Mandelbrot’s Math and The Markets

Closeup of the Mandelbrot set centered at (0.2...Image via WikipediaFractal Patterns – Farming To Financial Markets

Thanks to TheBigPicture, I was reminded that I wanted to show you something I found to be just fascinating.

Fractal geometries have been around for quite some time, but it was not until the past 50 years that we started really digging into that area of mathematics. As a matter of fact, the word ‘fractal‘ was coined just over 30 years ago by Benoit B Mandelbrot, the French-American mathematician.

When I was growing up in the red, rolling hills of central North Carolina, I was always in awe of the patterns I saw everywhere in nature. We were farmers, living close to the dirt. We walked with our eyes to the earth, watching each step across an uneven landscape.

As a boy back then, my great-grandfather was one of my best mentors. He taught me how to see the patterns in nature, the signs of the coming rains or snows. He taught me to smell the difference between an ice storm or a snowstorm in the winter, and how to use the moon to estimate the amount of rain we might get.

He taught me to look for patterns. He taught me to look for the similarities of things. He showed me trees in oak leaves, mountains in a freshly turned field. He taught me the practical applications of fractals before I ever learned to do long division.

I wasn’t much of a farmer. By the time I was 10 it was glaringly obvious that of all the young boys in our extended family, I certainly should be one to continue my ‘schooling’. My grandfather always told me, ‘Boy, you better be a doctor or a lawyer, cause you won’t ever be able to grow enough food to feed your family.’

I am pretty certain that was a brutal insult, but it was mostly true, so I took no offense. I just read another book, and then another, and then another. When I was 14, my father gave me a subscription to Scientific American magazine, and it was there that I first learned about fractals.

I remember being simply amazed that this French mathematician had created some way of describing patterns in the real world, the world my great-grandfather had shown me all my life. Pa Roberts wasn’t moving around much by then, but I sat and showed him these pictures, and we laughed at the fact that the ‘college folk’ were finally figuring out what his grandparents taught him, what he passed on to me: that the world wasn’t made of straight lines, and that the closer you looked, the more it looked like it did from far away.

Back in the early 60s, when Mandelbrot first started working with fractals, they were quickly applied to the financial markets. There was a consensus that somehow, this ‘new’ math could help to predict, and hence control, risk. Mandelbrot himself has written extensively on the subject, especially over the last 15 years or so.

Much of his later writing has been filled with attempts to correct misunderstandings which developed over time. I haven’t read all of it, and if you’d like to read his own words follow the link above to his Yale University pages. There you will find links to many of his papers dating back to 1960.

The Black Swan

Nassim Taleb is the author of the book, The Black Swan. In 2007, The Black Swan was the #1 selling nonfiction book listed by and spent 17 weeks on the New York Times bestseller list. So far it’s been translated into 27 different languages.

The Black Swan gets its name from the centuries-old belief that all swans were white. For thousands of years, the western world had never seen a swan of any other color. Then, Australia was discovered, just a few hundred years ago, and black swans were suddenly common.

Nassim uses this brief bit of human history to illustrate how easily and quickly long-held ‘knowledge’ can be radically altered by simple, though sometimes highly unpredictable events. If even only one black swan had been seen, it would still have changed the belief about the color of swans. Thousands of years of certainty would still have been wiped out.

For the past several years, Nassim has been seen on television and in news and magazine articles, warning of the Black Swan event in the financial markets. Ever-increasing complexity and mismanagement of that complexity by people who don’t understand it but think they do only increases the chances that a major event will happen.

Below is a short video interview, showing Nassim together with Mandelbrot. In the video, it’s obvious that they each agree that a major event is probably already playing itself out right before our eyes, now, in 2008. Watch the video, click the links above. Learn something new, something you already knew.

The Money Quote

‘Never in the history of the world have we faced so much complexity combined with so much incompetence in understanding it’s properties.’

I am Jon, still reminding myself: I am my great-grandfather’s great-grandson.

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