Skip to main content

Beyond Infinity - Eugenia Cheng ****

Popular maths writers have it much harder than authors of popular science books. Pretty well everyone loves science at junior school, even if they're put off it in their teens, so for science writers, it's just a matter of recapturing that childhood delight in exploring how the world works. But, to be honest, maths is a relatively rare enthusiasm at any age, so the author of a popular maths book has to really work at his or her task - and this is something Eugenia Cheng certainly does, bubbling with enthusiasm and trying hard not to put us off as readers as she explores infinity.

In Cheng's earlier book, Cakes, Custard and Category Theory, food played too heavy a role for me - here that tendency reigned in, though it still rears its head occasionally. We get a quite detailed exploration of infinity, infinitesimals and some additional material such as infinite dimensions and infinite-dimensional categories (we had to get some category theory), plus the usual enjoyment of quantum weirdness. I felt sometimes, because the book doesn't build on a historical basis, we were thrown in at the deep end a little too early with assertions like infinity+1=infinity and infinity x infinity = infinity. The process where Cheng shows us how infinity can't be a real number, or an integer, or a rational fraction etc. also felt a little repetitive and drawn out. There's always a difficulty in letting go a little when you work in a field that requires total precision. But we never lose Cheng's enthusiasm and light touch.

I think this book will particularly appeal to a reader who already has an interest in maths, but not much training, because it is purely focussed on the mathematics itself. For the more general reader, I suspect a book like A Brief History of Infinity, which gives historical context, brings and people and social implications to frame the maths, would work better as an introduction. With the appetite whetted, though, they should be encouraged to go onto Beyond Infinity, which as a wider mathematical context.

I really enjoyed this book, and though the author's desire to include food did still slightly intrude - and I felt it was just a bit too much about her, rather than the maths - it's a great addition to the relatively sparse popular maths shelf.

Paperback (US hardback):  

Kindle 
Review by Brian Clegg

Comments

Popular posts from this blog

The Demon in the Machine - Paul Davies *****

Physicists have a habit of dabbling in biology and, perhaps surprisingly, biologists tend to be quite tolerant of it. (I find it hard to believe the reverse would be true if biologists tried to do physics.) Perhaps one reason for that tolerance is Schrödinger’s lecture series and book What is Life?, which had a huge impact on molecular biology and with a reference to which, not surprisingly, Paul Davies begins his fascinating book. 

At the heart of the The Demon in the Machine (we'll come back to that demon in a moment) is the relationship between life and information. In essence, Davies points out that if we try to reduce life to its simple physical components it is like trying to work with a computer that has no software. The equivalent of software here is information, not just in the best publicised aspect of the information stored in the DNA, but on a far broader scale, operating in networks across the organism.
This information and its processing gives life its emergent compl…

The Cosmic Mystery Tour – Nicholas Mee ****

This is another book, like last year’s Enjoy Our Universe by Alvaro de Rújula, that sets out to provide a light-hearted introduction to physics and astrophysics for the general reader. It’s from the same publisher (OUP) and packaged in the same way: as a high quality small-format hardback with 200 glossy pages, the majority of them adorned with colour pictures. But that’s where the resemblance ends. Unlike its predecessor, this new book by Nicholas Mee delivers exactly what it promises.

It’s not that de Rújula’s book was a bad one, but he just wasn’t able to think his way into the reader’s mind. He kept saying ‘physics is fun’, but he was talking about the fun a professional physicist gets out of doing it – which is a very arcane, often highly mathematical, type of fun. The result, for a non-specialist reader, was actually quite alienating. Mee, on the other hand, understands exactly how his readers think, what they find interesting, and the details that – no matter how important they …

Professor Maxwell's Duplicitous Demon - Brian Clegg ****

‘It’s not uncommon when trying to give Maxwell his rightful place in the pantheon of physics to bracket him with Newton and Einstein’, Brian Clegg says towards the end of this book. In one sense that’s perfectly true. Dip into any physics textbook and you’ll see Maxwell’s name at least as often as the other two. His greatest achievement – Maxwell’s equations – did for electromagnetism what Newton had done for gravity, while laying the essential theoretical groundwork for everything Einstein was to do.

There’s a big difference, though. A few years ago, when I was offered the chance to write short biographies of Newton and Einstein, I jumped at it – because they addressed mysteries of the universe that anyone can relate to, and their lives outside physics were, if anything, even more fascinating. At the risk of sounding downright rude, you can’t say either of those things about James Clerk Maxwell. In spite of that, Brian Clegg has done a wonderful job here of recounting just what Maxwel…