How Not to Be Wrong: The Power of Mathematical Thinking in Science and Inquiry

Jul 10, 2015 David Rubenstein rated it it was amazing

Shelves: mathematics, nonfiction

This is a wonderful book about mathematics and its application to everyday life. Jordan Ellenberg shows that the certainty that people associate with math is often misplaced; some areas of math are devoted to uncertainty, and that's where things get very interesting.

Ellenberg starts the book with a beautiful example of application of mathematics, logic, and thinking out of the box. During World War II, a group of mathematicians working for the Statistical Research Group were given a problem by s This is a wonderful book about mathematics and its application to everyday life. Jordan Ellenberg shows that the certainty that people associate with math is often misplaced; some areas of math are devoted to uncertainty, and that's where things get very interesting.

Ellenberg starts the book with a beautiful example of application of mathematics, logic, and thinking out of the box. During World War II, a group of mathematicians working for the Statistical Research Group were given a problem by some Air Force officers. Fighter planes returning from missions were analyzed for bullet holes. The number of bullet holes per square foot were counted. For example, there were 1.11 bullet holes per square foot in the vicinity of the engine, 1.73 in the fuselage, 1.55 in the fuel system, and 1.8 in the rest of the plane. The officers wanted to add some armor to the planes; the question was where? The planes could only support so much weight, and where would additional armor be most advantageous? The officers thought that since the fuselage had the greatest density of bullets, that would be the logical location for more armor. A mathematician named Abraham Wald said exactly the opposite; more armor is needed where the bullet holes aren't, namely, around the engines. Planes with lots of bullet holes in the engine did not return at all!

The book discusses the issue of statistical significance. Scientific experiment often use a 95% confidence threshold as an indicator of statistical significance. This means that if a truly random outcome were expected, a positive correlation would be seen only 5% of the time. Ellenberg includes an xkcd cartoon that shows how easy it would be to perform a set of experiments that could come up with statistically significant results like "Green jelly beans linked to acne! at the 95% confidence level.

Some of the section and chapter titles are hilarious. For example, in the chapter titled "Are you there, God? It's me, Bayesian Inference", Ellenberg brings up a scary example of the use of "big data". Based on a teen-age girl's purchases of unscented lotion, mineral supplements, and cotton balls, the retail store "Target" began sending her coupons for baby gear, because of the (correct) inference that she was pregnant. Another great section title is "One more thing about God, then I promise we're done."

Another interesting title is "The Cat in the Hat, the Cleanest man in school, and the creation of the universe", in which Ellenberg reviews some of the probabilistic arguments for and against the existence of god. And I love the famous quote by Richard Feynman:

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW375. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!

I also love the chapter title, "If Gambling is exciting, you're doing it wrong". Ellenberg describes how several groups capitalized on several state lotteries. Due to some strange lottery rules, it is (was?) possible to reliably make a profit, given enough investment of resources. No illegal shenanigans--the states make money no matter what you do. You could make a profit by taking advantage of the rules, and of the people who buy lottery tickets without a coherent strategy. And, I did not realize that Voltaire made his fortune by taking advantage of state lotteries!

Ellenberg brings up the phenomenon of Nate Silver predicting the outcome of the Obama-vs.-Romney election. Silver predicted the probability of both candidates winning state by state, along with the margin of error. By adding up the probable errors, he estimated that he would be wrong by 2.83 states. Critics seemed to have ignored the fact that he was not wrong by this many states--in fact he correctly predicted the outcome in all 50 states!

I highly recommend this book to all people who are even vaguely interested in math, probability, logic, and the application to everyday life. This is an excellent book! ...more

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May 25, 2018 bup rated it it was amazing

Shelves: not-1001-but-the-list-is-stupid, oh-look-so-and-so-wrote-a-book, 2018, math

Ellenberg explains lots of real-world situations that math can help understand, and he does it really well.

I'm sure lots of people have compared this to Nate Silver's The Signal and the Noise and I will too. Both of these need to be required reading for everyone.

Don't be intimidated - he's a great writer and tailors this toward a non-mathy audience.

Somehow I missed that he's been writing for for many years, too. I've got a lot of catching up to do. ...more

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