Home >Opinion >Columns >What did one sand dune say to the other?

In September 1991, I climbed a sand dune. No ordinary dune, this was an enormous one in Sossusvlei, Namibia. Someone told me before I started that it was 400 metres tall. It’s actually only about 350m, but I don’t think that extra 50m mattered in any real sense. Because slogging ever upward through that pile of sand that day remains one of the hardest things I’ve ever done. So much so that when I finally reached the top, I couldn’t immediately admire the gorgeous view, or enjoy the breeze. Instead, I leaned over and threw up into the sand.

What made it worse was my travelling buddy, a genial German by name Jan. Though we had started the climb together, he chugged up the dune like it was a stroll in the park. He reached the top a good half-hour before me, and when I was able to look around after throwing up, I saw him sitting on the ridge, and of all things, he was smoking a cigarette, actually looking like he had just, yes, had a stroll in the park. Not the most encouraging sight.

But this is not a Namibia travelogue, it is a mathematics column. Why have I started with spectacular Sossusvlei and the dune there that’s popularly known as “Big Daddy"?

Because I have just learned that sand dunes “communicate" with each other. Not that Big Daddy whispered to one of the other dunes: “Hey, this creep in a pink shirt is throwing up all over my ridgeline!" Nothing that anthropomorphic (though hold that thought). More seriously, some scientists at the University of Cambridge have “experimental evidence that dunes interact over large distances without the necessity of exchanging mass" (Wake Induced Long Range Repulsion of Aqueous Dunes, Karol A. Bacik and colleagues, Physical Review Letters, 4 February 2020). This happens courtesy of winds that are constantly shaping and re-shaping the dunes. Winds blow swirls off the first dunes they encounter, and these swirls tend to push away the more “downstream" dunes, the ones the wind reaches later. This way, the “upstream" dunes effectively repel others, and this “dune-dune repulsion" prevents collisions between them. The scientists believe this explains “the observed robust stability of dune fields in different environments."

Stability indeed: Sossusvlei is spectacular, but it hasn’t changed much over the years. It has always been an enormous field of dunes, Big Daddy the largest of them. But even so, individual dunes are known to move (“migrate"). How does that happen, and what does that mean for a group of dunes? The Cambridge results will help us understand.

How did the scientists learn this about dunes? First, they built a circular track, enclosed in a tank, for experimental dunes. This allowed them to observe the dunes’ behaviour continuously, instead of being restricted to the time the dunes take to move off a linear viewing platform. They put two identical piles of sand close together on the track. Then they directed a stream of air at the sand. This shaped the piles into mini-dunes, and with the continuing flow of air, the mini-dunes started moving.

As you might expect, dunes move at speeds inversely proportional to their size: smaller dunes move faster than larger ones. So, when the researchers blew their simulated wind at the two identical dunes on their track, they expected that they would move at the same speed. In tandem, as it were. But this is not what happened; at least, not at the start of the experiment.

To start, the front dune—the one the wind struck first—moves faster than the one behind. But as time passes, the front dune slows down, until both are moving at about the same speed. What’s more, the front dune breaks up the flow of air so that it forms swirls, like the wake of a boat. These “turbulent structures" move on to strike the second dune, effectively making it move faster, pushing it away. So, the distance between the two dunes steadily increases, until they are as far apart as they can get on the circular track: diametrically opposite each other.

It’s as if the two dunes “didn’t like each other", the lead scientist, Karol Bacik, told CNN.

Now, it’s not that Bacik undertook this research because people think dunes are beautiful and photogenic, or, indeed, a challenge to climb. No, there’s a value to understanding how dunes move, because that movement can be a serious threat. It causes desertification. It can bury nearby roads and buildings under vast quantities of sand. For these reasons, it’s important to learn something about dunes and their movements. That’s the spirit behind the research.

And yet, that remark about the dunes that “didn’t like each other" is an arresting one. For, while it cannot possibly mean anything that there’s dislike between enormous piles of windblown (and occasionally thrown-up-on) sand, there’s a reason Bacik says that. It has to do with how his experimental sand dunes behave, and the qualities we easily ascribe to that behaviour.

What this brings to mind are Valentino Braitenberg’s “vehicles" (see my The Character of Cars here, 5 July 2012). This was a thought experiment involving simple model cars. Each has one or more motor-driven wheels, one or more wires, and one or more light sensors. The wires connect sensors to motors in different ways. Position such a car in front of a lit bulb, Braitenberg wrote in his fascinating little book Vehicles, and watch its behaviour.

Vehicle 1, the simplest, has a single sensor connected to a single wheel. The bulb gets the motor rolling and the vehicle sets off in whichever direction it is pointing, its speed proportional to the intensity of the light. But with changes in friction, it will change direction unpredictably. If you didn’t know it was a man-made device, Braitenberg wrote, and you watched it zip about, “you would say it is alive."

A model car, and it’s “alive."

Vehicle 2 has two sensors and two wheels, and comes in two avatars. Avatar 2A connects the left hand sensor to the left wheel, right to right. 2B has the wires crossed: left sensor to right wheel, right to left. Light the bulb. What happens?

Both avatars charge straight at the bulb, speeding up as they get closer because the intensity of the light gets stronger. But if the bulb is just slightly to the right, say, of 2A, the wheel on that side spins faster and the little car turns away from the bulb. On 2B, the wheel on the left spins faster and it will turn toward the bulb, finally smashing headlong into it.

Braitenberg called both 2A and 2B “haters" of light. But they express their hate in very different ways. 2A heads into the darkness, eventually coming to rest somewhere far from the madding light. 2B rounds on the light in a way that suggests that the goal of its “life" is to destroy the bulb. For Braitenberg, 2A is a coward and 2B an aggressor.

There’s much more to Braitenberg’s Vehicles, as there is to Bacik’s team’s work with dunes. Yet: Cars that “hate" light, dunes that don’t “like each other", who would have thought?

Consider how vividly these terms describe what the objects are doing, as opposed to saying merely that dunes move apart, or vehicle 2A turns away from the bulb. It’s fascinating to note how easily these scientists attributed profoundly human emotions to the inanimate objects they study.

Easy, and yet so revealing.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun

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