Day 19: Heart of Mathematics

• Announcements:
  • You've got a homework due on Monday.
  • More interesting images: results so far, using my web interface and your own images.
    Results from another class that I shared this with: some are just too creepy!

  • New assignment:

    Wed

    2/24

    The Fourth Dimension and Fractals

    Read 6.2; problems to come

• Today:
  • More Fourth Dimension:

    Name	Dimension	# of Vertices	# of Edges	# of Faces	# of 3D Faces
    Dot	0	1	0	0	0
    Segment	1	2	1	0	0
    Square	2	4	4	1	0
    Cube	3	8	12	6	1
    Hypercube	4

    Before we leave the 4th dimension, let's glance at #7, p. 321.

• Time now for Fractals!
  • Take a few minutes to examine the gallery of fractals in section 6.1
    What do you think of the gallery? Mathematics or Art?

  • What do you suppose mathematicians mean by dynamic models?

  • How many people do you suppose will be on the earth a hundred years from now?
    • Start Somewhere (collect data!)

      World Population clock

    • Apply a process and get a result
    • Apply the same process to that result to get a new result
    • Apply the same process to the new result to get a newew result
    • Repeat patiently and persistently, forever.

    Does this sound familiar? This is what was done in the Fibonacci spiral image process....

  • Why are simple rules that result in complex phenomena important? Here's an important example that affects our educational system these days....
    • Some people doubt the "theory of evolution", because they don't believe that simple rules can result in the complexity we see around us.
    • If scientists can demonstrate that complex phenomena can arise from simple phenomena, then that argument holds less water.

  • An introduction to the Game of Life:
    1. Is generally played on an infinite checkerboard, or on a world that wraps back around on itself.
    2. The rules are:
       • A living square will remain alive in the next generation if exactly two or three of the adjoining eight squares are alive in this generation; otherwise, it will die.
       • A dead square will come to life if exactly three of its adjoining eight squares are alive; otherwise, it will remain dead.

    3. Create your own creatures!
       • Can you think of one that will lead to extinction?
       • Can you think of one that will lead to a stable pattern?

Links:

• www.bitstorm.org/gameoflife/
• www.radicaleye.com/lifepage/
• Polls related to evolution (sorry about the ad)
• Public attitudes about evolution in the States (2005)
• Biological Science Department heads report "No controversy about evolution" in their departments.
• grid paper