25 May
2010
25 May
'10
5:48 p.m.
Related to my last reply to your question about "the tiling problem"
vs undecidability...
Ever since they started putting out relevant articles for computer
scientists (in the last year), the American Math Society monthly
"Notices" has gone from dull to fascinating; in the spirit of
open-source, all the articles are available free and online.
The latest ( http://www.ams.org/notices/201003/ ), focusing on
Cryptography issues, has an excellent article that goes into the
tiling problem in great detail -- and yet is a very clear explanation
(IMHO) that isn't predicated on incomprehensible (to the general
public) mathematical formalisms.
http://www.ams.org/notices/201003/rtx100300343p.pdf
Can't Decide? Undecide! by Chaim Goodman-Strauss
See also: http://www.srcf.ucam.org/~jsm28/tiling/
I've posted previously about other excellent articles in a previous
issue "Mathematics and the Arts" ( http://www.ams.org/notices/201001/
) with a though-provoking introductory essay by Sir Michael Atiyah :
In the broad light of day mathemati-
cians check their equations and their
proofs, leaving no stone unturned in
their search for rigour. But, at night,
under the full moon, they dream, they
float among the stars and wonder at
the miracle of the heavens. They are
inspired. Without dreams there is no
art, no mathematics, no life.
Niels
http://nielsmayer.com
PS: I think the "tiling problem" is actually a direct analogy to music
making... which involves fitting together "tiles" (musical passages,
patterns, etc) that are highly constrained in terms of "geometry"
(pitch, key, time-signature, BPM, starting and ending pitches or
chords). Music making is clearly an "undecidable" problem, which is
where human creativity comes in. Can computers help us "tile" music
more easily and therefore augment our musical creativity??