XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-10-22, olcott  wrote:   
   > On 10/22/2025 3:20 PM, Kaz Kylheku wrote:   
   >> On 2025-10-22, olcott  wrote:   
   >>> On 10/22/2025 2:52 PM, Kaz Kylheku wrote:   
   >>>> On 2025-10-22, André G  Isaak  wrote:   
   >>>>> On 2025-10-22 12:40, Kaz Kylheku wrote:   
   >>>>>> But that entire bundle is one fixed case DD, with a single behavior,   
   >>>>>> which is a property of DD, which is a finite string.   
   >>>>>   
   >>>>> I think part of the problem here is that Olcott doesn't grasp that the   
   >>>>> "finite string input" DD *must* include as a substring the entire   
   >>>>> description of HHH.   
   >>>>   
   >>>> Furthermore, he doesn't get that it doesn't literally have to be HHH,   
   >>>> but the same algorithm: a workalike.   
   >>>>   
   >>>> The HHH analyzing DD's halting could be in C, while the HHH   
   >>>> called by DD could be in Python.   
   >>>   
   >>> DD does call HHH(DD) in recursive simulation   
   >>> and you try to get away with lying about it.   
   >>   
   >> I'm saying that's not a requirement in the halting problem.   
   >>   
   >> DD does not have to use that implementation of HHH; it can have   
   >> its own clean-room implementation and it can be in any language.   
   >>   
   >> But nonetheless, yes, there will still be a nested simulation tower.   
   >>   
   >   
   > Thus proving that DD correctly simulated by HHH   
   > cannot possibly reach its own simulated final halt   
   > state no matter what HHH does.   
      
   I explained that a nested simulation tower is two dimensional.   
      
   One dimension is the simulation level, the nesting itself;   
   that goes out to infinity. Due to the aborting behavior of HHH,   
   it is not actually realized in simulation; we have to step   
   through the aborted simulations to keep it going.   
      
   The other dimension is the execution /within/ the simulations.   
   That can be halting or non-halting.   
      
   In the HHH(DD) simulation tower, though that is infinite,   
   the simulations are halting.   
      
   I said that before. Your memory of that has vaporized, and you have now   
   focused only on my statement that the simluation tower is infinite.   
      
   The depth of the simulation tower, and the halting of the simulations   
   within that tower, are independent phenomena.   
      
   A decider must not mistake one for the other.   
      
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