Re: Yet another contribution to the P-NP question

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.