Proofiness: The Dark Arts of Mathematical Deception

recommended by Steve Fey and NPR

This is actually a 4.5 star review with two 1-star deductions for howling errors that seem to stem mainly the author’s self-regard for his own mathematical savvy and the kind of “I’m clever in this area, so I must be clever in this area too” bias that trips up so many.

Overall, it’s a good update of the themes from some better but older books in the genre such as “Innumeracy” and “A Mathematician Reads the Newspaper” and Jordan Ellenberg’s “How Not to Be Wrong.” Chapter 7, “Alternate Realities” about the misuse of statistics in the criminal justice system is especially worthwhile and important, and the three short appendices explaining various examples of mathematical errors are quite good.

The deductions are for an early comment accusing Al Gore of cherry-picking data in his famous slide-deck presentations by showing what the Florida coastline would look like if the Greenland ice sheet melted, causing see levels to rise 20 feet. Seife notes that Gore is right to warn about sea level rise — but he wrote “It’s just that sea levels aren’t going to rise twenty feet anytime soon.” Here in 2024 — but also in 2010 — there was lots of evidence that our models of the effects of climate instability are persistently and systematically UNDERestimating both the pace and severity of changes. It reads as if Seife was dying to find an example of cherry picking that he could hang on a Democrat, so he simply asserted something that, alas, seems less certain every day, that we needn’t concern ourselves “anytime soon” with what a world without Greenland ice would look like.

The second star is deducted because Seife does only the most superficial gloss on the math of voting methods and ends up saying that it’s all just sport and that we like third party spoilers because it makes elections more interesting. Instead of noting that the entire gerrymandering problem he spends significant time covering is the result of the arcane single-member district system that is not constitutionally required, Seife simply asserts that we can simply use non-partisan redistricting commissions to abolish gerrymandering … which ignores the consequence of self-sorting, which is giving white rural voters a significant over representation in the US House to go with their significant overweight in power through the US Senate. Seife attacks ranked-choice voting and asserts — in direct contradiction to substantial evidence — that voter errors would “go through the roof” if ranked choice ballots are adopted.

ISBN 978-0-670-02216-8, 2010 Viking Press

I'm not really sure for whom Seife wrote this book. The majority of people who like math and/or statistics will already be very aware of most of the statistical concepts that Seife introduces in his book: significant digits, the importance of looking closely at how axes are labelled, appropriate population sampling and correlation vs. causation. And the people who don't like math won't voluntarily read a book on math. So that leaves...I don't know: people who like math but are bad at it? Middle-schoolers? And unfortunately, this book won't work great for those people either, because rather than using the actual names for the mathematical concepts, like I did, Seife makes up terms so that if this is your first exposure to the concepts, you won't actually be able to communicate about them or google more about them. I think my turning point with Seife was in an appendix about the difference between sensitivity and positive predictive value, where I was originally annoyed that he didn't name-check Bayes and then realized that he also didn't mention sensitivity or positive predictive value in the entire appendix even once! This appendix was literally about how just knowing the sensitivity of a test without knowing the prevalence of disease results in not being able to predict the positive predictive value and he didn't use the names for a single one of those concepts.

I found the latter half of the book more interesting: Seife largely moves away from mathematical concepts and investigates political hijinks, such as the Franken election, Bush v. Gore and gerrymandering. It doesn't really add to numeracy, nor have that many striking examples of “proofiness,” (except that humans can't count numbers to 6 digits worth of significant figures, which hopefully most people intuitively know) but it is interesting.

Overall, it's not a bad book. I might give it to a child who was interested in math, but I don't think most adults will enjoy it very much.