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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, 27 Oct 2024 21:55:13 -0500
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On 10/27/2024 9:26 PM, Richard Damon wrote:
> On 10/27/24 6:01 PM, olcott wrote:
>> On 10/27/2024 12:48 PM, Richard Damon wrote:
>>> On 10/27/24 10:17 AM, olcott wrote:
>>>> I am keeping this post in both sci.logic and comp.theory
>>>> because it focuses on a similar idea to the Curry/Howard
>>>> correspondence between formal systems and computation.
>>>>
>>>> Computation and all of the mathematical and logical operations
>>>> of mathematical logic can be construed as finite string
>>>> transformation rules applied to finite strings.
>>>>
>>>> The semantics associated with finite string tokens can
>>>> be directly accessible to expression in the formal language.
>>>> It is basically an enriched type hierarchy called a knowledge
>>>> ontology.
>>>>
>>>> A computation can be construed as the tape input to a
>>>> Turing machine and its tape output. All of the cases
>>>> where the output was construed as a set of final machine
>>>> states can be written to the tape.
>>>>
>>>> I am not sure but I think that this may broaden the scope
>>>> of a computable function, or not.
>>>
>>> Except that nothing you described related to what a "computabe function" 
>>
>> I intend to reply to other aspects of your reply later
>> on as long as your reply to this reply is not lame.
>>
>> When a Turing machine transforms the contents of its
>> input tape into the contents of its output tape this
>> seems to necessarily always be a computable function
>> no matter what the TM does in-between.
>>
> 
> Yes, a Turing Machine will always be computing the mapping from some 
> computable function.
> 
> It is NOT the "Computable Function" itself, as that is a thing of a 
> different ty[pe.
> 
> It just computed the mapping definied by that function.
> 
> Note, the mapping of the function might not be defined in terms of 
> "finite-strings", but will be something that can be described by a 
> finite string if we want to talk about it being computable.
> 

Yes. We are getting somewhere now.

> For instance, the Halting Function, that the Halting problem is about, 
> is defined with Turing Machines as its input (not finite strings).
> 

Not in the least little bit.
It seems totally crazy that you would say this.

It has always been finite string Turing Machine descriptions.
These finite strings do have a specific semantics associated
with them and that is the semantics of Turing Machines.

> The key point here is that different implementation of a attempted 
> Turing Machines to try to compute this might use different ways of 
> representing the machines, so the function can't just be thought of as 
> taking the string.
> 

A string that maps to the semantics of Turing Machines.
The bytes of x86 machine code have the precisely defined
semantics of the x86 language.

> We can look at the equivalent mapping based on the encoding of the given 
> decider, if the encoding has the required property that a given finite 
> string can only represent one Turing Machine by the rules of that decider.
> 

We simply hypothesize some arbitrary specific standard.
No need to actually do this WHEN WE UNDERSTAND THAT X86
EXAMPLE <IS> ISOMORPHIC TO LINZ.

> Note, This is one spot your HHH/DDD pairing fails, as what you want to 
> claim as the input reprenting DDD does NOT have that property, as the 
> finite string does not represent a specific computation, as it depends 
> on what HHH it is being pair with.

You really can't simply get away with simply ignoring
the self-reference by pretending that it does not exist
without looking foolish.

*MAYBE YOU NEED TO REREAD THIS 10,000 TIMES*
When HHH emulates itself emulating DDD this is different than HHH1 
emulating itself emulating DDD because the first case really happens
and the second case cannot possibly happen.



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