XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   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.   
      
   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.   
      
      
   --   
   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   
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