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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?=
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On 5/26/24 10:06 PM, olcott wrote:
> When Ĥ is applied to ⟨Ĥ⟩
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
>   Ĥ copies its own Turing machine description: ⟨Ĥ⟩
>   then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input.
> 
> It is an easily verified fact that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by
> embedded_H cannot possibly reach its own simulated final state of
> ⟨Ĥ.qn⟩ in any finite sequence of steps such as Googolplex ^ Googolplex
> number of steps. https://en.wikipedia.org/wiki/Googolplex

So, it can verify that if H / embedded_H was programmed not to halt it 
simulation, then the H^ built on that H will be non-halting, but that 
doesn't say anything about the DIFFERENT H^ built on an H that does 
abort its simulation and returns 0.

Remember, each H you start with becomes a SEPERATE problem with a 
SEPARATE input H^, and the results of one input say nothing about the 
results of other inputs.

EVERY H^, built on an H that answer qn for H (H^) (H^) will, when 
simulated for enough steps, reach a final state.


Your claim is the equivalent of looking at a 10-story office building 
when you are studing the behavior of cats.

> 
> UNLESS YOU CAN PROVE THAT A UTM CANNOT POSSIBLY BE ADAPTED TO COUNT
> THE NUMBER OF STEPS AND THEN STOP I AM CORRECT AND YOU ARE DISHONEST

As I said, it can be, it just isn't a UTM any more.

Just like if you take an electric car and change the engine to be an 
internal combusion engine, you no longer have an Electric car.

> 
> *Your dishonest dodge strawman deception is not me lying*
> *Your dishonest dodge strawman deception is not me lying*
> *Your dishonest dodge strawman deception is not me lying*
> 
> UNLESS YOU CAN PROVE THAT A UTM CANNOT POSSIBLY BE ADAPTED TO COUNT
> THE NUMBER OF STEPS AND THEN STOP I AM CORRECT AND YOU ARE DISHONEST
> 

As I said, it just isn't a UTM any more, and thus its partial simulation 
doesn't say anything about the input not halting, or that the correct 
simulation of the input would be non-halting.

Only that its partial simulation didn't YET reach a halting state.


You are just proving that you have no understanding of the field that 
you are talking about.

H can show that it didn't reach a final state.

It can't show that a correct simulation of its input would not reach a 
final state, as changing H / embedded_H doesn't change the H^ that was 
given to the origianl H, so the "new H" will get that same input for the 
arguement about what H could have done if it was different, as the 
question is still about the input that the original H was actually given.

And, there is no way to build an H^ whoes correct description will ask 
about the template that you tried to construct in your POOP theory, so 
you are stuck with looking at the set of posible H's all getting the H^ 
that was built on the original H that you need to show was correct. Some 
of your H's WILL beable to reach the final state, so yor claim is false.