- Homework:
Please read Sections 6.1 and 6.3: fractals for Wednesday.
To hand in next Monday (4/20): pp. 421-, #2, 3, 9, 13, 14, 17, 18, 21 - First of all, I want to alert you to the upcoming "show-n-tell"
(4/29). Some of you have already suggested a topic, but I know that
there are others of you who haven't yet even begun to think about
it. Show-n-Tell topics should be something you've seen, something
you've thought about, something you've encountered that means more
because of this class. If you need ideas, stop in and see me some
time...
Your show-n-tell item will require two aspects:
- A very short "presentation" (how will you explain your "item" to your peers -- imagine that you have three minutes)
- A two-page, typed, well-written, self-edited, peer-edited, perfect paper, explaining your show-n-tell item.
I've decided to have these all the very last day of class, which means that it will be a little crammed. We'll just do a kind of "round-robin" of show-n-telling.
- Exams returned.
- High: 91.5
- Mean: 63.56
- Median: 60.5
- Standard Deviation: 16.3
- As before, if you'll come see me, to discuss the exam and the points you've missed, I'll give you back 30% of the remaining points you missed. You should check out the key before coming to see me.
- Visit the Exam 2 key
first, however, before you come in. That way we only need to
talk about what didn't go well.
If you all do that, here's the (revised) distribution of the test,
- Just a reminder of the link to some problems relative to this stuff that I gave you prior to the exam....
- Today we finish our unit on dynamics.
- I begin with a few very current cultural references:
- Corruption Undercuts Hopes for Afghan Police (4/9/2009)
- police officials who steal truckloads of gasoline;
- judges and prosecutors who make decisions based on bribes;
- high-ranking government officials who reap payoffs from hashish and chromite smuggling;
- and midlevel security and political jobs that are sold, sometimes for more than $50,000, money the buyers then recoup through still more bribes and theft.
- This reminds me of a couple of my favorite dynamic rules
from my childhood:
- It's much harder to make something than it is to destroy it.
- The 90/10 rule: you get 90% of the work done in 10% of the time.
- A computer rediscovers Newton's laws -- in a day!
- Do simple rules result in complex phenomena? Stephan Wolfram says "Yes!"
- Gradual
treatment of peanut allergies shows promise A slow and incremental introduction of peanuts into the diet helps some children overcome an allergy to the food, but it takes time and close supervision. (Science News, 4/11/2009, p. 11)
(How does this contrast with "familiarity breeds contempt"?).
- Public tantrums defeat monkey moms too Rhesus macaque moms are more likely to give in to screaming babies when bystanders are watching and reacting (Science News, 4/11/2009, p. 8)
- Corruption Undercuts Hopes for Afghan Police (4/9/2009)
- I begin with a few very current cultural references:
- In section 6.2: The Dynamics of Change, our authors give examples of the use of dynamics:
- Personal Finance (more about this later, in our personal finance
unit).
- Biological populations. Example: How many people do you suppose
will be on the earth in 2109 (in a hundred years)?
- Start Somewhere (collect data!)
- 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 newer result.
- Repeat patiently and persistently, forever.
- Start Somewhere (collect data!)
- The Game of Life:
- Is a poster child to prove something important: simple rules, repeated over and over, can give very complicated dynamics.
- Is generally played on an infinite checkerboard, or on a world that wraps back around on itself.
- 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.
- the website's version
- Today let's check I.15, p. 423.
- Then let's have a look at the Wikipedia site for Life to learn about gliders, breeders, and some oscillators.
- Create your own creatures!
- Can you think of one that will lead to extinction?
- Can you think of a new one that will lead to a stable pattern?
- For the final, make sure that you know how to go from generation to generation!
- Personal Finance (more about this later, in our personal finance
unit).
Links:
