The Road to Reality: a Complete Guide to the Laws of the Universe

Book Review The Road to Reality: A Complete Guide to the Laws of the Universe

Reviewed by Brian Blank

The Road to Reality: A Complete Guide to the and a mathematical formulation of one of Nature’s Laws of the Universe interactions, gravity. Roger Penrose Many of the hallmarks of progress along the road Alfred A. Knopf, 2005 to reality can already be discerned in the first Sci- ISBN 0-679-45443-8 entific Revolution. Because Nature so deftly hides $40.00, 1,099 pages her secrets, a crazy theory is often a prerequisite for making any headway. Copernicus, for example, For the title of his latest epic, The Road to Re- defied not only established authority but also the ality, Roger Penrose has selected a metaphor that common sense of every observer who, under the appears frequently in popular expositions of illusion of being at rest, watched the sun move physics. It is no wonder that the phrase has become across the sky. Other necessities for progress— a favorite among physicists, for it suggests a mathematics for formulating and developing a the- single-minded pursuit of the ultimate destination: ory and a physical apparatus for testing it—were an understanding of all the underlying principles also essential components of the revolution. The that govern the behavior of our universe. Perhaps improved instruments for measurement devised by that may seem to be an ambitious program. After Tycho Brahe permitted Kepler to refute the orbits all, it was not so very long ago that Eugene Wigner of Copernicus’s system. Newton’s calculus allowed asserted, “The great success of physics is due to a him to extend Galilean dynamics and explain the restriction of its objectives.” Since that sober as- laws that Kepler had observed. The road to reality sessment, however, stunning progress has changed had taken its now familiar course of revolution fol- the outlook of physics so greatly that several of its lowed by successive approximation. leading proponents have been emboldened to sug- The nineteenth century witnessed the second gest that a complete grasp of the laws of nature lies Scientific Revolution. Between 1850 and 1865, fun- just ahead of us. damental notions such as energy and entropy were As Penrose asserts, the voyage of discovery has introduced. At first, many scientists deprecated en- lasted more than two and a half millennia and has ergy as a mathematical abstraction. By the end of been profoundly difficult. At the start of the jour- the century, however, energy was replacing force ney, around 500 B.C.E., Heraclitus identified the as the preferred attribute of reality around which major stumbling block: Nature is wont to conceal her- to organize physical theories. Several new branches self. Mathematical advances aside, the first signifi- of physics—thermodynamics, statistical mechan- cant steps on the road to reality were achieved in ics, the kinetic theory of gases—arose accordingly. the period between 1543, the year Copernicus pub- The second revolution in physics culminated in a lished his heliocentric theory of planetary motion, working awareness of our solar system’s place in and 1687, the year Newtonian mechanics was in- the Milky Way, the concept of a “disembodied” troduced. This era, the first Scientific Revolution, field, the mathematical description of a second culminated in a working awareness of the solar fundamental interaction, namely electromagnetism, system, a basic framework for studying dynamics, the discovery of an elementary particle (the electron), and, by virtue of the second law of thermo- Brian Blank is professor of mathematics at Washington dynamics, a stark new aspect of reality: the ther- University. His email address is [email protected]. modynamic arrow of time.

