Re: on "infinitely recursive" and "recursive"

From	André G. Isaak <agisaak@gm.invalid>
Newsgroups	comp.theory
Subject	Re: on "infinitely recursive" and "recursive"
Date	2022-05-01 13:35 -0600
Organization	Christians and Atheists United Against Creeping Agnosticism
Message-ID	<t4mnf0$57d$1@dont-email.me> (permalink)
References	(3 earlier) <d9KdnQZt_bn_T_P_nZ2dnUU7_8xh4p2d@giganews.com> <t4mkci$cj2$1@dont-email.me> <nbGdnW-d1Nd7RPP_nZ2dnUU7_83NnZ2d@giganews.com> <t4mmf8$t33$1@dont-email.me> <VYOdnd2cj9kcQ_P_nZ2dnUU7_8zNnZ2d@giganews.com>

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On 2022-05-01 13:24, olcott wrote:
> On 5/1/2022 2:19 PM, André G. Isaak wrote:
>> On 2022-05-01 13:05, olcott wrote:
>>> On 5/1/2022 1:43 PM, André G. Isaak wrote:
>>>> On 2022-05-01 12:33, olcott wrote:
>>>>> On 5/1/2022 12:30 PM, André G. Isaak wrote:
>>>>>> On 2022-05-01 11:08, Richard Damon wrote:
>>>>>>> On 5/1/22 8:37 AM, Mr Flibble wrote:
>>>>>>>> Recursive definitions are fine, infinitely recursive definitions 
>>>>>>>> (such
>>>>>>>> as The Halting Problem) are INVALID.
>>>>>>>>
>>>>>>>> RECURSIVE and INFINITELY RECURSIVE are TWO DIFFERENT THINGS.
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>>
>>>>>>>
>>>>>>> And the Halting Problem isn't recursive at all, so it can't be 
>>>>>>> infinity recursive. NOTHING in the definition refers to itself.
>>>>>>>
>>>>>>> The counter example is, in a way, "recursive", but that recursion 
>>>>>>> can only become infinite if the proposed Halt Decider turns out 
>>>>>>> to fail to be a Halt Decider.
>>>>>>
>>>>>> Actually, even the counterexample is not recursive. It only 
>>>>>> becomes recursive (or recursive-like) if one assumes that H bases 
>>>>>> its answer on the simulation of its input. And the proof certainly 
>>>>>> does not require that to be the case.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> Since the definition of H is wide open and can be anything at all 
>>>>> that meets the spec, if any of these definitions make the 
>>>>> "impossible" input decidable then this refutes the proofs.
>>>>
>>>> But the spec is as follows:
>>>>
>>>> Hq0 <M> w ⊢* Hqy iff M applied to w halts
>>>>            ⊢* Hqn otherwise
>>>>
>>>> Yours fails to meet this spec.
>>>>
>>>> André
>>>>
>>>
>>> You keep insisting that H must be a mind reader and base it decision 
>>> on something other than its input parameters when you already know 
>>> that all deciders compute the mapping from their inputs to their own 
>>> final state.
>>
>> Even if your view that TM's can only answer about their inputs were 
>> true, the spec is what the spec is. Not every spec can be met.
>>
> 
> I am saying that deciders are defined to compute the mapping from their 
> input parameters to their own accept or reject state, thus any 
> "specification" that contradicts this is fundamentally incorrect.

Specifications can't be 'correct' or 'incorrect'. They can be doable or 
non-doable.

Since you claim to be a software engineer, consider the following:

Someone hires you to write some program. They tell you what the program 
must do and what they ask for is simply not possible for a computer 
program to do (for example, they want you to solve an NP-hard problem in 
linear time).

Would you:

(a) Tell them that the specification is simply not doable

or

(b) Invest thousands of man-hours in writing a program that does 
something not exactly like the spec on the assumption that they will pay 
you for this after you explain to them that their specification was 
incorrect and that therefore this must be what they actually wanted?

The spec is what you WANT the Turing Machine to do. It may or may not be 
possible, but if it isn't possible that doesn't change what it was you 
wanted it to do.

