How to Figure Out Chaos Theory

Physics is a fascinating subject, one worthy of creative thought and contemplation. Newtonian physics is very elegant and neat with its immutable rules and all, but unfortunately, the world does not work as neatly and seamlessly.

In the beginning, there was chaos.

Then chaos became streamlined into elements. Elements were then described as particles and waves. Then came the proposal that these waves are actually strings, and now comes the suggestion that these strings are quite chaotic. So cutting edge physics is actually an elaboration of CHAOS THEORY.

Just what is chaos theory and how does it work? You probably first heard of chaos when it was introduced to popular media by Jeff Goldblum's character in the film, "Jurassic Park," to explain the harmful mutations apparent in the dinosaurs in that movie.

What is chaos? To paraphrase John Gribbin in his seminal book, "Get a Grip on Physics" (2002): To a scientist, chaos does not mean being messy and incomprehensible as most people understand the term. Instead, it is a kind of messy behavior that results from entirely predictable physical laws, like the ideal world as described by Newtonian physics. "It is unpredictable behavior obeying predictable laws" (p.178).

Here's a short demonstration of how chaos theory works.

Difficulty: Moderate

Instructions

Things You'll Need:

• a calculator or computer
• a little algebra
• your industrious fingers for punching in the data
• a sense of wonder at the beauties of quantum physics

1. Let's have some do-it-yourself chaos. Start with a simple mathematical expression like (2x^2-1). Work out a value for this expression, for any value you choose (x), by squaring x, multiplying the result by 2, and then subtracting 1.

2. Do the same thing with the number you are left with and repeat the whole process again and again. This is called iteration, which is a mathematical process that goes around and around in a loop. You start with a number or input, then run it though some mathematical manipulations, resulting in another number or output, which is then used as the input for the next round of the cycle.

3. Expecting to come up with similar answers since you started out with a couple of very similar numbers? Think again. After a few iterations, see what happens.

4. Try it with 0.51234, and make a note of each number you get at each step in the iteration. Now try it again, this time with 0.51235, again writing down the numbers at each iteration.
   
   After about 50 iterations, the two number sequences will be completely different. This is CHAOS at work! In chaos, a simple formula leads to very different places from very similar starting conditions!

Tips & Warnings

• For a more complete discourse on chaos theory and other physics-related phenomena, try reading "Get a Grip on Physics" by John Gribbin (Barnes & Noble Books, 2002). It's informative yet fun reading!

[RubyBayan]

on 1/3/2008 Very interesting!

[julz49221]

on 11/7/2007 Great Article!