Professor Richard Elderkin puts mathematics in service of preserving the environment.
Green Math
By Michael Balchunas
The gaping open-pit mines, the slag heaps and the burnt-orange stream seemed as natural to Richard Elderkin when he was growing up as the timbered slopes rising to the Continental Divide a short hike from his home.
"I grew up in a copper mining town near the headwaters of the Clark Fork River" in Montana, he says. "That stream was as orange as many of the books on my shelf, just from the water that was pumped out of the mines."
The landscape has changed in the ensuing years. The polluted water no longer goes into the stream, and the Environmental Protection Agency monitors the health of the Clark Fork, which is now a valuable recreational resource.
But it's not yet an environmental success story.
"No, all that's being done is that the water's being diverted, at the rate of six million gallons a day, into what used to be an open pit," says Elderkin, a professor of mathematics. The stream is cleaner, but that tapped-out mining district constitutes the largest Superfund complex in the nation.
"It's not yet critical, but eventually it will rise up to the point where things can no longer flow in. It's a problem people are working on, but it has yet to be solved," says Elderkin.
There have been a number of highly publicized achievements in environmental restoration in this country--such as the expected removal of the bald eagle in July 2000 from the list of threatened and endangered species, and the improvement in air quality in the Los Angeles basin--since Elderkin joined the Pomona faculty in 1974. But many serious concerns persist, he says, such as at the former copper mines, where a reckoning has merely been postponed.
"I'm not an evangelist. I'm not much of a sermon thumper. But I personally think we're going to be in deep trouble if we don't wake up and see the consequences of what we're doing," observes Elderkin, who played a major role in enlisting Pomona as a participant in Biosphere 2 and is now leading efforts to pave the way for an environmental studies program at Pomona.
For a professor of mathematics, those may seem unusual interests.
Mathematicians, he says, are seen as denizens of the ivory attic of the ivory tower, occupied with an arcane field of inquiry just for its own sake. "I've always believed mathematicians ought to be more forthcoming in making mathematics more applicable. But when I did look at how others were using mathematics, I saw them using it like somebody would use a crescent wrench, without giving a hoot about where the crescent wrench came from, whether it was really the appropriate tool for the job, and having no interest in the craft of using the crescent wrench. I think people involved in pure mathematics ought to be more interested in the application, and people involved in applying mathematics ought to be more interested in the study of pure mathematics."
Elderkin's research has generally been in mathematical ecology, and his publications have examined nonlinear differential equations, their topology, and their use in theoretical population and ecological models.
But when his daughter neared college age, she developed an interest on her own in environmental studies, which prodded Elderkin toward greater activism. He began to explore the possibility of establishing an environmental studies curriculum at Pomona, and how various scientific disciplines and humanities subjects could be related to the environment.
"I find that I can introduce fragments of environmental studies in my calculus classes, in my differential equations classes, in my mathematical modeling classes," says Elderkin, who is on sabbatical this year. "For instance, in calculus, one of the fundamental concerns is integration, and in years past, we seemed to be more concerned with how one does an integral, rather than what sort of tool for knowledge and understanding the integral can be. These days, I try to introduce integrals exactly as a tool for understanding society and for understanding the natural world."
One of the courses Elderkin teaches is Environmental Decision-Making. "I believe mathematics is a strong enabler in many endeavors," he says. In a description of the course for prospective students, he notes that "making decisions about our environment involves many aspects: ethical, political, scientific and economic," and that "frequently the decision-making process benefits from quantitative assistance, ranging from quick and rough estimates to sophisticated understandings of interactions within the environment and between policy makers."
Students in the class may consider a topic such as exponential growth in the context of an unconstrained population increase or the decay of radioactive wastes. They may examine population dynamics related to the growth and harvesting of resources such as fish and timber, and maximum sustained yield or maximum derived profit over a given time horizon.
Elderkin's interest in the environment also led to his involvement, along with Vice President for Planning Richard Fass, in helping arrange Pomona's participation as a partner school in studies at the Biosphere 2 Center in Arizona. Columbia University uses the giant enclosure, which contains a number of Earth's ecosystems in miniature, for a program of classes and research called Earth Semester. The center also offers a program of planetary studies called Universe Semester. The Biosphere was constructed by an entrepreneur as an experiment into how humans might live on Mars, and the original project sought to create a sealed, self-contained environment.
"It is a wonderful resource," Elderkin says. "They don't make any pretense about sealing people in anymore. As an experiment into how we interact with our environment here on Earth, it's a tremendous laboratory."
And what role does mathematics play in our interaction with the environment?
"My point of view," says Elderkin, "is that as we try to understand things, we generally formulate models for our own understanding, and most of us are not really conscious of that. In mathematics, we're very concerned with how the assumptions we make lead to the conclusions we take from them. So the assumptions we make are basically the stuff of the models we construct for our understanding of the world.
"And I, as a modeler and an analyst of mathematical models of populations and the environment, am especially concerned with how we formulate our understanding of the dynamics and interdependencies of population; what sort of mathematical formulations we can give them; and when we do choose one formulation over another, what the absolutely necessary consequences of those assumptions are. If we see consequences which don't seem to gibe with the natural world, then that says that probably the assumptions aren't so hot."
One verifiable assumption is that modern mathematics can seem increasingly impenetrable to those not well versed in it.
"In mathematics, like many other endeavors of inquiry, the problems, for the most part, are more and more advanced, so it gets harder and harder to talk about them in everyday parlance," says Elderkin.
Although the sciences and mathematics provide students with the knowledge and tools for in-depth study of the environment, the humanities also are indispensable, he believes. "It's really the humanities that tell us what sort of people we want to be, and ideally, what sort of relationship with our natural environment we would like to have," he says. "That's where we set our values. We don't set them in social sciences. We don't set them in natural sciences. We set them in humanities."
One of the lessons he tries to impart in his Environmental Decision-Making class is that to succeed as a society, we can no longer rely on individual decision-making. "We can't rely on Adam Smith's 'invisible hand,' assuming that people making their best individual decisions will lead to the best decisions for society, or even to environmentally viable ones. It's really important to say that to our students, and get them to realize that laissez faire could be disastrous."
If he needs examples, he has only to look back at his own childhood in Montana, where the mines are trenchant reminders of the conflict between preserving nature and exploiting its resources. It was there that the seeds of his environmental activism were sown.
"The Continental Divide was what I saw when I looked out my kitchen window," he says. "I was a Boy Scout and I loved the outdoors. I also grew up in a family that was involved in the outdoors and had a strong social conscience about how we ought to act."
His concern about the larger world, however, got its biggest boost from one of life's most powerful consciousness-raising events: parenthood.
"When your daughter says, 'I'm interested in doing something about the world, Dad,' you think, 'Oh my gosh, maybe I ought to be also.'"
Michael Balchunas is a free-lance writer living in Claremont.
--Photo by Phil Channing
