'Clouds Are Not Spheres, Mountains Are Not Cones' : Planet Money Benoit Mandelbrot, who argued that financial models oversimplified the world, died last week.

'Clouds Are Not Spheres, Mountains Are Not Cones'

We have to cut corners to understand the world. Otherwise, we'd drown in complexity.

But if we cut what turns out to be an essential corner, we're screwed.

For example: We get blindsided by a financial crisis that almost no one predicts.

At least that's what Benoit Mandelbrot, who died last week, said.

Widely used financial models were wrong to ignore the rare, huge swings in the market that are hard to predict but have a major influence on the long-term picture, according to Mandelbrot.

He made that argument for decades, and seemed to be vindicated during the financial crisis, when lots of financial models performed very poorly.

"For 50 years, people were sort of poo-pooing me," Mandelbrot said in a Ted talk earlier this year. "But I tell you, at this point, people listen to me."

Mandelbrot wasn't a finance or economics guy by training; he was a mathematician, best known for the development of fractal geometry.

In that work, too, he found a more complex world than what other experts were describing. He famously posed the question "How long is the coast of Britain?"

His answer: It depends on how close you look. From the NYT obit:

...On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

"Here is a question, a staple of grade-school geometry that, if you think about it, is impossible," Dr. Mandelbrot told The New York Times earlier this year in an interview. "The length of the coastline, in a sense, is infinite."

And, from the BBC obit, here's Mandelbrot making the same point in broader terms:

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.