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Fractals, Chaos, and Control Systems on Rails


7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays

Posted by Harry Seldon on December 14, 2009

Mandelbulb by Daniel White

As we are still at the beginning of the holiday season, maybe you haven’t bought all your gifts yet. In that case, here are a few lifechanging books you can offer to your loved ones.
By lifechanging, I mean you will never look at the world in the same way after reading one of these books. There is even a good chance you will find the world a lot more simple after your reading because these books give you keys to the behaviour of nature and mankind.

If you don’t like too much specialized books, you will like these ones because each one of them will speak about several topics among geology, economy, biology, social sciences, and climate.

Moreover, you will find some element of answers for several popular questions of our days like:


So, let’s go to the point, here are these absolutely marvellous books. Notice, they are somehow sorted by order of importance.

So, in case it was not clear, now you see why my Twitter name is @Fractalharry ;-)

You can propose other books in the comments.

Enjoy your reading.

PS I have linked to Amazon for your convenience but I don’t touch any commission!

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Simplexity: Things are a lot simpler than they seem and vice versa

Posted by Harry Seldon on October 20, 2009

Have you ever heard of simplexity ?

Some systems are a lot simpler than they look like. For instance, let’s consider the shape of a tree. It looks complex, especially if you compare it with a straight line. However, if you have read Mandelbrot or heard of fractals, you know that all you need to draw a tree is a 2 lines pattern, which you repeat a big number of times introducing at each step some light randomness. You can model pretty easily this tree shape. At least you can generate at your will tree shapes. That is typically the way used in computer graphics to generate natural virtual 3D scenes. However, this does not mean you can predict the accurate shape of a tree from its seed.

So, is the tree shape complex or simple? Thanks to Mandelbrot we know now that the shape is a lot simpler than it seems. Associating the notions of predictability and simplicity, the converse is also true: it is more complicated than you could think even if you have heard of fractals. Hence this notion of simplexity, contraction of simplicity and complexity.

Here are a few good books on the subject:

If you know about fractals and chaos, you must be already familiar with that fact that simplicity can bring complexity quickly and easily. But you might not know this term of simplexity.
More generally, each time you think “this thing is a lot simpler than I had imagined at first”, you experience simplexity: in fact, you changed your first impression of overall complexity by discovering the underlying simple principles.

While we are at it. There is a field where simplexity shows all its magnificence: it is in finance. International finance looks complex but there are a limited number of principles behind it. You can even fairly easily model a stock chart. (Even if this model has nothing to do with the actual models used by financial analysts). But even with a good model you cannot predict easily the stock chart of a determined company.
For more info, you can have a look at the Facebook group “Finance & Mandelbrot”.

And at last, because I cannot prevent from saying it again, If you want to keep things simple, then regulate them. Contrary to what you could think, you do not need very accurate models to control a system.

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Yes, he can save the world !

Posted by Harry Seldon on February 23, 2009

He is from a minority. He is American, lives in the US but has a dual culture. He studied in the best universities. He is one of the smartest guys on Earth. He had many awards for his outstanding work along his long and brilliant career. He has always fought received ideas. He is not afraid of complexity but knows to recognize simplicity in the middle of intricated systems that most people consider as infinitely complex. He is not afraid of telling people when they are wrong. He is not afraid of telling them what to do. He does not hesitate to fight alone against the majority but definitely prefers to be with the majority. If listened to earlier, many casualties would have been avoided. He wants to change the world and he has a plan.
No, I am not speaking about Barack Obama. Let me continue. He is Franco-American. He studied aeronautics. He deserves a Nobel prize in all categories: economy, physics, medecine (biology), chemistry, and even litterature and peace, because his work helped describing and understanding the geometry of nature. His work can indeed be applied to stock market, natural borders, lungs description, fluid mechanics, animal population evolution, clouds. He wrote many inspiring books. If more listened to the world would be way more peaceful because better understood and less submitted to crisis.
Yes, I am speaking about Benoit Mandelbrot and the good news is: his work on finance is slowly being recognized by the media and by economists.

Listen to Mandelbrot and global warming, crisis and wars will just be bad memories. OK I am exaggerating, but I am not sure how much ;-).

