Penrose, Penrose, Penrose. Oh, how I LONG to know thee.

I am becoming minorly obsessed with you and your work. I find myself pacing, for crying out loud. I am running in circles, opening and closing books, referencing and coming back, straining my eyes as if that will make me see the world as you do.

Why do you elude me so? Why does your tongue speak as if attached to the left temporal lobe itself? I catch glimpses of this reality you see. I feel myself drawn to it, longing for truth and understanding.

For some reason, I feel that to understand you, truly and completely, I would find some kind of wholeness within myself. Oh, someone save me, I am in love. I am falling madly and passionately in love with physics.

It has been coming on for a long time, this slow fever. This lingering low hum that is exploding in tiny bursts. As with lovers of old, your elusive and coquettish nature has wooed my heart, oh physics.

I want so badly to truly understand, not just some superficial knowledge, but some deep personal connective enlightenment. Cosmic, if you will.

I pledge to re-attend school. My career be damned, I have to know you, and I can't know you without the mathematical background to do so. I can't truly understand you until I can follow this terse and sometimes insipid language of higher calculus.

May the forces of this universe help me. I will not die until I know this form that physics takes. This is my pledge.

3.5 stars

This is an extremely thick mathematical and physics tome consisting of more than a thousand pages. It is essentially a comprehensive compilation of everything one should know about the universe, presented by the Nobel Prize winner himself, Roger Penrose.

The content is heavily reliant on formulas, which makes it quite challenging. Regrettably, many of the later chapters were beyond my level of understanding.

The writing style was just okay. I would have preferred to have more narrative elements to make it more engaging. However, I suspect that Penrose's open-mindedness led him to stay closely adhered to the established theories and not deviate too much.

Overall, it is a valuable resource for those with a deep interest in mathematics and physics, but it may not be accessible to everyone. Despite its shortcomings, I still rate it 3.5 stars.

Many of my all-time favourite books make the list as they offer a peek into the minds of extraordinary individuals. While reading Churchill's History of the Second World War and Yourcenar's Mémoires d'Hadrien, you can envision yourself as a great statesman at a crucial moment in history. Simone de Beauvoir's autobiography gives you the feeling of being a major literary figure, more so than any other book I know. Polugayevsky's Grandmaster Preparation, treated almost as a sacred text by many chessplayers, is the only truly honest account I've seen of how a top Grandmaster thinks.

Penrose belongs in this exclusive group. I finally have some inkling, however faint, of how a great mathematical physicist views the universe. Like the other books, it's not an easy read. To build such a comprehensive picture, a vast number of details are essential; without them, the entire texture of the world would vanish. Churchill requires maps, troop movements, and political networking. De Beauvoir has to assume (incorrectly in my case, alas) that you're familiar with most of French literature. And if you remove the chess from Polugayevsky, there would be no story.

In Penrose's case, it's mathematics and physics. He firmly refuses to simplify it and includes a rather intimidating quantity of Greek letters. If it were true that every equation halves your sales, he would have sold no copies at all. What saves him and makes the book readable for non-experts like me, who at least have some mathematical background, is his uniquely visual approach to experiencing mathematics. Penrose can clearly handle the equations, but he also has to see them, and he is astonishingly inventive in coming up with visualisations. The ones I liked most were related to Special Relativity. You may recall this fairly well-known picture by Escher.

What I didn't know was that it illustrates the "hyperbolic geometry" that underlies Einstein's Special Theory. In Special Relativity, the speed of light is an absolute limit, so velocities can't simply be added. The correct formula for combining them is the one shown in the picture. You can add any number of fish together and never reach the edge. Similarly, no matter how many times you add a velocity to itself, you never reach the speed of light. Believe it or not, the diagram precisely models the equation! And another geometrical argument he used here is nearly as beautiful. A great deal of nonsense has been written about the "Twins Paradox" (for example, by Robert Heinlein). Penrose's explanation is wonderfully concise and elegant. In Minkowski-space, a straight line is counterintuitively the longest distance between two points. The twin who flies out into space has a less straight world-line than his twin who stays at home, so he ages less. Thanks to Penrose, I can now see it.

