MLAP 31500

Natural Sciences Elective

 

Order and Chaos in the Natural World

 

Spring Quarter 2014

 

CLASS NOTES

FIRST CLASS

April 1, 2014

 

 

I. INTRODUCTION

 

A.      Housekeeping: Handout

 

1.       Course.

 

2.       Instructor.

 

3.       Texts.

 

4.       Organization.

 

(a)     Discussion.

 

(b)    Lecture demonstrations.

 

(c)     Papers.

 

(d)    No exams.

 

5.       Meeting times.

 

6.       Attendance.

 

7.       Liberal learning.

 

B.      Introductions

 

1.       Student Data forms.

 

2.       Introduce ourselves.

 


C.      Class Notes distributed in class and posted on the course web page <http://astro.uchicago.edu/~voort/pov.html> are essentially agendas for class discussions.  They will consist mainly of brief outlines of subject matter or questions about the subject matter.  The questions are intended to serve as guides in reading assigned material and as aids in preparing for class discussions.  Therefore, it is much more important to think about how one might arrive at the answers to the questions than it is to work out the answers explicitly.

 

D.      In our first two meetings, we shall discuss the introductory chapters of Chaos: Making a New Science by James Gleick, The Essence of Chaos, by Edward N. Lorenz, and Does God Play Dice? by Ian Stewart.  Our goal is to acquire a preliminary understanding of the phenomenon of chaotic behavior in dynamical systems, the nomenclature required for a systematic and precise discussion of the phenomenon, and the impact that investigations of the phenomenon during the second half of the twentieth century has had on the established fields of the natural and social sciences.  A review of the introductory chapters of the three books will be the subject of the first writing assignment.

 

II.      GLEICK, pp 1-8:  PROLOGUE

 

1.       On page 3, Gleick writes “Where chaos begins, classical science stops.”  What does he mean?

 

2.       According to Gleick, chaotic behavior arises in many different fields of the natural and social sciences.  Therefore, there must be something universal about chaotic behavior.  Why would that be the case?

 

III.    GLEICK, pp 11-31: THE BUTTERFLY EFFECT

 

1.       According to the description in the first paragraph of the chapter, Lorenz’s model of the weather in 1960 was very unrealistic.  Why might this have been the case?

 

2.       Why would the model have been useful, nevertheless, in early studies of dynamical weather forecasting?

 

3.       According to Gleick, Lorenz was looking for repetition of patterns in his model weather system.  Suppose that Lorenz had found cases in which a given state of his model system repeated itself exactly at some later time.  What would be the implication of such a result?

 

4.       What was it that Lorenz did that resulted in his famous discovery?  What result did he expect?  What result did he obtain?  Why would the result have been counterintuitive in the 1960s?

 

5.       On page 23, Gleick writes “Lorenz put the weather aside….  What was the point of that change in the direction of his research?  Was he giving up the study of meteorology?  Was he switching to mathematics?

 

6.       What was it about the Lorenz attractor that would have been surprising in the 1960s to a scientist with a traditional view of the behavior of dynamical systems?

 

IV. GLEICK, pp 33-45:  REVOLUTION

 

1.       The subtitle of Gleick’s book is Making a New Science.  The subtitle of Stewart’s book is The New Mathematics of Chaos.  Is chaos a science?  Is it a sub-discipline of mathematics?  Is there something new or revolutionary about the subject?  If so, then what is it? 

 

2.       On page 39, Gleick describes the pendulum as the “laboratory mouse of the new science.”  Why would the pendulum be a particular suitable system in which to investigate order and chaos in dynamical systems?  Under what conditions is the motion of a pendulum regular?  Under what conditions might the motion be chaotic?

 

V.   NOMENCLATURE:  For systematic discussions of the phenomena of order and chaos in dynamical systems we must develop a clear understanding of the precise meanings of a few technical terms.  Here are some examples in the first 45 pages of Gleick.

 

1.       Dynamical systems.

 

2.       The adjectives “linear” and “non-linear.”

 

3.       Fractal.

 

4.       Bifurcation.

 

5.       Random process.

 

6.       Butterfly effect.

 

7.       Deterministic dynamical system.

 

8.       Periodic and non-periodic motions.

 

9.       Sensitivity to initial conditions.

 

 

 

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/