JUNE/JULY 2006 NOTICES OF THE AMS 661 For all the successes of the second revolution, a theory that experimental physicists have re- physics faced several challenges at the beginning peatedly confirmed to exacting standards. Particles of the twentieth century. The debate over the wave continue to be discovered—notably the top quark versus particle nature of light, which had erupted in 1995 and the τ-neutrino in 2000—but they fit during the first revolution, was not definitively into the theory the way the man-made synthetic el- settled by the second, Maxwell’s characterization ements fit into the periodic table. of light as electromagnetic radiation notwith- During the same time span in which high energy standing. All experiments to detect a medium physicists probed the smallest bits of reality, as- through which light propagated, the hypothetical tronomers and astrophysicists revolutionized our luminiferous aether, failed. Newton’s law of grav- understanding of the largest objects of reality, in- itation remained a useful scorecard of gravity, but cluding our universe itself. By 1923 astronomers it neither explained the mechanism by which grav- had confirmed the existence of galaxies beyond the ity is effected nor permitted time to play any role Milky Way. Observations of distant celestial bod- in gravity’s action. The new theories of the second ies coupled with general relativity gave rise to a new revolution presented even more troublesome para- branch of physics, cosmology, that tells us much doxes, chief among which was the prediction of about how our universe came to be and how it will blackbody radiation having arbitrarily large en- cease to be. Though elementary particle physics and ergy. From an evolutionary point of view, our un- cosmology deal with objects at diametrically op- derstanding of reality seems to have advanced not posite ends of reality, the two fields have come to by a march down an orderly road but by an alter- be intricately intertwined. Knowledge gained from nating sequence of leaps between the frying pan the study of subatomic processes is the basis for and the fire. understanding the physics of stars and the syn- Historians of science often state that the twen- thesis of heavy elements in the universe. In return, tieth century witnessed two revolutions in physics: the exotic constituents of the universe provide im- quantum theory and general relativity. The first res- portant tests of particle theory. cued physics from the ultraviolet catastrophe of The whirlwind tour we have just concluded rep- blackbody radiation and resolved the dilemmas resents only a tiny fraction of what The Road to Re- posed by the properties of light. By blurring the dis- ality covers in its 1,100 pages. Anyone who casu- tinction between wave and particle, quantum the- ally flips through a few of those pages will recognize ory presented counterintuitive insights into the immediately that more than length distinguishes nature of matter and energy. The second revolu- The Road to Reality from other expositions that tar- tion, general relativity, combined space and time get a roughly similar audience. Here, uniquely so to provide a theory of gravity that is deeper than far as I am aware, we find an author presenting so- a mere bookkeeping formula. Both revolutions pro- phisticated concepts of physics by invoking so- foundly changed our conceptions of physical re- phisticated concepts of mathematics. Even an ex- ality. perienced mathematician who happens upon a The twentieth century was, indeed, a productive page illustrated with diagrammatic tensor nota- one for physicists; two revolutions may not give tion might shy away from Penrose’s Road. As the them their due. A second elementary particle, the author explains in his preface, “What I have to say photon, was detected in 1923. By 1932 both the pro- cannot be reasonably conveyed without a certain ton and the neutron had also been discovered. amount of mathematical notation and the explo- These nucleons led physicists to an additional two ration of genuine mathematical concepts.” Do not interactions: the strong and weak nuclear forces. take this declaration to be a contemporary version Within a few decades, a large menagerie of sub- of Copernicus’s Mathemata mathematicis scribun- atomic particles had been assembled: positrons tur: Penrose’s idea is that mathematics should be and muons in the 1930s, pions and kaons in the written not only for mathematicians but also for 1940s, Pauli’s long-conjectured neutrino in the anyone willing to learn. To that end, remedial 1950s, and a great many others. The ever increas- lessons begin in the preface, where rational num- ing particle zoo became ever more perplexing. Once, bers