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

This work is a masterpiece and belongs on the shelf of any aspiring mathematician or physicist. It is very lucid in the prose and extremely well organized. One of the other reviews states that there is a 900 page introduction to physics that is already known (to paraphrase). That's not how I read it. This work intertwines the history and culture of physics, the dilemma of mathematical "beauty" in the face of experimentation (which is an ongoing theme; i.e., see Sabine Hossenfelder's "Lost in Math"), and the pure hard sciences and theory that have brought us this far. The introduction of mathematical and physics formulae in the text is something that other authors have grappled with (such as Brian Greene's "The Elegant Universe"). It is all there. Read as deeply as you wish. Then, pick it up in a couple of years and read it even deeper. I view this as a timeless work from one of the brightest minds in the field.

As it happens, I'm an inhabitant of mathematical Slowland (somewhere between the author's level 1 and level 2 on what is an exponential scale of mathematical knowledge), but this book's preface charmed me into attempting a pilgrimage down "The Road to Reality," even though--or perhaps because--it has lots and lots of math. What is the lure Sir Roger uses in his preface? A profoundly simple explanation of fractions! I've always longed to find a 'Summa Philosophiae Naturalis' that wove together all the physical and mathematical strands of my education. Maybe this will be that 'summa' after its contents finally sink in (it will take multiple readings.) If not, there was still plenty of shock and awe on Sir Roger's Road to Reality. This author has the special gift of making his readers feel the beauty of scientific ideas through mathematics. Many of the books that have been published recently on the physical mechanisms of our Universe have been a little misty in this respect, probably for fear of losing readers. Not so Penrose. After a benign preface and opening chapter, his 'Royal Road' plunges his readers head-first into hyperbolic geometry. If it weren't for the Escher woodcut and its subsequent transformations, I might not have plunged in after him. As it was, I almost sank out of sight upon encountering Contour Integration in chapter 7. It was a long, hard 400-page slog to Minkowskian Geometry (chapter 18), after which the heavy physics finally kicked in. Extended side-trips into James R. Newman's classic "The World of Mathematics" were what saved me and kept me chugging through the first half of 'Reality.' I found I needed a bit of historical perspective on topics such as Riemann spheres, that Sir Roger necessarily had to explain in a formula and a paragraph--unless he wanted his book to bulk up into multiple volumes. So I highly recommend a supplemental mathematical source such as Newman for the parts in Penrose where you WILL get stuck in the Slough of Despond. Yes, friends, unless you belong to the author's level 4 mathematical elite you will flounder, but throughout your struggle, beautiful fireworks will be going off over your head: a promise of the grandeur to come. This book is full of glorious explosions, especially when the author is discussing a discrete, rather than real-numbered-base to physics: "Einstein, also, suggested, in his last published words, that a discretely based ('algebraic') theory might be the way forward for the future physics..." Wait a minute! Does that mean I should flush my 23 semester-hours of calculus down the same toilet that swallowed up phlogiston and Piltdown Man? Not at all. Penrose includes reams of calculus in this book, for those of you who like to twiddle around with infinitesimals. But do pay attention to the notion of a discrete reality. In the latter, 'physics' section of the book, Sir Roger refers back to discreteness when he discusses his twistor theory of Everything-

While this book is essentially an elaboration of Penrose's earlier books and theories, it appears it was worth the effort (both his and the readers). I agree with reviewer Lee Carlson's comment that "The chapter on the Big Bang and its 'thermodynamic legacy' is the best in the book", though experts in other fields may enjoy (or be challenged) by other chapters. In his chapter 27 on thermodynamics, Penrose seems to finally 'bury' dissenters who believe there is nothing unique or improbable about the universe. For instance in Vic Stenger's attack in his book Timeless Reality he says: "The initial entropy of the universe was also as large as it could have been, since it was also the entropy of a black hole. Thus, the universe has maximum entropy at the two extremes on the time axis. In each case, the universe is in equilibrium. At each time, the univserse is in a static state of total chaos. This is a point that has been missed by almost everyone, including Penrose." [Referring to his earlier book The Emperor's New Mind.] In his recent book Penrose counters: "Now let us return to the extraordinary 'specialness' of the Big Bang. The fact that it must have had as absurdly low entropy is already evident from the mere existence of the Second Law of thermodynamics. But low entropy can take many different forms. We want to understand the particular way in which our universe was initially special...It seems to me that this apparent thermal equilibrium in the early universe has grossly misled some cosmologists into thinking that the Big Bang was somehow high entropy 'random' (i.e. thermal) state, despite the fact that, because of the second law, it must have actually been a very organized (i.e. low entropy) state. A prevalent view seems to have been that the resolution of this paradox must lie in the fact that, soon after the Big Bang, the universe was 'small' so that comparatively few degrees of freedom were available to it, giving a low 'ceiling' to possible entropies. This point of view is fallacious, however, as was pointed out [earlier]. The correct resolution of the apparent paradox lies in the fact that the gravitational degrees of freedom have not been thermalized along with all of those matter and electromagnetic degrees of freedom...In fact, these gravitational degrees of freedom -providing a huge reservoir of entropy -are frequently not take into account at all...Rather than sharing in the thermalization that, in the early universe, applies to all other fields, gravity remains aloof, its degrees of freedom lying in wait, so that the second law would come into play as these degrees of freedom begin to become taken up. Not only does this give us a Second Law, but it gives us one in the particular form that we observe in nature. Gravity just seems to have been different!...physicists have tried to come to terms with this puzzle and related ones, concerning the origin of the universe. In my opinion, none of these attempts comes at all close to deali

