Adonis Diaries

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What Black Swan Theory has to do with Arab Spring uprising?

Posted on June 13, 2012

I have posted several articles on the Black Swan Theory and this link is in response to its application to Lebanon political/social structure

Zaher Yahya posted on Huffington Post an article (with slight editing) that is a general “refresher” post on the topic:

“The Arab Spring has been described and associated with a variety of symbolic designations.

At times, the term describes the series of protests that have swept across the MENA (Middle East and North Africa) region. It may also indicate a person’s political position on the wide and highly polarized spectrum.

The term ‘Arab Spring’ has even been criticized by some who support the pro-democracy (or anti-regime) protests, citing this description as being Orientalist and therefore inappropriate.

The ‘Arab Spring’  (protests and upheaval), which started on December 2010, has become a brand for the region, and has motivated and catalyzed many popular protest movements around the world.

International media generally refers to the term as a unified concept, largely citing its contagious aspects as well as the key links between the countries involved.

We now know that the Arab Spring will not be an easy ride for the countries that it has affected, though it cannot be denied that the region has been marked by a political paradigm shift.

People in the MENA region have:

1. Denounced the long-accepted principle that unelected officials and family dynasties can cling to power for decades without consequence.

2. People have broken the long-standing barriers of fear regarding corruption and intimidation,

3. People are adjusting to the ideological diversity of their societies (though many still have much to learn on this front).

For these reasons, I tend to be optimistic about the Arab Spring despite much rhetoric about it becoming an Arab “Winter.”

Having lived through the global financial crisis that has affected people of all walks of life, I view the Arab Spring as being related to these events that shook the world economy in 2007.

Are you surprised that I find a relation may exist between these two events, both vast and far-reaching, but seemingly distinct? It may appear a tad philosophical, but the answer lies with Nassim Taleb.

Nassim Taleb (see note 2) lays the foundations  in his two books Randomness (2001) and Black Swan (2007) for his theories about uncertainty, randomness and Black Swan events.

Black Swan theory describes unpredicted major-impact events that effectively appear sensible in hindsight.

Taleb theory is framed in a financial context, (many experts contend that Taleb forecasted the financial meltdown of 2007), and describes the biggest financial crisis since the Great Depression of the 1930s as one of these Black Swan moments.

Black Swan moments are characterized as being rare, high-impact and paradoxically unpredictable occurrences at the time of their occurrence. Most of us would assume black swans don’t exist, simply because we were only accustomed to seeing white swans in pictures and videos…

In the terms of the financial crisis, speculators assumed there is only one way for the markets to go; asset values would rise indefinitely with no limit to the amount of debt people could incur.

It has become clear afterward that the reality on the ground was different of what was written on their balance sheets and portfolios bottom lines.

The impact of the debt crisis was colossal and wide-spread that no expert envisaged at the time, with many talking about the failure of capitalism as a result. This global crash has really shattered the image and ultimate authority of the dictators of the finance sector (i.e. investment banks and hedge funds).

The Arab spring proved as difficult to predict as the financial meltdown showing economists, intelligence agencies, policy makers and analysts clueless about their own business, simply because they have never considered a Black Swan moment for the MENA region.

The Arab Spring was triggered by what could initially have been interpreted as an isolated event, spread surprisingly fast over a vast region, and led to major and unexpected developments.

In the same way, norms of the banking system that was held for generations collapsed with stunning speed and magnitude, the image and privilege of Arab dictators were shattered by popular revolts in a movement that took the world by surprise.

A Black Swan moment was never considered in the experts’ minds to apply to the Arab States: many Arab dictators held a seemingly unshakable iron grip on power and ruled undeterred for up to four decades, all while preparing their sons to someday take the reins after them, unshaken by popular and economic conditions in their country.

So the public witnessed only their moukhabarat (secret service agents) running the show, as well as the brutal backstage of the regime if you were unlucky enough to pay them a visit.

Years of tradition made this construction of power a social norm, a backbone of society so persevering it was often assumed (and reasonable at the time) to be unshakable.

