XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 12/13/2025 8:56 PM, Richard Damon wrote:   
   > On 12/13/25 9:30 PM, olcott wrote:   
   >> On 12/13/2025 5:02 PM, Richard Damon wrote:   
   >>> On 12/13/25 5:41 PM, olcott wrote:   
   >>>> On 12/13/2025 3:32 PM, olcott wrote:   
   >>>>> All of the textbooks require halt deciders to   
   >>>>> report on the behavior of machine M on input w.   
   >>>>> This may be easy to understand yet not precisely   
   >>>>> accurate.   
   >>>>>   
   >>>>> Since no Turing machine ever takes any Machine   
   >>>>> M as an input this  a category error even   
   >>>>> when this makes no functional difference.   
   >>>>>   
   >>>>> They simply glossed over this key detail because   
   >>>>> they thought that it made no difference.   
   >>>>>   
   >>>>> *Defining a halt decider with perfect accuracy*   
   >>>>> Turing machine halt deciders compute the mapping   
   >>>>> from input finite strings to an {accept, reject}   
   >>>>> value on the basis of the behavior that this   
   >>>>> input finite string specifies.   
   >>>>>   
   >>>>   
   >>>> By simply adding more detail we can make the   
   >>>> original definition more precise:   
   >>>>   
   >>>> A Turing machine based halt decider reports on the   
   >>>> behavior of machine M on input w thorough the   
   >>>> proxy of the finite string machine description of   
   >>>> ⟨M⟩ on input w.   
   >>>>   
   >>>> The above seems to be more precisely accurate   
   >>>> than any published proof. It includes a key   
   >>>> detail that all of them seem to leave out.   
   >>>>   
   >>>> If you know of any published proof that directly   
   >>>> refers to the idea of a proxy, please let me know.   
   >>>>   
   >>>   
   >>> And the use of a string proxy is just normally assumed by the theory,   
   >>> as that is how Turing Machine work.   
   >>>   
   >>   
   >> See that three agreements in one day.   
   >> That may be more than we have ever had.   
   >>   
   >> Because none of the textbooks ever directly said   
   >> that the finite string input is only a proxy for   
   >> the behavior everyone always took the proxy to be   
   >> exactly one-and-the-same thing as the actual behavior.   
   >   
   > But the behavior represented by the string *IS* exactly the behavior of   
   > the string, so you attempted point just falls flat.   
   >   
      
   Do you really think that I will keep going   
   on this for 22 years if it just falls flat?   
      
   Google Groups has a much better search so   
   you can see the 40,000 messages that I posted   
   in comp.theory since 2004.   
      
   My very first Halting Problem post Jun 6, 2004, 9:11:19 AM   
   Alan Turing's Halting Problem is incorrectly formed   
   It has lots and lots of replies.   
   https://groups.google.com/g/sci.logic/c/V7wzVvx8IMw/m/ggPE6a-60cUJ   
      
   > And, as I said, even your Linz book made that clear, as H took as it   
   > input Wm (the string) not M (the machine).   
   >   
      
   That is not the issue. All the textbooks say that.   
      
   The issue is that this finite string AS AN INPUT   
   is the ultimate basis of the halt decision even   
   when it is not a good proxy for the behavior of   
   the executed machine.   
      
   > Also, if you did any real study, you would have learned that the input   
   > to the machine is almost always just a "represemtation" of the input to   
   > the function, as we rarely are really interested in computing a result   
   > on the strings.   
   >   
   > The one exception is the very earliest exercises where you learn basic   
   > string manipulation with Turing Machines, but you rapidly get to wanting   
   > to do things like "arithmatic" and then learning you need to REPRESENT   
   > numbers as something. (and a common method which baffled you as I   
   > remember was unary, you wanted your Turing Machine to use UNICODE as it   
   > symbol set.   
   >   
   >>   
   >>> They almost ALWAYS work by a string representation proxy, as very few   
   >>> real questions are based on the "arbitrary" symbol set of the Turing   
   >>> Machines native operation.   
   >>>   
   >>> If you had bothered to learn the basics of the field, you would have   
   >>> understood that.   
   >>>   
   >>> Most works assume the basic knowledge of the field.   
   >>>   
   >>> Note, even the Linz proof you mention explicitly talks about giving   
   >>> the decider a representation of the machine in question, the Wm as   
   >>> the proxy for giving it M.   
   >>>   
   >>> So, why did you not understand the use of a proxy.   
   >>>   
   >>> Sometimes the problem when expressed for lay people will talk about   
   >>> the decider being given a description or representation of the machine.   
   >>>   
   >>> You just reject those as you think it too vague, when it is a well   
   >>> defined term, and even the general meaning is applicable, you just   
   >>> need to remember that it must be a SUFFICIENT description to convey   
   >>> the needed details of the machine.   
   >>   
   >>   
   >   
      
      
   --   
   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)