Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs
Date: Mon, 5 May 2025 21:32:01 -0500
Organization: A noiseless patient Spider
Lines: 78
Message-ID: <vvbsb1$1us1f$4@dont-email.me>
References: <TuuNP.2706011$nb1.2053729@fx01.ams4>
 <87cyd5182l.fsf@nosuchdomain.example.com> <vu6lnf$39fls$2@dont-email.me>
 <vugddv$b21g$2@dont-email.me> <vui4uf$20dpc$1@dont-email.me>
 <vuivtb$2lf64$3@dont-email.me> <vungtl$2v2kr$1@dont-email.me>
 <vuoaac$3jn5n$5@dont-email.me> <vuq81v$1hjka$1@dont-email.me>
 <vutefq$gmbi$3@dont-email.me> <vv22hs$puqs$1@dont-email.me>
 <vv89ll$2erlq$4@dont-email.me> <vv8en2$2kjgk$3@dont-email.me>
 <vv8ot8$2ub3p$1@dont-email.me> <vv8pqu$2ut5q$1@dont-email.me>
 <5YRRP.109778$_Npd.21893@fx01.ams4> <vv9142$35pgh$1@dont-email.me>
 <018f45d4807ba7b0092370889153d51d798e112e@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 06 May 2025 04:32:02 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="4d3877b25e07ae675aebb853b858fd37";
	logging-data="2060335"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19NX+9/6lYEN9gLtmXkcvxi"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:u9N2Yv6tcx55yeJCuEt879GrnqA=
X-Antivirus: Norton (VPS 250505-6, 5/5/2025), Outbound message
X-Antivirus-Status: Clean
Content-Language: en-US
In-Reply-To: <018f45d4807ba7b0092370889153d51d798e112e@i2pn2.org>

On 5/5/2025 8:19 PM, Richard Damon wrote:
> On 5/4/25 8:35 PM, olcott wrote:
>> On 5/4/2025 5:34 PM, Mr Flibble wrote:
>>> On Sun, 04 May 2025 23:30:54 +0100, Richard Heathfield wrote:
>>>
>>>> On 04/05/2025 23:15, olcott wrote:
>>>>> On 5/4/2025 2:21 PM, Richard Heathfield wrote:
>>>>>> On 04/05/2025 18:55, olcott wrote:
>>>>>>> Changing my words then rebutting these changed words is dishonest.
>>>>>>>
>>>>>>> Functions computed by Turing Machines require INPUTS and produce
>>>>>>> OUTPUTS DERIVED FROM THESE INPUTS.
>>>>>>
>>>>>> Counter-example: a Turing Machine can calculate pi without any input
>>>>>> whatsoever.
>>>>>>
>>>>>> As Mikko rightly said: a Turing machine does not need to require an
>>>>>> input.
>>>>>>
>>>>>>
>>>>> IT IS NOT COMPUTING FUNCTION THEN
>>>>
>>>> Quoth Alan Turing:
>>>>
>>>> (viii) The limit of a computably convergent sequence is computable.
>>>>
>>>>   From (viii) and TT— 4(1—i-|--i—...) we deduce that TT is computable.
>>>>
>>>> No input required.
>>>>
>>>>> IT IS NOT COMPUTING FUNCTION THEN IT IS NOT COMPUTING FUNCTION THEN IT
>>>>> IS NOT COMPUTING FUNCTION THEN
>>>>>
>>>>> Computable functions are the basic objects of study in computability
>>>>> theory. Computable functions are the formalized analogue of the
>>>>> intuitive notion of algorithms, in the sense that a function is
>>>>> computable if there exists an algorithm that can do the job of the
>>>>> function, i.e. given an input of the function domain it can return the
>>>>> corresponding output. https://en.wikipedia.org/wiki/ 
>>>>> Computable_function
>>>>
>>>> That's a very second-rate summary of computability. Turing was far more
>>>> interested in whether a computation was possible than whether it needed
>>>> inputs. Do most computations need inputs? Most useful ones that we care
>>>> about, sure. But all? By no means.
>>>>
>>>>> *Computer science is ONLY concerned with computable functions*
>>>>
>>>> Computer science is concerned with the Halting Problem.
>>>> The Halting Problem is concerned with an incomputable function.
>>>> Therefore computer science is concerned with at least one incomputable
>>>> function.
>>>
>>> The function is neither computable nor incomputable because there is no
>>> function at all, just a category error.
>>>
>>> /Flibble
>>
>> You can look at it that way or you can look
>> at it as simulating termination analyzer HHH(DD)
>> does correctly determine that DD cannot possibly
>> reach its own final state, thus is correctly
>> rejected as non-halting.
>>
> 
> Except that isn't the question that is being asked.
> 
> In fact, that question has a trivial answer, as we can make an H0 that 
> just aborts its emulation and returns 0 and it is correct by your 
> definition, 

No that is stupidly wrong as I have said at least 100 times recently.
The termination analyzer must compute the mapping from the input
on the basis of the behavior that this input actually specifies.

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