are defined as equivalence classes. after having given a speculative lecture at Colum- The first sixteen chapters of The Road to Real- bia, Wolfgang Pauli admitted, “This is a crazy the- ity are primarily devoted to the mathematics needed ory.” From the audience Niels Bohr called out, “Un- to express modern physical theory. By the time fortunately, it is not crazy enough!” In 1963 Murray page 383 is reached, the intrepid reader will have Gell-Mann and, independently, George Zweig pro- been introduced to a large number of topics in posed a theory of fractionally charged elementary analysis, algebra, and geometry. Of these, the particles (christened quarks by Gell-Mann) that demands of analysis are comparatively modest: cal- proved to be just crazy enough. In the next decade culus, Fourier series, hyperfunctions, Riemann sur- and a half, the so-called Standard Model of ele- faces, and enough complex function theory to state mentary particles and their interactions arose. It is the Riemann mapping theorem. The necessities

662 NOTICES OF THE AMS VOLUME 53, NUMBER 6 from algebra include quaternions, Clifford and find the backward references helpful. The forward Grassmann algebras, linear algebra, transforma- references may strengthen the incentives of some tion groups, and enough Lie theory to discuss the readers to slog through seemingly abstract math- classical groups and their Lie algebras and repre- ematics. sentations. The topics from differential geometry Those who reach the chapters on special rela- are the most arduous: parallel transport, geodes- tivity, general relativity, and quantum mechanics ics, curvature, the exterior derivative, calculus on will find excellent treatments that are filled with manifolds, connections, and fibre bundles. All told, physical insights and mathematical context. In par- Penrose has condensed the outline of a quite re- ticular, the four consecutive chapters that begin spectable education in undergraduate mathemat- with the quantum particle and conclude with Paul ics into the first third of his book. When he states, Dirac’s theoretical discovery of antiparticles are es- “I am an optimist in matters of conveying under- pecially enlightening. In the last of these chapters, standing,” we are inclined to believe him. Penrose shows how the integration of special rel- As a coping mechanism for the reader who turns ativity and quantum theory gives rise to the pre- off whenever a mathematical formula presents it- diction of antiparticles. Starting with the relativis- self, Penrose suggests “skipping all the formulae tic Hamiltonian of a quantum particle of rest mass and just reading the words.” Such advice surely µ , Penrose develops the Klein-Gordon equation transcends well-founded optimism for there is + (µ/)2 ψ = 0 for the wavefunction ψ. He scarcely a page on which mathematics and prose shows us how Dirac, by rediscovering Clifford al- are not thoroughly interwoven. Readers who shun gebras, factored the Klein-Gordon equation into mathematics would do far better seeking out the what we now call the Dirac and anti-Dirac equations. many excellent works that target a more general Exposure to this mathematical background pro- audience and that can be assembled to cover sim- vides the reader with genuine insights into Dirac’s ilar ground. Even those who do not flee from math- prediction of the positron, the antiparticle of the ematical symbols may prefer explanations of sci- electron, which was discovered only one year after ence in the style of Brian Greene or Stephen its conjectured existence. Hawking. Mathematicians who are interested in Dirac’s theory of the electron is a natural point physics, however, should give Penrose’s book more of departure for the Standard Model of elementary serious consideration. Some will choose to cut the particles and their interactions, a subject that does book down to size by passing over the first sixteen not lend itself well to popular exposition. One of chapters entirely. Others who want to brush up on the difficulties is that the Standard Model is filled a few topics will find that Penrose’s synopses pro- with jargon, much of which is whimsical rather vide a useful background for the physics that lies than intuitive. Even more problematic for the novice ahead. is the overlapping of terms, as illustrated by the With 382 pages of mathematical preliminaries following sentence from The Road to Reality: “The out of the way, Penrose turns his attention to the family of hadrons includes those fermions known various scientific revolutions that transformed as ‘baryons’ and also those bosons referred to as physics in the twentieth century. The second part ‘mesons’.” Hundreds of different particles—enough of his