The Road to Reality: A Complete Guide to the Laws of the Universe |  | Author: Roger Penrose
Publisher: Vintage
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Pages: 1136
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Dimensions (in): 9.2 x 5.9 x 2
ISBN: 0679776311
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Publication Date: January 9, 2007
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Product Description
Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.
Amazon.com Review
If Albert Einstein were alive, he would have a copy of The Road to Reality on his bookshelf. So would Isaac Newton. This may be the most complete mathematical explanation of the universe yet published, and Roger Penrose richly deserves the accolades he will receive for it. That said, let us be perfectly clear: this is not an easy book to read. The number of people in the world who can understand everything in it could probably take a taxi together to Penrose's next lecture. Still, math-friendly readers looking for a substantial and possibly even thrillingly difficult intellectual experience should pick up a copy (carefully--it's over a thousand pages long and weighs nearly 4 pounds) and start at the beginning, where Penrose sets out his purpose: to describe "the search for the underlying principles that govern the behavior of our universe." Beginning with the deceptively simple geometry of Pythagoras and the Greeks, Penrose guides readers through the fundamentals--the incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complex-number calculus, Riemann surfaces, and Clifford bundles, the tour takes us quickly on to the nature of spacetime. The bulk of the book is then devoted to quantum physics, cosmological theories (including Penrose's favored ideas about string theory and universal inflation), and what we know about how the universe is held together. For physicists, mathematicians, and advanced students, The Road to Reality is an essential field guide to the universe. For enthusiastic amateurs, the book is a project to tackle a bit at a time, one with unimaginable intellectual rewards. --Therese Littleton
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Showing reviews 1-5 of 173
 A panorama of science. February 26, 2005
Palle E T Jorgensen (Iowa City, Iowa United States)
502 out of 536 found this review helpful
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.
A paradise for autodidacts February 26, 2005
Royce E. Buehler (Cambridge, MA USA)
59 out of 65 found this review helpful
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 complex numbers at its foundation. So Road To Reality provides extensive summaries of two leading rival theories: loop quantum gravity, and the twistor theory which Sir Roger and his students have developed over the last several decades. He also discusses at length the notion he originally proposed in "Shadows of the Mind", that gravitational fields may be responsible for the collapse of Schroedinger wave packets.
No volume with the ambitions of this one has existed until now, and no one is better equipped than Penrose to achieve those ambitions, nor could one ask for a more congenial companion or a livelier guide. It belongs on the shelf of every one who aspires to know the real skinny on where physics is, and where it is likely to go in the near future.
There's Much More than Physics Here! October 9, 2006
Stephen Turnbull (Tsukuba, Japan)
30 out of 31 found this review helpful
Penrose's is a name I remember from reading Scientific American and NYT Book Reviews in the late '60s, which is most of the reason why I bought the book despite having never done any serious study of physics, and having recently been mildly disappointed by Lisa Randall's "Warped Passages". Surely someone who has dedicated so many years to the subject and been so influential will have something interesting to say! And I've always been a sucker for doing hard work in name of fun. I'm glad I did. "The Road to Reality" will have a permanent place on my bookshelf between Stephen Hawking's delightful "A Brief History of Time" and Saunders Mac Lane's "Mathematics: Form and Function".
Despite the number of claims that Penrose promised to write an accessible book, or to teach all of modern physics, or to teach all of the maths required for it, I can't find such a promise. What he offers is "some feeling for ... [the voyage] of discovery" that is modern physics' "search for the underlying principles...". Surely he succeeds in that! in the same way that Mac Lane's wonderful survey does in offering a feeling for modern mathematics. Hawking's exquisite little book takes the extreme opposite approach, equally successful in my opinion. If you profited from Penrose, then you must read Hawking. My disappointment with Randall's book stems from the fact that it steers a middle path between the "direct pointing" of Hawking and the "answer is in the details" approach that Penrose adopts. But I can read Penrose, skip the hard parts, and accomplish the same for myself. (That's admittedly unfair to "Warped Passages", which is worth reading. But this isn't a review of Randall's book.)
In the end, the answer *is* in the details, and Penrose manages his encyclopedic survey with taste and pace. It's not an easy read, but he didn't promise it would be. He promises to show you the doors, and he does. It's up to you to open them, and enter. Neither Hawking nor Randall does that.
What I found fascinating about this book, the "much more" of my title, is the wealth of insight into the psychology and sociology of mathematical science I found in it. Though I am unqualified to take a position on the question whether this book is mathematics or physics, I am not surprised that some find that Penrose has "left out the physics". (I wouldn't use those words myself to describe what he may have left out, but I can understand why some readers might.) But as I understand it, Penrose's purpose is to convey "a feeling" for the interaction of formal constraints on content and expression that the mathematics imposes, not to present a full graduate-level course in physics.
