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.

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

Guidance

Guidance refers to the questions ”where am I going to?”, ”How can the vehicle follow a trajectory?”. The trajectory itself is prepared by the Flight Planning System (FPS) (or Mission Planning System, MPS). During the flight, the Flight Management System (FMS) knows the trajectory and gives the current portion to the Guidance System (GS) . The Guidance System is in charge of converting the high level parameters (trajectory, waypoint positions) into a set of lower level orders that can be understood by the control, typically altitude, heading or directly a load factor, that is an acceleration. In some cases the guidance can have the role to compute a trajectory between 2 points.
It is also in charge of maintaining the trajectory and the other high level parameters. That means the guidance is itself a control loop. Typically the guidance is the Position Control System (PCS).
This is where things become tricky. Piloting and Guidance are essentially similar. The difference to keep in mind is that the pilot is a low level control loop whereas the guidance is a high level control loop. A nice world would be a world where guidance and pilot loops are two independent loops. Unfortunately both are coupled, and designing one, you need to keep the other one in mind.

Next chapter will be about GNC and human pilot.

Introduction
Navigation
Stability and Control
Guidance
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops
Conclusion

Stability and Control

Control answers the question ”How can the vehicle be stable?”. For an aircraft, it means “how can the aircraft accomplish basic moves such as flying straight, climbing, descending?”. A more technical definition of stability would be “the tendency of the vehicle to maintain or deviate from an established flight condition”. Control is the ability of the vehicle to be manoeuvred or steered from one flight condition to another.
It is very important to notice that questions regarding the stability (as opposed to a crash) are mainly addressed by the control and not the guidance nor the navigation. That is why one often speaks about Stability and Control System (SCS) and not only Control System.
The SCS is made of two parts: Stability Augmentation System (SAS) that stabilizes the aircraft (if it is naturally unstable) and improves its handling qualities. Then, the Control Augmentation System (CAS) typically allows the vehicle to maintain its altitude or heading. These functions are called altitude hold and heading hold modes in the AutoPilot (AP). The SCS creates the low level orders directly sent to the actuators (ailerons, rudder, elevator, engines, etc.). It is also sometimes called the Piloting System, meaning piloting is associated to low level, stabilization work.
Thus, how to fly is known by the control. Once it is done, higher level objectives can be achieved such as following a trajectory, that is going from a point A to a point B. High level orders will be sent by the guidance system.

Next chapter will be about Guidance.

Introduction
Navigation
Stability and Control
Guidance
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops
Conclusion

Navigation

Navigation (Nav) refers to the question ”where is currently the vehicle?”. A Navigation System (NS) aims at giving you your position. Nowadays the main sensor associated to navigation is definitely a GPS (Global Positioning System) sensor. More generally the Nav collects all the data from the sensors and processes them to make a precise, smooth and high frequency information about position and speed.
The main control theory tool for navigation is probably the Kalman filter. Typically, embedded on board an aircraft, the navigation will combine GPS data, air data, inertial data and the aircraft dynamical model into a Kalman filter.

Next chapter will be about Stability and Control.

Introduction
Navigation
Stability and Control
Guidance
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops
Conclusion

This post was quite long so I decided to cut it in several parts. Even cut in several parts, the point remains to consider GNC as a whole, it is not to make extensive explanations on each topic. Wikipedia would be fine for this, whereas it is not so good as far as the GNC topic is concerned. According to your comments, I may update Wikipedia with the little work made here.

The first chapter presents the Navigation System.

Here is the Table of Contents (TOC):

Introduction
Navigation
Stability and Control
Guidance
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops
Conclusion