Path: ...!Xl.tags.giganews.com!local-1.nntp.ord.giganews.com!nntp.brightview.co.uk!news.brightview.co.uk.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 29 Sep 2024 02:40:26 +0000
Subject: Re: Yet another contribution to the P-NP question
Newsgroups: comp.theory
References: <85955d539da522cf777ab489101c0e2a@www.rocksolidbbs.com>
 <4b415dd5a91ac648bee8224fc3c28aa19706e06f.camel@gmail.com>
 <a4cacd3261a32cb9a769fbfe6ed1cd15@www.rocksolidbbs.com>
 <87cykqgfax.fsf@bsb.me.uk>
 <MWqdnZDONIeEjWv7nZ2dnZfqnPudnZ2d@brightview.co.uk>
 <877cawhg6g.fsf@bsb.me.uk>
 <AqidnfQXj44K-Gr7nZ2dnZfqnPidnZ2d@brightview.co.uk>
 <87plonfgj9.fsf@bsb.me.uk>
From: Mike Terry <news.dead.person.stones@darjeeling.plus.com>
Date: Sun, 29 Sep 2024 03:40:25 +0100
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
 Firefox/91.0 SeaMonkey/2.53.18.2
MIME-Version: 1.0
In-Reply-To: <87plonfgj9.fsf@bsb.me.uk>
Content-Type: text/plain; charset=windows-1252; format=flowed
Content-Transfer-Encoding: 7bit
Message-ID: <HLScnXO2j7iHI2X7nZ2dnZfqn_idnZ2d@brightview.co.uk>
Lines: 88
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-k9mhVgUx9cHmtFqGFilYcW8bULHhiVZRFQiIPCMSV/aNHH/sFr6yYTlCSpCAElWar7N6ux4CtlkZNwE!d4Xj4+dDL/7ujBGwn+60gHg/y1MwonCIW2ropeAIErAO4njKdCOVMWv3zM0bTh6nE5D0HCzFY1l7!J4q+OEBagUACgGz5vxyGyUvT1Og=
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
Bytes: 6199

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?  :)

"homeomorphism" (with the 'e') is used in topology and is all to do with continuity.  "homomorphism" 
(no 'e') is a general algebra term (applied to groups/fields/whatever), not based on continuity.

   <https://en.wikipedia.org/wiki/Homomorphism>
   <https://en.wikipedia.org/wiki/Homeomorphism>

(This aside, you point could still apply.)

Mike.