Nature’s Language

Drop in to any lab at WHOI and you’re likely to see whiteboards filled with equations, diagrams, and inside-joke doodles. The telltale smell of dry erase markers has largely replaced the white chalk dust of yesteryear, and will likely also become a thing of the past as meetings and classrooms go virtual. So when a chalkboard in the Physical Oceanography department changed owners recently, that got me thinking: in this age of cloud-based computing and artificial intelligence, what value do analog methods still have? In fact, how do oceanographers explain dynamic Earth systems without tangible means?

WHOI scientist emeritus Joe Pedlosky. (Photo by Jayne Doucette, © Woods Hole Oceanographic Institution)

Well, who better to ask than scientist emeritus Joe Pedlosky, whose tenure at WHOI has withstood the test of time from the early 1960s to today? While he admits to preferring pencil and paper, Pedlosky says the chalkboard is still an essential tool for working out analytical theories, which later can be proven with lab experiments, computer models, and real-world observations.

“When they talk to you about science in school, they don’t tell you how much fun it is to predict things using basic physics and mathematics,” Pedlosky says with a laugh. “Pencil-and-paper mathematics is a very powerful and important part of a quartet of scientific approaches.”

Pedlosky was introduced to oceanography in the 1950s, when the field was fairly new. Nascent oceanographers, spurred by wartime investments in ocean science, were still cracking the code of ocean physics, using sound to determine depth and developing theories about circulation based on pure mathematics. In 1960, while in his fifth year studying aeronautical engineering at MIT, Pedlosky chanced upon a poster advertising the Geophysical Fluid Dynamics (GFD) program at WHOI, a summer course that had started the year before—and continues today.

“As I read the announcement, it seemed to say to me, ‘Come to the beach on Cape Cod, study fluid dynamics, and we will pay you,’” Pedlosky remembers. “It was irresistible on all counts and changed my life-path drastically. To this day, I think of myself as a GFD-er.”

After two summers in the GFD program and professorships at MIT and the University of Chicago, Pedlosky returned to Woods Hole as a senior scientist in the late 1970s, when such luminaries of physical oceanography as Henry Stommel and Fritz Fuglister roamed the halls. His collaboration with Stommel and Jim Luyten would result in the “ventilated thermocline” theory, which significantly advanced understanding of the physics that determine the temperature and the density structure of the ocean at mid-latitudes. As Pedlosky remembers it, about 40 years ago Stommel and Luyten were working on a numerical model that described how two layers of a subtropical gyre would mix. When they shared their results with Pedlosky, he realized they had gotten stuck by relying on a numerical model instead of an algebraic solution. So, he took out a pencil and paper to sketch the relationship between pressure at depth and “potential vorticity,” or the spin (due in part to Earth’s rotation) of parcels of water.

"When they talk to you about science in school, they don’t tell you how much fun it is to predict things using basic physics and mathematics.”
—WHOI Scientist Emeritus Joe Pedlosky

“Just like that—eureka! Within 20 minutes, I had a theory of the thermocline,” Pedlosky remembers. “That moment is as fresh in my mind as any emotional moment in my life. The story doesn’t always have that good an ending, but when it does work, it’s a little bit like falling in love and having it reciprocated.”

When Stommel and Luyten plotted Pedlosky’s theory with their numerical results, they got a match. And as their colleague Rui Xin Huang later showed in computer models, the analytical approach applied, no matter how many layers were added. For the first time oceanographers had a convincing theory to explain the thermal structure of the majestic subtropical, wind-driven gyres and the accompanying field of motion.

While today’s computers are much more sophisticated than they were in the early 1980s, the same situation applies: models supply answers. They don’t supply meaning.

“When you give a computer equations to solve, it’ll just give you a number. The big advantage of analytical work is that you get a formula for the result,” Pedlosky says. “It might not answer a specific question, but it will tell you the relationship between things.”

Today, whether he’s working out the potential hydrostatic balance of a gaseous planet or giving a lecture at Walsh Cottage, Pedlosky will first turn to a pencil and paper—or a chalkboard—to find patterns and order in the seemingly chaotic ocean.

“Mathematics is the language nature chooses to communicate with us,” Pedlosky says, paraphrasing Galileo. “To be using applied mathematics to describe something as beautiful as the ocean—I could be using the same equations on linoleum, but it wouldn’t be as meaningful.”