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?? _______________________________________________ Linux-audio-dev mailing list [email protected] http://lists.linuxaudio.org/listinfo/linux-audio-dev
