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The Road to Reality: A Complete Guide to the Laws of the Universe
**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS**The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book.Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections.The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit.'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin
1022 pages, Kindle Edition
First published January 1, 2004
About the author
Roger Penrose
89 books1,179 followersSir Roger Penrose is a British mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge, and University College London.
Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".
Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".
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September 5, 2011
Many of my all-time favourite books make the list because they show you what it's like to be inside the mind of an extraordinary person. While you're reading them, Churchill's History of the Second World War and Yourcenar's Mémoires d'Hadrien let you be a great statesman at a pivotal moment in history. Simone de Beauvoir's autobiography, more than any other book I know, gives you the feeling of being a major literary figure. Polugayevsky's Grandmaster Preparation, which many chessplayers treat almost as a sacred text, is the only truly honest account I've seen of how a top Grandmaster thinks.
Penrose belongs in this select company: I finally believe I have some idea, no matter how faint, of how a great mathematical physicist sees the universe. Like the other books, it's not an easy read. You can't build up this kind of picture without including a huge number of details; if you took them away, the whole texture of the world would disappear with them. Churchill needs the maps, troop movements and political networking. De Beauvoir has to assume (in my case, alas, incorrectly), that you're conversant with most of French literature. And if you removed the chess from Polugayevsky, there wouldn't be any story.
In Penrose's case, it's mathematics and physics: he resolutely refuses to dumb it down, and includes a seriously frightening quantity of Greek letters. If it really were true that every equation halved your sales, he would not have sold a single copy. What saves him, and makes the book readable to non-experts like me who at least have some mathematical background, is his uniquely visual way of experiencing mathematics. Penrose can obviously hack the equations, but he also has to see them, and he is astonishingly resourceful at coming up with visualisations. The ones I liked most had to do with Special Relativity. You may recall this fairly well-known picture by Escher:
What I didn't know was that it illustrates the "hyperbolic geometry" which 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 time you add a velocity to itself, you never get to the speed of light. Believe it or not, the diagram exactly 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 anything but 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 who came 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 pretty much the same as in Blake's version: the picture dramatizes the extremely low entropy of the Universe immediately after the Big Bang. I had not previously appreciated 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 ploughing my way 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 who's working on validation of 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 wrong 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 sprinkling of reviews here from people who give every appearance of having read and enjoyed it.
Penrose belongs in this select company: I finally believe I have some idea, no matter how faint, of how a great mathematical physicist sees the universe. Like the other books, it's not an easy read. You can't build up this kind of picture without including a huge number of details; if you took them away, the whole texture of the world would disappear with them. Churchill needs the maps, troop movements and political networking. De Beauvoir has to assume (in my case, alas, incorrectly), that you're conversant with most of French literature. And if you removed the chess from Polugayevsky, there wouldn't be any story.
In Penrose's case, it's mathematics and physics: he resolutely refuses to dumb it down, and includes a seriously frightening quantity of Greek letters. If it really were true that every equation halved your sales, he would not have sold a single copy. What saves him, and makes the book readable to non-experts like me who at least have some mathematical background, is his uniquely visual way of experiencing mathematics. Penrose can obviously hack the equations, but he also has to see them, and he is astonishingly resourceful at coming up with visualisations. The ones I liked most had to do with Special Relativity. You may recall this fairly well-known picture by Escher:
What I didn't know was that it illustrates the "hyperbolic geometry" which 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 time you add a velocity to itself, you never get to the speed of light. Believe it or not, the diagram exactly 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 anything but 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 who came 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 pretty much the same as in Blake's version: the picture dramatizes the extremely low entropy of the Universe immediately after the Big Bang. I had not previously appreciated 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 ploughing my way 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 who's working on validation of 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 wrong 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 sprinkling of reviews here from people who give every appearance of having read and enjoyed it.
August 4, 2016
I am finished, finally. All the 1050+ pages of this ambitious behemoth - including many exercises. What a ride!...
Finished? Well you are never finished with such a book, titled “The road to reality” but actually providing more than that: providing nothing less than a “road-map” to reality, and opening to the reader new beautiful vistas in modern mathematics and physics. I am sure that I will come back to this book in the future, as a source of inspiration and for future reference.
Before I start, I must confess that it feels slightly ridiculous for me to critique such a monumental work by a crazy genius like Penrose, who clearly lives in a higher realm of consciousness than the large majority of us common mortals. Never mind – the best I can do is to describe my personal, deeply humbling experience in reading this amazing piece of intellectual prowess. Penrose is clearly the Mozart of mathematical physics: genius, craziness, wild imagination and pure technical virtuosity all combined into a unique intellect.