PS If you know which conferences Mandelbrot is going to attend this year, please let me know in the comments because he is definitely the celebrity I would love most to meet.
mandelbrot antenna

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Good news from the combat against the crisis

Posted by Harry Seldon on February 22, 2009

Julia island
In my 2009 wishes, I wished that people better understand the world. For this purpose, I suggested they read The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward by Benoit Mandelbrot.
Actually, for one year and a half we have been inside this growing up crisis I have been appalled by the small number of articles in the media about Mandelbrot’s work on Finance and more generally by the small number of articles about chaos theory and economy. Indeed more than ten years ago, Mandelbrot explained why the finance world was walking on its head. To make it short, it is because financial theory fundamental principles are wrong and over-optimistic. These principles state that the hazard involved in the market theory is regular enough to be smoothed by the big numbers law. This hazard is “benign”. Basically, with the standard theory, crisis can’t happen. So yes, you must be dreaming, there is no crisis, unless you listen to Mandelbrot that tells you that the hazard is actually “savage” and potentially leading to a collapse of the market: a crash.

So where is the good news ?

It looks like main stream media are slowly understanding Mandelbrot’s work and they are speaking about it. I found yesterday an excellent article in one of the main French financial newspapers about Mandelbrot’s work on finance. The second good news, contained in that article, is that Mandelbrot’s book are being republished. A third good news, is that the author of the previous article, Philippe Herlin is very proactive and has just created a Facebook group called “Finance & Mandelbrot”. I joined immediately ! An instant interest of this group is that Philippe Herlin gives a list of news articles about the subject (given below). Please notice the link called How Fractals Can Explain What’s Wrong with Wall Street which is dated on February 1999. Yep, it is not a typo for 2009 !
Last but not least, there is a significant political news. Mandelbrot showed that the financial system was fractal, exhibiting the same behaviour at all scales. Actually that was the start of his long and brilliant career. Later on he showed the same behaviour for climate, geology, ecology, or biology. Actually about any natural system is fractal and even chaotical. However, there is a good way to smooth the behaviour of a system, it is called control. Our world needs more control (distributed control whenever possible). That is to say, more rules, more ways to enforce them and more ways to measure their efficiency. So the good news is today European leaders backed sweeping new regulations for financial markets. Questions remain, will the rules be good and will they be enforced?

By the way, if you want to understand a little better the whole world, if you want to hear about economy, climate, geology, ecology, or biology in less than 200 pages, just read these two amazing books. Your vision of the world will change and for almost free because these books are quite old (but have never been so fashionnable).

Nostalgia: I was offered these books 13 years ago. I read them then. They are definitely among the best gifts I have ever received. They stand in my bookshelf, one arm away from where I am writing these lines. Believe me these books are far easier to read than the Bible so you can give them to your children. I read them again 2 years ago after completing my studies in Dynamical Systems and Controls. I understood plenty of things I had missed in the first reading. So you can also offer these books to adults. They will learn quite a few things about the nature of our world.


In English

In French

If you know other good links about fractal, chaos theory and economy, please leave them in the comments.
Mandelbrot set

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Happy new year 2009! May we better understand the world!

Posted by Harry Seldon on January 02, 2009

I wish you all an excellent year 2009 filled with happiness in your private life as well as in your professional life.
Besides that, I wish you to better understand the world we all live in. For this purpose, here are some subjects that deserve all your attention and about which I will blog soon.

This beginning of the new year will be very busy around here. Indeed, I am going to make a major update for ThinkoSphere.com with the new design and I will start a blogging series about Control Systems. Later on I will blog about the fractal theory applied to finance because it is today the best theory explaining the crisis that I have found so far. I am currently reading the book “fractals, hazard and finance” from Benoit Mandelbrot*, father of the fractal theory. This book is amazing, it is ten years old but it looks like it was written 2 days ago, after the crisis.

Moreover, I also wish you to be better understood by your company, by your mayor, by your government. I wish you more democracy in your environment. This starts by giving more your opinion when you are polled. So I wish you more polls and finally I wish you to find your interest in ThinkoSphere.com.

* I am actually speaking about “fractale, hasard et finance” a book in French. Its equivalent in English is The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward. This is probably the best quality and best quality/price ratio book about finance you can buy nowadays!

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