It turns out that theoretical physics is far from a dry technical discipline. You come away feeling that these people are visionary poets who have chosen to write in mathematics rather than ordinary language. Blake is one comparison that comes to mind, and I can't resist the temptation to juxtapose Blake's image of God with Penrose's.

If you're wondering what God is doing, it's actually quite similar to Blake's version. The picture dramatizes the extremely low entropy of the Universe immediately after the Big Bang. I had not previously understood how remarkable this is, and the puzzle it represents is central to Penrose's exposition. Once again, the picture isn't gratuitous. He's illustrating, in a humorous way (the book is often funny), an extremely serious point.

As I've said, it's not an easy read. It demands a great deal of concentration, and I think I must have spent at least two or three hours a day over the last month struggling through it. A lot of that time, I was supposed to be doing other things, but I'm glad I ignored them and read Penrose instead. He's changed my way of looking at the world as much as Dante did when I read The Divine Comedy in 1999.

Now, if only it were in terza rima with animated illustrations by Gustave Doré and Terry Gilliam. Then it would truly be perfect.

We had another CERN physicist to dinner last night, an Australian post-doc working on validating the Standard Model. I asked her if she'd read Road to Reality.

"I stopped reading popular science books when I was an undergraduate," she said apologetically.

I said it wasn't really a popular science book, and she opened it for a few seconds. "Hm, yes, it does seem to have quite a lot of equations," she muttered doubtfully, and then she put it down again.

Something seems to have gone slightly awry with the marketing campaign for this book. Laymen think it's a book for physicists, and physicists think it's a book for laymen. I'm reassured to see a fair number of reviews here from people who appear to have read and enjoyed it.

This book is far too extensive to wait and review it all at once in the end. Therefore, I have made the decision to do it bit by bit as I progress through it.

I initially thought the prologue was rather unappealing. However, immediately after that, it became incredibly captivating. So, don't get disheartened. I should probably explain why I disliked it, though. It seemed as if the author was evaluating past eras and societies through a "presentist" perspective, as if all people have always been scientists since the beginning of time, and they were just really bad at it back then. It's a bit like a scientist's way of ignoring everything else about reality except for science, which made me feel a bit queasy, thinking "oh no, I hope he's not going to be this dull throughout the entire book." Fortunately, he quickly transitioned to extreme brilliance, and has continued to be so ever since. Even though he has been discussing seemingly simple things so far, his deep insights keep astonishing me, as they are things I have never considered before.

I am only in chapter 3 at the moment, and we are discussing integers, irrational numbers, and real numbers. I constantly have to stop and think hard about the things he is saying. He poses the question of whether integers would exist if we lived in a universe where everything was an amorphous soup. He also points out that calculus (and concepts like momentum, velocity, and many of our physical ideas that depend on calculus) is defined on the real numbers. If it turns out that the universe is discrete at the tiniest level, this math will no longer apply (except as an approximation). However, he also observes that the real numbers, which were first invented in Euclid's time when our physical evidence spanned only about 15 orders of magnitude (from the smallest to the largest known distances), are still relevant today when our knowledge spans something like 150 orders of magnitude. So, they are not doing too badly! These are the thoughts of someone who has deeply considered how math and physics are intertwined. I keep being dumbfounded by the things he casually asks about ostensibly simple things that I have known forever but never thought to question. This is really important stuff. He is breathtakingly brilliant! I am so glad I am reading this book!

Aside: The more I read, the more convinced I am that Platonic essences exist independently of the nature of physical reality and their instantiation in some physical reality.

