Jordan Ellenberg’s ambitiously-titled book How Not to be Wrong does a good job of teaching many broadly applicable ways of avoiding mistakes. It contains surprisingly little of what we’d recognize as math considering its subtitle The Power of Mathematical Thinking. Ellenberg explains that mathematical thinking often looks a lot like common sense. While this book isn’t specifically about personal finance or investing, it does teach lessons that are useful for our financial lives.
The book begins with one of the best answers I’ve seen to the question posed by many frustrated math students: “When am I going to use this?” I can’t do justice to the answer in just a few words, but I’ll give it a try. Just as you never see a professional soccer player “zigzagging between traffic cones” in the middle of a game, you may not spend much time doing algebra or calculus in your daily life. But the soccer player’s drills make him a better player, and math training helps you “understand the world in a deeper, sounder, and more meaningful way.”
Ellenberg follows up this explanation with an interesting story from World War II about examining returning planes for bullet holes to see where they need more armour. The correct answer comes from the observation that the bullet holes in the planes that don’t come back tell the true story of where to put the armour.
The rest of the book covers many ways that people get things wrong, such as false linearity. If current trends continue, we can project which year everyone will be obese. Another linearity error is believing that if some medicine is good for you, then more medicine must be better.
One amusing mistake of inference concerns scientific research. If you run enough experiments, you’ll eventually get a positive result by coincidence. A scientific paper demonstrating this problem “proved” to an accepted statistical standard that dead fish can read people’s minds.
I was pleased to see a section discussing whether “hot shooters” exist in basketball. Fans believe it happens but many researchers have crunched the numbers and found no evidence of hot shooting. One effect I’ve noticed as a fan has been confirmed by researchers studying the statistics: “players who had just made a shot were more likely to take a more difficult shot on their next attempt.”
Much of the more mathematical parts of the book are in the footnotes. Some of the humour is in the footnotes as well. “The natural logarithm [base e=2.718... as opposed to base 10] is the one you always use if you’re a mathematician or if you have e fingers.”
An interesting result concerned mean reversion and Scared Straight programs that “took juvenile offenders on tours of state prisons, where inmates warned them about the horrors that awaited them on the inside.” Of course, authorities selected the juveniles who had the worst records for this program and it seemed to work. However, any time you pick the worst samples there is some reversion to the mean where the worst ones become less bad over time. Once this was taken into account, “researchers found that the program actually increased antisocial behavior” among the juveniles.
In the end, Ellenberg is trying to add more tools for us to apply with our common sense, such as “more of a good thing is not always better,” “improbable things happen a lot,” and that you should make decisions “not just on the most likely future, but on the cloud of all possible futures.” These are valuable lessons in investing and in the rest of our lives.