For "artistic" reasons, he sometimes expresses a mutual constraint in adversarial terms, such as his conclusion in 33.14 that string theory and twistor theory are incompatible. But, as in this case, he also presents his speculations as to how the incompatibility might be resolved. He also is quite aware that the criticism of aphysicality he levels at string theory (especially superstring theory) is, at the present time, equally applicable to his own pet twistor theory.
One of the great achievements of this book is the great delicacy and sensitivity of his exposition of the sources of (note that I do not write "reasons for"!) his conviction that twistor theory is nonetheless better grounded in "physicality" than is string theory. Great Science is great Art; "The Road to Reality" provides any number of examples of one of the great scientific artists of our time introspecting about how he does it. I can only wish for an author with such insight for my own field (economics). Furthermore, Penrose acknowledges the very personal nature of such judgments, and on several occasions gives as a reason for questioning his own judgment the differing intuitions of others. This interaction among several individual thinkers, as well as the interactions of self-referential analysis of one's own thought processes, is extremely hard to characterize. It was very useful to me to see Penrose's thoughts on these issues.
I was also deeply impressed by his treatment of fashion in (mathematical) science. Mathematics promises unambiguous answers, and indeed, mathematical theorems are unambiguous (at least, I have never seen a "fuzzy proof" in my own field). Nonetheless, the applicability of theorems is often a matter of taste, and taste can be altered by any number of factors (such as a charismatic fashion leader) and constraints (such as the difficulty of getting citations for a contribution using a formalism unfamiliar to the herd of practioners, an interesting twist on the "not invented here" phenomenon familiar to software developers). Yet, rather than simply decry this reality as many "unfashionable" thinkers do, he treats it with respect (and regret, of course) as deserving of careful consideration, even as an indication of where the field "should" go, though he of course concludes that "voting" is ridiculous. Rather, he points out that if the fashionable direction should prove sterile, there are two ways out---the maverick genius who somehow perceives a different world, closer to the one we live in than is the "fashionable" one, and the brute fact of unexplainable experimental results forcing all reasonable observers to see a "crisis" of thought.
Is it worth slogging through over 1000 pages for these precious nuggets? I don't know how to give a direct answer. What I can say is that I found it so. First, the material is inherently interesting.
Second, an important theme (tacit until the footnotes of the last chapter!) is whether the "miraculous" coincidences of mathematical beauty and the resolution of theoretical paradoxes in physics are essence ("God" embodying the mathematics in physical reality) or accident (a mere consequence of the fact that mathematics is no more nor less than the set of tools we use to manipulate descriptions of order). The theme surfaces over and over in the second part of the book as discussion of whether various theories are lovely mathematical fantasy lacking a physical ground, or actual physical order manifesting itself in the mathematical description.
I'm not sure explicit discussion of this theme would have allowed a significantly shorter book to foster my understanding as "The Road to Reality" did. I turned all the pages, yet I can't claim to have loosely grasped, let alone actually understood, more than about a third of of it. Here and there I caught glimpses of ideas that I do not fully understand, yet were sufficient to leave me with much more sympathy for Penrose's Wignerian stance (i.e., that some of the "miracles" do expose a fundamental causal connection between mathematics and physical reality)---though I remain firmly in the Gleason camp, believing that the beauty of the maths may attract our eyes to correct theories, but that the maths' beauty does not "make" the theories correct. I'm afraid that a shorter book would have left me thinking that this is one of Penrose's blind spots, rather than wanting to further explore my own beliefs on the matter.
And that leads to my conclusion. If you want a comprehensive introduction to modern mathematical physics starting from the elements, this book isn't it. Rather, it is proof that there can be no such thing (unless, perhaps, you're already a highly accomplished mathematician with some physical intuition). If you are looking for a book that will provide a good "layman's grasp" of the principles and directions of recent theories in physics, there are much shorter ones, better adapted to that purpose.
But if you desire a riveting account written by one of the great voyagers in pursuit of scientific treasure, complete with sketchy maps to some charted and uncharted regions containing further troves, read this book. Roger Penrose delivers on what he promises.
Intuitive and insightful approach June 7, 2005
Dean Welch
28 out of 29 found this review helpful
In summary, this is one of my favorite books. A wide range of interesting topics in math and physics are covered. An especially nice aspect of the book is that the treatment of physics is more motivated by considerations of nature, rather than mathematical formalism. Given Penrose's immense mathematical talents that is very nice to see, but not surprising for anyone that has read some of his previous work. In fact a great deal of what appears in the book is based on earlier publications of Penrose. Sometimes the opinions of the author differ from those more commonly held by other physicists, but when this happens he provides justification for it and he is very clear that his opinion is in the minority (or at least not universally accepted).
