Chaos & the Butterfly Effect Theory

To those already initiated with Chaos and its theory, the article maybe not state something new (okay my interpretation maybe), but for those of you who don’t know what I am referring to, read on.

 

Chaos Theory: Contrary to the definition of the word chaos, which defines chaos as “a state of utter confusion or disorder; a total lack of organization or order”, Chaos theory attempts to identify outcomes in dynamic systems, whose behavior appears to be random but in fact are not random and are dependent on underlying variables.

 

The formal definition of Chaos Theory is thus “Chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

 

What the definition suggests is that a complex system (Such as Weather, population Growth, Stock Market etc) whose behavior, over an extended period of time, appears to be random with no underlying pattern and thus no predictability does in fact follow a particular order which is influenced by the underlying variables that work together as catalysts to generate the outcome (results). The theory thus focuses on identifying the underlying pattern (order) in apparently random data and attempts to predict outcomes in a given time frame.

 

The genesis of the Chaos theory is the butterfly effect (referred in the definition above).

 

Butterfly Effect: This theory describes the catalytic effect of small actions leading to a bigger consequence. It’s called the ‘Butterfly effect’ because the theory refers to the idea that a flap of a butterfly’s wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. The small action in the above is the butterfly flapping its wings and the bigger consequence is its effect on the tornado.

 

Formally butterfly effect can be defined as “Small variations of the initial condition of a dynamical system that produce large variations in the long term behavior of the system.”      

 

To illustrate the definition above, let’s take a simple example.

 

We know that 100*10 = 1000. Now let’s introduce a small variation of 1 in the original equation, thus 101*10 = 1010. The introduction of 1 lead to a variation of 1%. Lets extrapolate further 100^3 vs. 101^3. The % gap in data is 3% thus the difference starts to widen. Finally lets take 100^10 vs. 101^10. The difference is a staggering 10.46%

 

Thus an initial variation of 1% in the data has resulted in a variation of over 10.46% in a given outcome. This is the essence of Butterfly Effect.

 

In the next article I will try to explain the chaos theory, its implications and its effects on the Stock Market. Though I am not the first one to identify the correlation, I did identify it independently, so the topic is a lot closer to my heart than you think.