Skip to main content

How Not To Be Wrong - Jordan Ellenberg ****

In the preface to Jordan Ellenberg's chunky maths book (441 pages before the notes in the version I read) we are introduced to a hypothetical student moaning about having to work through a series of definite integrals and complaining 'When am I going to use this?' What Ellenberg sets out do is to show how we use mathematics all the time - and how important it is to understand it if we are not to get the wrong idea about the world. We'll see how well he does.

It was very interesting to read this book quite soon after Richard Nisbett's Mindware. Both cover how to interact with life better thanks to the support of mathematics. Nisbett drives from the psychology side and improving decision making, while this book drives from the maths. Perhaps surprisingly, How Not to be Wrong is the easier read of the two. Ellenberg has a delightful light touch and is often genuinely funny (it's important to read the footnotes, which Ellenberg, like Terry Pratchett, uses for a lot of his jokes).

Along the way he shows us the uses and risks of straight lines in forecasting and understanding data, the power (and danger) of using methods of inference, how to use expected value, the realities of regression to the mean and the interplay between correlation and causality, and some fascinating observations on why traditional statistics can be very misleading when it comes to public opinion. Here it is often not applied to either/or situations, and it's quite possible, for instance, for the public to both support the idea of cutting taxes while simultaneously supporting raising expenditure. Although there are a few cases where we lose the plot and the connection to the real world, mostly this all driven by real world examples - from lotteries where an appropriate strategy can result in big wins to the apparent prediction that everyone in America would be obese before the end of the century.

While I don't think is this as practical a book as Nisbett's, it is full of fascination for anyone who likes a bit of applied mathematics, but can't be bothered with the formulae - there is very little that is scary in that line here. What's more, if you have any exposure to scientists, this book contains by far the best explanation of p-values, what they really mean and where they are meaningless that I've ever seen. 

So would the student from the preface feel after reading this book that there's no need to complain? Satisfyingly for a book that doesn't limit us to predictable mathematical answers, the response is both yes and no. Yes, because it becomes very clear that maths is hugely useful in understanding the world and responding to it. No, because the vast majority of maths you will have suffered at school and may have suffered at university, isn't required here. At least 90 per cent of the content depends on probability and statistics, topics that are rarely covered well enough in the curriculum, given how important they are in getting a grip on reality.

Although it felt a bit too long and used US sports rather too often as examples for my liking, this is a book for anyone with an interest in the way that mathematics can give us a better understanding of what's really happening in our complex world.


Paperback 

Kindle 

Review by Brian Clegg

Comments

Popular posts from this blog

The AI Delusion - Gary Smith *****

This is a very important little book ('little' isn't derogatory - it's just quite short and in a small format) - it gets to the heart of the problem with applying artificial intelligence techniques to large amounts of data and thinking that somehow this will result in wisdom.

Gary Smith as an economics professor who teaches statistics, understands numbers and, despite being a self-confessed computer addict, is well aware of the limitations of computer algorithms and big data. What he makes clear here is that we forget at our peril that computers do not understand the data that they process, and as a result are very susceptible to GIGO - garbage in, garbage out. Yet we are increasingly dependent on computer-made decisions coming out of black box algorithms which mine vast quantities of data to find correlations and use these to make predictions. What's wrong with this? We don't know how the algorithms are making their predictions - and the algorithms don't kn…

Infinity in the Palm of your Hand - Marcus Chown *****

A new Marcus Chown book is always a treat - and this is like a box of chocolates: a collection of bite-sized delights as Chown presents us with 50 science facts that are strange and wonderful.

The title is a quote from William Blake's Auguries of Innocence: 'To see a World in a Grain of Sand, / And a Heaven in a Wild Flower, / Hold Infinity in the palm of your hand, / And Eternity in an hour.' It would seem particularly appropriate if this book were read on a mobile phone (so it would be literally in the palm), which could well be true for ebook users, as the short essays make excellent reading for a commute, or at bedtime. I found them distinctly moreish - making it difficult to put the book down as I read just one more. And perhaps another. Oh, and that next one looks really interesting...

Each of the 50 pieces has a title and a short introductory heading, which mostly give a feel for the topic. The very first of these, however, briefly baffled me: 'You are a third mus…

How to Invent Everything - Ryan North ****

Occasionally you read a book and think 'I wish I'd thought of that.' This was my immediate reaction to Ryan North's How to Invent Everything. The central conceit manages to be both funny and inspiring as a framework for writing an 'everything you ever wanted to know about everything (and particularly science)' book.

What How to Invent Everything claims to be is a manual for users of a time machine (from some point in the future). Specifically it's a manual for dealing with the situation of the time machine going wrong and stranding the user in the past. At first it appears that it's going to tell you how to fix the broken time machine - but then admits this is impossible. Since you're stuck in the past, you might as well make the best of your surroundings, so the aim of the rest of the book is to give you the knowledge you need to build your own civilisation from scratch.

We start with a fun flow chart for working out just how far back in time you are…