André

-- 
To email remove 'invalid' & replace 'gm' with well known Google mail 
service.

Thread

on "infinitely recursive" and "recursive" Mr Flibble <flibble@reddwarf.jmc> - 2022-05-01 13:37 +0100
  Re: on "infinitely recursive" and "recursive" Ben <ben.usenet@bsb.me.uk> - 2022-05-01 15:39 +0100
    Re: on "infinitely recursive" and "recursive" polcott <polcott2@gmail.com> - 2022-05-01 11:05 -0500
      Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 13:14 -0400
      Re: on "infinitely recursive" and "recursive" Ben <ben.usenet@bsb.me.uk> - 2022-05-02 00:50 +0100
    Re: on "infinitely recursive" and "recursive" Mr Flibble <flibble@reddwarf.jmc> - 2022-05-01 17:17 +0100
      Re: on "infinitely recursive" and "recursive" Ben <ben.usenet@bsb.me.uk> - 2022-05-02 00:44 +0100
        Re: on "infinitely recursive" and "recursive" Mr Flibble <flibble@reddwarf.jmc> - 2022-05-02 01:26 +0100
          Re: on "infinitely recursive" and "recursive" André G. Isaak <agisaak@gm.invalid> - 2022-05-01 18:29 -0600
            Re: on "infinitely recursive" and "recursive" Mr Flibble <flibble@reddwarf.jmc> - 2022-05-02 01:31 +0100
          Re: on "infinitely recursive" and "recursive" Ben <ben.usenet@bsb.me.uk> - 2022-05-02 01:49 +0100
  Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 13:08 -0400
    Re: on "infinitely recursive" and "recursive" olcott <polcott2@gmail.com> - 2022-05-01 12:23 -0500
      Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 14:04 -0400
    Re: on "infinitely recursive" and "recursive" André G. Isaak <agisaak@gm.invalid> - 2022-05-01 11:30 -0600
      Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 14:10 -0400
      Re: on "infinitely recursive" and "recursive" olcott <NoOne@NoWhere.com> - 2022-05-01 13:33 -0500
        Re: on "infinitely recursive" and "recursive" André G. Isaak <agisaak@gm.invalid> - 2022-05-01 12:43 -0600
          Re: on "infinitely recursive" and "recursive" olcott <NoOne@NoWhere.com> - 2022-05-01 14:05 -0500
            Re: on "infinitely recursive" and "recursive" André G. Isaak <agisaak@gm.invalid> - 2022-05-01 13:19 -0600
              Re: on "infinitely recursive" and "recursive" olcott <NoOne@NoWhere.com> - 2022-05-01 14:24 -0500
                Re: on "infinitely recursive" and "recursive" André G. Isaak <agisaak@gm.invalid> - 2022-05-01 13:35 -0600
                Re: on "infinitely recursive" and "recursive" olcott <NoOne@NoWhere.com> - 2022-05-01 14:43 -0500
                Re: on "infinitely recursive" and "recursive" André G. Isaak <agisaak@gm.invalid> - 2022-05-01 13:45 -0600
                Re: on "infinitely recursive" and "recursive" olcott <NoOne@NoWhere.com> - 2022-05-01 14:56 -0500
                Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 15:49 -0400
                Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 15:43 -0400
            Re: on "infinitely recursive" and "recursive" Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-01 12:21 -0700
              Re: on "infinitely recursive" and "recursive" olcott <NoOne@NoWhere.com> - 2022-05-01 14:27 -0500
                Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 15:52 -0400
              Re: on "infinitely recursive" and "recursive" Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-05-01 14:10 -0700
                Re: on "infinitely recursive" and "recursive" Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-02 02:53 -0700
                Re: on "infinitely recursive" and "recursive" olcott <polcott2@gmail.com> - 2022-05-02 08:31 -0500
                Re: on "infinitely recursive" and "recursive" Ben <ben.usenet@bsb.me.uk> - 2022-05-02 15:46 +0100
                Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-02 18:43 -0400
            Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 15:27 -0400
        Re: on "infinitely recursive" and "recursive" Richard Damon <Richard@Damon-Family.org> - 2022-05-01 15:13 -0400

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