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

The short version: If you are reading reviews in consideration of purchasing this book then just BUY IT. It has long been my wish for someone to a write a popular treatment of modern physics, one which includes the math, starts at the beginning, and then covers whatever is needed so that the reader can understand the theories described. For me, reading physics is fun; it is not a path to "becoming a physicist", but I want something beyond the popular science level. My goal is to become a READER of real physics, and I am willing to work to reach this goal. This wish describes "The Road to Reality" almost perfectly. Penrose literally intends to take the reader from basic math through calculus, and on to field theory, Lie Groups/Algebras, calculus of variations (Lagrangians & Hamiltonians), differential geometry with fiber bundles, and tensor analysis. He plans and prepares to explain both quantum physics and general relativity (gravity.) This book is both a popular science guide and introductory mathematics text (including introductions to advance subjects) at the same time. The book is a wondrous delight, while simultaneously being maddening for its flaws. If there were there a thousand similar books, it would be easy to criticise the flaws. The writing is at times simply awful (the worst and most common offense is 'pre-shadowing' for no useful purpose -- and without clearly warning the perhaps already struggling reader). Much of the math details are simple skipped or hand-waved, but the outline and structure provided for mathematical physics is both useful and significant With great persistence by the reader it is understandable. One reads this book both for what it contains, and also for the gateways it will open to other books. The book likely deserves only four stars, but due to it's unique nature I awarded the fifth as a reward for attempting and coming very close to what most would consider impossible. On the other hand, any criticism that it is "incomplete" (the subtitle says the "complete guide to the laws of the universe") is unrealistic and similar to criticizing a "complete guide to Europe" or "a complete guide to fishing" for not listing every hotel or restaurant, or for not including a picture of every fish and a map of every body of water. 'Complete' here means comprehensive and full in coverage and scope, not that every detail is specified. As to criticisms concerning Penrose's idiosyncratic views on physics, he is ABSOLUTELY clear when stating a personal opinion, or covering topics from his own point of view. His own less popular ideas for final theories in physics are a very small portion of the entire book. Pensore clearly delineates his own ideas whenever he mentions them in other sections. [A little about me, but only as a point of reference, might help you evaluate this review since those with significant college math and physics or those with no background in these subjects will approach this book differently: My prior background only includes high school calculus and physics, though I've read many popular physics titles. At the start, I was mathematically naive at the university level, but I was also completely undaunted by the prospect of learning the math and physics.] If you buy this book [highly recommend you do] just read it. Promise yourself that you will keep reading; determine to force your way through no matter what obstacles you encounter. If you have an interest in physics the rewards are immense. Using the book as a tour guide, outline, overview, and foundation you can find resources freely available on the Internet, or available for sale here on Amazon, to actually LEARN to READ physics. You should not expect to "become a physicist" without much more study, but you can develop a reading knowledge of the subject beyond the popular treatments, including the mathematics of tensor analysis, differential geometry, and group theory. An encouragement and warning to young people interested in Physics and Math (as well as those who might buy this book for them) is warranted: If you really want to read this book and work very hard it is possible, but forcing yourself (or being forced) to read it before you have either significant mathematicsal knownlodge and/or the ability to study and develope such know on your own is not a good idea. This book could convince the beginning student of physics or math that these subjects are more difficult than they actually are. Instead they are rather more like any significant skills: they takes some ability, some time to develop, and above all they require careful and persistent work on your part. Currently (three months after starting), I have finished the book (took two months for this) and also reached a rough, reading competence with advanced calculus, differential equations, lie groups/algebras, complex analysis, Lagrangians & Hamiltonians, and can now read introductory quantum mechanics texts and papers. Since reading this book, I have made a good start on Tensor Analysis and Differential Geometry. My estimate is about one year for me to fully understand the book and its topics, but the effort is well worth the results already. Even though, I have sought and used many other sources to improve my understanding, my successes are directly due to the incredible foundation provided by Penrose. In addition, I highly recommend "Deep Down Things" by Schumm, who is much more clear, but less mathematical, on Lie Groups and Gauge Theory. Schumm relates Lie theory directly to Gauge Symmetries, going beyond mere hand-waving while still remaining mathematically simple and clear. I further recommend "Understanding Quantum Physics" by Morrison which offers a much better guided, and step-by-step, introduction to the mathematics and postulates of Quantum Mechanics. (Only real criticism of Morrison is that there are NO solutions for exercise, but he does work many other problems in detail.) Although I bought Morrison's book several years ago and was unable/unwilling to read it, I can now read this one comfortably -- it's not a novel, but it is no longer a fight to read. Neither of these excellent books offers the scope of Penrose however, so read "The Road to Reality" first. (I might have missed the beauty of Schumm's treatment of Lie groups and Gauge theory had I encounted it first.) I am also working through "Quantum Mechanics Demystified" and "Relativity Demystified" both by David McMahon, and "A First Course in General Relativity" by Bernard F. Schutz. [Five months after starting Penrose's book, I now feel comfortable in reading the very imposing "Gravitation" by Misner, Thorne, Wheeler (MTW).] When I have finished these, my plan is to read "Quantum Field Theory in a Nutshell" by A. Zee and move on to Zwiebach's String Theory book. Notice that if you don't have the background in math or physics then this book is going to lead you to reading many others and learning many new topics. This truly great book doesn't end the journey but rather opens new worlds and capabilities for the interested reader. If you are asking "Should I buy it?", then: Yes, JUST BUY IT. If you do buy it, then JUST READ IT. No matter how long it takes you or how difficult it seems at time just keep reading.... You will be delighted to finish this book, and disappointed that it ends -- expect both emotions at the same time. Thank you Roger Penrose!

