books and arts The state of the Universe A bold attempt to make sense of relativity, quantum theory and cosmology. The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose Jonathan Cape: 2004. 1,094 pp. £30 Jeffrey Forshaw JOSE FUSTA RAGA/CORBIS JOSE FUSTA “The most important and ambitious work of science for a generation.”That’s the claim from the publishers of Roger Penrose’s latest book. The claim is vastly overblown. Certainly Penrose has written a remarkable book: it introduces many of the topics that lie at the cutting edge of research into the fundamental nature of space, time and mat- ter. Although the book aims at a complete survey of modern particle physics and cos- mology, its principal concern is to address the fundamental tension between the two pillars of twentieth-century physics: Einstein’s general theory of relativity and quantum theory. This is a fascinating tension and one that Penrose tries to communicate in a quite uncompromising fashion. Although advertised as popular science, this book will be far from accessible to most non-experts. I suspect that there has never been such a bold attempt to communicate ideas of such mathematical complexity to a general audience. It is Penrose’s hope that Up the junction? Despite progress in many directions, we still haven’t found the one “road to reality”. non-experts will be able to go with the flow and get a taste of the excitement of the field the future, critically assessing the way in of the necessary mathematics. The section without following the details.Unfortunately, which physicists progress in their quest for ends with a chapter — not strictly relevant the book is crammed full of details and is so an ever deeper comprehension of reality,and but entirely captivating — on the notion of utterly uncompromising that it will probably offering some personal views on the sociol- infinity, covering Cantor’s work on cardi- leave even the most enthusiastic of his non- ogy of contemporary research. In between nal numbers and Gödel’s incompleteness expert readership exhausted. Even those there are 32 chapters of serious mathemati- theorem. with a PhD in mathematics or physics are cal physics with little room for philosophical Then the physics starts, with a chapter on likely to find it very hard going. reflections. space-time.The earlier chapter on differential Having said that, the book is teeming So serious is Penrose in his desire to pre- geometry has paved the way and the reader with delights. Penrose’s ability to present sent the science in a worthy fashion that one is ready to understand Galileo’s principle of complex ideas in a logical, coherent manner, has to wait patiently (or struggle valiantly) relativity as implying that “space is a bundle often using geometry, reflect a deep under- until chapter 17 for the physics. The mathe- over time”.Einstein’s idea that space and time standing that will seriously engage a more matics of the first part of the book is a joy might constitute a unified whole is by now expert reader. There are even exercises, to read. Not all of it is needed for the later an entirely reasonable a priori possibility. graded “very straightforward”,“needs a bit of chapters, and the selection and presentation The following chapters introduce field thought” and “not to be undertaken lightly”, of material clearly reflects Penrose’s love of theory and quantum theory. Much of the which the reader is encouraged to attempt. the mathematical structures that underpin discussion on the measurement problem in I certainly found the classification of this the physics. quantum theory will be familiar to those final category quite appropriate. Penrose starts from a clean slate, encour- who have read Penrose’s earlier book The The opening chapter, on the roots of sci- aging the reader to question the dominant Emperor’s New Mind.In The Road to Reality ence and the notion of mathematical truth, role of real numbers, or the validity of he lays out his contention that quantum marvels over the ability of mathematics to euclidean geometry, in describing the world theory, as currently formulated, must be explain so much of the behaviour of the around us. Much time is devoted to com- incomplete, and this is a recurrent theme for world with such incredible precision. Some plex numbers and their “magic”. In typical the remainder of the book. scientists may balk at questions of ontology, fashion, Penrose does not shy from intro- There is a rather cursory chapter on the preferring to banish them to the realm of ducing Riemann surfaces, holomorphicity standard model of particle physics, which metaphysics, but this is not Penrose’s way. In and hyperfunctions. Hot on the heels of rather confusingly precedes the chapter on his subsequent assessment of the measure- these come quaternions, leading