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History of Mathematics
Just When Math Got Organized, Chaos Popped Up!



Just When Math Got Organized, Chaos Popped Up!
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     edHelper's suggested reading level:   grades 9 to 12
     Flesch-Kincaid grade level:   8.94

Vocabulary
     challenging words:    cyclically, pulsator, forefront, fractional, meteorological, analysis, unexplainable, mathematical, calculus, mathematics, wobble, mathematician, sunscreen, fractal, fractals, asteroid
     content words:    Edward Lorenz, In South Korea


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Just When Math Got Organized, Chaos Popped Up!
By Colleen Messina
  

1     What do you think of when you hear the word chaos? Your bedroom, perhaps? Mathematicians use the word in a different way. Chaos theory describes many normal things that seem unorganized, but that have a pattern after all. If this doesn't make sense to you, don't worry; it took a long time for mathematicians to understand chaos. Methodical mathematicians spent hundreds of years creating numbers and inventing calculus. Just when everything seemed perfectly organized, chaos popped up.
 
2     Where is chaos in real life? There is chaos in the flow of a dripping water faucet, in weather patterns, and in the ups and downs of the stock market. An excellent example of chaos is a human heartbeat, which sometimes has a chaotic pattern (and not just on Valentine's Day) because the time between beats changes depending on what the person is doing. Under some conditions, the heart beats erratically. The analysis of a heartbeat can help doctors and researchers find ways to make an abnormal heartbeat steady again.
 
3     Chaos theory quietly emerged in a meteorologist's office in 1960. Ironically, at about the same time, computers started organizing the mathematical world. Edward Lorenz wanted to predict the weather, or maybe he just wanted an extra way to figure out whether to recommend an umbrella or sunscreen to his friends. In any case, he programmed his computer to execute 12 equations to track weather patterns. After he ran the equations several times, Lorenz decided to save some time and paper by starting in the middle of the sequence of calculations rather than at the beginning. He also printed the results out to three decimal places instead of six. He expected to get a similar graph as before.
 
4     When Lorenz came back to check his printout an hour later, he saw something unusual. The graph was vastly different from earlier graphs! Lorenz thought about this new graph for a long time. He realized that he couldn't accurately predict the weather, but he wondered why the graph was so different. He realized that even though the difference between using three or six decimal places to run his equations seemed tiny, it had a huge effect on his results. Scientists eventually called this unusual phenomenon the "butterfly effect."
 
5     When a butterfly flaps its wings, the change in the atmosphere is small, but over time, that little difference can affect the entire planet. For example, after a month, the little change in the atmosphere from the butterfly's wings might cause a tornado off the Indonesian coast! The butterfly effect means that small differences in starting conditions can mean big changes in results. The butterfly effect, which affects chaotic systems, led Edward Lorenz to discover other elements of chaos theory. (Bugs of different kinds, like computer bugs, do seem to flit in and out of mathematics.)

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