Jordan Ellenberg’s bestseller How Not to Be Wrong: The Power of Mathematical Thinking is an insightful, challenging book which is designed to apply mathematical insights to the real world. As a non-mathlete, I found the book equal parts delightful and difficult. Below are a few illuminating parts which I found particularly engaging.
Abraham Wald was challenged with the problem of where to put armor on a World War II jet. They analyzed the bullet holes of planes in order to determine where best to place more armor. They couldn’t cover the plane in armor, after all, because the plane would be unable to fly fast with too much weight. The previous analysts argued for placing armor in places like the wings which had sustained the most damage. Wald opined that the bullets in the engine, however, resulted in more downed planes and therefore those holes would not be part of the data set. It caused me to think about our retention problems. Are we looking at the right data? Are we examining why people don’t enroll in our schools?
The Laffer curve is presented by examining perceptions of taxes. No one argues for a tax rate or for a full 100% tax rate. More than 0% is good but eventually the popularity drops. At what point? Too much of a good thing ends up being unattractive. Do we examine our programs (athletics? marketing?) in terms of the Laffer curve?
Regression to the mean appears in two separate sections. I thought of it while watching the Final Four. A player gets hot and scores 20 points in the first half. “He’s on track to score 40,” says the announcer. Inevitably, the player goes cold in the second half and ends up with around 26 points. That’s to be expected, according to Ellenberg. Do we examine outstanding student performance (or behavior) the same way? Ellenberg argues further that humans have a tendency to regress to the mean of performance—whether that’s teaching performance or student achievement. Our challenge is to keep raising expectations to the mean is on an upward trajectory.
Ellenberg presents interesting insight into the effectiveness of algorithms. The advent of Big Data and the Cloud have given tremendous power to mathematical insights in applications such as Facebook, Google, and NetFlix. He presents the theoretical underpinnings to these new developments.
Ellenberg presents insight into consensus and majority rules. The Equality Heuristic demands that all opinions and we’ve see how that plays out in the media when both sides demand equal treatment. In the face to different evidence, people tend to remain fixed in their opinions.
Finally, Ellenberg’s insights into correlation deserve our attention. In his chapter “Does cancer make you smoke cigarettes?” he presents an irreverent look at how doctors used to view the effects of smoking. The thought was that signs of lung cancer caused a patient to smoke in order to alleviate the symptoms. We aptly find that argument ridiculous but in how many other ways are we falsely attributing correlation? I often find Catholic school stakeholders arguing correlation for low enrollments—e.g. low devotion to Catholicism, high tuition, etc. instead of facing their brutal realities.
Worth a read, Ellenberg’s treatise belongs in advanced math classes and on the reading list of any curious school leader.