As college students head back to campus, they may be surprised by how
much thought some professors have put into making classwork just as fun
and fascinating as a summer vacation. Far from doing everything by the
book, the creative scholars featured here use everyday objects to put
even the most abstract subjects within reach.
Do-it-yourself dissonance
Even modern-art lovers sometimes run when they hear the dissonance
of 20th-century experimental music. But Anthony Brandt, an associate
professor of composition at Rice University in Houston, wants students
to see how those scores reflect the era's radical changes in thought
about the nature of such fundamentals as physics and consciousness.
Modern music provides "one of our safest and most enjoyable ways of
experiencing ... ambiguity," he says.
In his class on analysis of 20th-century music, Professor Brandt
challenges students to think about music from the ground up. They have
one month to invent an instrument out of an ordinary object and create
a composition for it. He's seen everything from toothbrushes to popcorn
poppers transformed. "It's one of my absolute favorite days when they
come in ready to perform their pieces," he says.
One standout: A student who "performed" the blackboard. (No, not the
fingernail screech.) He alternated using an eraser to make soft puff
sounds and chalk to make quick percussive dots. "You watched the
composition at the same time you heard it," Brandt says. "The class was
mesmerized. For about a minute, you thought the blackboard was an
instrument."
Another student composed with feedback from baby monitors placed at
varying distances apart. One woman used a metronome and kept returning
from the rhythmic clicks to the fixed tuning note - not realizing that
her concept was similar to that of a famous solo for oboe.
And then there was the toilet piece. To change the length of the
flushes for his composition, the student manipulated the toilet so the
water refilled to different levels. He couldn't perform in class, of
course, but he turned in a recording that gave his professor plenty to
chuckle about.
Crocheting what Euclid couldn't grasp
A visiting scholar at Cornell University has taken both the math
world and, more recently, the art world by storm with a touchable form
of advanced geometry. Daina Taimina,a mathematician and crocheter,
discovered a way to create durable and easy-to-use models of hyperbolic
space. People have been attempting this ever since the concept emerged
in the early 1800s and overturned Euclidean geometry's assumptions
about parallel lines.
Students are excited by the crochet creations, some of which
resemble curvy leaves of lettuce or kale. Straight lines of one color
of yarn are stitched into models made of another color. By bending the
forms, students see a new three-dimensional relationship between
parallel lines.
"Maybe there's something psychological about using the yarns and the
handicraft.... It just takes out the anxiety. It's not the same as
looking at some abstract formula," Dr. Taimina says. "People say, 'It's
very important that we can touch it - we can learn through feeling.' "
Taimina's models are on display at the Smithsonian in Washington,
and a virtual exhibit with mathematical explanations is available at
the Institute For Figuring, a Web-based educational organization
directed by Margaret Wertheim in Los Angeles (www.theiff.org).
"We tend to think of math as masculine, but this feminine activity has
had a powerful role in illuminating it," says Ms. Wertheim, who has
helped organized workshops for artists and other nonmathematicians.
Why spandex is like space/time
Who would have thought that spandex would come in handy to help people grasp Einstein's theory of relativity?
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IT'S A WHAT?
This crocheted 'hyperbolic pseudosphere' teaches students about three-dimensional relationships between parallel lines.
STEVE ROWELL/THE INSTITUTE FOR FIGURING
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Jim Borgardt, an associate professor of physics at Juniata College
in Huntingdon, Pa., brings out a stretchy membrane to represent space
and time, and places a marble or heavy ball on it to show how it's
affected by various objects. Dr. Borgardt explains that the moon orbits
the earth not because the two masses are attracted to each other, as
Newton theorized, but because the earth forms a dimple in the
space/time membrane, and the moon is trapped in that dimple. A heavier
ball gets the class talking about black holes, because the ball sinks
so deeply that it's surrounded by the membrane. "If you sit there and
try to explain that just with words, some people's heads are spinning,
whereas if you get something they can see - even though it's not a
perfect metaphor - at least it gives them a road map," Borgardt says.
A dog's expert calculus
Elvis has left the building. Actually he's jumped into a lake to
fetch a ball. Elvis is the Welsh Corgi that tours with math professor
Tim Pennings to illustrate a calculus problem at schools and colleges.
When Dr. Pennings noticed Elvis running along the beach part of the
way before jumping in to swim to a ball, he checked a hunch with some
calculations. Based on Elvis's running and swimming paces, Pennings
discovered his dog was instinctively choosing just about the quickest
route to the ball, known in calculus as the "optimal solution." In the
real world, factories calculate the optimal number of a product to put
out each day to maximize profits, and NASA finds the optimal time to
send out a spacecraft, says Pennings, who teaches at Hope College in
Holland, Mich.
After talking about Elvis's approach, Pennings puts younger kids to
the test by tossing a candy bar onto the lawn and telling them to walk
on the sidewalk and crawl once they hit the grass.
Turns out the children's instincts for finding the optimal path
aren't quite as good as Elvis's, but surely they have fun trying.
Links of interest
Most-viewed stories (for 08/30)
