XPost: comp.theory   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-16, olcott  wrote:   
   > That the information that HHH is required to report   
   > on simply is not contained in its input is what makes   
   > halting undecidable.   
      
   That is false. The information to decide D is entirely   
   in D and its subroutines. We can demonstrate a decider   
   (a simulating one, even) which can resolve D.   
   It just calls UTM(D) followed by executing "return 1;".   
      
   Rather the situation is that the information in the   
   input D is too complex for H to correctly handle.   
      
   It's not necessarily complex in some absolute sense, like "Kolgomorov   
   complexity".   
      
   D is targeted against H; D specifies a point in   
   the complexity space where H has a weakness.   
      
   H(D) does not require H to report on its caller whatsoever.   
   Everything necessary to understand D's behavior is   
   in that argument.   
      
   Undecidability of halting exists because programs are not able to   
   calculate the halting of some other programs which are more complex than   
   they are.   
      
   The diagonal case trick builds what is possible the smallest example   
   of this effect. The case is slightly more complex than the decider   
   it is aimed against: it includes that entire decider, plus a small   
   amount of additional logic.   
      
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