Harry Seldon's blog

Fractals, Chaos, and Control Systems on Rails


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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Launching ThinkoSphere Alpha, an accelerator of democracy

Posted by Harry Seldon on January 24, 2009

I am pleased to announce that the alpha version of ThinkoSphere.com is hereby publicly launched! I have finally integrated the new design. I hope you like it.

What is ThinkoSphere?
ThinkoSphere is a brand new experiment that publicly aims at implementing more Control Systems Philosophy into the democracy. That means I want to give each of you more power in:

  • Giving your opinion
  • Knowing the opinion of others
  • Analyzing thoroughly this data
  • Reacting accordingly to the results of a poll or vote

The Control Systems philosophy is pretty straightforward: you sense, you think, you act. This process is scale independent: it is the same that drives your personnality. It is also the same process that drives the society. So let us make it more transparent.

What is the current state of ThinkoSphere?
Currently, ThinkoSphere might look like a classical polling website. However, ThinkoSphere has 2 great features that are innovative, fun and very useful:

It means that, among the “sense, think, act” parts, the sense and think parts are currently the most developed ones.
To be precise, you can:

What comes next?
Plenty of things: widgets, API, internationalization (i18n), localization (l10n)… But for now, it is time to test in the real word what has already been done. So, what do you think about this project?. You are very welcome to leave your comments here. I am specifically appreciating negative feedback so that I can improve. It is all about control isn’t it?. Moreover, if there are features you want to see added, leave a suggestion here or create a poll.

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Control Systems 101: a Flight Control System example

Posted by Harry Seldon on January 03, 2009

Flight control system
The about page of this blog says this blog is about Linux, Ruby on Rails, Controls and the Thinkosphere project. It is now time to speak about controls.
First things first. What is a control system (CS) ? I am glad you ask because it is not an easy question. A way to answer is to give various examples which I will do in this post and next ones. Right now, I would say that a control system is a set of methods, processes and machines or humans that aims at shifting the state of a system from an initial state to a new determined state while keeping the behaviour of the system inside some bounds. OK, the definition is not very sexy. However, you notice immediately that many systems (if not all) will fall into this definition. That is the point of this blog. I want to show you that control systems are about everywhere. Everything and everybody is either a control system or a part of a control system.

What does a control system consist in ?
A CS is made of actuators, sensors, controllers. Another way to say it is: a CS is made of muscles, perceptors, brains. In order to enter the details of how a control system works I will take the example of an Aircraft Flight Control System (FCS) because it is what I know best as I am a Flight Mechanics and Controls Engineer, and a private pilot.

What is the aim of the FCS ?
Basically, nothing else than conducting the flight to move safely the airplane from a Point A to a point B minimizing the cost (Fuel consumption), minimizing the time and maximizing the passenger comfort… Yep quite a lot of things to do ! CS Design is not something very easy.

Actuators act on the system. For a mechanical system actuators apply forces and torques on the system.
For our FCS, actuators are:

  • Engines, they generate the thrust
  • Ailerons, they allow tilting the aircraft towards the left or right (along the roll axis, that is one of wings is higher than the other one) and thus they allow the aircraft to change its heading)
  • Elevator, it allows tilting the aircraft towards the up or down (along the pitch axis, that is the nose will be higher than the queue or the opposite)
  • Rudder, it allows tilting the aircraft (along the yaw axis, towards the left or the right in the plane of the aircraft)
  • Spoilers, slats and flaps to better act on the lift

Actuators receive their orders from the controller.

Some other things that fall into the actuators category: action mean, levers, muscles.

The sensors observe the state of the system. They measure critical parameters. For our FCS, sensors are:

  • Gyroscopes, they measure the angular velocities of the aircraft (roll, pitch, yaw rates)
  • Accelerometers, they measure linear accelerations.
  • Angle of attack probe, it gives the angle between the velocity vector and the pitch attitude angle.
  • Pitot tube measures the velocity with respect to the air.
  • Barometer allows estimating the altitude through the air pressure.
  • GPS to give the aircraft position

The controllers gets information about the system from the sensors.

