Posts filed under “Mathematics”
Nova discusses fractals, and the significance for various disciplines, such as Physics, mathematics and even markets:
Click for Video
In five parts:
They’re odd-looking shapes you may never have heard of, but they’re everywhere around you—the jagged repeating forms called fractals. If you know what to look for, you can find them in the clouds, in mountains, even inside the human body.
running time 11:36
THE MANDELBROT SET
In 1958, Benoit Mandelbrot begins using computers to explore vexing problems in math. They help him to understand repeating patterns in nature in an entirely new way. He coins the term fractal to describe them and develops the Mandelbrot set in 1980.
running time 9:51
ON THE DEFENSE
Though many colleagues initially scorned Mandelbrot’s work, his mesmerizing fractal images launched a popular culture fad. More importantly, his book The Fractal Geometry of Nature explained how his ideas could be applied in the real world. Mandelbrot’s ideas inspire an ever-increasing number of applications, including the fractal antenna.
running time 10:40
FRACTALS IN THE BODY
Fractal patterns turn up everywhere in biology, from the irregular rhythm of the heart to basic eye function. The fractal nature of such physiological processes, which obey simple mathematical rules, offers hope of better diagnosis and treatment of problems as well as new insights into how such processes work.
running time 10:15
NATURE’S FRACTAL NATURE
With carbon dioxide levels around the world rising, a team of American scientists travels to a rain forest in Costa Rica. They employ fractal geometry to analyze how much CO2 the rain forest can absorb.
running time 7:52
Economist Nassim Nicholas Taleb and his mentor, mathematician Benoit Mandelbrot, speak with Paul Solman about chain reactions and predicting the financial crisis.
click for video
RAY SUAREZ: Finally tonight, we return to a subject on many minds these days: the financial crisis. Our economics correspondent, Paul Solman, checked back in with one particularly prominent voice in the investment world and his colleague, who guided his thinking.
Here is the pair’s sobering conversation on what may lie ahead.
PAUL SOLMAN, NewsHour Economics Correspondent: One of the world’s hottest investment advisers these days, Nassim Nicholas Taleb, author of "The Black Swan," who’s been warning of a crash for years, betting on one, and winning big.
He’s been ubiquitous in the financial media of late, from cable TV’s "Colbert Report" to the BBC’s "Newsnight," where he was infuriated by what he called "bogus accounting."
NASSIM NICHOLAS TALEB, Scholar and Author: The first thing I would get immediately, immediately, I would suspend something called value at risk, quantitative measures of risk used by banks, immediately.
PAUL SOLMAN: We sat down with Taleb and the man he calls his mentor, mathematician Benoit Mandelbrot, pioneer of fractal geometry and chaos theory. And even more than feeling vindicated, they’re both scared.
NASSIM NICHOLAS TALEB: I don’t know if we’re entering the most difficult period since — not since the Great Depression, since the American Revolution.
PAUL SOLMAN: The most serious situation we’ve been in since the American Revolution?
Top Theorists Examine Rippling Economic Turbulence
PBS, October 21, 2008