XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/1/2025 3:23 PM, Richard Damon wrote:   
   > On 8/1/25 4:08 PM, olcott wrote:   
   >> On 8/1/2025 2:49 PM, Richard Damon wrote:   
   >>> On 8/1/25 2:49 PM, olcott wrote:   
   >>>> On 8/1/2025 1:36 PM, Richard Damon wrote:   
   >>>>> On 8/1/25 1:37 PM, olcott wrote:   
   >>>>>> On 8/1/2025 12:17 PM, Richard Damon wrote:   
   >>>>>>   
   >>>>>> Turing machines cannot directly report on the behavior   
   >>>>>> of other Turing machines they can at best indirectly   
   >>>>>> report on the behavior of Turing machines through the   
   >>>>>> proxy of finite string machine descriptions such as ⟨M⟩.   
   >>>>>   
   >>>>> Sure they can, since they CAN be given it as the representation.   
   >>>>>   
   >>>>   
   >>>> Do you understand that a finite string machine description   
   >>>> is not itself a directly executing Turing machine?   
   >>>   
   >>> But it can represent one.   
   >>>   
   >>> You don't seem to understand how representations work.   
   >>>   
   >>> A properly encoded representation of a Turing Machine fully defines   
   >>> the behavior of that machine, and that behavior becomes the MEANING   
   >>> of that string.   
   >>>   
   >>   
   >> That would intuitively seem to be impossibly false   
   >> until we see a counter-example that refutes it.   
   >   
   > No, it is a definition   
   >   
   >>   
   >> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞   
   >> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn   
   >> (a) Ĥ copies its input ⟨Ĥ⟩   
   >> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>   
   >> When ⟨Ĥ⟩ ⟨Ĥ⟩ is correctly simulated by Ĥ.embedded_H   
   >> even Mike was fooled into thinking that the simulated   
   >> ⟨Ĥ⟩ would reach its simulated final state of ⟨Ĥ.qn⟩ if   
   >> we just waited long enough.   
   >>   
   >>   
   >   
   > No, if ⟨Ĥ⟩ ⟨Ĥ⟩ is actually correctly emulated by H/Ĥ.embedded_H   
   it runs   
   > forever because neither H or Ĥ.embedded_H  will abort their simulation   
   > and that emulation doesn't reach a final state and H fails to be a decider.   
      
   In other words neither Ĥ nor any human being   
   could possibly see the repeating sequence even   
   after it has repeated 100 million times?   
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)