A key creative breakthrough occurred when Emory mathematicians Ken Ono and Zach Kent were hiking.
Original Article: Walk in the woods leads to math ‘aha!’
Walk in the woods leads to math ‘aha!’
Posted By Carol Clark-Emory On January 24, 2011 (1:03 pm) In Top Stories
EMORY (US) — The recent discovery that partition numbers—the basis for adding and counting—behave like fractals is a mathematical breakthrough centuries in the making.
A partition of a number is a sequence of positive integers that add up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. So we say there are 5 partitions of the number 4.
It sounds simple, and yet the partition numbers grow at an incredible rate. The amount of partitions for the number 10 is 42. For the number 100, the partitions explode to more than 190,000,000.
……
Seeing the forest
Ono’s “dream team” wrestled with the problems for months. “Everything we tried didn’t work,” he says.
A eureka moment happened in September, when Ono and Zach Kent were hiking to Tallulah Falls in northern Georgia. As they walked through the woods, noticing patterns in clumps of trees, Ono and Kent began thinking about what it would be like to “walk” through partition numbers.
“We were standing on some huge rocks, where we could see out over this valley and hear the falls, when we realized partition numbers are fractal,” Ono says. “We both just started laughing.”
The term fractal was invented in 1980 by Benoit Mandelbrot, to describe what seem like irregularities in the geometry of natural forms. The more a viewer zooms into “rough” natural forms, the clearer it becomes that they actually consist of repeating patterns. Not only are fractals beautiful, they have immense practical value in fields as diverse as art to medicine.
Their hike sparked a theory that reveals a new class of fractals, one that dispensed with the problem of infinity. “It’s as though we no longer needed to see all the stars in the universe, because the pattern that keeps repeating forever can be seen on a three-mile walk to Tallulah Falls,” Ono says.
….
A key creative breakthrough occurred when Emory mathematicians Ken Ono, left, and Zach Kent were hiking.
the likelihood note: Nature holds the keys – get outside!
[Photo Credit: Emory University]
