On 3/12/2017 6:25 AM, Ben Bacarisse wrote:
> peteolcott <peteolcott@gmail.com> writes:
>
>> http://LiarParadox.org/HP_Infinite_Recursion.pdf
>>
>> As this page 319 of An Introduction to Formal Languages and Automata
>> by Peter Linz 1990 indicates
>>
>> From H' we construct another Turing machine H-Hat. This new machine
>> takes as input Wm, copies it then behaves exactly like H'.
>>
>> q0 Wm |-* H-Hat q0 Wm Wm...
>>
>> Page 320 indicates that we apply H-Hat to itself as input.
>
> No, it shows H^ acting on w^ which is the representation of H^ in
> {0,1}*.
>
>> The problem is that every H-Hat needs a pair of inputs.
>
> No. H^ needs nothing. Like any TM, it acts on a tape and has no
> needs.
>
>> H-Hat takes an H-Hat as input
>
> No "an" H^. It takes *the* representation of H^ as input...
>
>> and copies it so that it
>> can analyze how its input H-hat would analyze the copy
>> of H-Hat that it just made.
>
> No, it copies it. It does this for no purpose at all. It might analyze
> the input or it may not. It might take the square root of the input, or
> it might immediately halt. H^ is simply H with an initial step. H is
> arbitrary. For every possible Turing machine M, M^ can be constructed.
>
>> The input H-Hat would have to copy its own input H-Hat
>> so that it can analyze what its own input H-Hat would
>> do on its own input, on and on forever...
>
> You write as H^ has some "intent" where in fact H^ just copies the input
> but is otherwise the same as H. If your humanising metaphors about what
> H^ "would have" to do is intended to explain why, in your mind, no H
> satisfying the requirements that were put on it can exist, then OK, but
> I doubt your explanation will help anyone else to understand the proof.
>
> <snip>
>

Do you agree that the definition of the Linz Ĥ on page 319
http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf

specifies infinitely nested simulation to the internal halt
decider of Linz Ĥ @Ĥq0 wM wM (the second q0 start state of Ĥ)
when this internal halt decider is based on simulating its input?

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein