MLAP 31500

Natural Sciences Elective

Order and Chaos in the Natural World

Spring Quarter 2013

CLASS NOTES

SEVENTH CLASS

May 14, 2013

I. A GEOMETRY OF NATURE: Gleick, pp 83-118

THE TEXTURE OF REALITY: Stewart, Chapter 11

1. What is the subject of these chapters? What is the organizing principle?

2. What is Gleick trying to accomplish with his introductory account of fractals? Is there a connection with Gleick’s earlier account of Thomas Kuhn’s model of scientific revolutions? If so, what is it?

3. How does Gleick characterize what Kuhn might call “normal mathematics?” In what respects would Benoit Mandelbrot appear to be unrepresentative of someone doing “normal mathematics?”

4. What is a fractal? What are the defining properties of a fractal? How do we recognize a fractal? Is the word a noun or an adjective? (And, are these four different questions?)

5. What, if anything, does Stewart’s account of fractals add to what is already described by Gleick?

6. What are examples of systems that exhibit fractal behavior or fractal structure? What insights about such systems are gained when their fractal character is recognized?

7. Does a common sponge have a fractal structure? How would you decide?

8. Suppose that you decide that two objects are fractals. How would you decide whether or not the fractal structures of the objects are similar?

9. On page 108, Gleick suggests that the human circulatory system has a fractal structure. What would be the advantage or benefit of such a geometry?

10. Is there a connection between fractals and properties of the logistic map? If so, what is that connection?

LINKS:

Return to Course Page: mla315spring2013.html

Return to Peter Vandervoort's Home Page: pov.html

Go to the home page of the Department of Astronomy and Astrophysics

of the University of Chicago: http://astro.uchicago.edu/