I spent about 4 months, on and off, and finally finished reading this great book. I have a dual purpose: (a) I wanted to quickly recover my knowledge in math and physics I acquired during my prior physicist career, and (b) I wanted to see if I could apply anything I learnt from here to the machine trading models as introduced in the book "Forecasting and Timing Markets: A Quantitative Approach." I really enjoyed this book and indeed found a lot of similarities and dissimilarities between building mathematical models for interpreting the real physical world and building models for forecasting market. Here is a summary of what I have found out to be very applicable and useful: (1) p.7: What laws govern our universe? How shall we know them? How may this knowledge help us to comprehend the world any hence guide its actions to our advantage? ... Eventually, even the much more complicated apparent motions of the planets began to yield up their secrets, revealing an immerse underlying precision and regularity. (2) p.18: Fig. 1.3 Three 'worlds' - the Platonic mathematical, the physical, and the mental - and the three profound mysteries in the connections between them. ... everything in the physical universe is indeed governed in completely precise detail by mathematical principles. ... all actions in the universe could be entirely subject to mathematical laws. (3) p.28: Euclid's first postulate effectively asserts that there is a (unique) straight line segment connecting any two points. His second postulate asserts the unlimited (continuous) extendibility of any straight line segment. His third postulate asserts the existence of a circle with any centre and with any value for its radius. Finally, his fourth postulate asserts the equality of all right angles. (4) p.45: We are to think of a light, straight, stiff rod, at one end P of which is attached a heavy point-like weight, and the other end R moves along the asymptote. (5) p.67: The system of complex numbers is an even more striking instance of the convergence between mathematical ideas and the deeper workings of the physical universe. (6) p. 109: What about the places where the second derivative f''(x) meets the x-axis? These occur where the curvature of f(x) vanishes. In general, these points are where the direction in which the curve y = f(x) 'bends' changes from one side to the other, at a place called a point of inflection. (7) p. 115: Armed with these few rules (and loads and loads of practice), one can become an 'expert' at differentiation without needing to have much in the way of actual understanding of why the rules work! This is the power of a good calculus. (8) p.151: Air, of course, consists of enormous numbers of individual fundamental particles (in fact, about 10^20 of them in a cubic centimeter), so airflow is something whose macroscopic description involves a considerable amount of averaging and approximation. There is no reason to expect that the mathematical equations of aerodynamics should reflect a great deal of the mathematics that is deeply involved in the physical laws that govern those individual particles. (9) p. 211: It seems that Nature assigns a different role to each of these two reduced spin-spaces, and it is through this fact physical processes that are reflection non-invariant can emerge. It was, indeed, one of the most striking unprecedented discoveries of 20th-century physics (theoretically predicted by Chen Ning Yang and Tsung Dao Lee, and experimentally confirmed by Chien-Shiung Wu and her group, in 1957) that there are actually fundamental processes in Nature which do not occur in their mirror-reflected form. (10) p. 217: For example, the configuration space of an ordinary rigid body in Euclidean 3-space is a non-Euclidean 6-manifold. (11) p.223: As in Sec 10.2, we have the notion of a smooth function (Phi), defined on manifold M. (12) p.388: He (Newton) had originally proposed five (or six) laws, law 4 of which was indeed the Galilean principle, but later he simplified them, in his published Principia, to the three 'Newton's laws that we are now familiar with. (13) p. 390: It is remarkable that, from just these simple ingredients (Newton's formula GmM/r^2), a theory of extraordinary power and versatility arises, which can be used with great accuracy to describe the behavior of macroscopic bodies (and, for most basic considerations, submicroscopic particles also), so long as their speeds are significantly less than that of light., (14) p. 392: Galileo's insight does not apply to electric forces; it is a particular feature of gravity alone. (15) p. 410: We shall also begin to witness the extraordinary power, beauty, and accuracy of Einstein's revolutionary theory. (16) p. 412: The geometries of Euclidean 2-space and 3-space are very familiar to us. Moreover, the generalization to a 4-dimensional Euclidean geometry E^4 is not difficult to make in principle, although it is not something for which 'visual intuition' can be