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Cicadas and the Mathematical Brilliance of Nature

Even as the U.S. East Coast braces for the arrival of the bizarre infestation of cicadas that happens with clockwork precision every 17 years, we’re already seeing an infestation of cicada stories, everything from how to grill a cicada to how to make a refreshing cicada cocktail. And that’s even before the Internet Meme Machine gets started. This will be the first arrival of the 17-year cicadas during the modern social media era, so get prepared for cicada hashtags (e.g. #Swarmageddon), “insect porn” of cicadas mating on Instagram and round-the-clock tweets documenting their arrival. But here’s one thing maybe you haven’t thought of: Why every 17 years? Why not every 18 years or every 16 years or every 15 years? What’s so special about the number 17?

The answer has to do with the mathematical brilliance of nature, the power of prime numbers and the mysterious process of natural evolution.

In 1977, Stephen Jay Gould was the first to examine what was so magical about the 17-year reproduction cycles of cicadas and the potential link with the mathematics of prime numbers. In the famous essay “Of Bamboos, Cicadas, and the Economy of Adam Smith” (which appeared in Gould’s first book Ever Since Darwin), the legendary Harvard scientist looked for examples of other species that take excessively long periods of time between reproductive cycles for clues. He found a potential counterpart to the cicada in the flowering cycles of Japanese bamboo. Somehow, both bamboo and cicadas were able to “time” their episodes of sexual reproduction over extended periods. There was one species of bamboo, for example, that first flowered in China in the year 999 and continued to flower and seed every 120 years. Even when this bamboo species was transplanted to places like Japan and Russia, it still kept rigorously to its 120-year cycle.

For Gould, the regular 17-year cycle of cicadas was even more puzzling. How was it possible that three different species of cicadas from different parts of the country could keep to their 17-year cycles, all while living underground the whole time while sucking juices from the roots of forest trees? How could they then emerge precisely at the same time, become adults, mate, lay their eggs and die — all within a span of a few weeks? That’s a long time to be dormant, and an incredibly short period to live and mate.

It turns out that the 17-year period is mathematically significant, since 17 is a prime number, as is 13 (the duration of the reproduction cycle followed by the 13-year cicadas in the South). By waiting 17 years, cicadas were basically gaming the evolutionary system. As Gould points out, most predators have 2-to-5 year life cycles, so the easiest way for cicadas to avoid regular predations over time was so minimize the number of coincidences when both life cycles overlapped. As Gould explains, the way to do this was to reproduce at exactly 17-year intervals, so that predators couldn’t feast on them at regular intervals:

“I am most impressed by the timing of the cycles themselves. Why do we have 13 and 17-year cicadas, but no cycles of 12, 14, 15, 16, or 18? 13 and 17 share a common property. They are large enough to exceed the life cycle of any predator, but they are also prime numbers (divisible by no other integer smaller than themselves). […]

Consider a predator with a cycle of five years: if cicadas emerged every 15 years, each bloom would be hit by the predator. By cycling at a large prime number, cicadas minimize the number of coincidences (every 5 x 17, or 85 years, in this case). Thirteen- and 17-year cycles cannot be tracked by any smaller number.”

Of course, in the 30 years or so since Gould first wrote about the bamboo and the cicada in his book Ever Since Darwinthere have been the skeptics. Some say that the long reproduction cycles of the cicadas are due to weather patterns. They point out the fact that cicadas date back nearly 2 million years, back to the Pleistocene epoch, when their was a need to burrow underground and remain for long periods of time until the glaciers melted. But that doesn’t explain the strange synchronicity of the 17-year incubation period. Why 17 years? Can it be any coincidence that 17 is a prime number?

So there you have it – the primary survival dynamic of the cicada – being “eminently and conspicuously available, but so rarely and in such great numbers that predators cannot possibly consume the entire bounty” – owes its success to the mathematical brilliance of nature. As long as cicadas keep to 17-year cycles, they can avoid their predators for as long a period of time as possible. Who knew that nature’s innate knowledge of prime numbers could be such a valuable survival skill?

image: Whirlwind of the simplest figures / Shutterstock


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