June 19, 2016

Review Corner

To them, the length of that hypotenuse had been revealed to be not a number at all. This caused a fuss. The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we'd now call mathematics, things we'd now call religion, and things we'd now call mental illness. They believed that odd numbers were good and even numbers evil; that a planet identical to our own, the Antichthon, lay on the other side of the sun; and that it was wrong to eat beans, by some accounts because they were the repository of dead people's souls.
I shall not solicit their opinion in the Tau vs. Pi debate. The quote is from Jordan Ellenberg's How Not to Be Wrong: The Power of Mathematical Thinking, recommended to me by a fellow named Bill Gates. Well, he did not text me, but I saw it was included on his Five Books to Read this Summer. And, it's a pop-math book: what could possibly go wrong?

I'm not sure about the title -- and, to be fair, Ellenberg takes a couple self-deprecating whacks at it. The whole book is a clarion call to use rigorous, structured mathematical thinking and reasoning in everyday problems. Many interesting historical math characters are trotted out, as are several fun facts. There is not enough math to chase anyone off; anyone could make it through. And yet there is enough depth to keep a geek immersed. That is the hardest part of a math/science book for public consumption, and he does better than most.

For example, there is a topological solution to picking every pair in a Powerball-style lottery that went over my head, but it did not despoil the interesting chapter on the MIT kids who would buy all pairs in the Massachusetts Lottery on certain conditions. (I just scared off three readers and sent three to buy it, but the book is completely accessible.)

The largest swath is devoted to debunking the misuse of statistics. If the TV news intones that a new study shows that watermelon cures dandruff or whatever, he offers good reasons for skepticism which has nothing to do with scientific or journalistic malfeasance.

You can do linear regression without thinking about whether the phenomenon you're modeling is actually close to linear. But you shouldn't. I said linear regression was like a screwdriver, and that's true; but in another sense, it's more like a table saw. If you use it without paying careful attention to what you're doing, the results can be gruesome.

It was once said of Colorado Governor Dick Lamm that if he encountered a baby born weighing seven pounds, and the little tyke grew to 14, Lamm would become upset that in the year 2040 the child will weigh a million tons! Ellenberg raps prestigious journals for the same thinking:
The Long Beach Press-Telegram went with the simple headline "We're Getting Fatter." The study's results resonated with the latest manifestation of the fevered, ever-shifting anxiety with which Americans have always contemplated our national moral status. Before I was born, boys grew long hair and thus we were bound to get whipped by the Communists. When I was a kid, we played arcade games too much, which left us doomed to be outcompeted by the industrious Japanese. Now we eat too much fast food, and we're all going to die weak and immobile, surrounded by empty chicken buckets, puddled into the couches from which we long ago became unable to hoist ourselves. The paper certified this anxiety as a fact proved by science.

Without using the term "common-core," he looks into different methods and teaching styles. A student of his that writes down a stupid answer "The Horse weighs -100 grams." with an annotation that the answer is stupid will get partial credit. One who provides only the stupid answer gets zero.
In fact, I'm not radical at all. Dissatisfying as it may be to partisans, I think we have to teach a mathematics that values precise answers but also intelligent approximation, that demands the ability to deploy existing algorithms fluently but also the horse sense to work things out on the fly, that mixes rigidity with a sense of play. If we don't, we're not really teaching mathematics at all.

On Review Corner even math books get graded on politics. I'd call him pretty middle of the road. For an academic, that is certainly a bruising right-wing neocon! He generally picks out Republicans to be the butt of a joke, but he always follows up with "Democrats do it too." Again, for an academic, I'm scoring that as "fair."
The Washington Post graded the Romney campaign's 92.3% figure as "true but false." That classification drew mockery by Romney supporters, but I think it's just right, and has something deep to say about the use of numbers in politics. There's no question about the accuracy of the number. You divide the net jobs lost by women by the net jobs lost, and you get 92.3%. But that makes the claim "true" only in a very weak sense.
[...]
But real-world questions aren't like word problems. A real-world problem is something like "Has the recession and its aftermath been especially bad for women in the workforce, and if so, to what extent is this the result of Obama administration policies?" Your calculator doesn't have a button for this.

And, one of my favorite, just how frequently improbable events happen in a nation of 300 million. People win the lottery all the time, get struck by lightening, bit by sharks, die of bee stings...
If a random Internet stranger who eliminated all North American grains from his food intake reports that he dropped fifteen pounds and his eczema went away, you shouldn't take that as powerful evidence in favor of the maize-free plan. Somebody's selling a book about that plan, and thousands of people bought that book and tried it, and the odds are very good that, by chance alone, one among them will experience some weight loss and clear skin the next week. And that's the guy who's going to log in as saygoodbye2corn452 and post his excited testimonial, while the people for whom the diet failed stay silent.

As the cleverer among you have inferred from the quotes, Ellenberg has a clever wit and a folksy attachment to Math. He decries those who leave the field when they see they're not the best, he provides lovable tales of odd mathematicians but underscores that they're outliers.

It's a pleasant and informative read. I do not mean to suggest that because it is easy it does not have much to offer even those with a good feel for statistics and probability. Even the chapter subheads are good "ARE YOU THERE, GOD? IT'S ME, BAYESIAN INFERENCE"

Five stars.

Review Corner Posted by John Kranz at June 19, 2016 10:43 AM
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