And this is exactly what Nassim Taleb focuses on, exactly on the things we don’t know rather than the things we think we do.

A small exception to a rule (events in the tails of the normal graph) in the future can have the ability to trigger large-scale change and dismantle norms, theories and paradigms that have been accepted for years.

The colossal impact of the Arab Spring across the region was beyond anyone’s realm of expectations – either idealistic or highly calculated.

In the world of risk management, this event appeared highly unlikely: The probability of such events spreading across such a vast region were not on the minds of political forecasters, in the same way so many bankers did not fathom their long-standing stability could be shattered so suddenly.

In hindsight, the Arab Spring may now appear to have been predictable.

How could we have assumed that despite torture, censorship, abuse, brutality, corruption, unemployment and poverty, regimes would remain sustainable?

Whatever your opinion of the Arab Spring, and whatever term you choose to designate it, what started in December 2010 has proven itself a Black Swan moment of the Middle East and North Africa, one that is far from over, and whose impact will perhaps take years to fully assess.

Note 1Michelle Ghoussoub, Blogger at Lebanon Spring, edited Yahya article.  Follow Zaher Yahya on Twitter:

Note 2: Nassim Taleb is a renowned Lebanese-American statistician, best-selling author and former Wall Street trader. His books Fooled by Randomness (2001) and Black Swan (2007) brought him to fame, with the latter described by The Sunday Times as “one of the twelve most influential books since World War II”.

Note 3: Opinion experts would like us to believe that the uprising were not expected by the US. Evidences are pointing that what was unexpected is the development, steadfastness and far-reaching movement of the Arab people to get away with their long established indignities and humiliation by usurping oligarchies.

Note 4: What is of most importance is to study how the colonial powers and Saudi Kingdom, and monarchic regimes went about taming this mass upheaval and re-instituting dictators power in the MENA region. Only the fomenting of the extremist religious movements were the major barriers in resuming these mass upheaval.

Fractals? Any connection with matters not related with nature?

And why should You care?

Georgemdallas posted this May 2, 2014 (selected as one of the top posts)

Fractal geometry is a field of maths born in the 1970′s and mainly developed by Benoit Mandelbrot. If you’ve already heard of fractals, you’ve probably seen the picture below.

It’s called the Mandelbrot Set and is an example of a fractal shape.


The geometry that you learnt in school was about how to make shapes; fractal geometry is no different.

While the shapes that you learnt in classical geometry were ‘smooth’, such as a circle or a triangle, the shapes that come out of fractal geometry are ‘rough’ and infinitely complex.

However fractal geometry is still about making shapes, measuring shapes and defining shapes, just like in school.

There are two reasons why you should care about fractal geometry:

1. The process by which shapes are made in fractal geometry is amazingly simple yet completely different to classical geometry. While classical geometry uses formulas to define a shape, fractal geometry uses iteration.

It therefore breaks away from giants such as Pythagoras, Plato and Euclid and heads in another direction. Classical geometry has enjoyed over 2000 years of scrutinisation, Fractal geometry has enjoyed only 40.

2. The shapes that come out of fractal geometry look like nature. This amazing fact that is hard to ignore. As we all know, there are no perfect circles in nature and no perfect squares.

Not only that, but when you look at trees or mountains or river systems they don’t resemble any shapes one is used to in maths.

However with simple formulas iterated multiple times, fractal geometry can model these natural phenomena with alarming accuracy. If you can use simple maths to make things look like the world, you know you’re onto a winner. Fractal geometry does this with ease.

This blog post shall give a quick overview of how to make fractal shapes and show how these shapes can resemble nature.

It shall go on to talk about dimensionality, which is a cool way to measure fractals. It ends by discussing how fractal geometry is also beneficial because randomness can be introduced into the structure of a fractal shape.

The post requires almost no maths and includes lot of pretty pictures

How to make a fractal shape

In normal geometry, shapes are defined by a set of rules and definitions. For instance a triangle consists of three straight lines that are connected.

