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

On 11/7/2024 3:56 AM, Mikko wrote:

On 2024-11-06 15:26:06 +0000, olcott said:
 

On 11/6/2024 8:39 AM, Mikko wrote:

On 2024-11-05 13:18:43 +0000, olcott said:
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On 11/5/2024 3:01 AM, Mikko wrote:

On 2024-11-03 15:13:56 +0000, olcott said:
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On 11/3/2024 7:04 AM, Mikko wrote:

On 2024-11-02 12:24:29 +0000, olcott said:
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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.

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Yes but not the particular mapping required by the halting problem.

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

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The halting probelm requires that every halt decider terminates.
If HHH(DDD) terminates so does DDD. The halting problmen requires
that if DDD terminates then HHH(DDD) accepts as halting.

>
void Infinite_Loop()
{
   HERE: goto HERE;
   return;
}
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No that is false.
The measure is whether a C function can possibly
reach its "return" instruction final state.

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Not in the original problem but the question whether a particular strictly
C function will ever reach its return instruction is equally hard. About

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It has always been about whether or not a finite string input
specifies a computation that reaches its final state.

 Not really. The original problem was not a halting problem but Turing's

Exactly. The actual Halting Problem was called that by Davis
in 1952. Not the same as Turing proof.
*So we are back to The Halting Problem itself*
has always been about whether or not a finite string input
specifies a computation that reaches its final state.
DDD specifies a non-halting computation to HHH because
DDD calls HHH in recursive simulation.
DDD specifies a halting computation to HHH1 because
DDD DOES NOT CALL HHH1 in recursive simulation.
*Ignoring these key differences is ridiculously foolish*

solution was so easily adapted to the halting problem that we can say
that Turing solved the halting problem before nobody had presented it.
 Turings original problem was to find a method to determine whether the
given Turing machine with given input ceases to write unerasable symbols.
Modern Turing machines don't even start as any symbol can be erased or
overwritten.
 

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