There's something odd about this chunky book on probability - the title doesn't mention the P word at all. This is because David Spiegelhalter (Professor Sir David to give him his full title) has what some mathematicians would consider a controversial viewpoint. As he puts it 'all probabilities are judgements expressing personal uncertainty.' He strongly (and convincingly) argues that while the mathematical approach to probability is about concrete, factual values, outside of the 'natural' probabilities behind quantum effects, almost all real world probability is a subjective experience, better described by more subjective terms like uncertainty, chance and luck. A classic way to distinguish between those taking the frequentist approach to probability and the Bayesian approach is their attitude to what the probability is of a fair coin coming up heads or tails after the coin has been tossed but before we have looked at it. The frequentist would say it's def...

There's a stereotype of computer users: Mac users are creative and cool, while PC users are businesslike and unimaginative. Less well-known is that the world of statistics has an equivalent division. Bayesians are the Mac users of the stats world, where frequentists are the PC people. This book sets out to show why Bayesians are not just cool, but also mostly right. Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant. If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on...

This is very much a book of two halves, the first a history of the development of probability theory and the second examples of where probability goes wrong and an attempt to explain why we're so bad intuitively at estimating chances. Steven Tijms has a rather old-fashioned writing style, which made me think this was a reprint of a book from the 1960s until I hit an entry on Covid-19. This means that the historical section is sometimes a little dry - but strangely, for me, this first half was by far the best part. The main reason for my preference was originality. Although the 'where probability goes wrong' section is arguably the reason books on probability are so much fun, whether it's dealing with the gambler's or prosecutor's fallacy - or the inevitably Monty Hall problem - Tijms was mostly treading very familiar ground here. However, there were parts of the the history section covering aspects that I've rarely seen before in a popular mathematics text. ...

I can't remember when I was last so frustrated that a book could have been so brilliant... but then managed to cut out 95 per cent of its potential audience. Matt Cook's book promises to deliver '75 ingenious paradoxes in mathematics, physics and philosophy'. And it does. Some are familiar, from Russell's paradox to the Monty Hall problem, but quite a few weren't to me. I absolutely loved reading about the paradoxes. But. There's a big but. The problem is that Cook does two things that make the book unreadable to many. One is to forget Richard Feynman's assertion that there's no point just learning labels for things. (Ironic, as Cook frequently cites Feynman, and even has a dedication that includes 'To Richard Feynman, who saved my father's life'.) Yet Cook insists on telling us all the technical language and what it means - which is totally unnecessary to explain the paradoxes. Who cares that something is called a bijection? We d...

Statistics have a huge impact on us - we are bombarded with them in the news, they are essential to medical trials, fundamental science, some court cases and far more. Yet statistics is also a subject than many struggle to deal with (especially when the coupled subject of probability rears its head). Most of us just aren't equipped to understand what we're being told, or to question it when the statistics are dodgy. What David Spiegelhalter does here is provide a very thorough introductory grounding in statistics without making use of mathematical formulae*. And it's remarkable. What will probably surprise some who have some training in statistics, particularly if (like mine) it's on the old side, is that probability doesn't come into the book until page 205. Spiegelhalter argues that as probability is the hardest aspect for us to get an intuitive feel for, this makes a lot of sense - and I think he's right. That doesn't mean that he doesn't cover...

Although this book dates back to 2007 (it was shortlisted for the Royal Society Science Book Prize in 2008), the information within doesn’t seem dated. Psychologist and behavioural expert Gerd Gigerenzer has written a number of books about risk and probability in recent years, and while this book has some of that, this book is focused on the secrets of fast and effective decision making. That is not to say that it is a self-help book, but rather a description, based on neurological and psychological research, of how the brain uses heuristics in order to make decisions with limited information, though readers will find much of the information useful when thinking about decisions. Gigerenzer explains how intuition works in easy to understand terminology and also uses numerous examples throughout the book to illustrate how intuition is the basis for decision making, such as how we are able to catch a ball without conducting calculations of its speed or distance.  In short, Gig...

I am really struggling to remember a book that has irritated me as much as this one, which is a shame because it's on a very interesting and significant subject. Pedro Domingos takes us into the world of computer programs that solve problems through learning, exploring everything from back propagating neural networks to Bayesian algorithms, looking for the direction in which we might spot the computing equivalent of the theory of everything, the master algorithm that can do pretty much anything that can be done with a computer (Turing proved a long time ago that there will always be some things that can't). As the subtitle puts it, this is the quest for the ultimate learning machine that will remake our world. So far, so good. Not only an interesting subject but one I have a personal interest in as I had some involvement in artificial intelligence many moons ago. But just reading the prologue put my hackles up. It was one of those descriptions of how...

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...

There's no doubt that Richard Nisbett's book, subtitled 'tools for smart thinking' is great, despite two issues. I want to get those issues out of the way first before we get onto the good stuff, with which it is packed. One issue is the writing style. This is a touch clumsy and could do with a little professional help. Nisbett has a tendency to overuse unnecessary jargon in sentences like this: Our construal of objects and events is influenced not just by the schemas that are activated in particular contexts, but by the framing of judgments we have to make. Nor ideally worded. The second issue I suspect comes more from the publisher, which is the attempt to frame this book (sorry, couldn't resist the italics) as a self-help title as much as popular science. It doesn't work particularly well as a practical self-help toolkit - it's not structured in a way to make this a good use, particularly because a large part of the book is focused on how we get thin...

There's a certain kind of maths title that delights. It's not the kind of pure maths you'd find in an Ian Stewart book , where maths is an intricate, latticework puzzle like a net of spun sugar that need have no connection to the real world. No, this is maths as impure and dirty as it gets. It sneaks up behind us and takes us by surprise, because this is the maths at the interface with psychology - maths that often challenges our beliefs and understanding of the world. It can be both deeply satisfying and quite interesting in a QI fashion, all at the same time. I suppose the classic of this field is Freakonomics , though I would also recommend The Tiger that Isn't and (in a modest way), my own Dice World . What William Poundstone does with great aplomb here is to unpick our dubious relationship with randomness. In the first half of the book he points out how we are particularly poor envisaging randomness, and how, as a result, if you understand how people get it...