Re: The philosophy of computation reformulates existing ideas on a new basis

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