XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 8:18 PM, Richard Damon wrote:   
   > On 8/4/25 6:42 PM, olcott wrote:   
   >> On 8/4/2025 5:34 PM, Mr Flibble wrote:   
   >>> On Mon, 04 Aug 2025 13:29:04 -0500, olcott wrote:   
   >>>   
   >>>> Diagonalization only arises when one assumes that a Turing machine   
   >>>> decider must report on its own behavior instead of the behavior   
   >>>> specified by its machine description.   
   >>>>   
   >>>> Everyone assumes that these must always be the same.   
   >>>> That assumption is proven to be incorrect.   
   >>>>   
   >>>> When one assumes a halt decider based on a UTM then the simulated input   
   >>>> remains stuck in recursive simulation never reaching simulated states   
   >>>> ⟨Ĥ.∞⟩ or ⟨Ĥ.qn⟩.   
   >>>>   
   >>>> 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⟩   
   >>>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩   
   >>>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>> on and on never reaching any simulated final state of ⟨Ĥ.qn⟩   
   >>>>   
   >>>> When embedded_H aborts its simulation and transitions to Ĥ.qn on the   
   >>>> basis that its simulated input cannot possibly reach its own simulated   
   >>>> final halt state of ⟨Ĥ.qn⟩ embedded_H is correct.   
   >>>>   
   >>>> This causes embedded_H itself to halt, thus contradicting its result   
   >>>> *only if a Turing machine decider can be applied to its actual self*   
   >>>> and   
   >>>> not merely its own machine description.   
   >>>   
   >>> Your Ĥ is not a halt decider as defined by the Halting Problem so has   
   >>> nothing to do with the Halting Problem.   
   >>>   
   >>> /Flibble   
   >>   
   >> You have this part incorrectly. Ask Richard because   
   >> of what he explained to you the other night he may   
   >> correct you on this.   
   >>   
   >   
   > Ĥ isn't a halt decider, H is.   
      
   That is quite a bit less than perfectly   
   accurate see if you can do better.   
   H is a what?   
      
      
   --   
   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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