The Truth Behind Chaos

What is chaos theory?

Chaos theory looks into nonlinear systems that cannot be predicted just given previous data.  If you look at a graph of chaos, it could look completely random (see the previous post about randomness at: https://foodforscientificthought.wordpress.com/2014/05/28/combating-data-manipulation-vii-patterns-and-randomness/).  As mentioned in that post, random processes will occur completely differently even if you use the exact same conditions again.  Chaotic systems, on the other hand, can be generated from an equation and change greatly based on initial conditions.  But, if you play the same chaotic system twice with the same initial conditions, you would likely get the same process both times.

File:PWL Duffing chaotic attractor plot.gif

Found at: http://commons.wikimedia.org/wiki/File:PWL_Duffing_chaotic_attractor_plot.gif

This graph may seem completely random, but it is dependent on initial conditions and can be described using an equation.  If you run that same equation many times, it will always turn out looking like that graph.

The big idea about chaos is that it is unpredictable; chaotic systems such as the weather and some aspects of the economy, among other examples, can not be predicted completely accurately.  This is why we have economic models and weather models; these are approximations because we cannot ever accurately predict these systems.

But, isn’t chaos theory just the butterfly effect?

With regard to chaos theory, many people have heard of the butterfly effect.  The butterfly effect states that a butterfly can flap its wings in one part of the world and it causes a hurricane in another part of the world; this is supposed to represent a chaotic system.  This effect illustrates that even very small changes in the initial conditions of a chaotic system can cause huge results.  More specifically, this effect describes the chaotic system of the weather, suggesting that the weather is so unpredictable that it is impossible to model, because no one could ever predict all the butterflies flapping their wings and generating wind which could effect the weather.  This makes the weather especially complex and unpredictable.

The butterfly effect itself is a little bit of an exaggeration, because just a butterfly flapping its wings could not solely cause a hurricane.  But the general idea holds that those small changes can cause much bigger events later on.

Misconceptions about Chaos

Chaos colloquially means disorder, but this is not necessarily true in mathematics and with regard to chaos theory.  Chaos is ordered in the sense that the processes are described by an equation and can be modeled, even if those models are approximations.

As far as media representations of chaos theory go, one of the most well-known is the movie Jurassic Park.  For those of you who have not seen this movie, there is a character who is a mathematician who uses chaos theory to explain why it is impossible to predict the outcome of a dynamic system like an unknown ecosystem and therefore the park cannot be deemed to be safe.  He does an interesting, albeit not entirely correct, demonstration of chaos theory in one scene.  He puts a drop of water on the back of his hand and lets it roll off, and then repeats the same procedure and sees that the droplet rolls in a completely different direction the same time.  He then declares that one cannot predict the path of the droplet of water and there is an example of a chaotic system.

While we have seen that chaos systems definitely cannot be predicted, so in a sense the character is correct, his demonstration is a bit flawed.  Instead of demonstrating a chaotic process, he demonstrated a random one.  As mentioned previously, chaotic processes will be largely the same if repeated many times, while random processes will be entirely different every time they are repeated.  What the character should have done is ask the woman he is demonstrating chaos theory to where the droplet of water would run on his hand and then do the experiment once, showing that her prediction was inaccurate and there are too many variables in this system to predict the path of the water.

Despite this little misrepresentation, Jurassic Park definitely did popularize the concept of chaos theory, so that’s a good thing!  Also it’s a great movie.

File:Jurassic Park, US.JPG

Found: http://commons.wikimedia.org/wiki/File:Jurassic_Park,_US.JPG

Works Cited

http://fractalfoundation.org/resources/what-is-chaos-theory/

http://homepages.ihug.co.nz/~sai/chaos_intro.html

http://www.crystalinks.com/chaos.html

http://www.math.tamu.edu/~mpilant/math614/chaos_vs_random.pdf

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