New twist(?) on old point-counting problem

[Jonathan Post]

Dear David,

I write a lot of papers, and other manuscripts.  I don't have the proper
tools (I can't make proper TeX for equation-filled papers, for instance, and
still don't own Mathematica). To have gotten 2200 things published (I
include the OEIS here, as well as all the conference proceedings, poems,
plays, short stories, broadcasts, and other categories) -- I first
accumulated over 5000 rejections.  By all means, short of a tenured
professorship or the like, we all have to "keep our day jobs" and do OEIS
and other fun Math on the side.

I'm not trying get all theological here, but the difference between miracle
and coincidence has been known for some time:

Most interesting to some Mathematicians is the use of Bayesian analysis.
See:
Mavrodes, George I. "David Hume and the *Probability* of *Miracles*",
International Journal for Philosophy of Religion, 43(3), (1998), pp.
167-182.

A general discussion begins:

" Aquinas (*Summa Contra Gentiles*, III) says "those things are properly
called miracles which are done by divine agency beyond the order commonly
observed in nature *(praeter ordinem communiter observatum in rebus*)." A
miracle, philosophically speaking, is never a mere coincidence no matter how
extraordinary or significant. (If you miss a plane and the plane crashes,
that is not a miracle unless God intervened in the natural course of events
causing you to miss the flight.) ..."
[Miracles*, First published Wed Sep 4, 1996; substantive revision Fri Sep
16, 2005, Stanford Encyclopedia of Philosophy]*
http://plato.stanford.edu/entries/miracles/

Hebrew and Arabic philsophers debated this for centuries, either taking a
pre-Aristotelian, or (in Medieval times) Aristotelian or contra-Aristotelian
stance. Modern Math and Logic has a different spin on such mysteries, but
the popular culture is still in a pre-modern condition.  I say this from a
country where rorughly half the citizens don't believe in Evolution by
Natural Selection, and I've had student to whom I was teaching College
Astronomy deny that human beings had actually walked on the Moon.  They had
weird hoax/conspiracy theories.  Of my hundreds of teenaged students (not my
thousands of adult students) a greater percentage, by show of hands,
believed in UFOs than believed the'd ever collect Social Security checks
upon retirement.

Innumeracy?  Tip of the iceberg.  "Against stupidity, the Gods themselves
contend in vain." [Friedrich von Schiller, but see also Isaac Asimov]

**

On 10/28/06, David Wilson <davidwwilson at comcast.net> wrote:
>
>  "Indeed, miracously, this backward difference scheme seems also to work
> for S_4(x)"
>
> Sometimes, when we are presented with some new idea in the absence of the
> path of reasoning that led to it, the idea might seem miraculous. And so it
> is in this case. I have background information that should demystify it
> somewhat, the practical limitations of my present trying life don't give me
> all the time I would like to present these matters. I would love to have the
> time and money to get the right tools to create proper manuscripts, but I
> don't. Even now, I have to get ready to go to work. As soon as time
> permits, I will show you the track of reasoning that led to this triangle of
> numbers. It is really nothing miraculous.
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20061028/d3960377/attachment-0003.htm>