More application in math (Was: Categories)

[Jonathan Post]

In one sense, I am one of the worst people to address this important
question.  Setting aside my thousand silly made-up sequences, and a hundred
or so actually tied to research that I intend to have (or already have)
cited in journal submissions, there are the cases of stumbling on a new (to
OEIS) sequence in a book or journal.

In such cases, I think that one should not only give the most important
reference (the book ar article itself), but also try to extract a short
statement of context from the abstract, or chapter introduction, or key
narrative text.  To pick my most recent example:

NEW SEQUENCE FROM Jonathan Vos Post

%I A000001
%S A000001 1, 3, 12, 123, 2536
%N A000001 The number of generalized Hantzsche-Wendt manifolds in
dimension n.
%C A000001 Rossetti and Szczepanski study the family of closed
Riemannian n-manifolds with holonomy group isomorphic to (Z_2)^(n-1), which
they call generalized Hantzsche-Wendt manifolds.  They prove results on
their structure, compute some invariants, find relations between them
which they illustrate with a graph connecting the family. A flat manifold
is a closed Riemannian manifold with zero sectional curvature.  From
Bieberbach's theorems, we know that in each dimension there are only a
finite number of such manifolds (up to affine equivalence), and efforts
are underway to classify them. Recently this has been completed up
through dimension 6.  In dimension 2, the Klein bottle belongs in this
family, and in dimension 3 there are 3 of them: a classical flat manifold
first described by Hantzsche and Wendt (now called "didicosm") and 2
nonorientable ones.
%D A000001 Juan P. Rossetti and Andrzej Szczepanski, Generalized
Hantzsche-Wendt flat manifolds, Rev. Mat. Iberoamericana 21 (2005) no. 3,
pp.
1053-1070.
%e A000001 This is adapted from the table on p.1061; beta is first
Betti number.
dim.|.beta=0.|.beta=1.|.orient.|.nonorient.|.total.|.holonomy reps|
.2.|..0.....|..1.....|..0.....|..1........|..1....|.1............|
.3.|..1.....|..2.....|..1.....|..2........|..3....|.2............|
.4.|..2.....|..10....|..0.....|..12.......|..12...|.2............|
.5.|..23....|..100...|..2.....|..121......|..123..|.3............|
.6.|..352...|..2184..|..0.....|..2536.....|..2536.|.3............|
%O A000001 2,2
%K A000001 ,hard,nonn,
%A A000001 Jonathan Vos Post
(jvospost2 at yahoo.com<http://us.f551.mail.yahoo.com/ym/Compose?To=jvospost2@yahoo.com&YY=57406&y5beta=yes&y5beta=yes&order=down&sort=date&pos=0&view=a&head=b>),
Dec 01 2006

This is a hard sequence based on topology not familar with most OEIS users.
But then again, the amazing coding and n-sphere packing citations of njas
are not well known to a majority of OEIS readers.

The problem is in walking the tightrope between comments redundant to
experts in the field, who alone really care about the sequence, but which
give a summary (even if oversimplified), and comments that crowd too much
data.

Illustrations are also relevant to this.  Sometimes a picture other than the
automatically generated graphs can be worth a kiloword. Sometimes this can
been done crudely in ASCII.  Other times, better to point to a rendering on
a web page somewhere else, even an animation.

This tightrope is parallel to the one of textbooks, since in a way the OEIS
is part of the greatest online textbook of Math.  Others, such as MathWorld
(frequently linked to or from OEIS) take the "encyclopedia" term somewhat
differently, as do wikipedia.

As Theodor Nelson, grandfather of the Web, put it: "Literature is debugged."
He was explaining why hypertext (which he invented) should not constrain the
network structure of literature (including the literature of math, of
Phjysics, ...) but rather enhance the human-friendly aspects of that
literature.

Just my $2 * 10^(-2) worth.

-- Jonathan


On 12/1/06, MARTIN FULLER <martin_n_fuller at btinternet.com> wrote:
>
> Very well put.  OEIS suffers from some of these
> problems too, e.g. some sequences do not give any
> context.  This could be how the sequence is used, or
> how it was reached.  What is the best way to improve
> this aspect of OEIS?
>
> --- franktaw at netscape.net wrote:
>
> > I'd like to put my plug in for more application in
> > math.
> >
> > I heard of a case some years ago where a paper was
> > published about some
> > kind of mathematical object (I think it was a kind
> > of topological
> > space, but it really doesn't matter).  Three or four
> > more papers were
> > published, establishing more and more properties for
> > this type of
> > object - until finally it was proved that they don't
> > exist!  This
> > wouldn't have happened if somebody had asked for an
> > example at an early
> > stage.
> >
> > There is a strong tendency in mathematics to start
> > at the end.  The
> > researcher pursues a line of thought, which
> > eventually leads to a
> > spiffy proof.  The proof is then published, with no
> > hint of the process
> > by which it was reached.  This is a disservice to
> > anybody who might use
> > a similar approach to solve some other problem.  It
> > is especially a
> > disservice when presented to students.
> >
> > On a more personal level, I find when looking a math
> > paper, I want to
> > know how this relates to problems that I am already
> > interested in or at
> > least familiar with.  If I can't get an answer to
> > that, I have a hard
> > time maintaining any interest.
> >
> > Franklin T. Adams-Watters
> >
> >
> ________________________________________________________________________
> > Check Out the new free AIM(R) Mail -- 2 GB of
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>
>
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