appealed to. (17) p. 455: Einstein's famous equation E = mc^2 tells us that mass and energy are basically the same thing and, as Newton had already informed us, it is mass that is the source of gravitation. (18) p. 462: Einstein originally introduced this extra term, in order to have the possibility of a static spatially closed universe on the cosmological scale. But when it became clear, from Edwin Hubble's observations in 1929, that the universe is expanding, and therefore not static, Einstein withdrew his support for this cosmological constant, asserting that it had been 'his greatest mistake' (perhaps because he might otherwise have predicted the expansion of the universe!). Nevertheless, ideas once put forward do not necessarily go away easily. The cosmological constant has hovered in the background of cosmological theory ever since Einstein first put it forward, causing worry to some and solace to others. Very recently, observations of distant supernovae have had most theorists to re-introduce /\ (greek lambda), or something similar, referred to as 'dark energy', as a way of making these observations consistent with other perceived requirements. (19) p. 466: The timing of these signals is so precise, and the system itself so 'clean', that comparison between observation and theoretical expectation provides a confirmation of Einstein's general relativity to about one part in 10^14, an accuracy unprecedented in the scientific comparison between the observation of a particular system and theory. (20) p.490: He (Hilbert) appears to have believed that his total Lagrangian gives us what we would now refer to as a 'theory of everything'. (21) p. 503: ... it took many years for Einstein's original lonely insights to become accepted. (22) p. 523: Heisenberg's uncertainty relation tells us that the product of these two spreads cannot be smaller than the order of Planck's constant, and we have Delta-p Delat-x >= h_bar / 2. (23) p. 528: I denote Schrodinger evolution by U and state reduction by R. This alternation between these two completely different-looking procedures would appear to be a distinctly odd type of way for a universe to behave! (24) p. 541: As the state of the arts stands, one can either be decidedly sloppy about such mathematical niceties and even pretend that position states and momentum states are actually states, or else spend the whole time insisting on getting the mathematics right, in which case there is a contrasting danger of getting trapped in a 'rigour mortis.' (25) p.686 (Chapter 27 The Big Bang and its Thermodynamic Legacy): What sorts of laws shape the universe with all its contents? The answer provided by practically all successful physical theories, from the time of Galileo onwards, would be given in the form of a dynamics - that is, a specification of how a physical system will develop with time, given the physical state of of the system at one particular time. These theories do not tell us what the world is like; they say, instead: 'if the world was like such-and-such at one time, then it will be like so-and-so at some later time'. (26) p.687: The usual way of thinking about how these dynamical laws act is that it is the choice of initial conditions that determines which particular realization of the dynamics happens to occur. Normally, one thinks in terms of systems evolving into the future, from data specified in the last, where the particular evolution that takes place is determined by differential equations. (27) p.689: What about evolution into the past, rather than the future? It would be a fair comment that such 'chaotic unpredictability" is normally much worse for the 'retrodiction' that is involved in past-directed evolution than for the 'prediction' of the normal future-directed evolution. This has to do with the Second Law of thermodynamics, which in its simplest form basically asserts: Heat flows from a hotter to a cooler body. ... This procedure of dynamic retrodiction is clearly a hopeless prospect in physics. ... For this kind of reason, physics is normally concerned with prediction, rather than retrodiction. (28) p. 760: Of course, it might indeed ultimately turn out that there is simply no mathematical way of fixing certain parameters in the 'true theory', and that the choice of these parameters is indeed such that the universe in which we find ourselves must be so as to allow sentient life. But I have to confess that I do not much like that idea! (29) p. 850: But to take this position is to part company with one of the basic principles of Einstein's theory, namely the principle of general covariance. (30) p. 935: ... A lot of these stem from the fact Einstein's theory is 'generally covariant' (Sec 19.6). Finally, I have to say that I really like so many drawings in the book, which are simplistic yet stupendously expressive. Thanks Professor Penrose for sharing your knowledge and achievements of many decades, which will benefit many on this planet called Earth!

