Chaos Theory

Here is a brief account of one of the most widely acclaimed theories of 20th century, the ‘Chaos Theory’; its origin, implications and myths.




Have you ever wondered, why it is difficult or rather impossible to predict,
• Weather few days/weeks/months down the line,
• The stock market future and trends,
• Human behavior or actions,
• Evolutionary patterns of various species,
• Future of our universe

Well, you may tend to think, given the advancement that has taken place in science and technology, especially physics, psychology and computers; it shouldn’t be really an impossible task to model the above-mentioned systems. However, the truth is, the scientists have come to a conclusion that we as humans will never be able to comprehend or model such systems.
The common underlying factors in the above systems are that they all are complex, dynamic systems, which are sensitive to their initial conditions.

Chaos theory attempts to explain the fact that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions.

History:

The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. It didn't predict the weather itself. However this computer program did theoretically predict what the weather might be.

One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning. He entered the number off his printout and left to let it run. When he came back an hour later, the sequence had evolved differently. Instead of the same pattern as before, it diverged from the pattern, ending up wildly different from the original. Eventually he figured out what happened. The computer stored the numbers to six decimal places in its memory. To save paper, he only had it print out three decimal places. In the original sequence, the number was .506127, and he had only typed the first three digits, .506.

By all conventional ideas of the time, it should have worked. He should have gotten a sequence very close to the original sequence. A scientist considers himself lucky if he can get measurements with accuracy to three decimal places. Surely the fourth and fifth, impossible to measure using reasonable methods, can't have a huge effect on the outcome of the experiment. Lorenz proved this idea wrong. This effect came to be known as the butterfly effect. The amount of difference in the starting points of the two curves is so small that it is comparable to a butterfly flapping its wings.

"Butterfly Effect," states that the flapping of a butterfly's wings in China could cause tiny atmospheric changes which over a period of time could effect weather patterns in New York


Limitations:

This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment. Such things are impossible to avoid in even the most isolated lab.

Complex systems usually have many variables involved that define the behavior of the system. Also, these variables are interconnected in ‘n’ number of ways. The human limitations come in firstly understanding and listing all the variables and their dependencies, and secondly in measuring the values of the variables accurately.

There are many variables associated with the weather: temperature, air pressure, wind speed, wind direction, humidity and many more. The equations, which control the weather, involve all of these variables.

Another system in which sensitive dependence on initial conditions is evident is the flip of a coin. There are two variables in a flipping coin: how soon it hits the ground, and how fast it is flipping. Theoretically, it should be possible to control these variables entirely and control how the coin will end up. In practice, it is impossible to control exactly how fast the coin flips and how high it flips. It is possible to put the variables into a certain range, but it is impossible to control it enough to know the final results of the coin toss.

Theories abound as to real-life examples of this phenomenon:

1. The weather: small changes in weather effect larger patterns.
2. The stock market: slight fluctuations in one market can affect many others.
3. Biology: A small change in a virus in monkeys in Africa creates a "thunderstorm" of an effect on the human population around the world with the appearance of the AIDS virus.
4. Evolution: small changes in the chemistry of the early Earth gives rise to life.
5. Psychology: Thought patterns and consciousness altered by small changes in brain chemistry or small changes in physical environmental stimuli.

Although chaos is often thought to refer to randomness and lack of order, it is more accurate to think of it as an apparent randomness that results from complex systems and interactions among systems. According to James Gleick, author of Chaos: Making a New Science, chaos theory is "a revolution not of technology, like the laser revolution or the computer revolution, but a revolution of ideas.”

Myths:

Over the years people have turned the chaos theory in some kind of philosophy and started applying it to anything and everything, including human life.

For e.g. some of the conclusions are:
• A butterfly flapping its wings in china results in producing a tornado in NewYork over a period of time.
• A person leaving from home 5 minutes late than usual, on reaching the bus stop may get hit by the bus and die.

It is important to note that the chaos theory does not predict anything but simply attempts to explain the fact that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions. In these systems, the cause and effects of many variables may well nullify each other such that they have no effect on the net result.

So if a person leaves from home 5 minutes late, he might on the way gain those 5 min owing to lesser traffic. Or a bus might in fact hit him if he actually leaves on time.

So the point is such kind of assumptions based on chaos theory is futile and improper.