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Mind your p's and q's

This article is more than 18 years old
Roger Penrose explains the laws of the universe in his monumental The Road to Reality. If only Nicholas Lezard could understand it

The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose (Vintage, £15)

It is not very often that a reviewer recommends a book which he or she is completely unqualified to review; and much less often that the reviewer admits the fact. But if one of the purposes of this column is to bring to your attention what, in my opinion, is one of the week's more important publications, then it would be remiss of me to mention anything else. Besides, just because the peak of a mountain is obscured by the weather, or the feebleness of one's own vision, it doesn't mean that you can't make a good guess that it is still bloody high up.

So here, then, are all the laws of the universe, in one handy 1,100-page volume. It would appear that they are even more complicated than the laws of cricket, although just as necessary. Moreover, it says on the front cover that it is a "Sunday Times Top 10 Bestseller", and on the back, next to the price, that it is "popular science". Open it up at random and you will see that Jordan's autobiography this ain't. Your reaction, I suspect, may be closer to Nigel Molesworth's than you may like: "It's just a jumble of letters sir i mean i kno i couldn't care less whether i get it right or not but what sort of an ass sir can hav written this book." That is Molesworth. Here is Penrose:

"For each pair of natural numbers p and q such that p + q = n, we can define a corresponding 'real form' of the complex group (Sp(*n, C) by taking only those elements which are also pseudo-unitary for signature (p, q) - ie which belong to U(p, q). This gives us the (pseudo-)symplectic group Sp(p, q)." A footnote by the word "gives" directs us to the words "Prove this", along with a little symbol glossed in the introduction as meaning "needs a bit of thought". For Penrose wants us to get involved in his extra-hard sums, and he doesn't think that the subject is so arcane that we need be completely ignorant of it.

And this is why this is such a wonderful book. If it is a quality of a great writer not to treat the audience like idiots, then Penrose is indeed great, and the position of this book on the bestseller lists makes sense. And did not A Brief History of Time lodge at the top of that very list for what felt, to other authors, like an eternity?

Penrose, incidentally, has worked with Stephen Hawking, and won the 1988 Wolf Prize for physics with him, "for their joint contribution to our understanding of the universe", so he knows whereof he speaks. And, for the first 100 or so pages of this book, he is able to communicate his knowledge; or, rather, I was able to receive it. In fact, he agrees with Molesworth about one thing at least: "Pythagoras as a mater of fact is the root of all geom." (That's Molesworth.) The first real bit of maths in the book - after a wonderful prologue and preface, which will get you quite worked up with excitement about how important mathematics is, how crucial to our understanding of the universe - is about the Pythagorean theorem (you know, the square on the hypotenuse and all that). You will sail through this and feel quite brainy indeed, even as you get to complex numbers - ones that are composed of combinations of real and imaginary numbers, imaginary numbers being multiples of the square root of -1. And you should not feel intimidated by these - after all, mathematicians have been working with complex numbers since 1545.

After this, it gets a bit hairy for the non-specialist, however engaging Penrose's prose style. But if you are at all interested in different sizes of infinity, or different dimensions, or quantum particles, the thermodynamic legacy of the Big Bang, then here is chapter and verse, at least until matters are sorted out by a grand unified theory once and for all. You can skate over the equations and let the more comprehensible assertions, or the more stimulating questions, lodge themselves in your mind and assume the character of poetry. Take it a page a day - which I was unable to - and you may even understand it all. It'll be worth it, surely. Good luck. To order The Road to Reality for £14 with free UK p&p call Guardian book service on 0870 836 0875.

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