It's a delicate balance for book: Encyclopedic vs well focused on a unifying theme! Penrose succeeds admirably. It's not boring! Books like this are few and far between. Indeed, there are preciously few authors who manage to successfully guide beginning students into serious scientific topics; and even fewer who can see the big picture, and do it all. And then keeping our attention through more than 1000 pages! Penrose's book is inspiring, informative, exciting; and at the same time it's honest about what math and physics are. It is modest when modesty is called for. You are not cheated. You do get the equations (not just hand waving!), but you are gently prepared in advance, so you will want the mathematical formulae. Penrose's book is likely to help high school students getting started in science; and to inspire and inform us all. There is something for everyone: for the beginning student in math or in physics, for the educated layman/woman (perhaps the students' parents), for graduate students, for teachers, for scientists, for researchers; and the list goes on. It is one of the very few books of this scope that is not intimidating. Not in the least! I can't begin to do justice to this terrific book. Get it, and judge for yourself. I will also not give away the ending, other than saying that the title of the book is a good hint. And you will be able to form your own take, and your own ideas on the conclusion. Like with all good and subtle endings, they can be understood and appreciated at several levels. I came across Penrose's book in my bookstore by accident, and I was at first apprehensive: The more than 1000 pages, and the 3.3 pounds are enough to intimidate anyone. But when I started to read, I found myself unable to put it down. And I didn't: Bought it; and I had several days of enjoyable reading. I am not likely to put it away to collect dust either. It is the kind of book you will want to keep using, and to return to. It will not surprise that one of Penrose's unifying themes is the compelling and pleasing geometric images that underlie both the mathematics (roughly one third of the book: modern geometry, Riemann surfaces, complex functions, Fourier analysis, visions of infinity), and the physics: Cosmology (the big bang, black holes), gravity, thermodynamics, relativity (classical and modern: loop quantum gravity, twisters), and quantum theory (wave-particle duality, atomic spectra, coherence, measurements). The pictures: In fact, this semester, I was just teaching a graduate course, and I had a hard time presenting of Riemann surfaces in an attractive way. It's a subject that typically comes across as intimidating in many of the classical books: Take Herman Weyl's book, for example. I also found it refreshing to see that Roger Penrose gave the many illustrations his own personal and artistic touch; as opposed to having flashy pictures generated by the latest in color-graphics and special effects. I think readers will relate better to Penrose's own illustrations: They isolate and highlight the core ideas and they are not intimidating: We sense that we ourselves would have been able to make similar pencil sketches. Or at least we are encouraged to try! The common theme in the pictures serves to bring to life the underlying and fundamental ideas;--- another attractive feature of the book! It is otherwise easy to get lost in some of the equations, and in the encyclopedic panorama of topics. Review by Palle Jorgensen, February 2005.

What laws govern our universe? Modern physics doesn't give a unified answer for this question, but only give partial answers. That is, we have two fundamental theories explaining our universe, relativity and quantum mechanics that conflict in some situations. There are theories like string theory which claims that it might be able to give a unified theory (as physicists say, the final theory). Among them is twistor theory formulated by the author, Roger Penrose in 1950s. As the inventor of twistor theory, he shows to readers how mankind has answered to the question from the ancient times until the present. Several distinguished features of this book include: 1. more than 1000 pages with neither typos nor grammatical errors. 2. almost all major roads to final theory: string theory, loop variables, twistor theory, non-commutative geometry. For descriptions, the book deals with classical mechanics, relativity, quantum mechanics, and chaos theory from the basics. And also it deals with classical and modern mathematics: irrational numbers, Euclidean geometry, hyperbolic geometry, projective geometry, real number calculus, complex number calculus, Riemann surfaces, Fourier decomposition, generalized functions, Clifford algebra, Grassmann algebra, vector fields on manifolds, Riemannian geometry, exterior derivative, Lie groups, Lie algebras, connections, fibre bundle theory, Cantor's set theory, Minkowskian geometry, Lorentz geometry, sheaf theory, and tensors. But in spirit, this book is for general audience. What is the most important for a reader? I think it is how much he learned from the reading. In this aspect, I could not give five stars. To finish the book, I spent almost two months. Of course, I learned a quite amount and it was a valuable time. But I think what I gained is just 35 percent of what the book contains. Comparing with Brian Green's popular books, the book is the next or the next-next level of a book. The difficulty was in concepts relating to relativity, in particular, tensors. In the book, the tensor notation is universal. Even the Maxwell equation is expressed in the tensor notation. I graduated in physics department and have a doctoral degree in mathematics. But I've never studied general relativity and its related Lorenz and Minkowskian geometry, and tensor notations. And I've never studied quantum field theory and its related tensor formalism as well. If you think that the book is difficult for you also, I would like to give some tips. They are all related to skipping. 1. As the author says, skip equations and difficult parts if you don't want to read it sometimes the whole chapter. If you realize that the part is important to understand the main stream of the book, you can always go back to that part when necessary. At page 74, the author says, My advice to such readers is basically just to read the words and not to bother too much about trying to understand the equations. 2. This book is not a textbook. If you want to learn relativity or tensor calculus or quantum physics, then you are referred to standard texts or Youtube lectures. You should not try to learn such subjects from this book. So when you meet some parts dealing with such a sophisticated level physics and think that it's too difficult, you should skip it without any regret. 3. As I said, in spirit, the book is for general audience. But if one can understand more than a half of the book, then I think that he would be at least a graduate student studying quantum field theory and relativity. If you are interested in the question, what laws govern our universe, you are entitled to read the book. But actually, if you are not already familiar with quantum mechanics at least at the level of popular science books, then it would be extremely hard for you to read. You have to make clever choices about what to read if you don't want to spend time frustrated. 