Wednesday, October 27, 2010

Sunday, October 17, 2010

RIP Benoit Mandelbrot

A portion of the Mandelbrot Set
The world lost a major scientific figure this week. Benoit Mandelbrot, who recognized that the geometry of nature is fractal, died on Thursday at the age of 85. The New York Times published a nice obituary, describing his life and work and recounting his story of how he got started on the research that led to the fractal concept.

This has always been one of my favorite stories about Mandelbrot, and I often told it to the students in my classes on nonlinear dynamics and complexity science, since it also provides a great illustration of what a fractal is.

The story begins when Mandelbrot tried to measure the length of the coastline of Britain and soon realized that the answer varied depending on the resolution of the map or photograph he was measuring. At a high altitude, say from the vantage of a satellite, the coastline appeared to be a certain length, but as the camera zoomed in, more bays and estuaries were revealed and the coastline length increased.

Mandelbrot knew that this could not continue indefinitely, because, if it did, the length of the coastline of Britain would be infinite and this was, obviously, impossible. He eventually hit upon a way out of this puzzling paradox, and the solution was a very clever idea: the coastline is best thought of, he realized, not as a one-dimensional curve with a length but as an object with a dimension somewhere between one and two.

Romanesco broccoli
A two-dimensional object would be a filled-in area, such as the land mass of Britain itself, so what Mandelbrot was suggesting is that the coastline is neither one-dimensional, like a curve or straight line, nor two-dimensional, like the entire island, but a "fuzzy" object with a fractional dimension. 

He called this type of object a fractal and soon found that nature is filled with fractals. Coastlines are definitely fractal, but so are trees, mountain ranges, the network of blood vessels in our bodies and even vegetables. One of my favorite examples is the Romanesco broccoli, which I wrote about in one of my earliest posts on this blog.

The BBC has published a beautiful photo essay of Mandelbrot and the fractals he discovered, including the beautiful one which bears his name: the Mandelbrot set, a tiny portion of which is shown at the beginning of this post.

Rest in Peace, Benoit. You will be deeply missed.

Friday, October 15, 2010

The Importance of Water

I'm working on a novel that is set in the western US and one of the main sources of conflict and tension in the story is the struggle over water: who owns it, who is entitled to manage it, what people do when there is not enough of it. When one of the major characters in my novel, Helen, discovers that her well has run dry and then (as if this is not bad enough) that the water management board will not allow her to divert or use any water from the spring on her own property, she becomes very worried.

A few of my writer friends have read early drafts of this story, providing me with lots of comments that have already improved my manuscript, but one particular comment left me a little unsure of how to proceed. "This dry well doesn't seem like a particularly big problem," the comment said. "Maybe Helen should be facing something really scary, like cancer or some other dire disease."

Maybe one has to have grown up in an arid environment, like I did, to understand that lack of water is really scary. When a person grows up with clean water literally available at the touch of a button, or turn of the tap, they may not fully appreciate just how frightening a prospect it might be to find that water is suddenly not available. 

Millions of people around the world face this sort of reality every day, and today's Blog Action Day has been undertaken to raise awareness of just how important water is to our survival.

Two years ago, I helped organize a workshop on "Applications of Complexity Science for Public Policy" for the Global Science Forum, part of the Organization for Economic Cooperation and Development (OECD). One of our participants, John Finnigan, the Director of the Center for Complex Systems Science at Australia's national science agency, the CSIRO, said that his agency is investigating the likelihood that the earth, and humanity, may be approaching a "tipping point" in which massive water shortages will occur.

Tipping points are those key transition points, like bifurcation points, where a tiny change can result in a huge effect. Finnigan spoke about the human-earth system as a complex entity that was nearing a tipping point largely because of social and economic factors. His agency has undertaken a number of research projects to develop smarter ways to address the complex problem of water management.

I don't find it surprising that this pioneering work is being carried out in Australia, a country that, for the most part, is as arid (or more so) than the western United States. If all of the US was as arid as Australia, perhaps our country would be one of the ones taking the lead on this most pressing of problems facing humanity.

Please help spread the word about how important it is to ensure a supply of clean water around the globe. Visit the Blog Action Day main website, where you can learn more about how you can help.

Wednesday, October 13, 2010

Nearly-Wordless Wednesday

Yellowstone: After the Fire

For more Wordless Wednesday, visit the main site.
For more of my photos, visit my page on Flickr.

Monday, October 11, 2010

Blog Action Day: October 15

I wanted to let you know about an important online event I'm taking part in on October 15th, called Blog Action Day. 

Each year bloggers from more than 100 countries come together and blog about a single important issue. This year's topic is clean water.

The event includes thousands of blogs - including the White House blog and The Official Google Blog. The organizers are looking for as many blogs to participate as possible, regardless of their size and focus.

I hope you'll think about joining me for this event. If you want more information, check out the Blog Action Day site at

Hope to see your post on the 15th!