naturally quantum field theory and makes the error ment problem in quantum mechanics, he to a discussion of Clifford and Grassman of stating that weak interactions couple argues forcefully for the need for a credible algebras. Chapters on differential geometry only to left-handed particles. It is also stated ontology. The book ends with reflections on and symmetry conclude the presentation that the only measured violation of charge NATURE | VOL 431 | 14 OCTOBER 2004 | www.nature.com/nature 741 © 2004 Nature Publishing Group books and arts parity, a symmetry that ultimately helps to and the book’s introduction shows just how account for the preponderance of matter important it is to link those three areas of over antimatter in the Universe, is in the Field guides and taxonomic study. study of neutral kaon mesons, a declaration The phylogeny of the monocots (such as that will not be popular with those working phylogenies lilies, grasses and orchids) has undergone on certain experiments based in the United Flowers of Ethiopia and Eritrea: radical change and restructuring with the States and Japan. Aloes and Other Lilies use of DNA sequence data. The number of The main thrust of the final part of the by Sebsebe Demissew, Inger Nordal & families recognized and their relationships book is the exploration of physics in those Odd E. Stabbetorp to one another have changed considerably often exotic places where both quantum Shama Books, Addis Ababa, Ethiopia: 2004. over the past decade (see Bot.J.Linn.Soc. 141, mechanics and gravity play a role, such as 227 pp. US$15 399–436;2003).Rather than brushing all this at the birth of the Universe or in the vicinity e-mail: [email protected] under the carpet,the authors clearly and con- of a black hole. The very existence of the Sandra Knapp cisely explain why phylogeny matters. Then, second law of thermodynamics is used to through the use of the field-guide format, argue that the Universe must have started Taxonomy has been much in the news in they show how such rearrangements make out in an extraordinarily special configura- the past year or so. Everybody seems to sense when looking at the plants themselves. tion (something else that will be familiar to want more of it, and in a slightly different They are also brave enough to admit what all readers of The Emperor’s New Mind), which way than it is currently done. Perhaps tax- taxonomists know: that the classification of Penrose takes as a hint that the quantum onomy should be done solely on the web, or such groups, where new data are emerging, theory requires revision. by using a set of DNA barcodes — opinions is still in flux. After a more detailed discussion of the differ. But just what is taxonomy and why Phylogenies and field guides are both of measurement paradox, Penrose is ready to is it suddenly in demand? I contend that obvious use, but both require a solid base expound his belief that quantum state reduc- taxonomy (or systematics, as some people of descriptive taxonomy. This book, and to tion is an objective process, arising as a prefer to call it) is composed of three inter- a certain extent the phylogeny to which it consequence of the gravitational energy locking spheres of scientific endeavour: adheres, rests on the descriptive work done difference between the different space-time phylogeny, description and identification. on the region’s flora. Major projects docu- geometries possessed by quantum states in This book is a sterling example of how all menting national floras (and faunas) have superposition. By now, Penrose is becoming three aspects of taxonomy can come together uncovered new species and provided the increasingly partisan, although he is careful to produce something of lasting value to a observations and taxonomic decisions that to announce when he is deviating from the variety of end-users. are needed for both phylogeny and field “accepted wisdom”.He is forceful in stating The book is a colour guide to the iden- identification. his objections to several mainstream ideas: tification of the charismatic flowers that Books such as this, with its numerous inflationary cosmology, low-energy super- characterize dry habitats such as Ethiopia — illustrations and accessible style, inspire symmetry, the electroweak phase transition ‘lilies’ in the broadest sense. Identification is others to study organisms, helping the accu- and string theory are all targets. Indeed, his aided by easy-to-use keys, simple descrip- mulation of information about uses and, to presentation of string theory is essentially a tions and lovely photographic plates, which my mind more importantly, conservation technical critique, and I suspect it will be make this a nice book for just exploring the status. How on earth can we conserve bio- inaccessible to non-experts.