Some other things that fall into the sensor category: feedback, detectors, observers, measures, references.

The controller gets the high level orders from the pilot (where do you want to go, heading, altitude, etc ?). Then, using the control laws it converts the order to low level electric orders sent to the actuators. Next, it checks that the aircraft does what it told it to do. The small discrepancy between the order and the measure is analyzed by the controller which sends an update to the actuators and the control loop goes on. The frequency of the whole process is typically 8 Hz.
The controller is made of computers and softwares. Softwares themselves are made of quite a lot of different parts, the core part being the implementation of control theory algorithms.
For sake of simplicity I am including the estimators, these algorithms that use several data measurements to filter the measurements or compute not measured data, inside the controller.

Some other things that fall into the controller category: guidance, navigation, control,stability, GNC, brain, think, computer, estimators, software, automatics, algorithms, methods, processes, regulator, commander, boss, manager.

In controls, we often speak about loop and feedback. The scheme at the top of this article is the representation of the order in which the parameters are sent and obtained. The pilot enters the parameters into the flight computer. The computer sends the first orders to the actuators. Actuators act on the aircraft. Sensors measure the state of the system and feed them back to the computer. Then, the computer verifies if everything behaves accordingly with what it expects, otherwise (for instance if there were external perturbations or modelling errors) it sends new orders. And the cycle goes on.
Finally, you should basically understand what a control system, controllers, actuators and sensors are. In future posts, I will explain the differences between Guidance, Navigation, and Control. I will give you more example of CS and what their controllers, actuators and sensors are. Some controlled (or not!) systems I have in mind are Economy, Climate, Politics, Society, Company, etc.
In the mean time, you can play the following game. Whatever you see, ask yourself if it is more a controller, a sensor or an actuator and for which CS. Or just do that for the following things: justice, police, lawyer, economist, trader, SEC, president, soldier, medical doctor, clothes, volcano, and ThinkoSphere.
Playing this game, you will quickly understand this motto I often have in mind: “It’s all about controls”!

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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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LEND to the rich, GIVE to the poor (not the opposite)

Posted by Harry Seldon on October 11, 2008

We are in the eye of a stock market cyclone. How did we get there ? One humoristic explanation of the subprime crisis can be found here. Another way to say it is that the financial world completely inverted the roles by lending a lot of money (I am not speaking about microcredit) to the weaker classes and by speculating on them instead of lending money to strong companies.

When I was a child, I was always surprised when hearing the French proverb “people lend only to the rich”. As many, I was surprised because the first reaction is to think rich people do not need money, poor people do need it. So the logical thing seems indeed to lend to the poor. However, to lend is not to give. In fact, lending money is not only a time exchange. I transfer you this money now, you will transfer it back to me later. But it is even a sale. I am selling you this money for this price (interest rate). So some of our great financial engineers sold expensive products (home and loans) to people who could hardly afford them. Worst of all they speculated on these products, resulting in destroying the value of both the home and the loan. While they did that they GAVE money to the rich. Lehman Brother’s CEO made 500 million dollars in eight years and he was already rich before being CEO. More generally, the whole finance world created crazy wages.

At the same time, companies in the industry got troubles borrowing money and went on a harder pressure to make profits whatever it takes. One such extreme solution is offshoring. On the paper, it seems to generate profits, but globally it destroys value because it destroys the experience acquired by the workers, engineers and management teams (about everyone is impacted by offshoring). This experience is something totally concrete which has a high value. Unfortunately, this value might not be easy to fit in the math models our finance guys came up with.

So let’s summarize : the poor got a money they could never reimburse, companies did not get a money they could reimburse, the rich were given a real part of a money virtually created by speculation. These last ten years, finance seemed to work with this motto in mind : Lend to the poor, give to the rich. Therefore, it looks like this remainder is not superfluous : LEND to the rich, GIVE to the poor (not the opposite). With this crisis, there will sadly be plenty of new poor people and there will be plenty of companies desperately needing credits.

Thus, now is the time to actually apply this advice. And finally, if you hear again the proverb “people lend only to the rich”, just think back to the 2008 great crisis to remind you what it precisely means.

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