4. Its style is informal and narrative, but in some parts, it is very dense. For example, the Newton mechanics is summarized only in three pages. After the section, the author assumes that you have mastered the Newton mechanics! Now I want to share my detailed appreciation. 1. If your major is related to science, then among many curriculum subjects, the linear algebra would be the most helpful to read this book, such as, basis, eigenvalue, linear transformations and matrices, basis change, dimension of a vector space. And if you know what a phase space is for a dynamical system, then it would be very helpful (Search the Wiki). And if your major is mathematics, I have something more to say. I've read the differential geometry book by O'Neil, Calculus on Manifolds by Spivak and studied one-semester courses of differential topology and Riemannian geometry. So I am familiar with concepts like curvature, 1-form, integration on forms, exterior derivative, Poincare lemma. But that was not so helpful to understand relativity and tensors in the book. Everybody who is interested in the subject knows that they are related, but I think that they live somewhat in different area. 2. The book is so concise that sometimes you can't understand what the author says. For example, I think that the Mach-Zehnder interferometer at page 514 cannot be understood only by the explanations of the book if the reader does not already know it. And for many extremely important experiments including EPR-experiment, the book describes them so briefly that if you are not already familiar with them, you may have difficulty to understand them. And as for quantum entanglement, it is a really amazing phenomenon of quantum mechanics. But if you didn't already know it, then you may not fully understand it only with this book. As one more example of physics part, while I read the book, I come to know that there is a projective postulate in quantum mechanics that seems to be a very important issue in the book. But I couldn't understand it even though I tried to read the related parts several times. There are such things on the mathematical part. First of all, although there are explanations about tensors, if you are not already familiar with it, you would have a rare chance of understanding it. As the second instance, at the extremely interesting section on covariant derivative on a fibre bundle (Section 15.8), the explanation is not sufficient for actually calculating the example of A=ik the conjugate of z. As another instance, in the sections on complex numbers, we see some logically vague explanations. I found that the author didn't explain the fact that if two holomorphic functions on a domain D coincide on a continuous set (in a sense), then they coincide on the domain D. 3. There seem to be unsatisfactory explanations. At section 14.3, introducing covariant derivative, the author introduces the concept of parallel transport. But there is some ambiguity whether covariant derivative is derived from the parallel transport or the converse is true (this case is true in mathematical literature). And at section 21.4, it explains the Blackbody radiation. Wien's formula was already there giving insufficient interpretation of Blackbody radiation and several years after Wien, Planck succeeded in explaining Blackbody radiation with introducing his Planck constant. If so, it is absurd that the Planck constant appears in the Wien's formula. 4. If you are a mathematician, I strongly recommend that you read sections on analytic continuation, hyper-functions, Fourier decomposition, fibre bundles. They are worth reading in the aspect that the book explains to readers the geometric meaning. Once you read them, you will not forget it for a long time. For example, we know that a conformal map is an angle preserving map. The author says that a conformal map preserves shape locally. Maybe this is a common sense to many researchers, but to me it was an astonishing insight. There are many things like that in the book. And there are some differences of point of view to mathematicians like me. For example, in Chapter 5, the author explains complex numbers from the basics, and in Chapter 13, symmetry groups. I thought I knew them. But the way he describes them seems to be strange. As for complex numbers, I skipped some parts and made a decision to retain my understanding. As for symmetry groups, I thought I have to learn more. 5. Until the author introduces the generalized function, he asks us what function is. What definition of a function can be satisfactory in theoretical meaning and in practical applications? In fact, I used to ask the same question also, although I was not so explicit. I think anyone who studied mathematics for several years may have conceived the question. His argument is very interesting and really thought-provoking. More than that, he gives an explicit answer about the question. 6. Diagrammatic notations and conformal diagrams don't seem to be helpful for non-specialists. 7. While reading through the book, I hoped that I could understand the following sentence. ... according to modern physics, all physical interactions are governed by 'gauge connections' which, technically, depend crucially on spaces having exact symmetries. (page 289) But even now after finishing the book, I still don't understand what the above sentence means concretely. My future goal would be to understand it. 8. What are the merits of the book? Does the book have a merit that other books do not have? I think it has. The author has no hesitation in expressing his explicit opinion about major current theories. Quantum field theory - mathematically inconsistent Inflation cosmology - suspicious String theory - Doubtful, especially due to its higher-dimensional spacetime. String theory regards spacetime as continuum but the author seems to believe that ultimately, spacetime also should be quantized. Loop variables - At this stage, it is far from being quantum gravity theory. Non-commutative geometry - The model does not incorporate special and general relativity. Quantum group - There is no very clear relation between a quantum group and quantum theory. Topological quantum field theory - It is hard to see them playing direct roles as models of serious physical theories. Another merit of the book is that it gave me a motivation to study relativity, tensors, and quantum field theory by showing a big picture of modern attempts to final theory. I am a group theorist, and I want to meet more various groups in physics. And I am interested in the question: what laws govern our universe? This is the motivation that I chose the book. I hope that I learn more about the area. As remarked above, ultimately, the spacetime also seems that it should have a discrete property at extremely small scale. So some scientists suggested a discrete number system other than real numbers. I thought that's the right way! But the author suggests that rather than a discrete number system, complex number system would be the right number system. Now I think that it is possible that to describe a discrete object, we may use a continuum like the complex number system. As a whole, the reading was valuable. While I read this book, I received the impression that the author is a very gentle, sincere, honest, kind, careful, and friendly person. Even though I was not totally satisfied with the book, I come to respect his attitude as a scholar.

