In an effort to increase public appreciation of the importance of mathematics, Cornell's Department of Mathematics is sponsoring its first annual public lecture as part of the nationwide Math Awareness Month.
On Saturday, April 29, John Hubbard, Cornell professor of mathematics, will give a talk titled "Chaos, Complication and Control" at 1:30 p.m. in Bache Auditorium, Malott Hall, Room 228.
An internationally renowned researcher, Hubbard is best known for his work on the Mandelbrot set, featured in James Gleick's best-selling book Chaos: Making a New Science. Hubbard also is a popular communicator of mathematics to nonmathematical audiences.
Hubbard will show how mathematics underlies every facet of science and technology, from computer games, cellular phones and the Internet to medical diagnostic tests, the design of new prescription drugs and minimally invasive surgery. Yet most people, he says, have little or no idea what mathematicians do or how their work is used.
Hubbard's talk will explain how a very "simple" differential equation modeling a very ordinary forced damped pendulum can exhibit extraordinarily complicated and unstable behavior. Such pendulums are the basic subunit in robots, so mathematical understanding of their behavior can contribute to the design of better robots in industry and even medicine.
One nonintuitive phenomenon exhibited by the pendulum is that chaos and controllability go hand in hand, said Hubbard, which can be seen in the history of airplane design. Because 19th century engineers identified control with stability, the first airplanes were designed to be extremely stable. But in World War I, pilots found that this stability made it impossible for them to dodge enemy fire. Making airplanes less stable made them safer, because they were easier to control. Similarly, Hubbard noted, a beginning skier aims for stability and is usually quite out of control, whereas the advanced skier with skis close together is quite unstable but able to maneuver at ease.
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