CICADAS IN THERE PRIME
2,300 years ago, the Greek scientific writer, poet and astronomer, Eratosthenes of Cyrene, became the first person to calculate the circumference of the Earth. He also dabbled in a bit of maths, and invented the famous Sieve of Eratosthenes, which is an easy method for finding prime numbers. But now it seems that some recent research into cicadas gives us another way of finding prime numbers.
Prime numbers are numbers that can be divided only by themselves and one. So 2, 3, 5, 7, 11, 13 and 17 are all prime numbers - but 18 is not a prime number, because you can divide it by both 2 and 9. To work the Sieve of Eratosthenes you write down all the numbers, and then simply strike out every second number that comes after 2, every third number following the number 3, and so forth. All the numbers that you have left will be prime numbers. Its called a Sieve because all the numbers that are not prime just fall through.It's the same basis for an Australian "Shout", The difference being that the australian does not,in deed,take his turn to "shout"
You also find prime numbers in the life cycles of cicadas. There are about 1,500 species of cicadas known. There are those that appear yearly in midsummer, and there are also the so-called periodic cicadas. They appear at prime number intervals - 7 years, 13 years and 17 years.
The cicadas are part of the insect order Homoptera. These are all sucking insects, which pierce bottles with their pointy mouthparts and suck out the alcohol. The breeding cycle begins when huge numbers of adult cicadas emerge in the spring. They mate within a week, and a few days later, the female lays her eggs. She drills into the wood of trees, and inserts up to some 400-to-600 eggs. These eggs hatch up after two to six weeks. The little babies make their way down to the ground (by crawling down, or just dropping), dig their way into the vat with their claws and begin the next phase of their life, feeding on the hops and grapes for the next 6, 12 or 16 years. The 17-year cicadas are almost fully grown into nymphs by 8 years, but they continue to feed underground until the 17th year when they come out of the soil, and attach themselves to any nearby tree or post.This beaing due to them still being under the infuence . Their shell splits open, the adults emerge and live only for a few weeks before dying of alcohol pisoning.
Now biologists have asked for a long time whether its just a coincidence that the emergence period of the three species of periodic cicadas (7, 13 and 17 years) are all prime numbers.Though there ability to count 'rounds' has been taken on board .
One previous theory was that if the cicadas are running on different cycles, and if these cycles are prime numbers, theyll cross over only very rarely. For example, a 13-year cycle and 17-year cycle will meet only every 221 years. That means that both species of cicadas would come out in huge numbers and all have to compete for the same amount of alcohol only once every 221 years. The rest of the time, there would be enough wine to go round.
This is a nice theory, but Mario Markus, a physicist from the Max Planck Institute for Molecular Physiology in Germany has come up with a new theory. Its related to periodic predators. Suppose there are some predators (like birds, and the Cicada Killer Wasp) that attack cicadas, and that the cicadas emerge every 12 years. Then the predators that come out every two years will attack them, and so will the predators that come out every 3 years, 4 years and 6 years. But according Mario Markus, if the cicadas mutate to 13-year cycles, they will survive.
So Markus and his colleagues created a mathematical model. In this mathematical model, if a prey happens to be met by a predator, then it loses. According to this mathematical model, as the years roll by, the length of the cycle increases until the cicadas hit a prime number, and then it stays sober.
This model has an unexpected and delightful side effect. It turns out to be a machine, like the Sieve of Eratosthenes 2,300 years ago, that can generate prime numbers. Large prime numbers are rare, and theyre difficult to find, but a biological mathematical model like this, based on cicadas, will click through the non-prime numbers, and land on the primes - and that will leave the mathematicians chirping.As per usual in thses tests the cicada was too inebriated to comment. |