book comprises 352 pages that are devoted to make your head spin or your eyes glaze over, to to general relativity, quantum theory, elementary quote Brian Greene—abound, all governed by a particle physics, and cosmology. The transition complicated theory of debatable mathematical con- from mathematics to physics is nearly seamless. sistency. In short, an author who attempts to ex- In part, that is because Penrose does not rigidly plain the Standard Model to a general audience compartmentalize the two subjects. Quantum num- faces many pitfalls; Penrose does not sidestep all bers are introduced in the chapter on the geome- of them. Consider, for example, the discussion of try of complex numbers, gauge connections ap- hadrons in The Road to Reality. Hadrons are, by de- pear in the chapter on fibre bundles, and, in the finition, the particles that interact through the other direction, Hilbert spaces, unitary operators, strong nuclear force. On page 101, Penrose intro- and spherical harmonics are found in a chapter on duces them in this way: “…the modern viewpoint quantum theory. Another reason for the smooth in- [is] that the ‘strongly interacting’ particles known tegration of mathematics and physics is that Pen- as hadrons (protons, neutrons, π-mesons, etc.) are rose speaks with the voice of a mathematical physi- taken to be composed of quarks.” It is a short ex- cist: even when topics from physics are not entirely cerpt that is laced with trouble for the newcomer: familiar to us, the method and language of pre- • Commas should delimit the participial clause; sentation are. For the selective reader, navigation as rendered, Penrose’s statement implies that the between mathematics and physics is facilitated by set of hadrons does not contain the set of the extensive collection of forward and backward strongly interacting particles. This confusion is references. The reader who has skipped over a bit not entirely resolved 500 pages later when Pen- of mathematics to speed ahead to the physics will rose’s next description of hadrons allows them

JUNE/JULY 2006 NOTICES OF THE AMS 663 to be a proper subset of the strongly interact- out this summary with a great deal of additional ing particles. detail. Penrose, on the other hand, dispenses with • Including the π-mesons in a list of familiar par- these matters in a mere two paragraphs, which he ticles intended to anchor the concept of hadrons finally presents more than one-third of the way into is counterproductive: the quoted extract is the the chapter. Standard expositions of the Big Bang only indexed entry for π-mesons. The problem walk the reader through the stages of the cooling propagates when, without explanation, Penrose universe from Planck time to the present. Penrose uses the alternative terminology, pions, the next does not. The notion of “freezing out” appears four times he mentions π-mesons (pages 436, briefly in his chapter on the Standard Model but 437, 494, and 628). The definition of meson fi- its role in the evolution of the early universe is not nally appears on page 646, but it is not indexed. made clear. For that matter, neither nucleosyn- • The subatomic particles represented by “etc.” are thesis nor star formation finds its way into The not revealed until 500 pages later. Road to Reality. There is a brief discussion of stel- • The use of the phrase “are taken to be com- lar evolution but it serves only to describe the cre- posed of” rather than the more concrete “are ation of black holes. By and large, the chapter fo- composed of” is baffling. The sentence has cuses on the thermodynamic puzzles of Big Bang begun not with “the fact is” but with the equiv- cosmology that Penrose has raised and studied ocating “the modern viewpoint is”. Why is fur- since the 1970s. While it is good to have an expert ther hedging necessary? present mysteries of the universe that have occu- • The assertion of the quoted excerpt, repeated on pied his thoughts for three decades, the downside page 645 as “All hadrons are taken to be com- is that readers will have to look elsewhere if they posed of quarks,” is contradicted when Penrose want to understand how the reality we now expe- later states that each meson is composed of one rience emerged from a plasma of elementary par- quark and one antiquark. Additionally, glue- ticles. balls, which are believed to have been detected As I have suggested, The Road to Reality com- at BNL, CERN, and DESY, are quarkless hadrons prises three books in one. The third part, which is comprising only gluons. nearly as long as each of the first two, concerns The problems highlighted by the preceding dis- the road ahead. It is here that Penrose fully lives cussion are neither isolated nor uniquely