Let me start by highlighting some of the peculiarities of this book (due, in my personal opinion, much to editorial/commercial choices/pressures, and only partially to personal choices by the author himself). This is also important to the proper positioning of this book within the overcrowded (and of hugely varying quality) world of popular science books:
A) this book is sold as a science “popularization” (probably with the objective to attract as wide an audience as possible): in reality this book requires a significant amount of background knowledge in mathematical physics; in fact there are some sections where the equivalent of a full maths/physics degree would be required to fully appreciate all the subtleties of some of the subjects being treated. I would personally recommend, as a prerequisite, the following minimum:
- calculus (including multivariate)
- ordinary and partial differential equations (at least at rudimentary level)
- complex analysis
- linear algebra
- basics of topology
- ideally, differential geometry at basic level
- in the physics area, some prior exposure to Maxwell's equations, the Lagrangian and Hamiltonian formalisms, the basics of quantum mechanics and relativity (at least special) would also be a great help.
If a reader tried this book with no prior exposure to any such topics, I am afraid that it all might prove a very steep learning curve indeed. I had all the above pre-reqs, and still it was, for me, an occasionally demanding if not challenging book in terms of required focus, time and intellectual stamina. But this is also a strength of this book - one of its greatly rewarding aspects is that the author does not refrain from exposing the reader to real maths (some of the exercises can be pretty hardcore), and to get into the heart of modern physical theories such as QFT and GR, if you want the real thing, you simply can't avoid getting into some real maths.
B) this book is not really a textbook, or at least not an ordinary textbook: it lacks the necessary structure and flow, and (too) many important derivations are left as exercises. The depth of mathematical analysis and rigour are uneven, and they seems also highly dependent on the occasionally whimsical personal level of the author's interest in the subject. Moreover, the formal treatment of many subjects is highly original and something that, unless you have had some previous exposure to them, might be confusing and certainly not easily reconcilable with what standard textbooks present. But this is part of the beauty of this masterpiece.
C) this book, contrarily to what stated in the title, is not a “complete” guide to the laws of the Universe. While managing to concentrate so many sophisticated and fascinating subjects into a single book, and at a serious level of detail (which is no mean feat, and something quite unique), I think that Penrose should have written two books (one on the mathematical underpinnings, and a separate one on the physical aspects) rather than trying to concentrate such a massive amount of information in one single big book.
This approach (admittedly less palatable from a commercial standpoint) would have allowed him to expand some important areas that he has unfortunately neglected in his otherwise magnificent book (such as finiteness and re-normalization issues in QFT) and which would have also allowed him to include other subject matters too – for example, the coverage of thermodynamics focuses mainly on the statistical view of the Second Law, neglecting all the other elements.
But make no mistake - this book feels like a "War and Peace" of mathematical physics – a colossal enterprise that just keeps giving and giving, a treasure trove of original insights, beautiful hidden connections, amazing stories and revelations. A fantastic and detailed exploration of quantum physics, relativity, of the current trends in the attempts to unify the two, and of cosmology. An exhilarating intellectual adventure in the company of a crazy genius.
Let me now make a few comments about the author's peculiar personal style and approach:
- Penrose's prose is beautiful, even if considered from a purely literary perspective; often very clear even if sometimes a bit too concise; it usually flows very smoothly, and it occasionally even acquires some poetical undertones in sections where aspects of philosophy of science and philosophy of mathematics are treated with insightful passion.
- Penrose relies heavily on a diagrammatical/pictorial/visual/topological representation of the concepts being treated. In doing so, many beautiful, eye-catching and highly informative hand-drawn diagrams/pictures are presented to the user. This approach generally works very well, but there are instances where (in my personal opinion) the most intuitive and simplest way to learn/teach a new concept is to present it analytically (in mathematical format), and where the purely visual approach might be quite limiting if not outright confusing. For example, the visual explanation of the concept of “covariant derivative”: while important and helpful, is in my opinion by itself not sufficient to get a real appreciation of the mathematical features of this entity: its analytical derivation, and its expression using the Christoffel symbols, would have actually better clarified its tensorial nature.
- In order to condense as many subjects as possible within the constraints of the space allowed by one single book (even one of 1050+ pages) Penrose has left the derivation of many important results as “exercises”. The exercises are therefore very important, they are a must in order to get a full appreciation of the underlying theory, and some of them are beautiful and rewarding (like exercise 22.32, which entails a beautifully elegant derivation of the Laplacian in spherical coordinates, using the curved metric and covariant derivatives). But some others should not have been left as exercises, and they seem no more than an editorial cop-out: there is one exercise that is even asking the reader to complete a significant derivation step of the GR field equations! (thankfully there is a website where many exercises have been solved by other readers (the majority of them clearly with a professional background in mathematical physics) – see https://sites.google.com/site/vascopr... ).
- I love Penrose's great intellectual honesty in not just debunking much of the hype behind String Theory and Multiverse Hypotheses in general, and in destroying the so-called “Strong Anthropic Principle”, but also in making very clear the speculative character of some of his own positions and theories. I also love his great originality and independence of mind, and his nuanced, multi-disciplinarian approach which includes aspects of philosophy of science and considerations of pure mathematical nature.
