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

Luna: Moon Rising (SF) - Ian McDonald ****

I'm not the natural audience for this book. Game of Thrones l eaves me cold - and it's hard not to feel the influence of GoT (and a whole lot of Dune )   underneath a veneer of science fiction and the trappings of a South American drug cartel in the cod-medieval family power battles and chivalric details. There are even dragons (of a sort). I'd be really sad if the future did involve this sort of throwback feudalism. However, remarkably, despite this I found Luna: Moon Rising kept me engaged. The fact is that Ian McDonald can put together a good plot with intricate machinations, which is enough to carry the reader through what can be a bewildering collection of characters. The two page scene-setter saying who did what to whom at the start was useful, but I could have done with family trees for the main family as I was constantly forgetting who was who - especially easy as McDonald endows many families with characters with the same first initial (e.g. Ariel and Al...
Post a Comment
Read more

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...
Post a Comment
Read more

The AI Paradox - Virginia Dignum ****

This is a really important book in the way that Virginia Dignum highlights various ways we can misunderstand AI and its abilities using a series of paradoxes. However, I need to say up front that I'm giving it four stars for the ideas: unfortunately the writing is not great. It reads more like a government report than anything vaguely readable - it really should have co-authored with a professional writer to make it accessible. Even so, I'm recommending it: like some government reports it's significant enough to make it necessary to wade through the bureaucrat speak. Why paradoxes? Dignum identifies two ways we can think about paradoxes (oddly I wrote about paradoxes recently , but with three definitions): a logical paradox such as 'this statement is false', or a paradoxical truth such as 'less is more' - the second of which seems a better to fit to the use here.  We are then presented with eight paradoxes, each of which gives some insights into aspects of t...
Post a Comment
Read more