Book recommendation: How Not to Be Wrong

Today, I finished reading How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg. This is a very enjoyable, very well-written, general-audience book about mathematics, which I recommend whole-heartedly.

Ellenberg, a math professor at the University of Wisconsin, does a great job weaving together a plethora of mathematical topics, including non-Euclidean geometry, probability, statistics, and mathematical analysis of voting systems. He writes in a way that someone who only vaguely remembers—or never really understood—high school algebra would be able to follow and enjoy. His exposition is made more lively by a cast of historical and contemporary characters, some famous and some primarily known only to mathematicians, including Abraham Wald, Bernhard Riemann, Teddy Roosevelt, Francis Galton, Voltaire, Nicolas de Condorcet, David Hilbert, Ronald Fisher, Antonin Scalia, and Nate Silver. (My favorite line in the book is the one in which Ellenberg describes Silver as a “Kurt Cobain of probability.”)

The best part of the book is about how the Massachusetts Lottery ran a game in which it was occasionally profitable to play (that is, there were some drawings in which the expected value of a ticket’s winnings was higher than the price of a ticket). Of course, some smart people (e.g. an MIT student) figured this out and recruited investors to buy absurd numbers of tickets for the profitable drawings. In the course of telling this story, Ellenberg weaves in discussions of finite geometries and error-correcting codes, both of which are relevant in describing how one buys thousands of lottery tickets without accidentally having to split winnings with yourself.

I think it would be awesome to use this book in a gen-ed math class.

In defense of FERPA

In an op-ed piece titled “College kids have too much privacy“, Michele Willens criticizes the Family Educational Rights and Privacy Act (FERPA) for making it difficult for families to monitor their college student children’s academic performance.

I can understand why some families are frustrated by FERPA. Many families spend a great deal of money to send their young to college. Consider the parents in Willens’s opening anecdote, who learned their daughter had not actually graduated and skipped class for the last two years. I think anyone would be angry to be in their shoes.

However, it’s just not true that FERPA means, as Willens puts it, that “you have to take [your kid’s] word for it when they say ‘everything’s fine.'” FERPA allows a student to voluntarily release their records to another party. I recall having at least one scholarship in college whose sponsors required me to send an official transcript every year. I don’t see why a parent couldn’t insist on this as a condition for continued financial support.

In addition, a student can sign a FERPA waiver allowing a third party to get their records directly from the school. Although Willens describes this as a “laborious process”, it really amounts to having a student sign a form or check a box on a web site.

Part of being in college is learning how to become an independent adult. The transfer of FERPA rights from parents to student is part of that process. So is students learning to take responsibility for their learning. All FERPA requires is for parents to deal with their adult children directly, as adults, rather than being able to go behind their back.

Some thoughts about online discourse

Sum question!

The American Mathematical Society made the following amusing post to their Facebook page today:

You can calculate 3???? = 26796, which of course is greater than 1000.

Continue reading

Not all cars


Imagine there was a serious manufacturing defect present in about six percent of cars. This defect caused a malfunction that could seriously injure the car’s passengers. Of course, consumers would demand action to eradicate this defect. Suppose auto industry representatives dismissed these concerns by protesting “Not all cars blow up because of this defect.”

Um, some conservatives DO dispute E=mc^2

A few times on my Facebook news feed, I’ve noticed a graphic with a photo of astrophysicist and (awesome) science popularizer Neil deGrasse Tyson and this quotation of him (emphasis and ellipsis in original):

Climate change has taken on political dimensions… That’s odd because I don’t see people choosing sides over \(E=mc^2\) or other fundamental facts of science!

It appears that Dr. Tyson has not checked out Conservapedia, a right-wing competitor to Wikiepdia. (I certainly don’t blame him for this—he’s got to have much better things to do than read a web site full of stupid garbage.) Conservapedia takes issue with relativity overall, and says of \(E=mc^2\) (emphasis in original):

Political pressure, however, has since made it impossible for anyone pursuing an academic career in science to even question the validity of this nonsensical equation. Simply put, \(E=mc^2\) is liberal claptrap.

(The whole \(E=mc^2\) Conservapedia article is actually pretty funny. My wife, who is a physicist, thought it was a joke.)

Conservapedia is a project of Andrew Schlafly, son of prominent conservative activist Phyllis Schlafly. Indeed, you can see from my link above (adorned with rel="nofollow", of course!) that the most recent edit to the \(E=mc^2\) article was by Mr. Schlafly himself.

Stop punching down at millennials

I absolutely hate millennial-bashing. While I don’t consider myself a millennial—I’m just a tad bit too old—I have a great deal of sympathy and affinity for that generation. That generation has been dealt a bad hand. Many of the manufacturing jobs that provide a path to prosperity for those without college degrees have been moved overseas, and as a result millennials desiring prosperity were told they had to go to college. Alas, millennials did not enjoy the same level of government subsidy for their college education as their parents, so many of them have been saddled with crippling amounts of student debt. Furthermore, many millennials came out of college right as the economy tanked due to the financial sins of their parents’ generation. Yet, it’s common to hear people blame millennials for their inability to launch.

Annoyingly, much of the millennial-bashing you hear boils down to complaints about how they were raised. Millennials, many baby boomers will tell you, were praised too much as children. There was too much emphasis on self-esteem. They were given too high of expectations by their parents. For whatever it’s worth, I think these complaints are over-wrought. In my experience, millennials don’t suffer from too much self-esteem and many have adjusted expectations—I think more than they should have to—to today’s economic realities. But even if these complaints were accurate, it takes quite a bit of chutzpah for someone to say, essentially, “Ha ha, your generation sucks because we did a poor job raising you!”

Millennial-bashing by older people is good example of “punching down”, that is, it’s people using their power to attack someone with less power—which I find very distasteful. And criticism of millennials is used as a convenient excuse to avoid questioning the policy decisions (such as financial deregulation, globalization, and defunding of post-secondary education) that have put that generation at a disadvantage.