I spent some time going over familiar ground in the complex plane. It has been so long since I studied or used this stuff that it is quite enjoyable and satisfying to do so. I think I have settled on the slow and savoring method of reading this book rather than the quick devour. This review is going to be very long, but I hope it will also allow for a bit of savoring. =)

I am now in chapter 5, and we are talking about e and logarithms. I wondered again why e is a more natural base for logarithms than any other number. So, I spent some time adding it up from the formula e = (1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)+(1/5!)+... and watched the digits slowly materialize as 2.7182.... So, I believe that much. =) Next, I am reading again about how e originally came up in playing around with logs and powers. This book has the effect of making me think again about things that I haven't thought about since I was young. I would really like to feel that I understand what we know of reality inside and out when I'm done. I want to see the whole chain starting from one cow, two cows, all the way up to the standard model and beyond. It has always been an obsession of mine just to understand how things work, what the universe is like, what nature is based on, and I have this feeling that I could get much closer by carefully going through this volume. The title keeps reminding me of the Royal Road to Geometry, which Aristotle reportedly told Alexander the Great did not exist, so that's some kind of warning, hah!

So far, I have resisted the urge to jump ahead, except for reading the section called "beauty and miracles" near the very end. You have to admit that's an attractive section name! Alas, I understood it only in the broadest sense, that beauty (mathematical elegance) and miracles (seemingly crazy mathematical coincidences such as all the complicated terms happening to drop out or whatever) act as a powerful but not unfailing guide so far to finding theories that fit how nature behaves. At that moment, my dear kitten Alai jumped up and sat right on the book, as if to say, "you want beauty and miracles? Just look at me!" As I petted him, I kept saying "beauty and miracles" affectionately.

**Title: A Review of a Mathematical and Physical Behemoth**

This book is an incredibly ambitious work.

When I first encountered it, I was highly impressed by the masterful construction of a mathematical framework in the initial dozen or so chapters (if my memory serves me right). This is one of the reasons for my rating, along with the aforementioned ambition. I believe this is the right approach, although popular expositors rarely take this path. Penrose presents it so efficiently and naturally that even the layman won't discard it in disgust after just a few pages. And the price is worthwhile for those beginning chapters alone.

There is an idiosyncratic emphasis in these chapters, but it doesn't detract from the breadth of the account and can't really be criticized as it sets the stage for what follows.

However, I never really delved into the "meat" of the book, which is the physics. I had hoped to, but then I realized I was procrastinating out of the fear that I would lack the formal first-year physics knowledge from university (which I happily escaped as soon as possible in favor of my chosen field of pure mathematics). This concern might be unfounded as when I skipped ahead to chapter 17 on spacetime, I could follow the account. Nevertheless, I closed the book at this point.

Perhaps I'll revisit it sometime with some other references at hand in case I need help. It would definitely be worthwhile if you can invest the required time and energy. You're bound to gain a wealth of knowledge in a way that almost no other popular science account can provide.

So we had a physicist over for dinner the other day and presented this to him. I can't mention T---- by his actual name. Let's just say his name rhymes with a dip made with chickpeas and tahini. The reason I can't use his real name is that he works at a place that begins with C and rhymes with a complete absence of humour. He enjoys his job, and I don't want to cause him to lose it by having him read Penrose.

He quickly flips through it, and the first thing I notice is that physicists can read in about 5 nanoseconds what it takes ordinary people ages to get through. He starts with the cover, of course. 'Reviewed in the Financial Times?' A derisive snort follows. 'Ah,' he remarks after the third nanosecond. 'He's written this kind of science book.' I like that. I have no clue what it means, but I like it.

After four nanoseconds, he is up to page 1050 or so. He reads out a question from it and says 'That is a good question. I don't know the answer.' He slaps the book shut. Really, for the most part, I get the impression that real physicists like him just wish those other physicists would just stop. Stop with all the philosophical 'should we be worried about this?' kind of stuff. Let's just get on with it, please.

And he says 'You didn't mention that the dinner invitation came with a catch.' I reply 'But I didn't say it didn't, did I?'

I am seriously considering reading this while skipping every page that doesn't have only words on it. Seriously.

Deciphering the laws of physics to create universal reality

This is an exhaustive review of the laws of physics as related to physical reality, with a significant emphasis on the mathematical component. The author, an outstanding mathematical physicist of our times, in this 1100-page book, describes the concept of space, time, and matter (energy) in terms of classical physics, quantum physics, string theory, and its derivatives.

