How Not to Be Wrong: The Power of Mathematical Thinking

Maths is a powerful tool, but in the wrong hands it can be pointless at best, dangerous at worst. Unfortunately, most human beings are a wrong pair of hands. We weren’t designed for handling numbers of any complexity, and tend to be out of our depths once they go beyond single digits. But a basic knowledge of numbers makes us overconfident and keen to interpret figures and statistics we don’t really understand as if they were cold hard facts. You only need to watch someone trying to work out which packet of washing powder presents the better deal when the supermarkets add a few percentages to the labels, or our reactions to opinion polls or the latest cancer-scare headlines.

Which makes books like this important, at least superficially. Ellenberg covers a lot of ground, explaining various ideas and highlighting common fallacies and paradoxes caused by our general weak understanding of basic statistics. He uses some excellent real-life examples to highlight what the numbers can teach us, but also what they can hide. Like how someone tasked with studying how to improve aircraft survivability in the Second World War realised that they were only analysing the bullet holes on the planes which made it back; the answer to this survivability bias was to increase armour to the places the raw data wasn’t showing them.

Another case in point is the classic disease afflicting the scientific community, that focus on statistical significance (and the Whorfian perversion of calling it significance at all). Papers tend to be published when they prove a point; negative science, for all its benefit, doesn’t enjoy the same kudos. Which fact alone means that many statistical outliers get published where the overwhelming unpublishable results tend to indicate the opposite. And that’s before taking into account how the researchers massage their results to hit the threshold of significance. After all, a few small tweaks here and fortuitous rounding decisions there can make all the difference for publication.

Aside from headline-grabbing scientific papers, Ellenberg uses other real-world examples to highlight his points. A large amount of space is taken up with the risks of playing state lotteries or the pitfalls of various electoral systems. Yet despite numerous practical applications, it remains a difficult book to recommend. For all its interesting asides, the title is just too schizophrenic to ever come to any real conclusions. Often it’s as if the author got carried away guiding the reader into some favoured corner of the mathematical jungle, only to forget why he ever led us there in the first place. Certain ideas are explained in fairly pedantic fashion, taking it a few steps further than even this particular pleb needed to grasp the concept. Other times it’s as if the target group has switched and the details become more turgid and difficult to follow.

[Photo by Roman Mager on Unsplash]

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Politics is not the art of the possible. It consists in choosing between the disastrous and the unpalatable.

— John Kenneth Galbraith

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