[seqfan] Intentional constructions and the importance of trivial information. Was: "Borderline numerology?"

[Antti Karttunen]

On Thu, Aug 28, 2014 at 12:34 AM,  <seqfan-request at list.seqfan.eu> wrote:
>
> Message: 8
> Date: Wed, 27 Aug 2014 14:19:39 -0700
> From: Andrew Weimholt <andrew.weimholt at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Borderline numerology?
> Message-ID:
>         <CAKPToLWc_zme8YTGoEZK-ZfY7B25MiriTNLTpENpxFCXfB=fqg at mail.gmail.com>
> Content-Type: text/plain; charset=UTF-8
>
> I noticed this comment in http://oeis.org/A000796 (Decimal expansion of pi)
>
> (quote)
> A 144 X 144 magic square of 7th powers was recently constructed by
> Toshihiro Shirakawa. The magic sum =
> 3141592653589793238462643383279502884197169399375105. Amazingly, the digits
> of its magic sum are exactly the 52 first digits of Pi! See the MultiMagic
> Squares link for details. - Christian Boyer, Dec 13 2013
> (end quote)
>
> Not really amazing if you ask me. Toshihiro Shirakawa intentionally chose
> the sum and constructed a magic square around it.
> I don't see any real relevance to pi, since almost any arbitrary sequence
> of digits can be made into a magic sum of a suitably sized magic square.
> Drawing any connection between pi and magic squares smells of numerology.
>
> So, does, this comment really belong here?

Somewhat tangential point:

I submit a lots of permutations of natural numbers, and I try to add
to each some comment about its behaviour. Something like: "this
permutation maps all number of the form ... (Axxxxxx) to the terms of
Ayyyyyy, in some order."

In most of these cases, there is _nothing deep_ (or "amazing") in
these observations (that would e.g. really link Axxxxxx to Ayyyyyy in
some secret way), but instead, they trivially follow from the
definition of the permutation itself (or the permutations, if the
sequence in question is a composite of two or even three).

Sometimes I have added a side-comment to a formula saying something
like "[Follows from the definitions of the sequences]." The intention
of this is to warn about the eventual ennui, in case the user thought
there were anything deep in those claims.

Similarly, with permutations, "As composition of related
permutations:" on the formula-line warns that if the user tries to
compute/understand the sequence based only on any sequences in the
formula-section BELOW that line, (s)he will probably just left in the
endless circle chasing links in the maze of cute permutations all
linking to each other.


Still, I consider it a good habit to add such comments, so that
potential users will at least get some initial grasp "for what" the
permutation is for, and to have at least some point to start from, for
maybe finding also "amazing" results at one day. (Maybe also my future
self, which would have forgotten all the details meanwhile, without a
help of the external memory, in which role the OEIS serves us.)


Moreover, I very much would like that every sequence had a link (on
the formula and/or crossrefs-section) to such sequences like +1/-1
variant, or an "inverse" sequence (of any injection, if inverse(s), if
these sequences exist), regardless of how "trivial" this information
might be. (So I thank e.g. Reinhard Zumkeller for adding many such
links).

Indeed, most of the time I'm not searching from OEIS any "deep" or
"amazing" information, but contrarywise, for just such trivial things
like, "what the heck was the A-number of that sequence, which was
otherwise like Azzzzzz, but was instead ..."



>
> Andrew
>

Best,

Antti