Monday, December 29, 2014


When his show premiered in 2005, comedian Stephen Colbert put the word "truthiness" into the English language as a description of something that sounds like it should be true but isn't. It's often used today when talking about how to state something so that it sounds like it is true, even if the speaker is uncertain or may even know it is likely false.

In 2010, mathematician and science writer Charles Seife used the same concept to title his book on misleading uses of math Proofiness, holding that politicians, public relations spokespeople, advertisers and others often used what sounded like solid and irrefutable mathematics to make their claims look true. But although the numbers might be real, there were always caveats in their preparation that were left to the fine print (or even left out), and overly credulous media outlets would not do the checking necessary to question them.

Seife spends the first third of the book talking directly about the ways that statistics can be manipulated and misunderstood. Survey size samples, margins of error, failure to adjust monetary amounts for inflation, lack of control groups, and so on are all brought out and Seife usually offers a real-world example of how they were used to mislead people. When he turns to elections, he points out how a small enough percentage gap between vote totals means that, for all practical purposes, the election is a tie. "Systemic error" in any method of tallying ballots prevents 100 percent accuracy -- so both the 2000 Florida presidential and the 2008 Minnesota senate elections should have been redone, because the size of the systemic error exceeded the gap between the candidates.

But he also spends a lot of time talking about public policy regarding the 2008 financial crisis and the electoral politics of redistricting and gerrymandering, which seem to wander afield from the central discussion of the misuses and trickery of math in modern media and politics. They have a tangential relationship to the core subject, but the extensive sections on financial regulation policies, the disputed elections and gerrymandering feel more like illustrations run amok. Seife's book might best be paired with some other examinations of the same problems, which may win out in sharpness of focus but which lag significantly behind him in writing style, liveliness and clarity of explanation.
Few things will more quickly bring terror to the eyes of many people than the equations of that most arcane and alchemical of mathematical disciplines, calculus. It is the Emperor Palpatine to algebra's Darth Vader, ramping up the insidious pairing of numbers and letters to the level that its letters stand not for mere variables, but for equations filled with other variables!

Most of those who do not flee calculus proclaim utter boredom at its existence and wonder when it will ever be of use in the real world. These people had better never meet Wellesley College assistant math professor Oscar E. Hernandez, whose 2014 book Everyday Calculus will answer their questions in detail.

Using his schedule of a "typical morning," Fernandez shows how everything from the amount of rain falling on his umbrella to the traffic levels during his commute can be approximated, if not precisely explained, by setting the situations up as equations which calculus can solve. After explaining a few key terms like "derivatives" and "differential equations," he is off to the races with his examples, explanations and equations.

Fernandez obviously loves both his discipline of mathematics and the job in which he uses it, teaching. He's amusing and works overtime to tune down the jargon volume and use as many everyday words as possible to describe the process of his reasoning. Equation-phobes will be leery of the book, which includes them at every relevant point and which does not do as well as it could at giving them some context to reduce the brain lock.

With that in mind, though, Everyday Calculus is an energetic and excellent introduction to the ideas of calculus and how complicated some of the simplest real-world phenomena actually are. In places it may be a bit of a slog, but it will also reward the perseverant who make the trip.

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