Skip to main content

The Infinite Book – John D. Barrow ****

Authors are often asked to review books on a topic they’ve written on themselves. The reasoning is sensible – they ought to know something about the subject – but there’s always that uneasy suspicion that there’s going to be a bit of bias creeping in. So I think it’s only fair to admit up front that I have written a book on infinity (of which more later).
Infinity is a wonderful subject, because it’s intimately mind-bending (if the combination sounds paradoxical, that’s what infinity is all about) and gives you the chance to pull in all sorts of different concepts and assocations along the way, something Barrow does with great gusto. There’s a surprisingly large amount of coverage here for God, and for the universe, and the book jumps around from Aristotle to Hilbert’s Infinite Hotel (explained at great length), from the paradoxes of infinite sets to the paradoxes of time travel. Overall it’s an enjoyable journey that gives plenty of opportunity to be amazed and surprised.
The only trouble I have with this book is the balance of content. Barrow spends a good half of the book on cosmology, which seems a bit of a cheat. Okay, there are links, and his thoughts on “is the universe infinite” are well worth reading, but in the end this wasn’t supposed to be a cosmology title. Because there is so much on cosmology, this only being a finite book (despite the title), he misses out important swathes of the history of infinity. There’s nothing, for instance, on the development of calculus – the first mathematical tool dependent on infinity – and the magnificent battle between Newton, Leibniz and Berkeley. Similarly, though Barrow does fill in a little bit of biography on Cantor, the man who devised the mathematics of infinity, he does so without explaining what Cantor’s set theory is about – a fundamental to understanding what Cantor was doing – and without even touching on important numerical concepts like cardinals and ordinals.
In a sense, the moan is that this is a book about infinity that isn’t really about maths or about mathematicians. As well as lots on cosmology, it has rather too much vague philosophical material (not helped by the illustrations from an obscure play, or the groan-inducing section titles).
Don’t think I’m putting the book down though – it is very good, and I would recommend reading it, but only after reading my own A Brief History of Infinity to fill in some of those gaps. If I were asked to compare the two, I would say that A Brief History of Infinity is better at providing a historical context, more of a feel for the people involved and more of the amazing mathematical consequences and paradoxes, while Barrow’s book is better at showing how infinity sits alongside our present day physical theories.
Paperback:  
Review by Brian Clegg

Comments

Popular posts from this blog

De/Cipher - Mark Frary ****

I was a little doubtful when I first saw this book. Although it has the intriguing tagline 'The greatest codes ever invented and how to crack them' the combination of a small format hardback and gratuitous illustrations made me suspect it would be a lightweight, minimal content, Janet and John approach to codes and ciphers. Thankfully, in reality Mark Frary manages to pack a remarkable amount of content into De/Cipher's slim form.

Not only do we get some history on and instructions to use a whole range of ciphers, there are engaging little articles on historical codebreakers and useful guidance on techniques to break the simpler ciphers. The broadly historical structure takes the reader through basic alphabetic manipulation, keys, electronic cryptography, one time pads and so on, all the way up to modern public key encryption and a short section on quantum cryptography. 

We even get articles on some of the best known unsolved ciphers, such as the Dorabella and the Voynich ma…

Paul McAuley - Four Way Interview

Paul McAuley won the Philip K. Dick Award for his first novel and has gone on to win the Arthur C. Clarke, British Fantasy, Sidewise and John W. Campbell Awards. He gave up his position as a research biologist to write full-time. He lives in London. His latest novel is Austral.


Why science fiction?

For one thing, I fell in love with science fiction at an early age, and haven’t yet fallen out of love with it (although I have flirted with other genres). For another, we’re living in an increasingly science-fictional present. Every day brings headlines that could have been ripped from a science-fiction story. Giant robot battle: Who knew a duel between chainsaw-armed mech suits could be so boring? for instance. Or, Roy Orbison hologram to embark on UK tour in 2018. And looming above all this, like Hokusai’s famous wave, are the ongoing changes caused by global warming and climate change, which is just one consequence of human activity having become the dominant force of change on the planet…

Karl Drinkwater - Four Way Interview

Karl Drinkwater is originally from Manchester, but has lived in Wales half his life. He is a full-time author, edits fiction for other writers and was a professional librarian for over twenty-five years. He has degrees in English, Classics and Information Science. When he isn't writing, he loves exercise, guitars, computer and board games, the natural environment, animals, social justice, cake and zombies - not necessarily in that order. His latest novel is Lost Solace.

Why science fiction?

My favourite books have always been any form of speculative fiction. As a child I began with ghost stories, which were the first books to make me completely forget I was reading. By my teenage years I was obsessed with fantasy, science fiction, and horror. Although I read literary and contemporary books, non-fiction, historical works, classics and so on, it is speculative fiction that I return to when I want escape and wonder. When I read reviews of my last book, the fast-paced novella Harvest Fe…