Penrose’s: up to his reputation as a recusant among physi- several well-regarded elementary treatments of the cists. According to an idea of cosmology that is now Standard Model, such as [3] and [10], are, in places, generally accepted, at some instant of time no just as exasperating. Where Penrose bests other later than 10−12 seconds “after the bang”, the uni- popularizers is that he gets the reader closer to the verse underwent an “inflationary” period of expo- underlying mathematical structure. By discussing nential growth in which its size increased by a fac- gauge connections and symmetry groups in a non- tor of at least 1030. The theory was conceived in trivial way, he alone allows his readers to under- 1979 by Alan Guth as an answer to the magnetic stand why the Standard Model is also called the monopole problem that signaled a conflict be- SU(3) × SU(2) × U(1) theory. tween Big Bang cosmology and grand unified the- With the chapter called The Big Bang and its ther- ories. At first, inflationary cosmology appeared to modynamic legacy, Penrose concludes the second be yet another crazy theory. However, inflation re- part of The Road to Reality by sketching our pre- solved so many significant difficulties of conven- sent knowledge of cosmology. In outline, the Big tional Big Bang theory that it gained serious con- Bang theory of an expanding universe originated sideration in short order. Inflation has also won when Alexander Friedmann (1922) and, indepen- over skeptics by being a predictive theory that has dently, Georges Lemaître (1927), solved Einstein’s not been refuted by the observations that have equations of gravitation without adopting Ein- been made since its formulation. Additionally, in- stein’s initial hypothesis of a static universe. Edwin flation, if correct, would indicate the presence of Hubble’s discovery (1929) of the recession of galax- the long-sought hypothetical Higgs field at an ear- ies provided early experimental evidence for the lier time of the universe. As Leon Lederman, one Friedmann-Lemaître model. Nevertheless, the Big of the leading particle hunters, declared, “The as- Bang explanation for the expansion of the universe trophysicists have discovered a Higgs thing!” seemed to be just one more crazy theory—the Against this cheery backdrop, Penrose will seem name itself originated in the 1950s from a sarcas- to be a killjoy when he demurs that “there are tic barb that was uttered by a dissenting cosmol- powerful reasons for doubting the very basis of in- ogist. Beginning in 1964 when the cosmic mi- flationary cosmology.” crowave background radiation predicted by Big The controversy over inflation might have been Bang cosmology was detected, an overwhelming avoided, but it fits into the theme of the final por- body of observational evidence has confirmed the tion of Penrose’s book. His thesis is that there are theory. Conventional treatments of cosmology flesh too many inadequately explained phenomena for

664 NOTICES OF THE AMS VOLUME 53, NUMBER 6 us to be near the end of the road to reality. Most Expounding the creation of the universe and its pressing is the provisional nature of the Standard ultimate fate invariably turns an author’s mind to Model. Because this theory requires fundamental philosophy, theology, or some other contemplative constants of nature as input parameters, it de- outlet. Penrose neither ponders why there is some- scribes the reality of a different universe just as con- thing rather than nothing nor engages in what sci- tentedly as it describes our own. That the values ence journalist Timothy Ferris terms God- of the fundamental constants now seem arbitrary mongering. Instead, The Road to Reality concludes and not prescribed is, presumably, a defect of our with a chapter in which Penrose muses upon beauty present knowledge. Of even greater concern is the and miracles, mathematically driven physics, the conflict between quantum theory and general rel- function of falsifiability in scientific theory, and the ativity in those realms where they should both role of fashion in physical theory. In the last of these apply. Until some verifiable theory of quantum topics, Penrose addresses the stam- gravity appears, we must consider ourselves far pede that is taking place along the from the road’s end. Indeed, there is now a fork in string theory road to quantum gravity. the road that has caused an often contentious de- Bandwagon effects, he worries, are bate over the correct continuation. Penrose de- drawing an ever increasing number of votes a chapter to each of three possible paths to theorists down a path he suspects to quantum gravity: string theory, loop variables (LQG), be a dead end. Penrose is also troubled and