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:  
Using these links earns us commission at no cost to you
Review by Brian Clegg
Labels:

Comments

Post a Comment

Popular posts from this blog

Phenomena - Camille Juzeau and the Shelf Studio ****

I am always a bit suspicious of books that are highly illustrated or claim to cover 'almost everything' - and in one sense this is clearly hyperbole. But I enjoyed Phenomena far more than I thought I would. The idea is to cover 125 topics with infographics. On the internet these tend to be long pages with lots of numbers and supposedly interesting factoids. Thankfully, here the term is used in a more eclectic fashion. Each topic gets a large (circa A4) page (a few get two) with a couple of paragraphs of text and a chunky graphic. Sometimes these do consist of many small parts - for example 'the limits of the human body' features nine graphs - three on sporting achievements, three on biometrics (e.g. height by date of birth) and three rather random items (GNP per person, agricultural yields of various crops and consumption of coal). Others have a single illustration, such as a map of the sewers of Paris. (Because, why wouldn't you want to see that?) Just those two s...
Post a Comment
Read more

The Bright Side - Sumit Paul-Choudhury ***

When I first saw The Bright Side (the subtitle doesn't help), I was worried it was a self-help manual, a format that rarely contains good science. In reality, Sumit Paul-Choudhury does not give us a checklist for becoming an optimist or anything similar - and there is a fair amount of science content. But to be honest, I didn't get on very well with this book. What Paul-Choudhury sets out to do is to both identify what optimism is and to assess its place in a world where we are beset with big problems such as climate change (which he goes into in some detail) that some activists position as an existential threat. This is all done in a friendly, approachable fashion. In that sense it's a classic pop-psychology title. For me, Paul-Choudhury certainly has it right about the lack of logic of extreme doom-mongers, such as Extinction Rebellion and teenage climate protestors, and his assessment of the nature of optimism seems very reasonable, if presented at a fairly overview leve...
Post a Comment
Read more

Rakhat-Bi Abdyssagin Five Way Interview

Rakhat-Bi Abdyssagin (born in 1999) is a distinguished composer, concert pianist, music theorist and researcher. Three of his piano CDs have been released in Germany. He started his undergraduate degree at the age of 13 in Kazakhstan, and having completed three musical doctorates in prominent Italian music institutions at the age of 20, he has mastered advanced composition techniques. In 2024 he completed a PhD in music at the University of St Andrews / Royal Conservatoire of Scotland (researching timbre-texture co-ordinate in avant- garde music), and was awarded The Silver Medal of The Worshipful Company of Musicians, London. He has held visiting affiliations at the Universities of Oxford, Cambridge and UCL, and has been lecturing and giving talks internationally since the age of 13. His latest book is Quantum Mechanics and Avant Garde Music . What links quantum physics and avant-garde music? The entire book is devoted to this question. To put it briefly, there are many different link...
Post a Comment
Read more