In physics, the behavior of objects is understood through the action of a force, a vector quantity with both magnitude and direction. The force acts on matter and produces a causative action that results in an effect. The cause-effect relationship is a fundamental aspect of classical reality, but it becomes fuzzy and uncertain at the submicroscopic level (quantum physical reality). The main objective of physical laws is to describe the reality we observe, which includes this universe composed of space, time, matter, and energy. All objects are made of matter, existing as complex structures composed of molecules, atoms, and fundamental particles. Matter is also a form of energy, and the two can interconvert as described by Einstein's famous equation. The fundamental particles have certain physical properties, and the way energy (and force) is expressed is through their association with the so-called force particles responsible for the four fundamental forces in nature: electromagnetism, gravity, strong and weak nuclear forces. These four forces mediate matter-matter interaction and facilitate matter-energy conversions in spacetime, thus explaining physical reality. The key to understanding nature and physical reality is to discover a theory that satisfactorily explains all four forces and is experimentally verifiable. Unfortunately, this has not been achieved so far, but we have theories that can be verified and explain only three forces. A single physical theory that explains both quantum and classical realities has not been successful mainly because the nature of the gravitational force (curved spacetime) is difficult to describe in a unified situation, as space and time at the most fundamental level are also quantized (exist in discrete quanta) and are dynamic (not a static background).

To understand this book, the reader is required to have an undergraduate level of physics and mathematics. The author explains in the introductory part of the book why he chose to include mathematics despite its potential negative impact on the book's marketing. Suffice it to say that the interplay between mathematical ideas and physical behavior played an important aesthetic role in the minds of great physicists, and Albert Einstein is one of the most important figures attracted aesthetically to a particular idea. You can skip chapters 1-16, and from chapters 17-30, a general discussion about the geometry of spacetime, quantum physics, quantum field theory, quantum cosmology, and the standard model of particle physics is presented. I found the last four chapters to be the most interesting.

A brief summary is as follows: The unification of special relativity and quantum theory led to quantum field theory (QFT), which produced a minefield of infinities. However, with some ingenuity, the infinity problem was circumvented, leading to the standard model of particle physics, which is in good agreement with nature. The controversy between the quantum relativity group and the QFT side is that the latter group tries to achieve renormalizability or finiteness as the primary goal, while the former group prefers to solve the conceptual difficulties between the two theories. The combination of two theories of particle physics into one framework to describe all interactions of subatomic particles, except due to gravity, is called the standard model. These two theories are the electroweak theory and quantum chromodynamics. They describe force interactions between particles in terms of the exchange of intermediary particles. The author also engages the reader in an insightful discussion of many other theories.

This article presents a challenging read due to the abundance of math involved.

However, for those individuals who possess the ability and determination to persevere through it, the effort is truly well worth it.

The complex mathematical concepts and equations might initially seem overwhelming, but they hold the key to a deeper understanding of the subject matter.

By grappling with the math, readers can gain valuable insights and expand their knowledge in a particular field.

It requires patience, focus, and a willingness to engage with the material on a more profound level.

Although it may not be an easy task, the rewards that come from successfully navigating through the math are significant.

So, for those brave enough to take on the challenge, this article offers a wealth of knowledge and a unique learning experience.

In my opinion, this is superior to most of the competitors.

It outshines works like Stephen Hawking's "A Brief History of Time", Brian Greene's "The Elegant Universe", Lee Smolin's "Three Roads to Quantum Gravity", David Albert's "Quantum Mechanics and Experience", and even the Feynman Lectures.

Penrose's attempt is comprehensive and uncompromising. He doesn't hold back. However, you can also flip through and get concise explanations. The difference is that they are not cheesy, and you don't have the feeling of being left with a weak metaphor that lacks substance.

This is highly recommended to those who wish to understand quantum mechanics or the "deep meaning" of physics.

It might take you a few years to read, along with many visits to Wikipedia. But it is far more worthwhile than spending your time on something that doesn't truly explain it to you.

You will gain a deeper and more profound understanding through this book, which makes the effort well worth it.

This book delves into an extensive array of topics, ranging from Euclid's postulates to Schrodinger's cat.

