How Not to Be Wrong, by Jordan Ellenberg: A Book Review

Yesterday, I wrote about mistakes I’ve made in the past and how I am using that experience to avoid being as wrong—at least in the same way—in the future. So, you can certainly see why a book with “How Not to Be Wrong” as the title appeals to me. The subtitle, “The Power of Mathematical Thinking,” is also attractive, as math is one of the great organizing principles of my profession. On the face of it, this sounds like exactly what anyone in my position should be looking for.

Identifying potential traps

In fact, How Not to Be Wrong, by Jordan Ellenberg, lives up to the title. Its five parts walk readers through all of the major math-based thought errors that trip us up so often: 

1. “Linearity” takes on the folly of trying to turn a straight line into a prediction.
2. “Inference” looks at the details behind lies, damn lies, and (of course) statistics.
3. “Expectation” discusses how to really think about expected values.
4. “Regression” focuses on causality, correlation, and regression to the mean.
5. “Existence” reviews the criticality of assumptions—and why they are not always what they seem.

Each of these topics is a core source of error in economics and investing. Every single one—even if you know what you are doing—is a potential trap if you are thinking too quickly.

Entertaining, but useful, stories

In each part of the book, Ellenberg provides illuminating and memorable illustrations and stories that help you internalize and remember the points to watch for. The stories I remember immediately include one about the dead salmon that could (with statistical significance) recognize human emotions in pictures, a projection of the date when everyone in the U.S. will be obese (2048, if you were wondering), and an in-depth discussion of the problem of oracles who divine the future by examining the entrails of deal animals (chapter 9, “The International Journal of Haruspicy”). While completely out of the box, these examples provide useful and very entertaining ways to look at material that otherwise could be dry and complex.

For economists and investors, there are also many directly applicable examples. The Laffer curve appears early, as does the Baltimore stockbroker story—one every investor should know. The stories here are many and varied. But, for analysts and investors, they are also an incredibly effective way to present the information.

Don't let the math scare you

The thing that might keep readers away is the subtitle, as math creates a sense of foreboding for many. But make no mistake: although this is a math book, it is math in the sense of “the extension of common sense by other means,” a phrase Ellenberg uses early and often. By using the tools of math to aid understanding and help define the limits—and probable errors—of the solution, readers can benefit not only in their own work but also in reading and reviewing anything else.

Verdict: Highly recommend

This is reputed to be one of Bill Gates’s 10 favorite books, and I can certainly see why. It combines a sound analytical foundation; practical and relevant, if whimsical, examples; and clear explanations as to why each point matters and how it can be used—providing the best introduction about how not to be fooled by math that I have seen. Read this book and you really will learn how not to be wrong.