It is clear that I love books, learning, and just the simple act of reading. While there are whole sections of the bookstore I will never enter, I do read rather broadly. Even so, there are some books that I find so stunning that I marvel to even hold them in my hands. This book, "The Road to Reality" by Roger Penrose is one of those books. It is a wonderful achievement and a gift to every one of us. It has a breadth to it that is quite unique. No matter how specialized you are, even if you have a Ph.D. in mathematics, this book covers so many topics that you will find yourself reading as a generalist saying to yourself, "Yeah, that's neat, I always wanted to learn a bit more about that." And while there is much there for the advanced specialist, it is written in such a way that a person with just an ordinary exposure to mathematics can ignore the math notation (equations) and still get a huge value from reading the text. This book allows you to dip into it here and there without having to read it front to back. If the ordinary book on cosmology is like taking a trip across an inland lake in a boat, this magnificent volume is like having an ocean to explore. There is a wonderful primer on the roots of science, an exploration of the mathematics based on the Greeks, number theory, logarithms, various forms of calculus, Fourier hyperfunctions, hypercomplex numbers, symmetry groups, and then on to physics. Penrose gives us the basics of spacetime, 4 space geometry, Lagrangians and Hamiltonians, quantum particles, quantum algebra, the standard model of particle physics, quantum field theory, an examination of the Big Bang and other speculative theories of the early universe, gravity, and much more. He ends with a wonderful section on "Where lies the road to reality". I particularly admire his modesty in stating his feeling that we are not "just about there" in wrapping up physics and that our current best lines of thinking may all indeed be dead ends. Nevertheless even the dropping of a theory represents an advance in knowledge. You can spend years with this book and should. There are probably four audiences for this book. The advanced specialist who wants to read in areas connected to but other than his expertise, the student (or teacher) who wants to get some context for and supplement to their studies, the generalist (like me) who loves the challenge of learning new things and exploring challenging thought, and someone who simply values having something marvelous on their bookshelf in the odd chance that having all this wonder in one volume might prove valuable one day. While I could only give "The Road to Reality" five stars, I really view it as a six star event. I recognize that this book is not for everyone, but if you enjoy intellectual mountaineering this is a wonderful peak to climb.

The stunningly ambitious subtitle to Penrose's latest gift to the world, "A Complete Guide to the Laws of the Universe", is at one and the same time tongue in cheek, since Penrose is cheerfully aware of how far we are yet from knowing the deepest laws of the universe, and perfectly serious, since Penrose wants to equip the diligent reader with the tools to understand all the central issues at the frontiers of 21st century physics. The key word here is "diligent". How tough is this book? For anyone with three or four years of university math under their belt, it will be pretty straightforward going, with tons of beauties and "ah-hahs" along the way. Penrose aims to provide the central intuitions, and not get bogged down in petty details. As one of a handful of the world's premiere mathematical physicists, he has a firm (and all the more valuable for being slightly idiosyncratic) grasp on what is truly central, and that lets him condense his enormous subject into a mere 1040 pages. He provides just enough in the way of exercises, unobtrusively tucked into footnotes and handily classified as easy, medium, and hard, to let you check that you are really following along. When dealing with tensors and bundles, which are the language of general relativity and of all the unified theories, he takes care to say most things three times: in the coordinate free language preferred by mathematicians, in the "Einstein summation convention" language preferred by physicists, and in his own diagrammatic notation; so he gives you three chances to get it. His intent is to be accessible to anyone who isn't mathphobic. A determined reader with a rough grasp of basic calculus concepts is likely to find he has achieved that intent. The learning curve is steep, but all the steps are in place. If you've read any two of Penrose's "Emperor's New Mind", Green's "Elegant Universe", and Hawking's "Brief History of Time", and found them stimulating rather than daunting, then you're ready to tackle this one. The book deals with all the mathematical machinery it will need in the first 300-odd pages. Relativity follows, then quantum theory, then particle physics and quantum field theory, then cosmology. Penrose always has a fresh perspective, spending a few paragraphs to take a step or two back for a broader, more philosophical view of the territory than the textbooks offer; but all this material, up to page 780, has become standard physics. Then the pure fun begins. Roger Penrose has never allowed his considerable stature to get in the way of the pleasure of contrarianism, and his take on the Big Kabloona Question, how to reconcile quantum mechanics with general relativity, is as well defended as it is unusual. His longest chapter respectfully spells out the details of the most popular approach to a unified theory, that of strings and branes. But he has always been skeptical of string theory, not just on grounds of verifiability, but also because he feels it fails to involve c