his own twistor theory. (These approaches are by the curious jawboning that marks also discussed, at a more elementary level, by Lee the landscape. If you have already in- Smolin, a proponent of LQG, in Three Roads to vestigated string theory, then it is likely Quantum Gravity [8]. Given that string theorist that you are acquainted with the slo- Brian Greene’s recent book [1] has a section titled gan, “String theory is the only game in Roads to Reality, we infer that there is at least town.” One well-known string theory agreement about the metaphor that is to be used.) textbook, quoted by Penrose, dismis- Penrose may have taken off his gloves in the sively pronounces, “There are no al- chapter on inflationary cosmology, but it is in the ternatives…all good ideas are part of string theory chapter that bare-knuckle fisticuffs string theory.” Similarly, the author of break out. In the first paragraph of the chapter, Pen- a new book on string theory declares [9, p.357], “As rose writes, “Very few [physicists] appear to an- much as I would very much like to balance things ticipate that there will be fundamental changes in by explaining the opposing side, I simply can’t find the framework of quantum mechanics. Instead, that other side.” Overwhelmingly outnumbered, they argue for strange-sounding ideas like the need Penrose can do no more than remind us that, “With for extra dimensions to spacetime, or for point ideas that are as far from the possibility of exper- particles to be replaced by extended entities known imental confirmation or refutation as those in as ‘strings’.” Five sections later, the rhetoric esca- quantum gravity, we must be especially cautious lates: “To its most extreme detractors, [string the- in taking the popularity of an approach as any real ory] has achieved absolutely nothing, physically indication of its validity.” The mathematician who so far, and has little chance to play any significant peers in, unable to take sides, will begin to appre- role in the physics of the future.” Although the ciate the hard-liner’s position: This is what comes reader may suspect that Penrose is not putting of debating philosophy. words in other detractors’ mouths, he allows only A very long book is almost certain to generate that he is “less than positive about a good many some annoyances. For me, the professionally com- aspects of the current string-theory programme”. piled yet abysmal index of The Road to Reality Unlike the theoretical objections to string theory proved to be an enduring irritant. The electron that Penrose raises, many physicists object on prin- neutrino’s rest mass m (νe) makes a good case in ciple: their tradition is to dismiss theories not point. Determining the value of this parameter, tested by experiment as either philosophy or reli- and, in particular, establishing that it is nonzero, gion or mathematics. In his recent book on parti- is of great current interest. Penrose introduces cle physics [10, p. 308], Nobel laureate Martinus neutrino mass on pages 636 and 637 and then Veltman expresses his justification for omitting provides an upper bound for m (νe) on page 872. string theory and supersymmetry with language However, this second discussion has no index entry that is as blunt as Penrose’s: “The fact is that this and the first is indexed only under the misspelled book is about physics, and this implies that the the- nutrino. Another source of frustration is the hap- oretical ideas discussed must be supported by ex- hazard handling of the physicists behind the perimental facts. Neither supersymmetry nor string physics. Many of their given names are reduced to theory satisfy this criterion. They are figments of initials, and some physicists are not even accorded the theoretical mind. To quote Pauli: they are not that much: James Cronin, Val Fitch, John Clive even wrong.” Ward, and George Zweig rate neither a first name,

JUNE/JULY 2006 NOTICES OF THE AMS 665 nor an initial, nor an index entry. Other physicists and the unity with which he conveys the essential are entirely invisible. Thus, we learn about the developments of twentieth century physics. In his Stern-Gerlach apparatus, but we do not encounter review, Wilczek cites “serious blunders”, drawing the two eponymous pioneers of quantum theory, attention to three. These problems, perceptible Otto Stern and Walther Gerlach. Indeed, when a only to sophisticates of physics, should be placed prominent physicist is mentioned, it is often only in perspective with a particular audience in mind. by chance. Eugene Wigner, for example, makes two If Penrose brings his typical reader to the level of tangential entrances, but not in the chapter that understanding the concepts that compose the