As I see it a rough breakdown of the book's material would be: the first third primarily mathematics, the second third mainly universally accepted laws of physics and the remaining third more speculative (and controversial) possibilities for physics not currently well understood.
This first third includes discussions of geometry, complex analysis, number theory, symmetry groups and much more. It's not a text book from which one would master the details of doing the calculations (if you've never done a contour integral this probably wouldn't be the best place to learn), but it does provide many interesting insights that one could miss by only reading a traditional type text book. His treatment of complex analysis was wonderful, especially his discussion of holomorphic functions. Among the other things I especially enjoyed was his discussion on what one means by something being a function and some of the bits of history he sprinkled in.
Penrose then moves on in the second third of the book to covering fundamental physics, this includes quantum mechanics, relativity, quantum field theory and cosmology. The material and its excellent treatment consists of physics that is more or less universally accepted. Again the approach is motivated much more by physics rather than mathematical formalism, however it's done without sacrificing any mathematical elegance. I found the treatment of entropy and phase space evolution in the big bang to be especially interesting. One kind of idiosyncratic thing in the book is his use of tensor diagrams, I've never seen anybody besides Penrose use these. But, if Roger Penrose has found them useful (as he states he has for many years) who am I to argue against their inclusion.
The remaining chapters of the book cover more speculative ideas in physics. Mainly fundamental aspects of quantum mechanics (for lack of a better term) and quantum gravity.
A fairly in depth discussion of the "measurement paradox" is given, presumably because as he puts it, "present-day quantum mechanics has no credible ontology". While many (most?) physicists might say "So what? It works" or consider the problem solved via environmental decoherence and consistent histories approach (for example see Omnes "The interpretation of quantum mechanics"). Penrose is of the opinion that quantum mechanics needs to be modified to have objective state reduction. This is a position he has advocated for quite awhile and he warns the reader that this is not a universally embraced point of view. This is as he does throughout the book when strays into more controversial areas of physics. While a new discussion of something like the "measurement paradox" might seem to be needed as much as a new table of integers, Penrose believes that quantum mechanics is incomplete and considerations like this are important in that they will give some clues to finding a quantum theory of gravity. To be clear, this is not just a rehash of the usual (and in my opinion tired) "interpretation of quantum mechanics" discussion, it is a proposal for possible new physics. Although alternatives to objective state reduction are also considered, the presentation isn't quite balanced.
He also covers three approaches to quantum gravity: string theory, loop quantum gravity and twistor theory.
Not surprisingly he is not very optimistic about the prospects of string theory providing the correct quantum theory of gravity. More generally he has a pretty dim view of Kaluza-Klein models, believing that spacetime has only four dimensions (not more with some of them compactified). I think the fact that he is "less than positive" about string theory is a good thing for a couple of reasons. One is that string theory has probably been oversold, often being presented as "the quantum theory of gravity", rather than as "a plausible candidate for a quantum theory of gravity". Two, there are many excellent books (popular and technical) that provide a more positive outlook on string theory, I think Penrose's perspective helps provide some balance. Still, I think the reader should keep in mind that most physicists in the field consider string theory to be the leading candidate for the quantum theory of gravity.
The treatment of loop quantum gravity is brief, but good. Twistor theory was essentially created by Penrose himself and it is a bit more esoteric than the other approaches. The treatment of it is excellent, but mostly the same as has appeared in print many times.
Given his view of string theory and his belief in the need to modify quantum mechanics I wasn't surprised that he is unconvinced that information is returned from a black hole as it evaporates via Hawking radiation. However, I was surprised that he is so skeptical of inflation and the approach of using complex periodicity (outside of a narrow range of applicability) to get the temperature of a black hole. I believe these two things are generally pretty widely accepted.
Despite the amount of material in the book there are a few topics that were omitted or covered only briefly that I would have loved to have seen Penrose's approach to: positive energy theorems, stability of black hole Cauchy horizons, the chronology protection conjecture, missing mass, cosmic censorship (covered only briefly) and quantum cosmology (the no-boundary proposal was only briefly considered).
In summary, considering the breadth and depth this is a unique book. I believe a wide range of people would benefit by reading it, however without a fairly strong background in math I think it would be quite a challenge. I think perhaps the "sweet spot" for readership would be advanced undergraduates in physics or astronomy.
Likely will become one of the Great Books: Buy it! May 19, 2006
H. Martin (Austin, TX United States)
29 out of 31 found this review helpful
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!
Showing reviews 1-5 of 173
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