Day 05: Heart of Mathematics

Last Time

Next Time

Announcements:
- I'll have your first homework assignment graded by Monday
- New assignment:
  Fri 1/22 Estimation Assignment: there are two parts (due Monday, 1/25):
  
  Read section 2.2: Fibonacci numbers
  Bring in some object that illustrates Fibonacci numbers
- Current Estimation Assignment (due Wednesday, 1/27): Estimate the following (remember our classroom list of the fundamental mathematical elements of an estimate):
  1. How much do you spend in groceries for a year?
  2. How much gasoline do you use in a year? (CNN website) What percentage of your budget is fuel?
  3. How many times will you breathe today?
  4. How tall is the Lucas Administration building?
  5. The southbound lanes of I-471 are backed up from the Big Mac bridge at the Ohio river, to Nunn drive. How many cars are stuck in traffic on that section?
  These should not be "one-liners": you should give reasons for things, justifications, draw pictures, use data, etc.
Last time: Estimation
- We introduced estimation (and the pigeonhole principle) via the example of section 2.1 (do two people have the same number of hairs on their bodies?)
  - Indirect attack: they didn't need to actually count the number of hairs on anyone's body.
  - They used bounds, and the pigeonhole principle
- We learned:
  - The importance of bounds: it's not enough to give an estimate: you need to give bounds as well. (which gives some idea of how bad your estimate can be): e.g.
    A CNN-Opinion Research Corp. poll of 1,346 adults conducted July 31- August 3, 2009 found that 50 percent favored Obama's Health care plan, but 45 percent opposed it. The results had a margin of error of plus or minus 3 percentage points. (source)
  - It's good to have useful referents for things (e.g. you need to know some things! You need to be a resource, not just a consumer of information. It's not enough to be able to google....).
    - Close your eyes
    - Show me a centemeter between two fingers
    - Prepare to laugh
    - Hold your measure, and look around you!
    - There are 2.54 cms/inch
  - You can approximate some things using mathematical objects (e.g. box areas for skin areas) for which you will, however, need to know some mathematical formulas
  - It's good to have several different plans of attack from which to choose.
  - It's okay to be wrong: "make a suitable number of mistakes!" If you're not making any mistakes, then you're not trying hard enough. Just do it!
Today:
- What are some other fundamental elements of a good estimate?
  1. Collection of (quality) Data
  2. Knowing units and unit conversions
  3. Formulas and Computation (putting it all together)
  4. Sometimes it suffices to be rough!
- At the end of the hour you were estimating the number of dice that would fit into the room. How did we do? Let's compare answers. If you have an estimate, come up and write it down.
- Something interesting: if you let a bunch of people (ants, etc.) independently do a task (that is, without consulting each other), then they may well find the optimal answer (see Swarm Savvy: How bees, ants and other animals avoid dumb collective decisions)
- By the way, what is "the pigeonhole principle"?
  - Have you ever played a game, perhaps at a birthday party as a young child, that relies on the pigeonhole principle?
  - When have you ever used it?
- Another problem to consider (exercise in estimation):
  1. Do you have a temporal twin (someone who was born on the same day as you, and will die on the same day)?
    - Is there anyone who obviously does?
    - Is there anyone who obviously doesn't?

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