RIP: Benoit Mandelbrot – Discoverer of Chaos

October 16th, 2010 by xformed

From the New York Times:

Benoit Mandelbrot, Mathematician, Dies at 85

Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.

His death was caused by pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge.

Why is this important to this blog? His work was the inspiration for the title.

I first bumped into his work, not having a clue about him in 1988. I was at Naval War College and had bought a Mac II, equipped with a graphics card which would provide 256 color displays.

I’m not sure exactly where I found it, I’m guessing on GEnie (yep, before the ‘Net), but I got a program to draw fractals, the Mandelbrot set, and later the Julia set. I’d set a bunch of parameters in the computer when I was heading to bed, then get up in the morning to see some way down inside the Mandelbrot fractal scene. They’d take 2-4 hours to draw, depending on the “magnification” factors (the power to) I had set. Then I had working material to slice up in PixelPaint.

I was fascinated by the detail, and it was not the “chaos” or disorder, but the very subtle silightly offset order.

My worldview shifted as a result, somewhat then, but moreso later. In 1996, I was sent to attend two courses in Software/Systems Safety at the University of Southern California. Wandering through the University’s book store and picked up “Chaos: The Making of a New Science”.

In reading that book, and seeing the development of this body of science, my views of life shifted quite a bit. When I hear “chaos,” I usually consider the topic and think about if it’s just order too subtle that has escaped the examination, or it’s really something out of control. Usually, it’s related to the subtle organization. Beyond that, how his formulas have affected the computer graphics world. The scenery in the background of the big screen, like the “Lord of the Rings,” and many, many others, is generated using fractal formulas.

So, in 2004, when I began blogging, the moniker of the blog, Chaotic Synaptic Activity, came from a subtle reference to the far beyond the decimal point changes, normally allocated as disorder, in those things I think about. Before I read the James Gleick book, to me, chaos was chaos. After? It just means you have to consider things further.

In addition, about a year ago, the scientists figured out what I did in 2004: The brain runs on chaos!

For years, I’ve told myself I needed to write this piece to explain my naming convention, and I haven’t. Today, on hearing of Dr. Benoit Mandelbrot’s passing, I could delay no longer.

He was a pioneer in his field, and changed mathematics forever. In mapping, in fluid dynamics, in population growth and an offshoot into market economies and how they preform.

In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.

Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.

His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.

“I decided to go into fields where mathematicians would never go because the problems were badly stated,” Dr. Mandelbrot said. “I have played a strange role that none of my students dare to take.”

We need more minds like this.

RIP, Dr Mandelbrot.

Update: This YouTube bideo gives you a 10 minute view of the Mandelbrot math, hosted by Arthur C Clark



Now, hear from 2008 on how this math gave insights to the then coming economic collapse:



Category: Economics, Education, History, Leadership, Mathematics, Public Service, Science | Comments Off on RIP: Benoit Mandelbrot – Discoverer of Chaos

Go Figure: The Brain runs on Chaos!

July 13th, 2009 by xformed

Well, I’m not a real scientist, but I play one on this blog sometimes. The naming of this blog had this concept in mind, as formulated by the reading of “Chaos: The Making of a New Science” by James Gleick, about 15 years ago. Actually, my entire point, I think missed by many, is James Gleick pointed out that chaos is actually organization at a level we fail to take the time to dig for. It’s in the way past the decimal point places, that we round off before we get there, either out of “good enough,” laziness, or computational limitations. It’s order at a very subtle level, while looking exceptionally random to those who don’t take the time to take the journey. Over 20 years ago, I began playing with the creation of fractals on my Macintosh II, sometimes leaving it running all night, just to generate the image way down in the insides of the fractal form. Now, such things are easy to make quickly, and are widely used to generate scenery for movies.

I had always planned, from day one of the blog, to write about this, yet…almost 5 years later, and three iterations of this blog at different places, I have failed to get there yet, however, I feel vindicated today, by real scientists. Fallen rip

HAVE you ever experienced that eerie feeling of a thought popping into your head as if from nowhere, with no clue as to why you had that particular idea at that particular time? You may think that such fleeting thoughts, however random they seem, must be the product of predictable and rational processes. After all, the brain cannot be random, can it? Surely it processes information using ordered, logical operations, like a powerful computer?

Actually, no. In reality, your brain operates on the edge of chaos. Though much of the time it runs in an orderly and stable way, every now and again it suddenly and unpredictably lurches into a blizzard of noise.

Neuroscientists have long suspected as much. Only recently, however, have they come up with proof that brains work this way. Now they are trying to work out why. Some believe that near-chaotic states may be crucial to memory, and could explain why some people are smarter than others.
[…]

Lets go to the video:

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Take some time to read the article. When Harry Met Sally… video Maybe you’ll get a grasp on the chaos that reigns sometimes.

So, here I sit on the domain “Chaotic Synaptic Activity,” before the brain scientists figured it out. Sometimes even a blind squirrel finds an acorn in the snow.

A Crude Awakening: The Oil Crash divx

Category: Biology | Comments Off on Go Figure: The Brain runs on Chaos!

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