of DDD by HHH never stops running.
>>>>>
>>>>>
>>>>
>>>> IF you are going to change an define that *THE* HHH is just a 
>>>> program that does unlimited emulation, than it fails to give the 
>>>> answer that the input is non-halting.
>>>>
>>>
>>> HHH correctly predicts...
>>> HHH correctly predicts...
>>> HHH correctly predicts...
>>> HHH correctly predicts...
>>> HHH correctly predicts...
>>>
>>> I will get the another piece of this sentence
>>> after you fully understand this first piece.
>>>
>>
>> How can HHH correctly predict something that won't happen?
>>
> 
> How do we know there is no greatest prime?
> 

Because we can form a proof that show it.

Something that seems to be beyond your ability to comprehend,


We CAN form a proof from a partial emulation that Infinite_Loop and 
Infinite_Recursion that the unlimited emultion of them will not halt, in 
part because they do not depend on the emulator they are paired with 
(since they are not defined to be paired with an emulator).

A Given DDD, that has been paired wtih a given HHH, can be shown to Halt 
if that HHH(DDD) returns an answer, and to not halt if (and only if) 
that HHH(DDD) will never return. This means we can PROVE that no HHH can 
correctly predict that the DDD that calls it is non-halting, becuase the 
act of making that prediction renders it false.