BOOK REVIEW

The Whole Megillah

The Road to Reality: A Complete Guide to the Laws of the Universe. Roger Penrose. xxviii + 1099 pp. Alfred Knopf, 2004. $40.

Roger Penrose's latest book, The Road to Reality, is so generous in scope that it is difficult to absorb the breadth of its offerings. The text will seem gloriously variegated to some readers but frustratingly inaccessible to others. It's a physically huge book, but every ounce of the content was designed with great care. There is no single road here, though; rather, Penrose has provided a bundle of interlaced narratives that must be teased out by the reader.

The first half of the book is devoted to mathematics and the second to physics. The math portion is pure delight. Penrose starts with the simplest ideas, such as counting, and builds gradually, with great care, until he has taught us most of the kinds of math that physicists wield these days (covering, for example, Riemann surfaces and complex mapping, hypercomplex numbers, manifolds of n dimensions, symplectic groups and tensors). It is simply astounding that he has accomplished this feat. He does invoke equations, but they are perfectly chosen for explanatory power and simplicity.

Reading this math section is eerily liberating. It is shocking that so much can be explained so well. The obvious comparisons are to The Feynman Lectures on Physics or George Gamow's One, Two, Three . . . Infinity, but the achievement here is greater, because the book starts at such an elementary level and soars to such heights, without any glitches along the way. It's a magical escape from the bounds of gravity.

All readers will profit from being swept upward by Penrose, even if only for a fraction of the journey, and beginners will be amazed at how far Penrose can take them. Even so, it's unlikely a novice reader will get through more than perhaps the first hundred pages of the book without help.

Mathematicians will find Penrose's unconventional presentations of familiar ideas amusing and will be introduced to new gems and curiosities. Computer scientists and other technical readers who haven't used this sort of math since school days will enjoy both the review Penrose provides and the overview of recent advances.

The first half of The Road to Reality can be read as a love story about a little boy who adored numbers—especially complex numbers—like life itself, and who never grew up. Penrose's warm, funny temperament comes across in an understated way, and the reader is able to feel a little of what it would be like to have his superlative mathematical ease and intuition. There is a sense of drama as modern mathematics is reconstructed. An early brush with true love is depicted when Penrose explains in an utterly simple way why the "almost mystical" formula -1=e^iπ is true. Consummation awaits in the chapter about hyperfunctions.

Penrose uses illustrations frequently. Peculiar yet perfect, the drawings in some cases look as though they might have been sketched by the underground comic artist R. Crumb. Unlike the sterile draftsman's renderings usually seen in math books, these drawings present metaphors. Some of the sketches depict the cute mental mnemonics that Penrose employs to keep ideas clearly in his mind. When he shows us a little bubble universe with assorted junk flung about, bursting out of a representative point in a potato chip-like configuration space, we know he has shared an intimate thought with us.

Penrose takes absolutely nothing about numbers for granted. For example, he expresses profound doubts about the most basic counting numbers and wonders whether aliens might find a different way to be mathematical. This attitude comes as no surprise, because he has had one of the most eccentric careers in the sciences, combining superlative contributions to physics and mathematics with excursions into philosophy and speculative neuroscience. The constant returning to first principles may not be to everyone's taste. For Penrose it is a source of inspiration and part of a quest for clarity, whereas for others it might come off as an ivory-tower indulgence. I loved it.

The Road to Reality is the lifetime statement of a devoted thinker who has defied the mainstream and can cast powerful if unusual light on a canon of familiar thoughts. I was reminded of Camille Paglia's Sexual Personae: Art and Decadence from Nefertiti to Emily Dickinson. Both are big books that at turns amaze and infuriate many readers.

