XPost: comp.theory, sci.math   
   From: mikko.levanto@iki.fi   
      
   On 19/12/2025 16:52, olcott wrote:   
   > 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.   
      
   WHich one?   
      
   > A bunch of irrelevant   
   > questions distract away from this one point.   
      
   A sufficient answer to an irelevant question is "doesn't matter".   
   If a quetion is irrelevant it is sufficient to say "doesn't matter".   
      
   > 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}.   
      
   The terms "computation" and "decider" are not parallel. The suffix   
   of "decider" means that it is an agent. The word "computation" has   
   a diferent suffix bedause it is an action. A decider performs a   
   computation but it isn't one. But you can say that a decider is a   
   computer although more ofthen the term "automaton" is used.   
      
   One should also note that definitions are not principles.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)