XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 12/17/2025 11:01 AM, olcott wrote:   
   > On 12/17/2025 7:51 AM, Tristan Wibberley wrote:   
   >> On 17/12/2025 13:33, olcott wrote:   
   >>   
   >>> I am trying precisely define the exact essence   
   >>> of the architecture of Turing Machine computation.   
   >>> Things like writing to a tape are not of the essence.   
   >>   
   >> It might be good to refer to "Idealised Turing Machines" instead of   
   >> "Turing Machines". Real Turing Machines will only do what you say   
   >> /contingent/ /on/ /their/ /environment/ while Idealised Turing Machines   
   >> might do so contingent only on your accuracy as perceived by your future   
   >> readers.   
   >>   
   >>   
   >>> Things that are outside their scope:   
   >> ...   
   >>   
   >>> finite string transformations to inputs.   
   >>   
   >> A cautionary note about the term "strings": there is a formal term   
   >> "string" as well as an intuitive programmer's term "string" the latter   
   >> of which is often misconceived as any of the various programmer's   
   >> language's respective /sequence/ concepts.   
   >>   
   >> It might be good to avoid the term "string".   
   >>   
   >   
   > If I said a set of sequences of space delimited   
   > binary digits each stored in the cells of a Turing   
   > machine tape this would make it impossible for people   
   > to see the essence of the error of the halting problem   
   > and its proofs.   
   >   
      
   The simplest essence of the error of the halting   
   problem itself is that it requires a halt decider   
   to make a halt decision on the basis of something   
   that its finite string input does not actually say.   
      
   Everyone assumes that it does say this yet never   
   exhaustively tested the truth of this.   
      
   I bet not even one person here even knows what   
   "exhaustively tested the truth of this"   
   actually involves.   
      
   In this forum it seems to mean to totally understand   
   the conventional wisdom and construing this mere   
   "conventional wisdom" as infallibly correct.   
      
      
      
   --   
   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)