Monday, November 9, 2009
CICADAS & MATH - AN AMAZING STORY
DO NOT BACK OUT OF THIS BLOG BECAUSE YOU ARE INTIMIDATED BY MATH. WHAT YOU WILL READ IS MOST FASCINATING IF YOU JUST DON'T GET HUNG UP ON "PRIME NUMBERS" AND "INTEGERS."
One of my favorite bloggers, Tom McMahon, finds all kinds of interesting things to talk about. I found this on his blog but he had found it earlier on the blog "Neatorma." It's fascinating. For us who are totally stupid when it comes to math (that includes ME!), it isn't the math that is special, it is the result of the math that astounds! So give it a read.
CICADA-GENERATED PRIME NUMBERS
Cicadas are winged insects that evolved around 1.8 million years ago during the Pleistocene epoch, when glaciers advanced and retreated across North America. Cicadas of the genus Magicicada spend most of their lives below the ground, feeding on the juices of plant roots, and then emerge, mate, and die quickly. These creatures display a startling behavior: Their emergence is synchronized with periods of years that are usually the prime numbers 13 and 17. (A prime number is an integer such as 11, 13, and 17 that has only two integer divisors: 1 and itself.) During the spring of their 13th or 17th year, these periodical cicadas construct an exit tunnel. Sometimes more than 1.5 million individuals emerge in a single acre; this abundance of bodies may have survival value as they overwhelm predators such as birds that cannot possibly eat them all at once.
Some researchers have speculated that the evolution of prime-number life cycles occurred so that the creatures increased their chances of evading shorter-lived predators and parasites. For example, if these cicadas had 12-year life cycles, all predators with life cycles of 2, 3, 4, or 6 years might more easily find the insects. Mario Markus of the Max Planck Institute for Molecular Physiology in Dortmund, Germany, and his coworkers discovered that these kinds of prime-number cycles arise naturally from evolutionary mathematical models of interactions between predator and prey. In order to experiment, they first assigned random life-cycle durations to their computer-simulated populations. After some time, a sequence of mutations always locked the synthetic cicadas into a stable prime-number cycle.