## December 09, 2005

### 17 year itch

Magicicada septendecim is a cicada, a harmless and rather nondescript insect that grows up to 2 inches long. It might be truly nondescript if it was not what is called a "periodical cicada". This means that the life-cycles of these little creatures are synchronized; put another way, they become adults at about the same time.

(Imagine all humans -- all 6 billion of us -- going through puberty in the year 2006).

This is surprising enough. But there's something even more astonishing about this insect. They have very long life-cycles. How long? Try 17 years. Every 17 years, these cicadas emerge from under the ground in North America in huge clouds, fly around, find mates, lay eggs, and then die: all in a matter of weeks. Then they are gone for another 17 years. In the intervening years, you will find no adult Magicicadas.

Why such a long life-cycle? But more intriguing, is there any significance to that number 17?

(Hint: a cousin, Magicicada tredecim, has a life-cycle of 13 years. Why 13? Why 17?)

Any speculation welcome -- except if you've read Simon Singh's Fermat's Last Theorem, or have heard about this from somewhere else. Let's hear the speculation first.

Varun Singh said...

Primes? too naive.

I thoroghly enjoyed Singh's last book - The Code Book. Should get my hands on this one soon. Wasn't this published BEFORE the code book?

Anonymous said...

Since I have read Simon Singh I will not speculate. But if I am not mistaken Gould also has at least one chapter devoted to this phenomenon (Ever Since Darwin, perhaps?) so you should exclude Gould readers as well.

Ravi

Abi said...

I have read Simon Singh's 'Fermat's last theorem', but I am still at a loss!

My first shot would be that it gives them some advantage in terms of evading their predators.

That it has something to do with primes is quite clear, but why these primes? In what way are these particular figures are optimal?

I give up!

Dilip D'Souza said...

Varun and Abi, you're on the right track with primes and predators -- but flesh that out a bit more, won't you?

Varun, Fermat's Last Theorem was Singh's first book. He has "The Code Book" and (most recently) "Big Bang" too.

Sailesh Ganesh said...

3^2 + 2^2 = 13
4^2 + 1^2 = 17

How does that help? Of course, Fermat's last theorem is that there is no whole number solution to an equation of the form
x^n + y^n = z^n for n > 2. My pride's going for a huge toss here.

Sailesh Ganesh said...

At first it sounded like a problem of Fibonacci series, but since 17 isnt in the series, that theory goes out of the window.

Advantage in terms of predators? Is it something like 17 years being a long time, and the life span of many animals is less than that, they simply forget about these creatures?? Sounds like a load of drivel, and then it doesnt explain the primes though.

Sailesh Ganesh said...

Are you going to post a solution or what?