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From: Ben Bacarisse <ben@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: Yet another contribution to the P-NP question
Date: Sun, 29 Sep 2024 22:56:24 +0100
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Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

> On 29/09/2024 01:30, Ben Bacarisse wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>> 
>>> On 27/09/2024 23:42, Ben Bacarisse wrote:
>>>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>>>
>>>>> On 27/09/2024 00:34, Ben Bacarisse wrote:
>>>>>> nnymous109@gmail.com (nnymous109) writes:
>>>>>>
>>>>>>> Also, I did not know this yesterday, but alternatively, you can access
>>>>>>> the document directly through the following link:
>>>>>>> https://figshare.com/articles/preprint/On_Higher_Order_Recursions_25SEP2024/27106759?file=49414237
>>>>>> I am hoping that this is a joke.  If it is a joke, then I say well done
>>>>>> sir (or madam)[*].
>>>>>> But I fear it is not a joke, in which case I have a problem with the
>>>>>> first line.  If you want two of the states to be symbols (and there are
>>>>>> points later on that confirm that this is not a typo) then you need to
>>>>>> explain why early on.  You are free to define what you want, but a paper
>>>>>> that starts "let 2 < 1" will have the reader wrong-footed from the
>>>>>> start.
>>>>>
>>>>> You mean q_accept and q_reject?  It looks like they are just to represent
>>>>> the accept and reject states, not tape symbols?  Calling them symbols is
>>>>> like calling q_0 a symbol, which seems harmless to me - is it just that you
>>>>> want to call them "labels" or something other than "symbols"?
>>>> Later he/she writes
>>>>      (Omega U {q_accept, q_reject})*
>>>> where * is, presumably, the Kleene closure.  Omega is the set of
>>>> non-blank tape symbols of the TMs under discussion so these states are
>>>> used to make "strings" with other tape symbols.
>>>> I agree that what the states actually are is irrelevant, but that two of
>>>> them are later used like this is presumably important.
>>>>
>>>>> I don't fully get the notation though - e.g. it seems to me that the TMs
>>>>> have tape symbols and states, but I don't see any state transition
>>>>> table!
>>>> Right, but that's line 2 and I was starting at line 1!
>>>> I thought it might be joke because of the way the author just piles
>>>> definition on definition using bizarre notations like integral symbols
>>>> but apparently not.
>>>>
>>> Not a joke, for sure.  Stuff like the integral sign needs explanation.
>>> Paragraph [5] looks like a definition? or is it standard in some branch of
>>> computation theory?  I haven't seen it used like that, but wouldn't really
>>> know.
>>>
>>> When someone turns up from outside the established academic establishment
>>> with their own proof it can be hard work deciphering what they're really
>>> trying to say - so many private notations to clarify and so on.  Many
>>> experts reasonably decide they're unable/unwilling to invest enough time on
>>> something very likely to turn out a lost cause.  Anyhow, I hope this thread
>>> gets somewhere as it's likely I'll learn something here!
>> I tried to make one major suggestion to the author: explain (in English)
>> in what way the core of the argument differs from the usual "it must
>> examine all the cases" non-proofs that keep cropping up.
>> 
>>> Of course the paper is very very likely wrong, and likely for a common
>>> underlying reason for such proof attempts, but the author says as much and
>>> asks for assistance rather than insisting they know better than all the
>>> experts - so a million miles from the usual class of usenet cranks we
>>> typically see.  [PO, WM, AP, Nam/KD, JSH etc... all duffers in the sense of
>>> lacking background + ability to express themselves and reason technically,
>>> but not recognising this for whatever reasons.  Ok, WM might be in his own
>>> category as he supposedly has more background than those others.].
>> But there are some worrying signs.  If someone knows little mathematics,
>> why describe a mapping as a homomorphism when there is no topology in
>> play?  Does he or she just mean a bjection?  What has continuity to do
>> with it?  There's a whiff of "that's a nice sounding word, I'll use it"
>> here.
>
> Like PO using words like "isomorphic" and "tautology" without any
> understanding of their technical meanings.  That's possible...
>
> It looks like you might be confusing "homomorphism" and "homeomorphism"
> though.  God knows they deserve to be muddled!  Who invents these names?
> :)

You are right.  I had seen "homeomorphism" where it was absent.
....

> (This aside, you point could still apply.)

It's unclear as the algebra is unspecified.  There's a lot that's unclear.

-- 
Ben.