MLA 31500

Natural Sciences Elective

 

Order and Chaos in the Natural World

 

Spring Quarter 2008

 

CLASS NOTES

FOURTH CLASS

April 12, 2008

 

 

I.   LORENZ, CHAPTER 1: GLIMPSES OF CHAOS

 

1.    What does Lorenz accomplish in the introductory chapters of his book?  Does what he accomplishes there differ from what Stewart and Ruelle accomplish in their early chapters?

 

2.    Consider again what we should understand as the meanings of the terms Òdeterministic systems,Ó Òrandom processes,Ó and Òchaos?Ó  Do Stewart, Lorenz, and Ruelle agree on the meanings of these terms?

 

3.    Stewart and Lorenz introduce the reader to chaotic behavior in the first chapters of their books.  They get to the point of introducing the subject by rather different routes.  What is the difference?

4.    The two authors illustrate their introductions to chaos by describing the behaviors of particular dynamical systems or models of dynamical systems.  What are those illustrative examples?

 

5.    In what respects are the systems that Stewart and Lorenz use in order to illustrate chaotic behavior similar?  In what respects are those systems different?  Why do the authors choose systems that are so similar or so different?  Which is the better system with which to illustrate chaotic behavior?  Why?

 

II. LORENZ, CHAPTER 2: A JOURNEY INTO CHAOS

 

1.       In this chapter, Lorenz introduces many of the principal concepts encountered in a general study of order and chaos.  He does so with the aid of a particular set of dynamical models.  It is illuminating that one such family of models can provide examples of so many elements of the subject.  As you read the chapter, you might find it instructive to compile a list of the definitions, concepts, principles, tools, phenomenologies, etc. that Lorenz illustrates with the aid of these models.

 

2.       Early in the chapter, Lorenz designs a computer model of a snowboard on a ski slope containing a regular array of moguls.  What are the relevant physical laws underlying the model?  What are the forces acting on the board?  What are the variables in the phase space in which we describe the state of the system?

 

3.       On page 38, Lorenz replaces the model of a ÒboardÓ with a model of a Òsled.Ó  What is the difference between these two dynamical systems?  Why does Lorenz turn to the model of the sled for his subsequent discussion?

 

4.       On page 62, Lorenz returns to the model of the snowboard, but he makes the system frictionless, and he replaces the ski slope with a horizontal snowfield with the array moguls.  Why does he make these changes?  What are the important consequences?

 

 

LINKS:

 

Return to Course Page: mla315spring2008.htm

 

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/