I love the contrast between these cute spherically pruned trees and the majestic naturally shapped oaks behind. Notice that the apparent complexity of the fractal shape of the tree does not imply it is very difficult to prune a tree. It is more the size and the hardness of the branches that will decide how hard it is to prune the tree into a round shape.
Which tree shape is complex, the natural fractal shape or the artificial round shape? In terms of time, to accurately describe the shape, it is quicker to draw a circle than a fractal, so the circle is much simpler.
In terms of work to obtain the shape, it is the opposite. To get the fractal shape all you need to do is let nature do its job (with simple algorithms). To get a nice spherical shape you will need to prune the tree regularly. It is thus complex to get simple shapes.
Pruning a tree might not sound a complex process. However, the complexity comes from the fact the gardener will want to minimize his work on each tree. He will want to know the minimum frequency at which he needs to prune each of his trees. When in the season, which branch length (according to the tree halth), which tools, that makes many questions that complexify the control algorithm.
So yes gardeners as many other people do optimal control engineering without knowing it. Each time you ask yourself a question such as at which frequency should I do this, you are asking you the central question of control engineering. Too slow and you don’t get the performance you want, too fast and you overwork, you overconsume your energy.
A key factor of success is to do things at the good frequency. Unfortunately, this optimal bandwidth is complex to obtain.

To get back to the simple vs complex question, the key of the simplexity paradox lives in these points:

• A simple natural algorithm leads to a complex shape.
• A complex control algorithm leads to a simple shape.

More generally, we can sum this up like explained in this figure:

Notice that the line from nature to artificial world is continuous. I am not excluding mankind from nature.
Notice also that this separation between a chaotical world and a controlled world is very similar to Nassim Taleb’s separation between extremistan and mediocristan. I had already quickly talked about this description of extremistan and mediocristan as unstable (chaotical) and stable (controlled) systems in a previous post.

Then, here are a few more pictures of the snowed gardened.

Garden with naturally shaped trees in the background

Trees pruned in a conic shape.

Trees pruned in a cubic shape.

Feel free to leave your comments.

Part 2

Part 3

Part 4

Part 5

Part 6

Enjoy!

Enchanting ghost trees.

Sceaux Castle Forest under the snow.

Sceaux Castle under the snow.
This picture will be the inspiration for a future post. Can you see why?

If you have pretty winter pictures you want to show, you are welcome to link to them in the comments.

Do not hesitate to contact me if for some reason you want the pictures in full size (5 MegaPixels).

Happy new fractal year!

PS: In the first picture the tree is not the only one to be naked, can you see the naked young lady in the picture?

Wow, this naked young lady under the naked tree must be freezing. ;-)

So, as you follow where I am heading to, yes I do wish you to be a full pilot of your own life, not a passenger. And do not forget “Goals are dreams with a deadline” as one says.

If you find your life is too much of a fractal it might be because you don’t control enough your life. It is normal to perceive the world outside of you as a fractal, with its good and bad news, with positive or negative black swan. But inside of you the way news affects you is very much under you control. The way you behave is under your control. World might be fractal, your mind might not if you master it.
All the fun of life is knowing what you can change and what you cannot.

To read more about the duality Fractals vs Control check this article about extremistan and mediocristan.

Be in control of the first thing you can readily control in that world: yourself ;-)

If you are interested in knowing more about how you actually control yourself, check the subject of NLP: Neuro-Linguistic Programmation.

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:

• How does the climate evolve?

• Why are we in the middle of a great economical crisis? (By the way, if you want good new about the crisis)

• Why politicians appear to be “all rotten anyway”?

• Is the key to success luck or hard work (or both)?

• Why species disappear?

• Why can’t we predict the weather nor the stock market?

• Can Chaos Theory be actually useful to something? (Chaos theory is also about knowing what you can’t predict exactly so that you can prepare for the worst)

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

• The Fractal Geometry of Nature, by Benoît Mandelbrot; W H Freeman & Co, 1982

• Chaos: Making a New Science, by [James Gleick] (http://www.around.com/)

• The Black Swan: The Impact of the Highly Improbable by Nassim Nicholas Taleb (If you have already read it, be sure you have read this post about mediocristan and extremistan)

• Simplexity: Why Simple Things Become Complex (and How Complex Things Can Be Made Simple)

• The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward.

• Fooled by randomness by Nassim Nicholas Taleb

• Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, 1977

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!

My conclusion (1) is that in order to be able to predict a system behaviour you need to be able to stabilize it, that is you need to be able to control it or equivalently speaking to regulate it.
I cannot predict what you are going to do tomorrow. But If I can order you what you are going to do tomorrow, then there is a good chance I can also predict what you are going to do !

