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 Art of Logic - Eugenia Cheng ***

This is an important book, though I'm not sure Eugenia Cheng would agree with my logic in saying so. 

Going on the marketing, what we have here is a counter to fake news and dodgy argumentation in the form of mathematical logic. The back cover tells us 'Newspaper headlines and social media use emotions to warp the facts. Politicians and companies master rhetoric to mislead us. What one book could help us make sense of it all?' Admittedly they don't answer their rhetorical question, but I assume the answer is intended to be The Art of Logic. (Did the company behind this book realise it was using rhetoric, though presumably not to mislead us?) 

What we actually have is a combination of a lucid and interesting explanation of the basics of logic with the mathematical equivalent of those books such as Algorithms to Live By that were so popular a couple of years ago. They used the logic of algorithms (differently worded, and, to me, easier to understand), the heart of computer…

Quantum Economics - David Orrell ****

David Orrell's earlier title Economyths is one of my favourite popular science books of all time. Or, perhaps, I should say popular non-science, as Orrell shows just how devastatingly traditional economics uses the tools of science without having a scientific basis. I was, therefore, really looking forward to reading Orrell's new book - until I saw the title. As anyone involved with physics can tell you, there's nothing more irritating than the business of sticking the word 'quantum' onto something to give a pseudo-scientific boost to waffle and woo. Was Orrell doing the same thing? Thankfully, his introduction put my fears aside.

Orrell, a mathematician with a physics background quickly makes it clear that the way he is using quantum theory is not just employing magic words, but involves making use of strong parallels between the nature of quantum objects and concepts like money (more on money in a moment). Yes, this is to some extent a metaphorical use of quantum …

The Ashtray - Errol Morris *****

Wow. When someone suggested I read a book called The Ashtray, written by a documentary film-maker, it didn't strike me that it would be a book that gave deep insights into the history and philosophy of science - while also being a remarkable reading experience. In fact, I almost didn't bother with it, but I'm glad that I did.

The titular ashtray was thrown at the author when he was a grad student - thrown by one of the two best known names in the philosophy of science, Thomas Kuhn, he of The Structure of Scientific Revolutions and the concept of paradigm shifts. Kuhn didn't like the young Errol Morris daring to challenge his ideas and reacted with what some would regard as a less than philosophical reply by hurling a heavy glass ashtray at him.

Part of the reason that reading The Ashtray is a remarkable experience is because it's a book that feels in some ways like watching a documentary. I have to confess I've never seen any of Morris's work, but he uses vis…