XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 12/19/2025 4:09 AM, Mikko wrote:   
   > On 18/12/2025 15:07, olcott wrote:   
   >> On 12/18/2025 5:10 AM, Mikko wrote:   
   >>> On 18/12/2025 06:29, olcott wrote:   
   >>>> On 12/17/2025 4:41 AM, Mikko wrote:   
   >>>>> On 15/12/2025 16:31, olcott wrote:   
   >>>>>> On 12/15/2025 3:20 AM, Mikko wrote:   
   >>>>>>> On 15/12/2025 02:15, olcott wrote:   
   >>>>>>>> On 12/14/2025 4:46 AM, Mikko wrote:   
   >>>>>>>>> On 11/12/2025 16:38, olcott wrote:   
   >>>>>>>>>> On 12/11/2025 2:53 AM, Mikko wrote:   
   >>>>>>>>>>> olcott kirjoitti 10.12.2025 klo 18.27:   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> DD() executed from main() calls HHH(DD) thus is   
   >>>>>>>>>>>> not one-and-the-same-thing as an argument to HHH.   
   >>>>>>>>>>>   
   >>>>>>>>>>> If the last sentence is true then this is not the counter   
   >>>>>>>>>>> exmaple   
   >>>>>>>>>>> mentioned in certain proofs of noncomputability of halting and   
   >>>>>>>>>>> therefore not relevant in that context. The halting problem   
   >>>>>>>>>>> reuqires   
   >>>>>>>>>>> that HHH can determine whether the counter example halts.   
   >>>>>>>>>>> That is,   
   >>>>>>>>>>> you must be able to replace "???" in   
   >>>>>>>>>>>   
   >>>>>>>>>>>    #include  // or your replacement   
   >>>>>>>>>>>    int main (void)   
   >>>>>>>>>>>    {   
   >>>>>>>>>>>      int Halt_Status = HHH(???); // put the correct argument   
   >>>>>>>>>>> here   
   >>>>>>>>>>>      printf("HHH says: %s\n", Halt_Status ? "halts" : "does   
   >>>>>>>>>>> not halt");   
   >>>>>>>>>>>      return Halt_Status;   
   >>>>>>>>>>>    }   
   >>>>>>>>>>>   
   >>>>>>>>>>> with whatever specifies the behaviour of DD to HHH. If you can't   
   >>>>>>>>>>> do this then HHH is not a halt decider nor a partial halt   
   >>>>>>>>>>> decider.   
   >>>>>>>>>   
   >>>>>>>>>> When the halting problem requires a halt decider   
   >>>>>>>>>> to report on the behavior of a Turing machine this   
   >>>>>>>>>> is always a category error.   
   >>>>>>>>>   
   >>>>>>>>> That you don't know what "category error" means does not   
   >>>>>>>>> justify your   
   >>>>>>>>> claim. Apparently you can't apply definitions.   
   >>>>>>>>   
   >>>>>>>> Turing machines only compute functions from finite   
   >>>>>>>> strings they never compute functions from Turing   
   >>>>>>>> machines.   
   >>>>>>>   
   >>>>>>> True, but irrelevant to questions about category errors.   
   >>>>>>>   
   >>>>>>>> A halt decider can at best compute the behavior of   
   >>>>>>>> a Turing machine through the proxy of a finite   
   >>>>>>>> string machine description it never computes it   
   >>>>>>>> directly from another Turing machine.   
   >>>>>>>>   
   >>>>>>>> Whenever any textbook says that a halt decider   
   >>>>>>>> must compute halting for machine M on input w   
   >>>>>>>> is it wrong.   
   >>>>>>>   
   >>>>>>> Which textbook actually says "must"? It is not wrong to say   
   >>>>>>> "must" in   
   >>>>>>> the sense that any decider that does not compute whether machine M   
   >>>>>>> halts on input w is not a halt decider. But using "must" is not the   
   >>>>>>> clearest way to say it because the word "must" other meanings.   
   >>>>>>>   
   >>>>>>>  > It actually computes halting that this input pair specifies   
   >>>>>>> (⟨M⟩, w).   
   >>>>>>>   
   >>>>>>> There is an unbalanced parenthesis above.   
   >>>>>>   
   >>>>>> No halt decider ever computes the halt status   
   >>>>>> of a machine except through the proxy of finite   
   >>>>>> strings.   
   >>>>>   
   >>>>> No halt decider computes anything because there are not halt deciders.   
   >>>>   
   >>>> I am trying to state the gist of this and not get so   
   >>>> bogged down in tedious details that the gist cannot   
   >>>> possibly ever be understood because we have too much   
   >>>> detail for the capacity of the human mind.   
   >>>   
   >>> If you can't state the gist without causing more confusion than   
   >>> clarity you should try something else.   
   >>>   
   >> When people demand too many irrelevant details   
   >> I must so no.   
   >   
   > You should put the whole story to GitHub. Then you can add any detail   
   > aomeone asks. If the same quiestion is asked again you only need to   
   > give a pointer as the answer.   
   >   
      
   I am making one single point. A bunch of irrelevant   
   questions distract away from this one point.   
      
   I have gone over these things thousands of times   
   and what seem obvious to me cannot possibly be   
   understood by anyone besides LLM systems.   
      
   These are the correct first principles of all   
   computation.   
      
   Computations: Transform finite strings by finite   
   string transformation rules into values or non-termination.   
      
   Deciders: Transform finite strings by finite string   
   transformation rules into {Accept, Reject}.   
      
   >>> You still havn't answered the question which textbook says "must".   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)