Math in the Real World

My kids' high school had a "Career Day" yesterday and the school invited business people to co-teach classes, in order bring "real world" examples of what the kids are learning into the classroom. I was assigned to co-teach Seniors taking pre-calculus. The kids had been continually wondering how they would ever use calculus in the real world.

I gave a talk on the use of math models and how nearly every profession uses math models to create understanding out of all the data they assimilate. I made the point that math can help, not just scientists and engineers, but nearly everyone make sense of data that affects all aspects of our lives. We read of studies predicting that certain foods will help us live longer or kill us sooner, problems with new medicines, economic data that influences our savings and jobs, and problems like global warming that even influence who we should vote for. I emphasized that they should develop a healthy skepticism about much of what they read since it is often based on poor math (primarily poor statistics).

One of the points I emphasized over and over was that "correlation is not causation". This point is largely lost on the public, as all correlations are deemed by the media to be the result of some cause (often the cause is based on the biases of the writer or researcher). I told this story from a Simpson's episode "Much ado about nothing". After a bear attack , the town creates a "Bear Patrol" to keep bears away:

Homer: Not a bear in sight. The "Bear Patrol" is working like a charm!
Lisa: That's specious reasoning, Dad.
Homer: [uncomprehendingly] Thanks, honey.
Lisa: By your logic, I could claim that this rock keeps tigers away.
Homer: Hmm. How does it work?
Lisa: It doesn't work. (pause) It's just a stupid rock!
Homer: Uh-huh.
Lisa: But I don't see any tigers around, do you?
Homer: (pause) Lisa, I want to buy your rock.

The world is full of Homers' who don't have the a clue about the difference between correlations and causation. And a college education doesn't prevent people from falling into this trap. Often it even does the opposite (I work with PhD's that do this all the time in areas outside their field of study).

We talked about how most of the models used calculus to some degree (or should use it). We also discussed the difficulty of developing a model for global warming. I presented this partial list of variables that might impact global warming:

Solar flux
Gravity, Pressure, Density, Humidity
Urban Heat Island Effect
Earth’s rotation and “wobble”
Currents in the ocean
Surface temperatures/ atmospheric temperatures/ water temperatures
Green house gases (CO2, H2O)
CO2 Dissolved in the ocean
Size of polar ice caps
Infrared radiation
Earths magnetic fields
Evaporation
Precipitation
Cloud formation
Reflection from clouds
Volcanic eruptions
Aerosol formation (soot, dust, sulphur)
Trace compounds
Ozone levels
Cosmic rays
Many, many others

I only had 27 minutes to get my points across, but it was obvious that the kids had not been exposed to much out of the conventional wisdom. Our education seems mainly geared to pumping information into kids, but really doesn't help them learn to think independently.