Day 32: Heart of Mathematics

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Announcements:
- You have an assignment due Friday (Dynamics)
- 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...
Today: a tad more dynamics
- For homework, use Excel (if you don't have Microsoft Office on your computer, you can get Free Open Office -- nearly as good, if not as good).
- Some financial dynamical systems
  - What characteristics have we seen in dynamics?
    - Equilibrium
    - Steady Growth
    - Steady Decay
    - Oscillations
    - Chaos!
  - How might we characterize the "dynamics" of these systems?
Our new unit is called "Lying with Graphs"...
- and though I've called it that, I should actually have called it "Truthtelling and Lying with Graphs". The point is that graphs can be done well, and they can be done poorly. And there are even resources that one can buy, like the book How to Lie with Charts, that illustrate that people are out there, thinking about how to pull the wool over your eyes. So practice self-defense.
  You've actually seen some of this before, if you read section 7.6 -- What the average American has -- carefully. If not, please re-read 7.6 soon!
  According to our authors, "Our goal is to create an image that reveals the structure that the data contains." (p. 588).
- Homework:
  - Problem #30, p. 608; and then adapt the exercise by replacing the word "statistics" with the word "graphics". Due Wed., 11/19.
- There are several take-home messages that we want to become aware of:
  - Scales on graphs:
    - Where do they start?
    - Why do they start there?
    - How do they grow?
    - Why do they grow that way?
    - Does size matter?
    - Let's look at some examples:
      1. Consider our authors' example on page 589: two histograms of heights.
      2. Let's revisit our financial dynamical systems to see how scales were used.
      3. This site describes a personal experience with a graphic along the same lines as my financial graphics above -- only with a scaling twist.
      4. Here is a humorous view of scales that also illustrates something about those lyin' statistics.
      5. In the "Does size matter?" category, we have the following emotionally charged graphic (and several alternatives), representing abortion
      6. Here's another, with less emotional content, about the Shrinking value of a dollar
        What determines the brain/eye's perception: length, or area?
      7. Here's another one: The Incredible Shrinking Doctor
      8. And another, slightly different: Alcohol and Tobacco Use
      9. And finally, often it's not our objective to lie, but rather to clarify, that leads us to "change scales". For example, let's consider how to choose bin size to view a histogram:
        
        Cicada-killing wasps and their prey
  - Dimensions of content
    - that is, how many dimensions of information does a graph contains?
    - A bar or pie chart contains only one dimension of information; a histogram, or scatterplot of two variables x and y, contains two. Graphs can contain more.
    - It's easy to make a bar chart do double duty.
    - The classic example (containing at least four dimensions) is
      
      Napoleon's March to Moscow, by Charles Joseph Minard
      Edward Tufte, who is a great fan of this graph, talks about "simple design, intense content". This graphic illustrates it. This might be Tufte's version of "Our goal is to create an image that reveals the structure that the data contains."
      Charles Joseph Minard did a similar map for the
      March of Hannibal from Spain to Italy
  - The type of a graphic: we have choices, afterall!
    - Our authors propose pie charts: others argue against them
      Notice that pie charts use areas proportionally to the values represented (not heights or widths, as we saw in the doctor and dollar graphics above)
- Tufte fights not just for "simple design, intense content", but also against the flattening of information that has occurred with the advent of PowerPoint. Here is a classic example of PowerPoint abuse.

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