The rules are that if you have the length of all three sides of the triangle it is completely defined. If you have the length of one side and two corresponding angles the triangle is also defined.

Though the rules defining a triangle are simple, huge amounts of useful maths has come out of it, for instance Pythagoras’ Theorum, sin() cos() and tan(), the proof that the shortest distance between two points is a straight line, etc.

Fractal geometry also defines shapes by rules, however these rules are different to the ones in classical geometry.

In fractal geometry a shape is made in two steps:

First by making a rule about how to change a certain (usually classically geometric) shape. This rule is then applied to the shape again and again, until infinity. In maths when you change something it is usually called a function, so what happens is that a function is applied to a shape recursively, like the diagram below.



After it has repeated an infinite amount of times, the fractal shape is produced. What are these functions then? What do you mean by repeating infinitely? As always, this is best explained by an example…

A good fractal shape is called the von Koch curve. The rules, or function, are extremely simple. First you start with a straight line. This is your ‘initial shape’:


The rules are as follows:

1. Split every straight line into 3 equal segments.

2. Replace the middle segment with an equilateral triangle, and remove the side of the triangle corresponding to the initial straight line.

The process is shown in the figure below:




This is what happens to the straight line, our initial shape, when it goes through the function the first time, the first iteration.

Now, the shape it has produced is fed back into the function again for a second iteration:





Remember the rule was that any straight line would be split into thirds, so now 4 lines are split up and made into triangles. The shape that is produced after the second iteration is then fed through the function for a third time. This gets hard to draw in MS paint so I’ve used a couple of pictures from this website for the next few stages:

von_Koch_curve (1)

After this has iterated an infinite amount of times the fractal shape is defined.

This may sound bewildering but it is still possible to analyse it mathematically and visually you can see what the shape starts to look like.

The gif below (from Wikipedia) is a good illustration of what the curve looks like by zooming in on it:



The von Koch curve is a great example of a fractal: the rule you apply is simple, yet it results in such a complex shape. This kind of shape is impossible to define using conventional maths, yet so easy to define using fractal geometry.

So who cares about the von Koch curve?

Isn’t it just mathematicians wasting time on weird shapes?

I guess that depends on how you look at it, but I’m convinced it’s useful because it looks exactly like a snowflake. This is made more clear if the initial shape you start with is a triangle rather than a straight line:


There’s a whole debate to be had on the purpose of maths, but as an Engineer I am inclined to say that one of its purposes is to try and replicate the world around us. The shapes that come out of fractal maths are so different to conventional mathematical shapes and so similar to the world around us that I cannot help but be seduced by this topic. Two other shapes that are favorites of mine are the Barnsley Fern:


And fractal trees:


These aren’t drawings or pictures, but mathematical shapes. If you look at the shapes you can see what function repeats itself. For instance on the Barsley Fern the function is to draw 30 or so perpendicular lines out of each straight line. The function repeats itself to and looks like a fern. On the tree you can see that each line branches out twice, which will be the function that repeats itself. Another property about these shapes (though strictly not for all fractals) is that they are self-similar. This means that the shape looks like itself however much you zoom in or out. For instance on the tree above, if you snapped a branch off it and stood it up, it would look like the original tree. If you took a twig from the branch and stood it up, it would still look like the original tree. Again, this is a property that occurs in nature, but until fractal geometry there was not a good way to put it into maths.

Not only do these shapes look like natural objects, but the process of iteration sounds intuitive when thinking about nature. When a tree is growing, its trunk will create branches, these branches create further branches, these branches create twigs. It’s as if the function is a genetic code telling the branch how to grow and repeat itself, eventually creating shapes that are ‘natural’. This may sound like pseudo-science (it definitely is) but I think these are concepts worth considering when you are able to imitate nature so closely.

Right enough about nature, time to talk about how fractals have crazy dimensions.


So now we know what fractal shapes are and how to make them, we would like to know a few things about them. One of them first things to try and figure out is the length of some of these shapes. Let’s go back to the von Koch curve.

