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

The Art of Statistics - David Spiegelhalter *****

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 all …

The Best of R. A. Lafferty (SF) – R. A. Lafferty ****

Throughout my high school years (1973–76) I carefully kept a list of all the science fiction I read. I’ve just dug it out, and it contains no fewer than 1,291 entries – almost all short stories I found in various SF magazines and multi-author anthologies. Right on the first page, the sixth item is ‘Thus We Frustrate Charlemagne’ by R. A. Lafferty, and his name appears another 32 times before the end of the list. This isn’t a peculiarity of my own tastes. Short stories were much more popular in those days than they are today, and any serious SF fan would have encountered Lafferty – a prolific writer of short fiction – in the same places I did.

But times change, and this Gollancz Masterworks volume has a quote from the Guardian on the back describing Lafferty as ‘the most important science fiction writer you’ve never heard of’. Hopefully this newly assembled collection will go some way to remedying that situation. It contains 22 short stories, mostly dating from the 1960s and 70s, each w…

David Beerling - Four Way Interview

David Beerling is the Sorby Professor of Natural Sciences, and Director of the Leverhulme Centre for Climate Change Mitigation at the University of Sheffield. His book The Emerald Planet (OUP, 2007) formed the basis of a major 3-part BBC TV series ‘How to Grow a Planet’. His latest title is Making Eden.

Why science?

I come from a non-academic background. None of my family, past or present, went to university, which may explain the following. In the final year of my degree in biological sciences at the University of Wales, Cardiff (around 1986), we all participated in a field course in mid-Wales, and I experienced an epiphany. I was undertaking a small research project on the population dynamics of bullheads (Cotus gobio), a common small freshwater fish, with a charismatic distinguished professor, and Fellow of the Royal Society in London. Under his guidance, I discovered the process of learning how nature works through the application of the scientific method. It was the most exciting t…