To get to the infuriations, we must turn to the second half of the book, which is devoted to physics. This portion reads more like a suspense novel than a romance. Right at the end the reader becomes aware of elaborate setups put in place hundreds of pages back, in anticipation of the spectacular climax—the unveiling of Penrose's best shot at promoting further research into his twistor theory. Despite that structure, this second ascent to the heavens from scratch is almost as smooth and inviting as the brilliant math presentation that precedes it. The big difference is that here Penrose is giving us a tour of controversies, and he's in fighting form.

Penrose veers into irony in the lengths to which he goes to point out where his ideas deviate from the mainstream. He is then excruciatingly polite as he eviscerates concepts he believes to be overrated, such as string theory and M theory. Why all this high drama? Through no fault of Penrose's, theoretical physics has become a rough sport lately. Heated debate is nothing new—one recalls the immortal put-down attributed to Wolfgang Pauli: "This isn't even wrong." And yet something new does seem to be happening, in that a mob mentality is taking hold.

For those who haven't been keeping score, here's a very quick summary: Quantum field theory and the theory of general relativity have such superb power that no experiment yet has shown a crack in either of them, even though they both predict wildly counterintuitive properties in physical reality. And yet the two theories seem to be deeply at odds with each other, which suggests that there must be some other as-yet-unknown theory that incorporates them both in a consistent way, a theory of quantum gravity. It is fervently sought. The mainstream, and extremely cocky, school of thought is that string theory or M theory is inevitably going to be accepted as this unifying theory.

The second-most-studied approach is loop quantum gravity. There has sometimes been an almost thuggish dismissal of it by the string crowd. As it happens, loop quantum gravity makes extensive use of some of Penrose's ideas, such as spin networks. Penrose, however, has been most identified with yet a third approach, twistor theory, which was intensely studied in the late 20th century but has been on a back burner for most physicists lately, although not for Penrose. This makes him twice the outcast, yet he is still one of the most creative and productive individuals in his field.

A quick look at responses to Penrose's book on the Internet turns up some—a noisy minority—that are shockingly negative in tone. Science is always under siege by charlatans, and theories of gravity are among the most attractive to con artists and self-deceiving megalomaniacs. But to dismiss someone like Penrose in harsh tones is to diminish the power of such language when it is applied to more appropriate targets.

One gets the impression that some physicists have gone for so long without any experimental data that might resolve the quantum-gravity debates that they are going a little crazy. If that's the problem, help is on the way, because measurements of cosmic background radiation and ingenious new experiments will soon present a new generation of physicists with beguiling data.

Why did Penrose put all these elements together into such a big book? His presentation of the whole megillah makes a point that, had Penrose stated it explicitly (which he does not), might have gone something like this: "I'm going to bypass the physicists who have succumbed to a mob mentality and make my case by addressing everyone else—whether they have the technical background to understand me or not. None of us really knows what the right theory of quantum gravity will turn out to be, and unfortunately it's hard to do experiments, so we'll have to be patient to work this out. But in the meantime, just look at what a creative thinker I am and how productive I've been, despite my inclination to explore the unusual. The fact that I can explain my ideas to novices also shows that I am thinking clearly. Are you really ready to close your mind off and believe those string people, who are so sure of themselves? None of us has real evidence, but I'm the kind of guy you want to pay attention to." I found him persuasive.

Finally, Penrose presents us with a cosmic, romantic sense of human history fused with his technical autobiography. To him, the great adventure of history is the quest to understand what is going on in this weird reality we find ourselves in, and his personal story is that same quest in miniature. The book opens with a fantasy about an artisan in ancient Egypt who wonders about the cosmos, and it closes with another fantasy, about a young woman sometime in the future who is on the verge of the next big intuition about quantum gravity. Penrose gives us something that has been missing from the public discourse on science lately—a reason to live, something to look forward to. After all, why should religious types be the only ones to offer this? One of the problems with the pompous triumphalism of string theory is that it suggests a premature decrease in mystery. One can practically hear Peggy Lee singing "Is That All There Is?" If it's true that that is all there is, that message would be fine, but Penrose makes a persuasive case that we are still surrounded by a sea of inviting mystery.

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