In order to figure out how long the full von Koch curve is (after being iterated an infinite amount of times), it is useful to consider what happens at the first stage again:


The line is split into three, then the middle section is replaced by two lines that are as long as it (as it’s an equal triangle). So if the original straight line had a length of 1, the length of the curve after the first iteration is 4/3. It turns out that every time you iterate the shape, it gets 4/3 longer. So the length of the curve after the second iteration is 4/3 x 4/3 = 16/9:


As 4/3 is greater than 1, the line gets longer every time it is iterated through the function. As you iterate the function an infinite amount of times, the full von Koch curve has a perimeter that is infinitely long! This is the case for all fractal shapes: they have infinitely long perimeters. That isn’t useful for mathematicians so they don’t measure the perimeter of the shape. Now the next few paragraphs require a bit of abstract thought, but if you think a bit outside the box it does make sense.

The perimeter measures the length around something. Length is a 1 dimensional measure of space. Length is 1D because it only measures a straight line. A 2D measure of space is area, 3D is volume. Now we’ve shown that it isn’t useful to measure fractal patterns in 1 dimension as they are infinitely long, but what is odd is that fractal shapes are not 1D, 2D, or 3D. Each fractal shape has it’s own unique dimension, which is usually a number with a decimal place.

The dimension of a fractal shape is a measure of how quickly the shape becomes complicated when you are iterating it. What do we mean by becoming complicated? Well in the von Koch curve you can see that the first few iterations produce quite simple shapes, however at about iteration 4 it starts to become quite small and complex.

The way to measure how fast a shape becomes complicated, and hence its dimension, is to measure how much longer the perimeter gets after each iteration. This makes sense intuitively, as if the line gets much longer after each iteration it is probably becoming very complicated very fast, whereas if the line stays pretty much the same length after each iteration then it probably isn’t getting very complex.

As we’ve already shown, the von Koch curve gets 4/3 longer each iteration. This means that the von Koch curve is 4/3 D, or 1.3333…D. Pretty crazy right? It exists somewhere between 1D and 2D. But this measure is really useful to mathematicians as it gives information about the shape (whereas perimeter doesn’t, it’s always infinite). For instance if there was another fractal shape which was 1.93D, you could say with confidence that that shape gets complex quicker than the von Koch curve, as the perimeter gets 1.93 times longer after each iteration rather than 1.3333, implying it gets complex more quickly. When studying a fractal shape, knowing its dimension is of integral importance.


The last thing I’m going to talk about is the fact that randomness can be inserted into fractal shapes. Random (or seemingly random) events occur in nature all the time and affect different things in a variety of different ways, for instance a large part of Information Engineering is dealing with noise, which randomly fluctuates an electronic signal. When trying to replicate this, you usually add randomness on top of a signal. For instance in electronics you would create a nice sine wave and then add noise on top of it (borrowed from this website):


The bottom image is the ‘pure’ wave, and the top image is the wave with noise added on. An inherent assumption when doing this is that there is an underlying ‘pure’ signal which is randomly altered. While this may be true for a lot of electronics, the same cannot be said for nature. Often there isn’t a ‘pure’ shape that is randomly altered around the edges (for instance there are not many fuzzy squares in nature), but rather randomness effects the structure of the shape itself at each stage of its evolution. Classical geometry is not good at incorporating randomness into shapes, whereas fractal geometry can do it easily. For the last time lets turn to the von Koch curve. However this time we will insert randomness into it.

We know the rule is that for each iteration a triangle is created in the middle third of a line. However every time the triangles always faced ‘outwards’. We could insert randomness by saying that for each triangle created, it goes either above the line or below the line depending on a coin toss:


Now the shape will develop at random according to the coin toss. For instance after multiple iterations the von Koch curve can look like this:


Or it can look completely different. What is cool about this is that you can insert randomness into the shape itself rather than adding it on top of an existing shape. This has exciting potential, for instance (going back to nature) this may be a good way to model random genetic mutations.


This blog post has provided a brief introduction to fractal geometry. I hope you’ve found it interesting!




June 2023

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