It particularly appeals to me as it presents scientific principles in chronological order. This allows readers to witness the evolution of knowledge. Additionally, a sprinkling of historical facts about scientists can assist the audience in digesting these challenging concepts.

However, his captivating narrative has a downside: learning science concepts chronologically may not be the most optimal approach. In some instances, it can be more difficult to understand an older concept. Sometimes, it is preferable for a beginner to become acquainted with more modern techniques before delving into more traditional ones. Also, the necessary subject continuity may not be present in timely consecutive items.

Nevertheless, if you are already familiar with these principles, it is incredibly enjoyable to see them all laid out over a broad timeline and gain the big picture.

"Road to Reality" is similar to Stephen Hawking's "A Brief History of Time," but unlike that, it is by no means a brief history, and Hawking is indeed a better tutor. If you find some chapters a bit intimidating, I guarantee you can find alternative sources with simpler explanations. In particular, I had a difficult time understanding several chapters in the math section. The same material is presented with more clarity and accessibility in Thomas' Calculus or Kreyzig's Advanced Engineering Mathematics.

There is one more thing I should mention, but I truly hope no mathematicians read this. Life is too short to waste time on the Riemann sphere and Fourier series in the earlier chapters, which are just dry mathematics. Consider them as tools and familiarize yourself with their capabilities in case you ever need to use them. The real excitement begins after chapter 17 when physics, astrophysics, and quantum are covered.

I am truly desperate to make it through this book. Maybe I'm crazy, but I think part of my intense desire to finish it stems from compensating for not graduating from engineering school. I can tell you this much:

It would have been a whole lot easier to read if I had actually obtained my degree and learned the relevant material along the way. Nevertheless, this book commences in the most interesting and captivating manner, which speaks volumes about a book that endeavors to explain the universe by traversing the history of mathematics.

A couple of years ago, I noticed a man reading it while on the treadmill at the gym. The book is a hefty 1000 pages long, and after seeing the title, I inquired about it. I asked him if one needed to have a solid understanding of advanced mathematics to read it (which, despite having completed Calculus 1 - 4, I do not possess). He replied, "Oh no, I don't know much math but I'm enjoying it anyway."

Well, it soon became evident early on in the book that the guy at the gym was completely off his rocker (or rather, off his treadmill). After the attention-grabbing opening, the author meticulously details the origins of mathematics, the definitions of "proof", "theorem", and "postulates", and aims to start from "point A" and progress through to whatever lies beyond mathematical "point Z".

So, with an initial sense of excitement, I began reading the book. Soon, I had a scratch pad at the ready. Then, I was reading and re-reading sections in an attempt to understand before moving on. It reminded me of my struggles during my calculus classes at Michigan Tech. I have a strong interest in the material and a longing to learn it, but it really strains my little brain.

In conclusion, I am still grappling with the first 100 pages, but I would still highly recommend this book, especially to those with an interest and aptitude for math and science. I'll persevere.
~ Mike - February 2009

In this remarkable book, Roger Penrose delves into an extremely fundamental issue.

He endeavors to seek a single metric that can describe everything.

However, this is not a unit of reality, despite the way he formulates the problem.

The challenge of choosing a metric, as he repeatedly demonstrates, lies in how different metrics emerge from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics may be on the verge of collapsing. In numerous cases, the metrics (and their associated relationships) will no longer be applicable. In the Kantian (and Badiouian sense), this implies that the applicability of these relationships will become "undecidable". In some extreme situations, the relationships may even break down. For example, black holes pose a problem because the relationships expressed through physics experiments prove to be unviable in black holes (and the big bang) as these relationships decohere and infinities and zeros emerge everywhere.

This search for a metric leads Penrose to reject string theory as a viable form of relationship. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, and the weak force is a dimension. Each dimension is an independent mathematical vector of a different "inertial" influence. Additionally, the mathematics of string theory, as well as other theories, prove to be overly illusory. Similar to post-structural critiques of modernism, Penrose points out that the consistency of string theory depends on theoretical supplements/signs that are attached to the positions of various types to maintain coherency. For example, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions and its inherent effects prove to be unmanageable for Penrose because the coherence of the relationships is maintained by theoretical enforcement rather than any direct correlation between math and physical experimentation.

