XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/1/2025 3:48 PM, Richard Damon wrote:   
   > On 8/1/25 4:33 PM, olcott wrote:   
   >> 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?   
   >>   
   >   
   > Doesn't matter if is can determine what will happen, to correctly   
   > simulate the behavior, you have to do it.   
   >   
      
   It seems that even after hundreds of corrections   
   you still do not understand that this infinite   
   sequence can be correctly detected in finite steps.   
      
   --   
   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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