Having thoroughly enjoyed The Emperor's New Mind and Shadows of the Mind, I was looking forward to this book by Roger Penrose. I was initially slightly intimidated by the book when it arrived: it looked suspiciously like one of those textbooks that I'd had to wade through years ago. But I need not have worried. The book is a model of clarity, and you do not need to be put off by the equations. Roger Penrose is a member of a prodigiously talented family and a former collaborator of Stephen Hawking. He has a remarkable ability for explaining complex concepts, and his passion for his subject shines through. I think that many people will be surprised at the amount of progress that has been made toward a comprehensive model of the physical universe. Penrose is extremely good at connecting the dots: showing how different areas of mathematics fit together. Just over twenty years ago I was asked to give a lecture about the brain and consciousness to a lay audience. During the question and answer session, I was asked something that set a group of us off in a new direction. "Why," I was asked, "Are these models complicated? Any true insights into the natural world should be simple enough for a child to understand." Is that really true, I wondered? Is it really possible to reduce the brain or the physical universe to a small number of ideas that could be explained in a high school textbook? The answer is, I think, no. And certainly on the evidence of Roger Penrose's book, the universe is multi-layered, and we need some sophistication to understand it. This book does require intellectual effort, but it is well worth it. A bit of brain stretching is good for all of us! Unless you are a die hard math or physics buff, I recommend reading the book in small bite size chunks and contemplating what you have learned. That way it almost becomes a daily meditation. After a little while, you will probably find yourself looking forward to the next installment. This is a book to which you want to return, and I think that it will be remembered as a classic long after many popular science books have been remaindered. Highly recommended.

The book gives a beautiful tour of "fundamental physics"; it is certainly not about all of Physics. It is an attempt to review the basic aspects of our current picture of the fundamental elements and laws of the reality, from which some understanding of the very small and the very large of the universe can be gained. Who is this book NOT for: someone without some college level math background, OR someone without enough patience to spend months to slowly progress in learning the book's invaluable content. Who is this book GREAT for: anyone with a college level math background. Students of science or engineering, in particular. Who is this book PERFECT for: an udergrad student of Math or Physics, with some interest in theoretical physics. Graduate students or PhDs of those fields, will still certainly find the book indispensable, but will most probably wish they had read it earlier. The first half of the book is a wonderful coverage of a nice selection of math topics, important for theoretical physics, and that with a good number of exercises, which combines with a clear and exciting narration to make it pedagogically fantastic! It indeed revived my deep interest in math after a long time. Among the topics in the first half are: algebra (groups and representations in particular), geometry (manifolds, differential forms, fiber bundles and connections in particular) and complex analysis (Cauchy's theorem, Riemann surfaces and Fourier decompositions in particular). A chapter on infinities, Turing machines and the Godel's theorem, beautifully ends the math lectures before starting the physics. The physical discussions (starting with "Spacetime") are both pedagogical and bold: pedagogical because so much insight is conveyed through a very readable text. Bold, because the author dares expressing his sometimes unconventional views on the controversial topics. In the second part, among the topics presented are: Quantum Mechanics, Quantum Field Theory, the Standard Model, early universe Cosmology, the Measurement problem, Superstrings and Loop Quantum Gravity; all these fascinating things and more you will learn from a brilliant thinker and expositor! What could be better? In sum, for people interested in fundamental physics (or as the branches are often called, Mathematical Physics, High Energy Theoretical Physics, Particle Physics, Quantum Physics, and Cosmology), with a college level background in math (including Calculus), THERE IS NO ALTERNATIVE SINGLE BOOK FOR THIS HUMONGOUS AMOUNT OF KNOWLEDGE AND INSIGHT TO BE GAINED FROM!

