Science

- Mitch Wright

Chaos intrigues Austin Davis—so much so that he’s structuring his remaining undergraduate courses around studying it. Davis was already interested in chaos theory when he was handed the assignment of mathematically modeling a complicated differential system. He chose a triple pendulum to demonstrate the chaotic system and astonished his professor, Dr. Anthony Quas (math and statistics), by going far beyond the assignment parameters and actually building the pendulum at home.

“It’s not unusual to build this, but it’s usually done by graduate students in a laboratory setting,” says Quas. “It’s pretty astounding for an undergrad to go ahead and build this in his backyard. It’s a very advanced topic for an undergrad.”

For Davis, the course—Math 379: Nonlinear Dynamical Systems and Chaos—provided a natural opportunity. He’d mulled the idea for the pendulum for some time and had even sat down with a previous instructor a couple years ago to work on a different, ultimately unsuccessful, attempt. He moved on to other things, but the interest in the math involved with chaos theory lingered.

While taking Quas’s class, Davis realized he was not only acquiring the tools and ability to delve deeper into what had been a passing interest in chaos theory—also known as dynamical systems or more popularly, the “butterfly effect”—he was actually ready to leap into the chaos.

The former construction worker knew while working on the math that he’d follow through on attempting to build it, although he now admits it was far more complicated than he originally expected, even with that earlier unsuccessful attempt under his belt.

“Anthony’s class was the first opportunity to apply the tools to a physical system,” Davis says. “A lot of the point in making it was to actually visualize it. I’ve got quite a lot of information from actually building it, rather than just equations.”

The excitement comes from delving into the unknown.

A common analogy for a chaotic system is weather. Much about weather and how and why weather systems form is known, yet it is near-impossible to get any degree of accuracy in a forecast. That’s because all those knowns interact and affect each other in dynamic, or chaotic, ways.

Likewise, in a dynamical system such as Davis’s triple pendulum, much is known—as he says, a single pendulum is a completely known entity. But connect it with two others, and it becomes chaotic, each pendulum affecting the others in myriad unpredictable ways.

“They’re both incredibly difficult to predict,” Davis says. “It’s so close to a system we know everything about, and then you add a couple of things, and it’s completely different.”

With the realization he had the tools to really push into the unknown, Davis began changing his course load to facilitate the pursuit of what had by now grown from latent to burning interest.

“It’s become the central thing to his course work,” says Quas.

Davis admits he spends far more time thinking and tinkering on the theory than he probably should, but he can’t help it. And he plans to continue the effort, “until life tells me I can’t,” or until it opens up a new line of inquiry that captures his interest.

Watch Davis’s triple pendulum do its crazy dance: http://bit.ly/12IEDY5

In this story

Keywords: mathematics, machinery

People: Austin Davis, Anthony Quas