Botanical Mathematicians

When I clicked on a blog post called “Bamboo Mathematicians,” I assumed it would be about the bamboo multiplication table recently cleaned up and analyzed by researchers at Tsinghua University in Beijing. Those bamboo strips, dating from approximately 305 BCE, contain the oldest known base 10 multiplication table.

A forest of mathematicians. Image: JFXie, via Flickr.

A forest of mathematicians. Image: JFXie, via Flickr.

But the “Bamboo Mathematicians” I clicked on was a post by Carl Zimmer, a science writer who specializes in biology and evolution, about bamboo plants with decades-long flowering cycles. He reports that researchers have developed mathematical models that explain how a bamboo forest ends up synchronizing to these long cycles. The main idea is that if some plants mutate to have a flowering cycle that is an integral multiple of the dominant flowering cycle, they will tend to outcompete the shorter-cycled plants. Over time, this has led to plants with 32-, 60-, and 120-year cycles, all products of small primes.

On the other hand, periodical cicadas favor larger primes: 13 and 17.This year, broods of both 13- and 17-year cicadas are scheduled to appear in the midwest and southeast US. Cicada Mania reports that they have started emerging in Illinois and should be around for about a month. The cicadas and the bamboo have long life cycles for similar reasons: by appearing at once, they flood the market, so to speak—their predators can’t eat all of them, so the species has a better chance of survival. Steve Mould has a nice Numberphile video about this predator satiation strategy. It’s interesting that the cicadas’ survival strategy led to (relatively) large prime numbers while the bamboo ended up with composite numbers with small prime factors. It’s interesting to think about the evolutionary factors that may have contributed to that difference.

Bamboo isn’t the only mathematical plant. Two years ago, there was a flurry of articles claiming that plants do math when they change their starch consumption at night. The Aperiodical mentioned it, and Christina Agapakis had a nice post about it at her blog, Oscillator

The plants in question aren’t spitting out numerical answers to word problems on their leaves, but doing normal plant stuff: using energy stored as starch at different rates depending on environmental conditions. Plants get their energy from sunlight, so at night the rate of starch consumption has to be smooth in order to maintain energy until dawn and prevent a “sugar crash.” The researchers found in a previous study that that plants will consume their starch almost completely every night and that the rate of consumption will stay mostly constant after “sunset,” regardless of whether the lights go out earlier or later than the plant “expects” based on their circadian rhythm. Based on these results, the researchers proposed a mathematical model whereby the plants are “dividing” the level of starch stores by the number of hours until dawn in order to determine the proper rate of consumption.

So plants can multiply, at least by small numbers, and divide! I wonder what other mathematical tasks they’ve been doing in secret.

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