|
Mathematician Catherine Roberts
is helping to
regulate traffic on the Colorado River
By Donald N.S. Unger
 We
see the world through the lens of our experience and the
filters of our specialized knowledge. Ask a mathematician,
and she'll tell you that the world is made up of numbers,
from the natural world geometry that defines snowflakes,
to the engineering equations that define the construction
of the buildings in which we live and work.
In focusing her students' attention on this fact,
Catherine Roberts, an associate professor in the department
of mathematics and computer science, introduces them to a
topic that interests many of us as we start our day: coffee.
"My first assignment in ‘Mathematical Models,'" she
says, "is to create some equations that help judge
the quality of a cup of coffee. There are many variables
that can be considered (quality of the bean, method of roasting,
manner of making the coffee, characteristics of the water
...). The challenge is to find a balance between including
enough variables to obtain realistic results and having resultant
math equations that are simple enough to solve. We spend
much of our time fine-tuning our judgement skills in this
regard."
More sophisticated math can be applied to a more complex
mix of disciplines and personal interests. "I majored
in both mathematics and art history as an undergraduate," Roberts
continues, "and I've always been particularly
interested in the interfaces between science and art. For
example, calculus techniques were used to prove that a purported
Vermeer masterpiece from the 17th century was actually a
fake." Someday, she'd like to integrate examples
like that into a course on "the science of art."
At the present time, however, one piece of her work might
better be described as "the science of recreation," or
of "environmental impact." For several years
now, Roberts has been working on the Grand Canyon River Trip
Simulator, a computer program that is designed to help park
managers regulate rafting traffic on the Colorado River.
The program marries a database of trip reports to an integrated
statistical and artificial intelligence-based computer simulation
that models the impact of rafting trip launch schedule changes.
If this sort of software strikes one, at first blush, as
an approach better suited to modeling traffic in and out
of a busy airport or through a heavily used tunnel, consider
that the current wait for people who want to book a non-commercial
rafting trip through the Grand Canyon is on the order of
12 years: book today so you can travel in the year 2014!
According to an article that Roberts co-wrote with Joanna
Bieri, then an undergraduate at Northern Arizona University,
for the Association for Women in Science (available on the
Web at www.awis.org/v_maggrandcanyon.html), the full trip
runs some 279 miles, and takes anywhere from three to 22
days, depending on how far people choose to go, and whether
they use motorized or non-motorized rafts. Some 20,000 passengers
currently take this trip annually.
As Roberts and Bieri point out, "Without reasonable
restrictions on the number of people allowed to raft on the
Colorado River, river trips could cease to be considered
a true wilderness experience." The GCRTsim, then, is
an example of using technology to preserve nature.
Her experience with river rafting isn't just abstract,
of course. And Roberts takes particular pleasure in puncturing
the cliché image of mathematics as a sedentary, lab-bound
field. "As an applied mathematician," she says, "I
enjoy breaking down the stereotypes that I encounter. It's
fun to surprise mathematicians by sharing my other interests
with them, such as art and river rafting, as much as I enjoy
explaining to non-mathematicians that my research is both
interesting and relevant."
There are a number of characteristics of the math and computer
science program at Holy Cross that made both the department
and the larger institution appealing to Roberts. At or near
the top of the list are issues of scale and issues of balance.
Northern Arizona University, the institution from which
she came to Holy Cross, is a significantly larger place.
This made mentoring students much more difficult. As she
wrote in her cover letter when she applied for her current
position at Holy Cross: " … one personal disappointment
for me working here at a large, comprehensive university
(NAU has some 20,000 students) is that I have rarely seen
the same student in more than one course. At graduation,
I'm lucky if I know even one senior. The students are
so distributed that mentoring them, in the manner that I
was mentored [as an undergraduate] at Bowdoin, is simply
impractical."
Those structural difficulties notwithstanding, she continues,
she did everything she could in that context to include undergraduate
participation in her research work in a meaningful way. "My
one success in this venue has been engaging students in undergraduate
research," she says. "I am the leader in my department
in this regard, having had 12 students work on three distinct
funded research projects. I established the Modeling and
Simulation Lab, using my grants to purchase computers and
pay student wages. Now, in addition to my students, two other
faculty have begun using the lab resources. Our students
have been successful getting into REU and graduate programs.
Their names are on research publications, and they have presented
at several national conferences. I've found this work
to be incredibly rewarding."
As to the matter of balance, as a woman in a field that
remains dominated by men, as an active member of the Association
for Women in Mathematics, Roberts stresses that, "It
is crucially important to encourage all students to consider
nontraditional careers as viable and rewarding alternatives," and
happily points out that, "the mathematics and computer
science department here at Holy Cross is close to 50 percent
female. This is, simply put, astounding. While national trends
show an even gender split in undergraduate majors, women
still make up approximately 20 percent of the new doctorates
each year."
Roberts remains committed to increasing those numbers, to
mentoring and advocating for her students, to creating possibilities
and opportunities for them, and—for those of us whose
training and experience don't dispose us to see the
mathematical components of our daily lives—to opening
our eyes to the stream of numbers that compose the world
around us.
Donald N.S. Unger is a free-lance journalist from Worcester,
Mass.
|
