XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/24/2025 5:10 PM, Richard Damon wrote:   
   > On 12/24/25 5:01 PM, olcott wrote:   
   >> On 12/24/2025 3:38 PM, Richard Damon wrote:   
   >>> On 12/24/25 3:56 PM, olcott wrote:   
   >>>> On 12/24/2025 2:33 PM, Richard Damon wrote:   
   >>>>> On 12/24/25 3:11 PM, olcott wrote:   
   >>>>>> On 12/24/2025 1:28 PM, Richard Damon wrote:   
   >>>>>>> On 12/24/25 2:20 PM, olcott wrote:   
   >>>>>>>> *This defines the scope of computation*   
   >>>>>>>> A Turing-machine decider is a Turing machine D that   
   >>>>>>>> computes a total function D: Σ∗ → {Accept,Reject},   
   >>>>>>>> where Σ∗ is the set of all finite strings over the input   
   >>>>>>>> alphabet. That is:   
   >>>>>>>>   
   >>>>>>>> 1. Totality: For every finite string input w ∈ Σ∗, D   
   >>>>>>>> halts and outputs either Accept or Reject.   
   >>>>>>>>   
   >>>>>>>> *This is semantically entailed from this definition*   
   >>>>>>>> Any requirement that requires more than the above   
   >>>>>>>> definition can provide is a requirement that is outside   
   >>>>>>>> of the scope of computation.   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> FALSE, proving you don't understand the meaning of "Scope".   
   >>>>>>>   
   >>>>>>   
   >>>>>> Instead of spouting off dogma any idiot can do   
   >>>>>> that, you define what you think that the term   
   >>>>>> "scope of computation" actually means.   
   >>>>>   
   >>>>> You are using the wrong term.   
   >>>>>   
   >>>>> It is the Scope of the Theory of Computation, which is the list of   
   >>>>> problems that we are allowed to ask a Turing Machine/Computation to   
   >>>>> try to compute.   
   >>>>>   
   >>>>> That list of problems is ANY mapping of a source domain (expressed   
   >>>>> to the machine via some representation) to an answer domain (again   
   >>>>> expressed via some representaiton)   
   >>>>>   
   >>>>>>   
   >>>>>> This is what Google AI said.   
   >>>>>> The "scope of computation" refers to the range   
   >>>>>> and limits of what can be solved or processed   
   >>>>>> using algorithms and computational methods.   
   >>>>>>   
   >>>>>> That is what I mean. What do you mean?   
   >>>>>>   
   >>>>>   
   >>>>> Which isn't the Scope of the Theory of Compuation, but a descption   
   >>>>> of what is actually computable,   
   >>>>   
   >>>> The scope of computation is the boundary of   
   >>>> what is and what is not computable.   
   >>>   
   >>> Which is NOT the boundry of what you can ask of a decider, as it is   
   >>> allowed for the Function to not be computable.   
   >>>   
   >>> You are confusing the boundary of ABILITY with the boundry of allowed   
   >>> REQUIREMENT.   
   >>>   
   >>   
   >> You are confusing that requirement can exceed an ability.   
   >> Some idiot could "require" the a Turing Machine to   
   >> compute the last digit PI.   
   >>   
   >   
   > Sure, and that IS one operation that a Turing Machine (in a different   
   > model) could do, One of his early paper talked about using Turing   
   > Machines to compute real numbers, by continuing to compute the next   
   > digit of the number, and then the one after that, and so on.   
   >   
   > Of course, there machines never stop to complete if the number is   
   > irrational.   
   >   
   >>>>   
   >>>> Turing machine deciders: Transform finite string   
   >>>> inputs by finite string transformation rules into   
   >>>> {Accept, Reject} values.   
   >>>>   
   >>>> *Translated into this formal specification*   
   >>>>   
   >>>> *DEFINE the actual limits of computation*   
   >>>> *DEFINE the actual limits of computation*   
   >>>> *DEFINE the actual limits of computation*   
   >>>   
   >>> Of what is COMPUTABLE, not what can be asked to try to compute.   
   >>>   
   >>   
   >> Asking it try try to compute anything outside the   
   >> scope of computation is nuts.   
   >   
   > But it is in the Scope of Computation Theory and a valid request for a   
   > decider.   
   >   
   > You just don't understand what you are talking about.   
   >   
      
   I have proven that I am correct and you   
   are merely biased by the conventional view.   
      
   >>   
   >>>>   
   >>>> A Turing-machine decider is a Turing machine D that   
   >>>> computes a total function D :  Σ∗ → {Accept,Reject},   
   >>>> where Σ∗ is the set of all finite strings over the   
   >>>> input alphabet. That is:   
   >>>   
   >>> And, to be an XXXX Decider, must produce the mapping of the XXXX   
   >>> function,   
   >>>   
   >>   
   >> Not when no such mapping exists as transformations   
   >> from finite string INPUTS INPUTS INPUTS INPUTS   
   >> INPUTS INPUTS INPUTS INPUTS   
   >> INPUTS INPUTS INPUTS INPUTS   
   >> INPUTS INPUTS INPUTS INPUTS   
   >> According to the specification of the limits of computation.   
   >   
   > Right, and that input *IS* the string that specifies fully the algorithm   
   > of the machine, and thus it if valid to ask about semantic properties   
   > that derive from the running of siad machine.   
   >   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
   INPUTS INPUTS INPUTS INPUTS TO H DO NOT SPECIFY THIS   
      
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