How to Understand Chaos Theory

Chaos theory is popular in movies and books because it has such a unique name for a scientific/mathematical theory. Typically, Science is all about precision and prediction, however chaos theory is all about describing the inability to predict certain system. Interestingly enough, contrary to it's name, chaotic systems do not operate randomly, they just appear to.
Read on if you wish to have a brief understanding of the Chaos theory... to impress a girl or something.

Difficulty: Moderately Easy

Instructions

Things You'll Need:

• A Functional Brain

1. The first step to understanding chaos theory is realizing that it describes system that appear to behave randomly, yet actually follow deterministic (predictable) laws. A great example of this is a dice. We use it in games because it appears to show us a set of numbers ranging from 1 to 6 at random. In reality however, the behavior of a dice can be completely predicted using the laws of science. There are two things stopping us from predicting where a dice will land however.
   
   Firstly, there are several variables and equations involved in predicting the role of a dice. One most know the exact moment of inertia of the body of the dice, all the vectors of the forces applied, air resistance, elasticity of the surface it hits, etc. It is just too complicated of a problem to solve accurately.
   
   Secondly, the dice is extremely sensitive to the initial conditions of how it is rolled. All of the forces involved must be known past a reasonable level of precision in order to predict the dice. It is like trying to balance a spoon upright on a piece of cardboard. The smallest air current will cause it to fall one way instead of the other.
   This is called the "butterfly effect."

2. The butter fly effect describes a hypothetical phenomena where a butterfly flapping it's wings in Brazil can eventually cause a Tornado in Texas. It was coined after Edward Lorenz attempted to model weather using a 12 equation system on a computer 40 years ago. He discovered that a very small change in input values, on the order of .001, could change the output of his weather simulation on the order of thousands. Thus, the butterfly effect was discovered. This effect is a common trend in chaotic systems. The smallest nudge in one direction or another will cause them to completely change their outcome. Just like our spoon. A piece of dust landing on it can cause it to fall one direction instead of the other.

3. This is the basic premises of chaotic systems. What do they look like in real life though? Believe it or not, most systems in nature would be considered chaotic. Even a human being could be considered a chaotic system. This is because they satisfy the two basic rules of the chaos theory. A human body operates on the laws of science, and therefore, should be completely predictable. It is not however, because a human is far too complex, and the smallest change in it's environment can cause a series of neurons to fire, which in turn, can cause it to behave completely differently than expected. This is why a human body can be explained with the laws of science, but never predicted.

4. There are of course systems in nature that are still chaotic, unpredictable, and easier for scientists to study. One of the primary methods of studying the chaos theory is using chemistry. I am currently researching chemical chaos for my thesis. The system I am studying is called the Belousov-Zhabonisnski reaction. It consists of a complex chemical concoction that oxidizes and reduces in acid back and forth numerous times at unpredictable time intervals. When it does this, it changes color back and forth, over and over. There are of course a set of equations we can use to predict the behavior of this system using a computer, but when the experiment is done in real life, it behaves differently every time. This is because it is extremely sensitive to temperature, the rate it is stirred, how many molecules of each of the chemicals i put in the mixture, etc. I use a set of electrodes to monitor the reaction using electrical voltages that can be recorded on a computer. Th strange thing is, even though the data appears random and different every time, when we graph the data a special way using something called phase space, it produces the same pattern every time!

5. 
    
   Electrode data of Platinum electrode over time collected from BZ reaction

   How can it be that data that is different every time follows the same pattern? This is because even though it seems random, it is in fact following very ordered rules. I have included two photographs. The first is the data, and the second is what is called a strange attractor. A strange attractor is what we use in chaos to describe how a system changes according to the previous value to the next instant in time, usually one second. It is clearly seen that the reaction is following a beautiful order even though it appears chaotic!

6. 
    
   Strange Attractor of Electrode Data

   This is just a short introduction to chaos theory of course, hopefully it has not bored you. If you do find it boring, I recommend you try reading it again until you understand everything I have said. I believe once you do this, you will find chaos theory extremely interesting! A great book to read would be: Chaos: The making of a New Science. By James Gleick.

[Upon-Request]

on 1/17/2009 Well written! (said the impressed girl!)