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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a
 new basis
Date: Sun, 3 Nov 2024 09:13:56 -0600
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On 11/3/2024 7:04 AM, Mikko wrote:
> On 2024-11-02 12:24:29 +0000, olcott said:
> 
>>
>> HHH does compute the mapping from its input DDD
>> to the actual behavior that DDD specifies and this
>> DOES INCLUDE HHH emulating itself emulating DDD.
> 
> Yes but not the particular mapping required by the halting problem.
> 

Yes it is the particular mapping required by the halting problem.
The exact same process occurs in the Linz proof.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨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⟩
(g) goto (d) with one more level of simulation

The initial input to the directly executed
embedded_H never reaches its own ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩.

embedded_H is not allowed to report on its own behavior
it is only allowed to report on the behavior of its input.

>> HHH1 does compute the mapping from its input DDD
>> to the actual behavior that DDD specifies and this
>> DOES NOT INCLUDE HHH1 emulating itself emulating DDD.
> 
> The behavour specified by DDD is the same in both cases, 

*That is counter-factual*

DDD emulated by HHH
CANNOT POSSIBLY reach its own return instruction.

DDD emulated by HHH1
DOES REACH its own return instruction.

Are you so totally clueless that you can't see this?

> incuding
> the behaviour of HHH(DDD). The mapping computed by HHH1 is different
> from HHH so at least one of them is not the mapping required by the
> halting problem (and in fact the other isn't, either).
> 
>> It seems ridiculously stupid for everyone here to simply
>> ignore how pathological self-reference DOES IN FACT
>> change the behavior of DDD.
> 
> The pathological self-reference does not change anything.

*That is counter-factual*

DDD emulated by HHH
CANNOT POSSIBLY reach its own return instruction.

DDD emulated by HHH1
DOES REACH its own return instruction.

Are you so totally clueless that you can't see this?


>  It just
> is there. But it is not very pathological as HHH can detect it
> and terminate anyway.
> 



-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer