* Astronomy

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Roger Penrose’s new book Road to Reality: 'A Complete Guide to the Laws of the Universe.'
Reviewed by Joe Kauzlarich.

Flipping through the eleven-hundred pages, you notice the gratuitous inclusion of mathematical formulae and the chapter titles on the page headers -- "Quantum algebra, geometry, and spin," "Gravity's role in quantum state reduction," "Calculus on manifolds" -- suggest a far more exclusive audience than yourself, a lowly paper-pusher with a four-year degree.
"But then, what's this doing in the popular new releases?" you ask yourself, "Shouldn't it be hidden away in the darkened corner of the store's physics section?" But that's where you're wrong, you realize, glancing through the author's preface; this book is for you: Penrose has, it seems, composed a mathematical physics book for the general audience -- and not merely an introductory one, but one that takes you to the frontiers of modern theory.
The trouble with the common popular-science books that propose to illustrate modern physical theories is in their implicit premise of avoiding mathematical notation and concept in favour of plain English. This works to an extent, but ultimately breaks down when the nature of the subject matter itself is mathematical. Indeed, after reading the wonderful Dancing Wu Li Masters, the reader is no more prepared to plunge into a textbook on modern physics or to comprehend even the titles of the latest mathematical physics papers on Arxiv.org. Physicists know about the fundamental particles or the nature of space only through the mathematics that model the phenomena. Which is not to say that such English language renderings are useless, but they skilfully devise to distance themselves from what physicists actually do, as well as to reinforce readers' natural aversion to numbers and formulae.


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Penrose's approach is not to dive head-first into the most strenuous material or to assume a proper background for the comprehension of advanced physics; instead, the first several chapters are devoted to building the necessary mathematical subtext for the remaining bulk of the book. The volume's length is not, as is often the case, a result of lengthy diversions or pedantry (needless complexity); Penrose keeps his eye on the ball throughout, consistently informing the reader how the topic at hand is related to the over-arching theme and infusing the more well-known pedagogy with creative insight, so that even a talented math major may learn from the introductory chapters on number systems or geometry. What's more, the careful organization of the disparate topics permits a fluid drift from one to the next. The effect is a single cohesive book and not a collection of notes or essays.
With 390 illustrations and a generous supply of endnotes and bibliography entries, it's clear that Penrose didn't consider the work completed with the text alone. The inclusion of short problems within the footnotes hints to the reader what concepts are important to understand. The usual footnote-commentary is withheld for the endnotes at the end of each chapter.
It's probable that the name "Roger Penrose" might excite some memories you may have of his previous works, published over a decade ago, both of which explore the mind-brain relationship. At least one of these (Shadows of the Mind -- the other is the more popular The Emperor's New Mind) proposes a quantum theoretical explanation for consciousness which was perhaps too liberal to have been taken seriously by neurologists. Penrose's efforts in quantum theory have, however, been more successful than those in neurology: in 1988 he was awarded the Wolf Prize, one of the very highest honours in mathematics (perhaps second only to the Fields Medal), along with Stephen Hawking, and has made invaluable contributions to quantum physics for the past several decades, proving himself to be one of the finest scientific minds of our day. In consequence to his stature, it's certainly a treat for laypeople that Penrose has donated the time and energy to the creation of a monumental expository work for general consumption.
Whereas the average pop-science journalist reaches upwards to accrue a book's material, Penrose's acknowledged expertise on the subject forces him back towards the ground again. If you think about it, I suppose this is as difficult a task, since much of what Penrose describes he's known for forty or fifty years (he was born in 1931). He apologizes in the final chapter for the necessity of handpicking among the dozen or so "theories of everything," sometimes according to his own professional biases. Today's leading theory, "String theory" along with the theory of "Loop Quantum Gravity," and the little known "Twister Theory," are all covered in the later chapters; the first portion of the book builds the mathematical foundations for the succeeding chapters, which give an in-depth treatment of quantum physics and quantum field theory. These topics are followed by the previously described "theories of everything."
A glance at the table of contents may make or break your purchasing decision; chances are, if you find the mysteries of the terms somehow galvanizing, then you'll enjoy the book. On the other hand, if the eclectic terms frighten you, you should perhaps look at the preface (where Penrose gives solace to anxious readers), or it may be best to avoid the book altogether.
As I mentioned earlier, little has been done for the general audience to explore the wide expanse between physics and mathematics. The Road to Reality is, in this respect, a virtually pioneering effort, and given its size, scope and quality, I would venture to guess it will remain the de facto text in its area for many decades to come, and may safely be placed on your bookshelf next to E.T. Bell's Men of Mathematics, Douglas Hofstadter's Gödel, Escher, Bach, or Benjamin Yandell's recent (*highly* recommended) The Honour’s Class: Hilbert's Problem's and Their Solvers.
I am fortunate to have had some mathematics education and so am familiar with the basic principles of complex numbers, calculus, and geometry, making the first several chapters, while still insightful, less toilsome than it might've been. I suspect that the average bright high school graduate would have no trouble with Penrose's quick treatment of these concepts. I would recommend the reader have at least some familiarity with the basic terms of mathematics and physics (i.e. when Penrose mentions "set" you know he's referring to a particular mathematical structure) or the book could overwhelm you quickly. Additionally, readers would be at an advantage having read "English-based" modern physics books such as The Dancing Wu Li Masters, Michio Kaku's Hyperspace, Brian Greene's The Elegant Universe or a similar book about 20th century quantum physics. Either way, it's safe to say that despite the virtuosic readability of the text, it's still going to take an intellectual commitment on the part of the reader to reap all of the available knowledge."
FROM THE PUBLISHER
"What Roger Penrose accomplishes in this book is threefold. First, he gives us an overall narrative description of our present understanding of the universe and its physical behaviours - from the unseeable, minuscule movement of the subatomic particle to the journeys of the planets and the stars in the vastness of time and space." "Second, he evokes the extraordinary beauty that lies in the mysterious and profound relationships between these physical behaviours and the subtle mathematical ideas that explain and interpret them." "Third, Penrose comes to the arresting conclusion - as he explores the compatibility of the two grand classic theories of modern physics - that Einstein's general theory of relativity stands firm while quantum theory, as presently constituted, still needs refashioning."
Along the way, he talks about a wealth of issues, controversies, and phenomena; about the roles of various kinds of numbers in physics, ideas of calculus and modern geometry, visions of infinity, the big bang, black holes, the profound challenge of the second law of thermodynamics, string and M theory, loop quantum gravity, twistors, and educated guesses about science in the near future.

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Listen to 20 minute interview with Penrose (available in RealPlayer and Windows Media streaming formats)



-- Edited by Blobrana at 23:08, 2005-05-11