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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. In his paper, Kuhn argues that rival paradigms are ______, meaning that it is not possible to understand one paradigm through the conceptual framework and terminology of another rival paradigm.

2. Where was Robert May born?

3. When was Steven Smale born?

4. James Yorke realized that one of the largest problems with his work was that mathematicians and physicists were often worlds apart because they did not what?

5. In mathematics, what is a system which does not satisfy the superposition principle, or whose output is not directly proportional to its input?

Short Essay Questions

1. What were the biggest issues with weather forecasting during Lorenz's time as described in Chapter 1, "The Butterfly Effect"? How is the Butterfly Effect defined?

2. How is Edward Lorenz described in Chapter 1, "The Butterfly Effect"? Where was he working at the time?

3. How did Lorenz's work influence James Yorke in Chapter 3, "Life's Ups and Downs"?

4. What was the early life of Benoit Mandelbrot like, as described by the author in Chapter 4, "A Geometry of Nature"?

5. In Chapter 3, "Life's Ups and Downs," one of the biggest questions came to be how different parameters affected the ultimate destiny of a changing population. What was the answer to this?

6. How is James Yorke described in Chapter 3, "Life's Ups and Downs"? What term did he coin?

7. What did Benoit Mandelbrot and Hendrik Houthakker agree on about the chart in Chapter 4, "A Geometry of Nature"?

8. Describe the weather simulator discussed in Chapter 1, "The Butterfly Effect." What weather conditions did it create?

9. When and where was the National Meteorological Center founded in Chapter 1, "The Butterfly Effect"? What existed before it?

10. What two technologies contributed to the development of global forecasting in Chapter 1, "The Butterfly Effect"?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe Mitchell Feigenbaum and Michael Barnsley. How did the two mathematicians meet and what discoveries arose from their conversations?

Essay Topic 2

Describe and discuss the Cantor set and the Noah and Joseph Effects. What is Cantor Dust and how was it discovered?

Essay Topic 3

Discuss the history of chaos theory as it relates to the biological and ecological sciences. When and how did ecologists come to use chaos in their theories?

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