Did you ever play a game with yourself as a small child, "I wish..." --- I did and I got very serious about it. I very quickly progressed through the stages of wishing for a million dollars. By the time I was a teenager I used to wish that I could understand everything in the universe. By the time I was an undergraduate student in college I used to wish I could be arrested, put in jail for a few years and just catch up enough to do justice to the courses I was taking "THAT" semester. By the time I was finishing up my graduate degree I used to wish I could get all the Mathematicians and Physicists in one room and force them to behave themselves and write some content that would give the rest of us a clue. Since graduate school I have spent many many hours reading popular accounts of the latest 'bandwagon-theories' of mathematics and physics and loving every bit of it. My wish slowly evolved to the point where I wished I could stay aware and awake enough to appreciate the new stuff as it came out. Well; folks like Roger Penrose in this book and Brian Green in his two books and even Robert Laughlin in his book about emergent phenomena have basically granted my wish. I really fell in love with Brian Green's books and found myself constantly flipping to the back of the book and reading the end notes and saying to myself, "Wow, wouldn't it be great if someone could sort of flesh all this out without requiring the reader to have a PhD in physics and math." I read Roger Penrose's book The Emperor's New Mind some years ago and it only made me wish for more. I can only applaud the Physicists and Mathematicians of our age for writing these types of books. And I must say if you have even an undergraduate degree in math, physics, or any other physical science where you enjoyed the math and physics courses you took then this book is for you. And even if you do NOT have a degree in math or some physical science but enjoy reading the best of the best then this book is for you. I hope everyone will enjoy it as much as I have.

The book is excellent but the quality of the paperback leaves a lot to be desired unfortunately. The paper is extremely thin and this deters from the reading experience. At the same time, the hardcover is expensive. It’d been ideal if there were a higher quality paperback which was slightly more expensive than the one we have.

A very good book. The concepts are explained in simple language so that after reading this we can follow it up in other texts covering these topics. Gives a fast overview of the physics of spacetime and gravitation.

まだ腰を据えて読み出してはいなくても、パラパラと見ただけで力作であることはわかる。図表やグラフ、説明のために趣意工夫された概念図の数々がぎっしりと配置されている。非常に難解なテーマであるだけに使われている言葉数も多いが、一流の学者が皆そうであるようにこの著者も教えることを楽しんでいる節がある。英検一級程度の読解力があれば大した苦もなく読み通せるような英文だと思う。ズッシリ重い本だが週末を使えば1年程度で熟読できる本である。買ってよかった。

Roger Penrose hat mit „The Road to Reality“ eine Art Kompendium der mathematischen Physik vorgelegt, mit dem ehrgeizigen Ziel das gesamte Rüstzeug zu präsentieren, um die heutigen Theorien der Physik, die eine fundamentale Beschreibung der Realität liefern, – jedenfalls im Prinzip – verstehen zu können. Theoretische Physik wurde im Laufe des 20. Jahrhunderts immer abstrakter, d.h. es werden immer komplexere Bereiche der Mathematik nötig, um die fortgeschritten Theorie überhaupt formulieren zu können; dabei haben Relativitätstheorie und Quantenmechanik – beide wurden bereits in ersten Viertel des letzten Jahrhunderts entwickelt – mehr über Raum, Zeit und Materie enthüllt, als es 2000 Jahre Philosophie vermocht haben. Die 'übliche' Weise moderne Physik einem größeren Auditorium zu vermitteln, sind Sachbücher, wie die von S. Hawking, P. Davis, J. Barrow oder B. Green nur um einige zu nennen, die sich wohl verdienter Weise großer Beliebtheit und Verbreitung erfreuen, leider weichen diese Darstellung – mit unter im entscheidenden Moment – in Metaphern aus, z.B. wird das oft zitierte Gummituch als Gleichnis für die gekrümmte Raumzeit der Relativitätstheorie bemüht. Das ist natürlich keine üble Absicht, um die Dinge genauer zu verstehen, ist ein gewisses Maß an Einsicht in mathematischen Zusammenhänge unerlässlich; aber jeder Formel in einem Sachbuch halbiert die Verkaufszahlen – wie es Hawking in der Einleitung seiner „... kurzen Geschichte der Zeit“ kolportiert. Aber es gibt sicher ein 'Publikum' für eine differenziertere Sicht, abgesehen von Fachwissenschaftlichern, Leonard Susskind hält seit Jahren Vorlesungs- Zyklen 'The Theoretical Minimum' zu allen Bereichen der Theoretischen Physik im Rahmen des Continuing Studies Program der Stanford Universität, das interessierten Nichtakademikern die Gelegenheit bietet, spezielle Kurse zu hören, die aber durchaus akademischen Ansprüchen genügen. Diese Kurse wenden sich unter anderem an all jene, die bereits einmal ein Studium absolviert haben, dann diverse Jobs ausgeübt haben, um am Ende wieder den faustischen Drang , zu hören “...was die Welt im innersten zusammenhält...“. Gerard t'Hooft hat aus ähnlich Gründen eine Webseite zu Thema „How to become a GOOD theoretical physiscist“ zusammen gestellt, mit Material, das zu wissen notwendig ist, wenn man einen 'Fuß' auf das Terrain der theoretisch Physik setzen mag, auch außerhalb des üblichen universitären Umfelds, das ist – nicht zuletzt dank des Internet – keine Unmöglichkeit. Genau in diese Richtung zielt auch das vorliegende Buch, man darf sich nicht der Illusion hingeben hier ALLES zu finden ist, was man zum Verständnis der theoretischen Physik benötigt, vieles ist angerissen, aber um es tatsächlich zu Verstehen, wird man wohl je nach Topic noch etliche Fachbücher konsultieren müssen; aber das Werk stellt einen wundervollen Leitfaden dar, der den interessierten Leser mit dem notwendigen Überblick und der Zusammenschau der verschieden Themen versieht. Unter diesem Gesichtspunkt ist das Werk einzigartig, der Autor müht sich um präzisen Darstellungen, ohne sich in unnötigen Formalismen zu verlieren, er ist bemüht die verschieden Konzepte stets zu motivieren, so dass sich für den geduldigen Leser ein roter Faden spannt; die Kapitel sind mit vielen Beispielen versehen, jedes Kapitel wird mit weiterführenden Notes abgeschlossen, und die Bibliographie verweist auf ein Unzahl spezieller Textbooks und Original Papers.

