MLA 31500

Natural Sciences Elective

 

Order and Chaos in the Natural World

 

Spring Quarter 2014

 

CLASS NOTES

TENTH CLASS

June 10, 2014

 

I.      LORENZ, CHAPTER 4: ENCOUNTERS WITH CHAOS

 

1.     The first few sections of this chapter address subjects that we have encountered previously in Stewart.  Is there anything new or distinctive in Lorenz’s account, or are the first few sections redundant for us?

 

2.     Lorenz makes a distinction between “chaos,” which he also calls “full chaos” and “limited chaos.”  What is that distinction?  (The glossary in the book is helpful on such points.)

 

3.     Lorenz takes up the question as to whether or not Poincaré considered the phenomenon of full chaos in the modern sense in which Lorenz describes the concept.  What conclusion does Lorenz draw?

 

4.     In accounts of the history of the subject, we find Smale introducing the term “differentiable dynamical systems,” Ruelle and Takens the term “strange attractor,” Li and Yorke the term “chaos,” and Lorenz the “butterfly effect.”  Lorenz remarks that, for some years, he resisted the term “chaos” in favor of “irregularity.”  And he describes his work as a search for “non-periodic” behavior in models of weather and turbulent convection.  What does this history tell us about the scientific tastes and perspectives of pioneers in the field and about the role of nomenclature in promoting the development of a field?

 

5.     In his computer investigation of a model of terrestrial weather, what was Lorenz looking for?  What did he find?  Was what he found inconsistent with what he was looking for?

 

6.     Lorenz makes a link between non-periodic or aperiodic behavior and unpredictable behavior.  How do we explain that link?  (Hint: Why can’t periodic behavior be chaotic?)

 

7.     What are the attributes of the Lorenz attractor that make it a strange attractor?

 

 


II.    LORENZ, CHAPTER 5:  WHAT ELSE IS CHAOS?

 

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

 

2.     “Complex behavior (or structure) can result from simple recipes.”  How does the Mandelbrot set illustrate this proposition?   How and why might this be an important principle in nature?

 

 

 

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/