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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Tue, 12 Mar 2024 20:47:03 -0500
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On 3/12/2024 8:05 PM, immibis wrote:
> On 13/03/24 01:18, olcott wrote:
>> On 3/12/2024 7:10 PM, immibis wrote:
>>> On 13/03/24 00:56, olcott wrote:
>>>> On 3/12/2024 6:38 PM, immibis wrote:
>>>>> On 13/03/24 00:24, olcott wrote:
>>>>>> On 3/12/2024 6:05 PM, immibis wrote:
>>>>>>> On 12/03/24 23:53, olcott wrote:
>>>>>>>> On 3/12/2024 5:30 PM, Richard Damon wrote:
>>>>>>>>> On 3/12/24 2:34 PM, olcott wrote:
>>>>>>>>>> On 3/12/2024 4:23 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/12/24 1:11 PM, olcott wrote:
>>>>>>>>>>>> Not exactly. A pair of otherwise identical machines that
>>>>>>>>>>>> (that are contained within the above specified set)
>>>>>>>>>>>> only differ by return value will both be wrong on the
>>>>>>>>>>>> same pathological input.
>>>>>>>>>>>
>>>>>>>>>>> You mean a pair of DIFFERENT machines. Any difference is 
>>>>>>>>>>> different.
>>>>>>>>>>
>>>>>>>>>> Every decider/input pair (referenced in the above set) has a
>>>>>>>>>> corresponding decider/input pair that only differs by the return
>>>>>>>>>> value of its decider.
>>>>>>>>>
>>>>>>>>> Nope.
>>>>>>>>>
>>>>>>>> ∀ H ∈ Turing_Machines_Returning_Boolean
>>>>>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>
>>>>>>>> Every H/TMD pair (referenced in the above set) has a
>>>>>>>> corresponding H/TMD pair that only differs by the return
>>>>>>>> value of its Boolean_TM.
>>>>>>>>
>>>>>>>> That both of these H/TMD pairs get the wrong answer proves that
>>>>>>>> their question was incorrect because the opposite answer to the
>>>>>>>> same question is also proven to be incorrect.
>>>>>>>>
>>>>>>>
>>>>>>> Nobody knows what the fuck you are talking about. You have to 
>>>>>>> actually explain it. The same machine always gives the same 
>>>>>>> return value on the same input.
>>>>>>>
>>>>>>
>>>>>> It has taken me twenty years to translate my intuitions into
>>>>>> words that can possibly understood.
>>>>>
>>>>> You failed.
>>>>>
>>>>>> A pair of Turing Machines that return Boolean that are identical
>>>>>> besides their return value that cannot decide some property of
>>>>>> the same input are being asked the same YES/NO question having
>>>>>> no correct YES/NO answer.
>>>>>
>>>>> https://en.wikipedia.org/wiki/Turing_machine#Formal_definition
>>>>> A Turing machine is ⟨Q, Γ, b, Σ, δ, q0, F⟩
>>>>> Show me two ⟨Q, Γ, b, Σ, δ, q0, F⟩ that are identical besides their 
>>>>> return value.
>>>>> You can't because you are talking nonsense. they don't exist.
>>>>
>>>> Turing machine descriptions that are identical finite strings
>>>> except for the the 1/0 that they write the their exact same
>>>> tape relative location.
>>>
>>> So which part of ⟨Q, Γ, b, Σ, δ, q0, F⟩ is different?
>> Exactly one element of Q differs by writing a 1 instead of a 0.
> 
> That's part of δ but this mistake doesn't matter.
> 
> It wasn't clear whether you were talking about a Turing machine that was 
> somehow identical but gave a different return value, or one that was not 
> identical. Now you have explained it is not identical.
> 
They are identical except for their return value that is specified
in a single state that is different.

*This means that they implement the exact same algorithm*

A protocol can be defined so that Turing machine descriptions always
implement their return value in their state with the largest Natural
Number value. This allows other Turing machines to determine identical
algorithms except for return value.

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