Bonus thought
Linear systems are very rare. Most systems are non-linear. But control engineers use and abuse of linear systems. The important reason is that systems can be locally linearized. Then, locally, you can apply linear control tools. You can stabilize your system and because it is stable you remain in the initial local place and you remain stable. That is all the beauty of it. So yes, somehow, linear systems are not as rare as they seem. Otherwise, there would be no aircraft autopilots because aircraft or spacecraft dynamics are not linear systems.
About Economics / Aerospace comparisons, you can also read this post:
2 lessons Economics should learn from Aerospace

(1) (not engaging Taleb, he does not seem much against regulation, for instance he wants companies to be prevented from becoming “too big to fail” but he is probably less regulation prone than I am. I am for instance for a safety authority on financial products like there is an aviation safety authority in charge of certifying airplanes (FAA).)

I had read this little comparison a year ago already in a French newspaper. The author was Jacques Attali, a French economist. As a pilot, I have wanted to blog about this since that time.

To be a little more accurate, an analogy would assimilate companies to airplanes and market to Air Traffic Control (ATC). The problem is the market does not control anything. Imagine air traffic without ATC. Air space would be a mess. Aircrafts would collide all the time and basically nobody would trust air traffic. Finally nobody would take the plane. The air traffic system would be quickly dead. Yet, that is what is happening with the economy. Companies crash and collide because they have secant routes and nobody to help them. Economy is a mess. Most of the time ATC helps pilots by guiding them among the traffic and by giving them slots to take off and land. But sometimes ATC prevents pilots from going too fast to their destination because they would compromise safety of other airplanes. Unfortunately companies have no “market controllers” to talk to, hence the crisis.

Economy should learn 2 lessons from aerospace system engineering:

• Systems must be controlled.
  An airplane is highly unstable. It can fly because it is very actively piloted. Air traffic is unstable too, it is controlled by ATC. In the same way economy needs guidance, navigation and control. To say it differently economy needs regulation.

• Systems must be robustified.
  Even once an airplane is controlled and made stable there is still a lot of work to do to ensure that it is robust to all kinds of failures, even some non-anticipated failures.
  Economy needs safety engineers. Currently there is only one safety engineer for the economy. He is Nassim Nicholas Taleb, the author of the Black Swan and Benoit Mandelbrot’s spiritual son. Else financial engineers behave more like terrorists than safety engineers. OK it is a bit harsh.

I began this post by the first point. So let’s develop now the second point.
An airliner has redundancy by design. It has 3 flight computers (and more). It has 3 fly by wire circuits. It has 3 hydraulics circuits. It has 2 wings (just kidding). It has 2 pilots. To design the airplane there is a whole team of engineers whose only role is to evaluate and improve the aircraft safety. They will verify that the airplane is as black swan proof (rare catastrophic event proof) as it can be. For instance, they will check that in the case of an engine explosion the projections won’t cut all the flight control wires. Obviously, propulsion engineer (in engine companies) will make sure an engine does not explode but, all the same, aerospace safety engineers do not take anything for granted. So they study the worst cases and they robustify the system. Moreover, they also robustify the system without any specific case of failure. For instance, the logic behind having several circuits is as simple as “something could happen”. You do not always need to know the exact failure scenario to robustify the system. Obviously, nothing (and no human pilot) being perfect, there are crashes. However, it is still safer to be in an airplane than in a car.

To come back to business, notice that safety by redundancy is the 6th point in the absolutely excellent article ”The Six Mistakes Executives Make in Risk Management” by Taleb. The mistake is “We are taught that efficiency and maximizing shareholder value don’t tolerate redundancy”. (A blogger sums up the six mistakes here).
If you are a manager, don’t leverage too much your department. Don’t think that each competency must be hold by only one person. Don’t make your best to reduce all redundancies. On the contrary identify your key activities and put redundancy on it. On the short term, reducing all redundancy gives you more profits but on the medium term it leaves you exposed to very easy failures (a sick person, an expert who leaves, etc.).

To conclude I will point out that Taleb loves to compare financial analysts to blind drivers. Here is one of his last sentence: “There were so many wise people around, but whom does Obama pick? The same people who were driving a schoolbus blindfolded, who have now been given a bigger bus.” You can find the citation in this article: Black swan now elephant in the room

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:

• Simplexity: Why Simple Things Become Complex (and How Complex Things Can Be Made Simple)
• Chaos: Making a New Science, by James Gleick
• Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, 1977
• In French, La simplexité by Alain Berthoz

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.