Chaos and the Evolution of Consciousness, Syllabus
  • Week 00, beginning August 25
    Report 00 due Monday, September 12, 11:59 pm.

    List resources you have on hand:
    • RAD1 = first edition of Radiance
    • RAD2 = 2nd edn
    • DYN3P = monochrome hard copy of Dynamics, all four parts
    • DYN4.1 = eBook of Dynamics on CD in color, Part One
    • WIT = Mentalities article
    • NLOGO2 = NetLogo 2.1  
  • Week 01, beginning August 29
    Report 01 due Monday, September 12, 11:59 pm.

    Part A. Interpret the five mentalities in terms of your own experience with math.
    Let us code them with the letters RGADX:
    • R for aRithmetic,
    • G for Geometry,
    • A for Algebra,
    • G for Galilean dynamics, and
    • X for chaotic or complex dynamics.
    Part B. Discuss the relationship between Culture (in Thompson's title) and Consciousness (in Combs' title).
  • Week 02, beginning September 05
    Report 02 due Monday, September 12, 11:59 pm.

    Read the first chapter of the Dynamics text, and the front matter (Forewords and Introduction) of Radiance. Identify as many dynamical concepts as you can (as described in Dynamics, Ch. 1) in the front matter of Radiance.

  • Week 03, beginning September 12
    Report 03 due Monday, September 19, 11:59 pm.

    Part A. Iterations, or discrete dynamical systems, are covered in my book, Chaos in Discrete Dynamical Systems. It is found online in PDF form at: http://www.visual-chaos.org/jpx/book/
    I call it JPX for short (for Just Plane Xaos).
    This week, please read sections 1.1 to 1.5 in Chapter 1 of JPX, and all of Chapter 2. These chapters are separate PDF files on the JPX website.  

    This material is supported by a exploratory laboratory, a Flash applet found at: http://www.visual-chaos.org/lab/Flash/
    along with instructions. The instructions and the applet will appear in your browser. Please do the suggested experiments this week.
    Your lab report of these experiments will comprise Part A of your Report 03.

    Part B. Consider Combs' list of DCs. This is found in the first part of Appendix I. In RAD1, pp. 270-280. In Rad2, pp. 289-292. Extract from this list all terms either in italics or preceded by an *.

  • Week 04, beginning September 19
    Report 04 due Monday, October 10, 11:59 pm.

    Part A. The second lab may be found at: http://www.visual-chaos.org/lab/NetLogo2/.
    Record your experiments and observations, relate them to page numbers or illustration numbers in DYN, Part One, Chs. 1 and 2.

    Part B. Read Chapter 1 of RAD, excavating the DCs and unpacking them.

  • Week 05, beginning September 26
    This week conflicts with Esalen for some of us.
    Report 05 due Monday, October 10, 11:59 pm.

    Read Chapter 2 of RAD, excavating the DCs and unpacking them.
    No lab suggestion for this week.

  • Week 06, beginning October 03
    Report 06 due Monday, October 10, 11:59 pm.

    Part A: Draw the response diagram (that is, attractors and repellors) for the logistic family, with R from 2.7 to 3.3. Use the Flash applet.

    Part B: Refine your list of DCs from the Appendix of RAD. Add page numbers for Chapter 1 only. Consulting the index of RAD is fine, but you should scan each page of Chapter 1 for instances of DCs on your list.
    Each DC on your list should:
    • be explicitly contained in Comb's Appendix I
    • appear explicitly in Chapter 1 of RAD
    • be followed by all page numbers for pages on which that DC is found
    • include line numbers where the DC is found
      example: static, p. 7, para 3, line 4
    Please indicate if your pages numbers are from RAD1 or RAD2,.
    NOTE: Due date for Report 06B is extended to Oct 17.

  • Week 07, beginning October 10
    Report 07 due Monday, October 17, 11:59 pm.

    Part A: Draw the attractor-basin portrait for several values of a and b in the cusp family. Use the NetLogo 2D flow applet #2 in the chaos lab.

    Part B: Refine your list of DCs from the Appendix of RAD. Add page numbers for Chapter 2 only. Consulting the index of RAD is fine, but you should scan each page of Chapter 2 for instances of DCs on your list. My list has 115 instances involving 44 DCs. Please follow the instructions for Week 06B.

  • Week 08, beginning October 17 (halfway point)
    Reports 08 due Monday, October 24, 11:59 pm.
    Suggested readings:
    • DYN Part 2, 3rd and 4th chapters (ca 60 pp)
    • RAD Ch 3 (ca 30 pp)

    Part A. Explore the Dorband map family, using the NetLogo applet "Lab #3" found here:
    www.visual-chaos.org/lab/NetLogo/
    Your Report 08A should be your lab notes, following the suggestions posted with Lab #3. Try to find all attractors, for several values of the control parameter.
    This is the last lab.

    Part B. List all DCs (from RAD Appendix I) occurring in RAD Ch 3, in alphabetical order, with page numbers. (Please indicate if page numbers are from RAD1 or RAD2.)
    This list should be your Report 08B.
    This is the last DC list.

  • Quiz #1, due Monday, October 24, 11:59 pm, via email
    This quiz must be completed and received by by midnight on Monday. There is only one question.

    This question concerns the work of Walter Freeman described in the section "Chaos in the Head" of RAD Ch 3 (RAD1, p. 50 and Fig. 4; RAD2, p. 38 and Fig. 3a).

    In 500 words or less, unpack "chaotic attractor" as it is used here. Please distinguish the state space of the dynamical model, the actual states of the empirical domain, and the conventional interpretation. These are discussed in DYN 1.1, and also in paragraph 16 of RAD, Ch 2.

  • Week 09, beginning October 24
    No Report 09 due Monday, October 31, 11:59 pm.
    Read the first three chapters of DYN, Part Four.
    This is the last reading from DYN.

  • For information regarding late quizes and the final project,
    please consult the: Course Home Page
  • Week 10, beginning October 31
    Report 10A (lab report for volunteers) due Monday, November 07, 11:59 pm.
    Download NetLogo 3-D Preview 1 from ccl.netlogo.edu/netlogo
    Go to http://www.visual-chaos.org/lab/NetLogo3D/
    Download the three models: ueda, lorenz, and rossler
    Explore these three classic chaotic attractors of 3D flows
    Practice using the 3D controls (rotate, zoom, etc)
  • Quiz #2, due Monday, November 07, 11:59 pm, via email
    This quiz is intended only for those who did not submit Quiz #1.
    Submit your quiz by email to abraham@vismath.org.
    It must be completed and received by midnight on Monday.
    There is only one question, on the work of Charles Tart described in RAD Ch 3.
    In 500 words or less, describe a model for conciousness similar to the brain model from Quiz #1, and unpack Tart's "discrete states" using the concept "catastrophic bifurcation" from DYN Part Four.
  • Week 11, beginning November 07, due Monday, November 14, 11:59 pm.
    Report 11A (lab for volunteers) Repeat 07A, use Experiment #3 to locate repellors
    Report 11B: please post your project proposal

    Revised by Ralph 08 November 2005