ChaosDate: 01/27/2001 at 14:27:39 From: Justin Subject: Chaos Edward Lorenz came up with the branch called "Chaos", and The Butterfly effect. How can a butterfly flapping its wings in South America cause a tornado in Texas? Date: 01/27/2001 at 16:42:38 From: Doctor Douglas Subject: Re: Chaos Hi Justin, and thanks for sending your question to Ask Dr. Math. Here'a different example, like the butterfly scenario, that illustrates the "sensitive dependence on initial conditions" that is the trademark of chaos. I'll assume that you're familiar with (American) football. If you're not, write back and I'll try to come up with a different example. Suppose a football is punted and is oriented so that the points are up and down. It is falling, and headed right for the 50 yd line. The football is not spinning. The punt returner decides that it is too dangerous to field, and lets the ball bounce. Which way will it bounce? The answer is that it depends. If the downwards point of the football is just a little bit to one side, it will tend to bounce away from that side, say, towards the goal of the home team. But if the point is just a little bit to the other side, it will bounce toward the other goal. And if the point is just a little to the side, it will bounce towards one of the two benches. In this way a tiny difference in the position, or the movement of the air molecules around the ball that influence its orientation on the way down could have a big difference on where the ball ends up. The direction of a small 1 mph breeze might make a difference of 30 yards in where the football ends up. It is in this spirit that the butterfly's flapping its wings might affect things many days later, many miles away, and either create a tornado or suppress one from forming. I hope this helps clarify the concept of "sensitive dependence on initial conditions." If you have more questions about the fascinating topic of mathematical chaos, please write back. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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