If Penrose were familiar with Badiou, Kant, and Derrida, he would be able to recognize that the undecidability of supersymmetry and string theory results from these theoretical supplements. The supplements provide the missing pieces to coherently form the theory, so physical experiments prove to be incomplete in their testing. As Penrose notes, string theorists, in the absence of finding superpartners, can always adjust the calibration of their theory to include these partners, just at higher energy levels that are always beyond the reach of technology to generate.

In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose makes a mistake when he theorizes that Quantum Field Theory can be modified (rather than Einstein's general relativity) by changing the cut-off metric. This is in line with all his discussions about "renormalizing" the math to eliminate the variance accumulated by extending localized relations beyond the area of origin on the manifold. We can always enforce the consistency of a given domain in two ways.

1. To provide a "superpartner" to supplement the terms and keep the phenomena visible to each other within the domain, as a movement of immanence, as Derrida suggests.

Or.

2. To encapsulate a domain by limiting its identity to its other. From there, we can radically reduce the other to zero, thereby hiding the limitations of a domain, as in the case of Moffe & Laulau with their Hegemony or as with Badiou with a basic atomic "cut" to center the domain as in Being and Event II.

Both of these strategies amount to the same kind of forced coherency by rigidly mapping a domain.

Penrose does offer his own favored solution; his Twistor theory, which eliminates the need for extra dimensions beyond 3 + 1. Additionally, he conceives of this theory by collapsing all the different vector differences held cosmically in string theory into immanent relations that are founded on the very "knots" of space, so that the pre-space twistors contain the information that wider "vibrations" are intended to express. Both theories are incompatible in this regard due to their significant difference in scale.

And while Penrose admits that twistor theory adds nothing physically; that it's just another way of viewing a situation mathematically, he also realizes the need for us to see things differently than we have.

It is this adherence to a particular view that causes all the problems in the first place. If you examine how these different views are constructed, you'll observe that mathematicians switch from one domain to another through various class equivalences whenever it suits them. When they need to express vectors, they will jump to a manifold model or a more generic (abstract) deformation of an algebra. In other words, we lack sufficient views. So we supplement the one we have in an attempt to normalize them.

Even more curiously, Penrose has a brief discussion of consciousness in which he attempts to "renormalize" consciousness in terms of objective reduction. He theorizes that the waveform reduction that collapses due to quantum gravity may be at the core of consciousness's ability to complexly project different sensory views into coherency. This suggestion is of the same nature as his forced synthesis of twistor theory. The satisfaction of attempting to find a single metric, a single complex knot of relations that cannot be unraveled but contains all the "moves", is like a physicist trapped on a chessboard recognizing the orthogonal formation of the board or, as in Futurama, the Professor discovering that the smallest unit that constitutes the universe is the pixel.

In a real sense, Penrose aims to calibrate physics to the mathematical domain. He doesn't desire beautiful math that doesn't apply or is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth onto which the entirety of the physical is mapped; although mentality is generated from the physical and the mathematical/Truth is generated from that.

The Platonic ideologue he adheres to lies in the equivalence of function, on the purity of the sameness of process from point to point of the same type. Never mind that the subatomic particles we discover today are largely generated through artificial means. Penrose would assume a sameness of process that forces a universalization, but that is the way both metaphysics and science operate, to equate different phenomena as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we can see, all relations are born locally, within a limited scope. Their cosmic extension creates the basis for which we begin to witness a degradation of the relationship in terms of variance (pollution, or various forces of form-fitting). After all, we can have no irrationality without first being able to posit a rational sheet of complete consistency.

Nonetheless, although this is a lengthy book, it is still beautifully written. I wonder who Penrose's intended audience is, as he approaches a great deal of mathematical complexity in such a short time, discussing basic principles like polynomials and trigonometry before leaping into Lagrangian manifolds and so on. Still, if you have a hunger for complexity and abstraction, it is here. Much of his explanations of very complex concepts are very clear, although at times we could use more guidance. His illustrations are also very interesting and complement his points nicely.

Well worth the effort to read.