Beautiful, Simple, Exact, Crazy - Apoorva Khare and Anna Lachowska ***

This is a rare example of a book that is pretty much a textbook, but works well as entertaining educational maths for a certain section of the audience. To be honest, that's probably quite a small section - but for those it does appeal to, I can heartily recommend to it.

What the authors set out to do is to give those who aren't mathematicians or scientists a feel for how useful mathematics is in the real world. All too often, the maths we are taught at school seems strangely abstract. Okay, they might give you those irritating problems about people filling baths or meeting each other part way on a journey to make the 'numbers come to life' - but these aren't real world applications. And all too often we are just presented with, say, an abstract geometric or algebraic problem to solve and expected to get on with it, with no idea of what the point is in anything vaguely connected with normal life.

The authors assume that the reader has maths to high school algebra level, but then takes off down a whole host of application routes, such as velocities and accelerations, interest and mortgages, the strange behaviour of fractals, the benefits of being able to estimate, ciphers, probability and statistics.

Some of the problems still do seem painfully artificial - a question picked at random is 'Suppose an entire school goes on a picnic - as many boys as girls. The boys all wear jeans; a third of the girls wear skirts, and the rest wear jeans. Given that a randomly picked student is wearing jeans, what is the odds that the student is a girl.' There's no doubt that Bayes' theorem is hugely valuable in real life, but this probably isn't an application many people are going to make of it, so doesn't really fit the book's philosophy of moving away from the artificiality of ordinary textbooks.

Is it going to work? I think the main problem is finding an audience. It's too simplistic for most university science students, and it's too much of textbook to read for fun. (I'm sorry, it just feels like a textbook, and no one remembers those fondly - the eyes tend to skip off the page in protest unless you force them to continue.) So that limits the size of the popular science audience. However, if you have high school maths combined with sufficient drive to find out more about usable mathematics to go along with a textbook approach, you will find that your mathematical toolkit is impressively expanded by this title.

Paperback:

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

It's On You - Nick Chater and George Loewenstein *****

Going on the cover you might think this was a political polemic - and admittedly there's an element of that - but the reason it's so good is quite different. It shows how behavioural economics and social psychology have led us astray by putting the focus way too much on individuals. A particular target is the concept of nudges which (as described in Brainjacking ) have been hugely over-rated. But overall the key problem ties to another psychological concept: framing. Huge kudos to both Nick Chater and George Loewenstein - a behavioural scientist and an economics and psychology professor - for having the guts to take on the flaws in their own earlier work and that of colleagues, because they make clear just how limited and potentially dangerous is the belief that individuals changing their behaviour can solve large-scale problems. The main thesis of the book is that there are two ways to approach the major problems we face - an 'i-frame' where we focus on the individual ...

Introducing Artificial Intelligence – Henry Brighton & Howard Selina ****

It is almost impossible to rate these relentlessly hip books – they are pure marmite*. The huge Introducing … series (a vast range of books covering everything from Quantum Theory to Islam), previously known as … for Beginners , puts across the message in a style that owes as much to Terry Gilliam and pop art as it does to popular science. Pretty well every page features large graphics with speech bubbles that are supposed to emphasise the point. Funnily, Introducing Artificial Intelligence is both a good and bad example of the series. Let’s get the bad bits out of the way first. The illustrators of these books are very variable, and I didn’t particularly like the pictures here. They did add something – the illustrations in these books always have a lot of information content, rather than being window dressing – but they seemed more detached from the text and rather lacking in the oomph the best versions have. The other real problem is that...

The Laws of Thought - Tom Griffiths *****

In giving us a history of attempts to explain our thinking abilities, Tom Griffiths demonstrates an excellent ability to pitch information just right for the informed general reader. We begin with Aristotelian logic and the way Boole and others transformed it into a kind of arithmetic before a first introduction of computing and theories of language. Griffiths covers a surprising amount of ground - we don't just get, for instance, the obvious figures of Turing, von Neumann and Shannon, but the interaction between the computing pioneers and those concerned with trying to understand the way we think - for example in the work of Jerome Bruner, of whom I confess I'd never heard. This would prove to be the case with a whole host of people who have made interesting contributions to the understanding of human thought processes. Sometimes their theories were contradictory - this isn't an easy field to successfully observe - but always they were interesting. But for me, at least, ...

Search This Blog