Popular Science Review - The Road to Reality

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Review - The Road to Reality - Roger Penrose

Just occasionally you come across a popular science book that is so different from anything else you've ever seen that it stuns. From the first sight it's pretty obvious there's something special about Road to Reality - it's absolutely huge. The postman complained of a potential hernia on delivering it. We are talking over 1,000 pages here. And then there's the approach Roger Penrose has decided to take. It's not so much the scope - we've seen plenty of books on all of science in the last couple of years, some excellent (like Bryson's A Short History of Nearly Everything or Calder's Magic Universe) - and in fact Penrose doesn't cast his net so wide, only covering physics and its mathematical basis. But the stunning thing is the way he does this.

A few popular science books have succeeded in the past despite being almost impossible to read and understand. The classic example is Hofstadter's Gödel, Escher, Bach (though I disagree with those who put Hawking's Brief History of Time into this category, as I think it is surprisingly approachable). There is no doubt at all that The Road to Reality is archetypal. The first 350+ pages are almost pure mathematics, intended to provide a grounding that will be needed to follow the rest of the book. Penrose tells us that it isn't essential to understand all this - that's just as well. I think it's unlikely that many people with physics degrees will understand all the maths that Penrose presents in that first part.

He then goes on to explore the world of physics in pages that range between delightful and frustrating (this is also true of the basic maths pages). In a few sentences he can spring from very readable and enjoyable prose to dense formulae, expressed with the most complex set of typographical conventions I've ever seen. There's brilliant stuff in here - I'm just not sure anyone other than professional physicists and mathematicians are going to be able to penetrate it.

There just seems a total detachment between the author and the real world. Perhaps the most hilarious example of this is the exercises with which he scatters the book. If anyone other than a budding Richard Feynman or Andrew Wiles can be bothered with these, I will be amazed. Early on Penrose says "The reader will find that in this book I have not shied away from presenting mathematical formulae, despite dire warnings of the severe reduction in readership that this will entail. I have thought seriously about this question and have come to the conclusion that what I have to say cannot reasonably be conveyed without a certain amount of mathematical notation and the exploration of genuine mathematical concepts." This seems a perfectly reasonable attitude - unfortunately it's wrong on two important levels.

Firstly, many great popular science books have shown it is possible to give a good understanding of complex principles without diving into high level maths. It IS hard for the author - not everyone can do it - and it usually takes a writer rather than an academic to succeed, but it certainly is possible. Secondly there isn't a "certain amount" of mathematical notation here. It's an avalanche, a flood of biblical proportions. You drown in mathematical symbols. I think it's also worth saying that Penrose doesn't always explain things very well - I've never seen Cantor's elegant infinity proofs presented in such a confusing way.

So why does it get four stars? Because it's a tour de force. Despite all its flaws, it is arguably a work of genius. This is a book that everyone ought to try, because the few (and it will only be a very few) who succeed in reading it will get a tremendous amount from it. This is an Everest of a book. Finish it and you'll feel both the exertion and the exhilaration of climbing a great mountain. But don't expect it to be easy. Do you like a challenge? Please do take it on. But don't say I didn't warn you.

Also in paperback (September 2005):

Reviewed by Brian Clegg

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