3 ms·
http://en.wikipedia.org/wiki/Bernard_Chazelle http://en.wikipedia.org/wiki/Bernard_Chazelle
by hc 18y ago
http://en.wikipedia.org/wiki/Bernard_Chazelle http://en.wikipedia.org/wiki/Bernard_Chazelle
- jcl 18y agoI had a post prepared saying basically the same thing (Chazelle's algorithm work is awesome), but then I realized that bdr is, strictly speaking, correct: the number of combinations of notes you can play is a factorial of the number of notes, and factorials grow faster than exponential functions. http://en.wikipedia.org/wiki/Factorial#Rate_of_growth http://en.wikipedia.org/wiki/Factorial#Rate_of_growth Of course, when you're writing an essay on the relationship of music and very simple math, I think it's forgivable to use "exponential" to mean "growing at or faster than an exponential rate". Using a more specific term like "factorial", "combinatorial", or "super-exponential" sounds pedantic and out-of-place.
- akd 18y agoI don't understand. If you have 300 notes, and 12 tones, the number of different melodies you can play is 12^300 (12 choices at each step). Why is it 300 factorial? You don't have 300 distinct entities to permute.
- bdr 18y agoIt was in the context of drawing the diagonals on the polygon, so I thought of quadratic growth. I guess everyone interpreted it differently, and the author is justified in using 'exponential' in an informal way.