dis- contains the circle of ideas once known as Wigner- puted statements, then he has done a service in ism. comparison to which the impact of his occasional Though these cited complaints are genuine, they miscues pales. do seem niggling when considered alongside the For mathematicians with a general interest in astonishing scope of Penrose’s endeavor. The rel- physics, Penrose’s book will be self-recommending. atively few lapses that have been mentioned are not Other mathematicians may find it useful to scan evidence of general carelessness. Given its length, The Road to Reality, if only to glimpse the extent breadth in both mathematics and physics, and its to which mathematical constructs infuse theoret- eight year gestation, The Road to Reality must be ical physics. There are a great many competing deemed extraordinarily accurate and coherent. If books that seek to explain the state of the art in any nontrivial grievance is to be found, then I think fundamental physics. If you compare Penrose’s we must look to an imbalance between the math- work to any of the recent ones ([6], [7], [9], for ex- ematical description of physical law and the pre- ample), then you will understand a reviewer’s in- sentation of observational support for it. Figments of the theoretical mind are part and parcel of math- clination to hold The Road to Reality up to the ematics, but when it comes to separating the crazy highest standards, for it is, indeed, sui generis. theories that represent physical reality from the And that makes my bottom-line recommendation crazy theories that are just plain crazy, we rely on a cinch. For anybody who wants to learn up-to-date empirical facts for conviction. Even Dirac, anti- physics at a level between standard popularization electron equation in hand, hesitated to predict an- and graduate text, The Road to Reality is the only timatter. (As he later said, “The equation was book in town. smarter than I was.”) Penrose’s concentration on theory is perhaps best illustrated by his omission References of CERN’s Large Hadron Collider, which is sched- [1] BRIAN GREENE, The Fabric of the Cosmos, Knopf, 2004. uled to begin operations in 2007, from the chap- [2] LILLIAN HODDESON, LAURIE BROWN, MICHAEL RIORDAN, and ter titled Where lies the road to reality? To obtain MAX DRESDEN, The Rise of the Standard Model: Particle viewpoints drawn from the experimental side of Physics in the 1960s and 1970s, Cambridge University Press, 1997. physics, readers can supplement The Road to Re- [3] GORDON KANE, The Particle Garden, Basic Books, 1995. ality with the excellent books ([4], [5]) of Leon Le- [4] LEON LEDERMAN with DICK TERESI, The God Particle: If the derman and Don Lincoln, both of Fermilab. Refer- Universe Is the Answer, What Is the Question?, ence [2] is an especially valuable resource containing Houghton Mifflin, 1993. articles written by many of the experimental and [5] DON LINCOLN, Understanding the Universe from Quarks theoretical physicists who contributed to the Stan- to the Cosmos, World Scientific Publishing Company, dard Model. 2004. The Road to Reality was published in Great [6] ROBERT OERTER, The Theory of Almost Everything: The Britain and discussed by critics prior to the re- Standard Model, the Unsung Triumph of Modern lease of the American edition. Before Penrose’s Physics, Pi Press, 2006. Road came into my hands, I was familiar with sev- [7] LISA RANDALL, Warped Passages: Unraveling the Mys- eral reviews that damned it with faint praise. Typ- teries of the Universe’s Hidden Dimensions, Harper- ical of the bottom-line assessments is this one Collins Publishing, 2005. from Nobel laureate Frank Wilczek [11]: “There’s [8] LEE SMOLIN, Three Roads to Quantum Gravity, Basic much to admire and profit from in this remarkable Books, 2001. [9] LEONARD SUSSKIND, The Cosmic Landscape: String The- book, but judged by the highest standards The ory and the Illusion of Intelligent Design, Little Brown, Road to Reality is deeply flawed.” With such criti- 2006. cism in mind, I approached my reviewing task ap- [10] MARTINUS VELTMAN, Facts and Mysteries in Elementary prehensively. As I progressed through the first few Particle Physics, World Scientific Publishing Company, hundred pages, unconvinced by Penrose’s con- 2003. ception, I found myself thinking nothing kinder [11] FRANK WILCZEK, Review of The Road to Reality: A Com- than The Road to Reality is paved with good inten- plete Guide to the Laws of the Universe, by Roger Pen- tions. And yet, all my misgivings eventually yielded rose (Jonathan Cape, London, 2004), Science 307 (11 to the sheer quantity of Penrose’s valuable insights February 2005), no. 5711, pp. 852–853.

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