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I run across a lot of books that I add to my to-be-read list and then forget about until after their publication dates or I stumble upon the book in the library or bookstore. How Not to Be Wrong was initially one of those books, but it sounded so good that I found myself obsessively thinking about it and started a search for a pre-publication copy. Since I'm not a librarian, didn't win a copy via First Reads, and don't have friends at Penguin Press, it took some time and effort, but having procured a copy and read it, I can say that it was well worth my time and $6.00. How Not to Be Wrong is a catchy title, but for me, this book is really about the subtitle, The Power of Mathematical Thinking.
Ellenberg deftly explains why mathematics is important, gives the reader myriad examples applicable to our own lives, and also tells us what math can't do. He writes, “Mathematics is the extension of common sense by other means”, and proceeds to expound upon an incredible number of interesting subjects and how mathematics can help us better understand these topics, such as obesity, economics, reproducibility, the lottery, error-correcting codes, and the existence (or not) of God. He writes in a compelling, explanatory way that I think anyone with an interest in mathematics and/or simply understanding things more completely will be able to grasp. Ellenberg writes “Do the Math” for Slate, and it's evident in his column and this book that he knows how to explain mathematical ideas to non-mathematicians, and even more so, seems to enjoy doing so with great enthusiasm. I won't pretend that I understood everything discussed in this book, but it's such an excellent book that I also bought the hardcover (so I have an index which my pre-pub copy does not), and reread the book so I do have a much more thorough understanding. I've wished for a book like this for a long time, and I'd like to thank Jordan Ellenberg for writing it for me!
I've already been recommending this book to family and friends, so I thought I'd take a few moments to recommend it to strangers on the internet, too.
This book, as anyone who is familiar with Jordan Ellenberg's writing (or speaking!) would expect, is written in an entertaining, witty, and engaging style. Each chapter of the book is framed by one or two major, motivating questions, such as:
- What parts of military aircraft should get the most armor? - Is it ever a good idea to play the lottery? - How should votes be counted in a democracy?
The answers that mathematical thinking asks you to accept are often surprising and unintuitive, but Jordan guides the reader through the fog of potentially-complicated arguments with a conversational style rife with clear, succinct examples and amusing historical anecdotes. In the hands of other writers, the mathematics in this book may be dull, or technical and complicated, or all of these things; but with How Not To Be Wrong, Jordan has instead created a book that you will eagerly and (mostly) effortlessly consume.
To put it another way: Steven Pinker said that "assumption of equality between writer and reader makes the reader feel like a genius, [while] bad writing makes the reader feel like a dunce." Jordan Ellenberg makes the reader feel like a genius.
Finally, regarding another reviewer's comments about the author's "liberal bias", I'd like to point out that I had the exact opposite impression while reading this book. Whenever politics were considered, I thought Jordan was even-handed and stuck to the mathematics at hand without wading into any political commentary. While I have liberal political ideals, and I avoid talking about politics with the more conservative members of my family, I would not feel uncomfortable recommending or gifting this book to any of them. This simply is not a book about politics, and I'm surprised that anyone would would have their political feathers ruffled when reading it.
Despite the "mathematics" title, this is mostly about statistics and probability (my own speciality), interpreted broadly. Many existing such popular (general audience) books exist, written either by popular science writers or by academic specialists, each alternative having characteristic virtues and faults. This book, by a mathematician with a different speciality, mostly succeeds in embracing the virtues and avoiding the faults. My main reaction is that, by telling entertaining stories that will be new to most readers, and by following a rambling path that meanders outside the statistics-probability core, the author disguises the fact that the main topics here are the same topics found in standard textbooks and in existing popular accounts -- regression and correlation and causality, misuses of tests of statistical significance (data-snooping, file-draw, ignoring size of effect), wise and foolish usage of proportions, seeing patterns in noise, a little Bayes and utility theory. The downside of this style -- trying too hard not to be a textbook, leading to entertainment via deliberate disorganization -- is that I suspect it leaves the reader with no memorable take-away message. The style of Kahneman's Thinking, Fast and Slow -- short focused chapters with entertaining stories but also with clearly stated points and little problems for the reader to ponder -- is surely more effective.
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This item: How Not to Be Wrong: The Power of Mathematical Thinking
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