By Shalosh B. Ekhad and Doron Zeilberger
Written: May 1, 1997.
Last Update: July 9, 1997.
At this time of writing, we still need human creative
geniuses, like John Horton Conway, to DEFINE such
marvelous things as surreal numbers and the audioactive
sequence 1, 11, 21, 1211, 111221, 312211, ....
But given the definition, all the rest can be done by
computerkind (with, at present, routine programming
still done by humans.) In ref. [C] of the present
paper, Conway begs: `Can you find a proof in just
a few pages? Please!' (p. 186)
If you count pages modulo routine verification and
programming, then the present proof is about .1-page-long.
Most importantly, download the Maple package
HORTON , without which the present
paper makes little sense.
To understand the present paper, you are advised to
read first
Steve Finch's fascinating essay on Conway's constant..
If you are skeptical, your computer can reproduce the proof
by downloading the
input file for Cosmo , and after about two weeks
(on nice) you should get
the
output file for Cosmo .
If you want to construct the periodic table ab initio, and
at the same time find how each atom splits after it is
acted on by Conway's audioactive operator, the relative
abundance of each element, the minimal polynomial
for Conway's constant lambda, and its value (to 50 digits),
all you have to do (assuming that you have maple and HORTON)
is run
input file for PTlam , and after less than half an
hour, you should get
the
output file for PTlam .
.pdf
.ps
.tex
(Appeared in
Electronic Research Announcement of the Amer. Math. Soc.
3(1997) 78-82.)
Added Sept. 26, 2007: Noam Zeilberger kindly told me about
Kevin Watkins's interesting paper
.
Doron Zeilberger's List of Papers