In many a high school math class, a student raises his hand and asks, “Why do we need to know this?”
Sometimes the teacher responds, “Because math teaches you how to think.”
Leaving the strengths and weaknesses of that answer aside, let’s talk about some books that can teach you something about how to think.
You won’t see many topics from your high school math classes in these books. but all of them deal with quantitative concepts. What’s more, all have helped me understand the world more clearly.
In no particular order:
1. The Signal and the Noise
The Signal and the Noise is a book about prediction. Nate Silver discusses how real-world data always contains a mix of “signal,” meaningful patterns that hold useful information, and “noise,” which are things that look like useful patterns but are really just random.
To make accurate predictions, it’s important to get good at distinguishing the two. If, say, a stock’s value ticks up, is it about to skyrocket, or just fluctuating a bit? If the former, the uptick might be considered part of the signal. If the latter, then the increase was just noise.
The book is well-written, though a little dense. It has chapter-long examples of good and bad prediction techniques: there’s a poker chapter, a baseball chapter, an earthquake chapter, and so on. Reading this also taught me a lot about how to understand and interpret statistics – which is a great thing to develop an intuition for, whether or not you care about prediction.
2. The Drunkard’s Walk
The Drunkard’s Walk is a book on randomness by one of my favorite authors.
I, like most people, sometimes see meaning in things that are really just random: if my favorite athlete is on a winning streak, or I draw an all-black poker hand, it seems like that event should have a specific cause. Making that kind of mistake a pretty basic human tendency. But, to make these mistakes less, it helps to know what randomness looks like.
This book explores randomness and how it shows up in daily life. Mlodinow explains the math, works through examples, and points out the situations where common sense tends to fail. The Drunkard’s Walk totally changed how I think about patterns and coincidences. And like The Signal and the Noise, it helped me a lot with understanding probability and statistics.
Even though it can be technical, this is a fun book. Mlodinow’s explanations of randomness are peppered with history and with character sketches of important figures. And it’s hilarious.
3. Thinking, Fast and Slow
There’s practically a whole genre of books that draw on the work of Thinking, Fast and Slow. The book details the psychology research that won the author a Nobel Prize in economics. Much of the book is dedicated to intuitive snap judgements that people make all the time – things like interpreting a mayor’s expression, choosing to donate to a wildlife reservation, or estimating how long a project will take.
Those judgements are all examples of what Kahneman refers to as “System 1,” or “thinking fast.” Sometimes those quick decisions work, but often they don’t. They can fail in systematic, predictable ways. The book teaches you how to understand these errors, and how to get tripped up by them less often. I’ve found it incredibly valuable for my day-to-day decision making.