It is really an encycopledia of both Mathematics and Physics. The author succeeded in doing a great synthesis of modern physics at the classical, quantum and cosmological levels by stressing on the mathematical tools which helped to realise this synthesis. Penrose also emphasized the many conceptual ideas and difficulties which arose in the physics of this century and he indicates path which could help in solving many problems. It is one of the great intellectual achievements of this century.

Orientación> Cómo ya lo indica Penrose en el Prefacio, "El propósito del libro...es la búsqueda de los principios subyacentes que gobiernan el comportamiento de nuestro universo" y algo más adelante "...este libro trata realmente de la relación entre los matemáticos y los físicos..." y "de hecho puede ser utilizado como una guía genuina de las ideas centrales de la física". El libro es estructurado en varias partes sobre matemáticas, física y cosmología. Se recogen varios capítulos que desarrollan diversos conocimientos matemáticos y físicos, entre ellos: Mundo real de Platón; Pitágoras; Euclides. Números reales, complejos, hipercomplejos. Superficies. Geometría de logaritmos, potencias y raíces. Fourier. Simetría. Infinito. Espaciotiempo. Geometría de Minkowsky. Langragianos y hamiltonianos, campos clásicos de Maxwell e Einstein. Modelo Estándar de partículas. Mecánica cuántica (partícula, álgebra, geometría, mundo, QFT, gravedad y su influencia, paradoja de la medida, Copenhague, Schrödinger, etc.). Teoría de cuerdas, teoria de twistores, etc. Llegando a los capítulos de Cosmología (Big Bang, teorías especulativas sobre el universo temprano, agujeros negros, etc. Finalizando con un capítulo de reflexiones sobre las grandes teorías físicas del SXX y ¿Qué es la Realidad?. Entre otras teorías no aceptadas por Penrose, en la época de desarrollo del libro, podemos destacar: GUT, M, F, Universo inflacionario, teoría del BigBang, teorías que se apoyan en más de 4 dimensiones del e-t (Kaluza-Klein, cuerdas), etc. poniendo la esperanza en teorías como la QFT, teoría cuántica de la gravedad, en un profundo entendimiento de los ingredientes del universo más allá del modelo estándar de partículas y una teoría cuántica que englobe las cuatro fuerzas fundamentales. Respecto a donde se invierte el dinero en la Ciencia, deja claro que la moda y los grandes proyectos nublan a los pequeños ."Afortunadamente , los criterios de la ciencia no son los de los gobiernos democráticos". Opinión> Ante las tres grandes dificultades que entraña esta gran obra de Penrose, "contenido, volumen y densidad" y no siendo yo un especialista en muchos de los temas planteados, decidí iniciar su lectura por aquellos capítulos que podría entender o recordar mejor. Así inicié con el 34 (el último), 28, 17, 26, 27, 25 y 1. Conseguí sobrevivir; así que, pasé a lo "duro" el 8, 5, 6, 7, 9, 10, 11, ... algunos de los cuales conseguí terminar y otros los dejé a medias o a principias. Penrose tardó 8 años en escribir el libro (1996a2004). Los mismos años que yo tardé, desde que lo compré en 2013, hasta empezarlo, 2021. Es decir: Si no eres matemático o físico y no tienes altos conocimientos de estas disciplinas y de cosmología, mejor no intentarlo. 1.100 páginas. Libro bien escrito, con amplia bibliografía (el libro se publicó en 2004), amplio índice alfabético y notas al final de cada capítulo. Han pasado 16 años desde su publicación y 24 desde su inicio de escritura...y la Cosmología avanzó, avanza y avanzará. Es complaciente que Penrose en su prefacio aconseje que "si tienes miedo a las fórmulas, lee las palabras", "o si te encuentras saturado evita los capítulos o parte de ellos" Yo lo hice y aún así..."las palabras se las lleva el viento" y las referencias constantes del autor a capítulos anteriores o posteriores te dificultará su entendimiento, salvo que también los evites... y entonces, para qué compraste el libro.