- Penrose has reached such a higher, rarefied level of proficiency in mathematical physics that he must have completely forgotten how common humans think in relation to mathematical formalism. Just as an example: after getting into pretty advanced stuff such as hyperfunctions, and treating it like if it is the simplest thing on Earth, the author then refuses to get into a detailed definition of differentiability of a many variable function (which is quite simple, really) because "it is too technical"!! So his ideas of what is complex can occasionally be significantly at variance with what the common mortal might think.
Finally, let me add here some miscellaneous notes about selected individual chapters of this majestic book (it is a very incomplete list, only a severely reduced sample, as there is simply too much stuff in this book for me to be able to analyse in just one review):
- In the first few chapters, after a fascinating introduction of overall philosophical character, Penrose briefly addresses some of the basic fundamentals of mathematics, including a short but intensely interesting discussion about the Axiom of Choice and its relationship to the Zermelo–Fraenkel set theory. A totally fascinating subject that unfortunately Penrose only touches, without developing into more detail.
There is also a fascinating treatment of hyperbolic geometry, and of the number system/s. However, when dealing with the relationship between real numbers and reality, the author does not make any reference to important aspects such as computability and irreducible complexity, as for example addressed by the excellent work done by G.Chaitin.
- The author then gets into one of the most beautiful and fascinating realms of mathematics - complex analysis. The treatment is concise but done well, and I completely share Penrose's enthusiasm and love for the aesthetically as well as functionally beautiful world of complex numbers, which he calls “magical” with good reason.
- Another subject of interest treated are the fascinating quaternions, which extend the complex numbers and provide the uncommon and interesting features of a non-commutative division algebra. There are in the book a couple of minor missing things in relation to the algebraic structure of quaternions: an algebra is a vector space that must also be equipped with a bilinear product, and a ring (being also an abelian group under addition) must be provided with an additive inverse.
Moreover, Penrose is dismissive of the utility of the quaternions in the development of physical theories – this is correct, but it must also be said that quaternions find important uses in Information technology applications, in particular for calculations involving three-dimensional rotations, computer graphics and computer vision.
- Penrose could not have forgotten the extremely important Clifford/Grassmann algebras, which are foundational to the entire architectural structure of mathematics, and he didn't; they are treated well, but a bit too succinctly in my opinion, considering their importance.
- Symmetry groups are treated really well, clearly and concisely. Very nice.
- Manifolds and calculus on manifolds: all is treated quite well, but I would have found quite helpful some more analytical detail rather than a focus almost exclusively on the visual/topological approach. I confess that here, in order to get a proper detailed handle of tensor calculus and exterior calculus, I had to consult other more traditional, “textbook-type” sources.
- Chapter 16 (Cantor's infinities, continuum hypothesis, Godel's incompleteness, Turing computability and similar) is OK and well written, and it would be utterly fascinating to a neophyte – but of course it could not have been detailed nor exhaustive, considering the complexity and width of such subjects.
- The “Physics” part proper starts with Chapter 17. Chapter 17 on spacetime, and chapter 18 on Minkowskian geometry (and special relativity of course) are succinct, but riveting and beautifully written. Just one small note: Penrose has a fetishism for non-standard, or uncommon, notational or representational choices, not always justified: for example, by using a non-standard metric tensor in page 434, Penrose gets himself into an error at the end of page 435 (c^4 should have been used rather than c^2) and I think that he would not have fallen into this typo, had he used the more standard and simple-to-use metric.
- Chapter 19 (Maxwell and Einstein) are beautiful; Maxwell equations and Einstein field equations in tensorial/differential form are mind-blowing for their mathematical conciseness and beauty, and this is where the reader can start to see the value of the mathematical apparatus described in the previous chapters: things such as manifolds, tensors, exterior derivatives and bundle connections. Einstein's fields equations of general relativity are beautiful. Very rewarding. It all seems so neat and perfect, but then, the bombshell (at least to me, who was never told of such a thing!): the energy/momentum stress tensor does not account for the energy density of the gravitational field itself, and it seems that conservation of energy/momentum is non-local !
- Chapter 20: Lagrangians and Hamiltonians: I must say that they are too hastily discussed - the derivation of the Euler–Lagrange equation (one of the most classic proofs in mathematics) is not treated, the Legrende transform to derive the Hamiltonian from the Lagrangian is not treated, the derivation of Hamilton's evolution equations is not treated either. Not very happy with this chapter.
- The subsequent chapters on quantum mechanics are beautiful, and the description of the EPR issue is really nice. The derivation of Dirac's equations is equally beautiful. I also love Penrose's discussion and perspectives about the measurement paradox. Beautiful stuff indeed. An exception to the overall masterful treatment of Quantum Physics is chapter 26 (Quantum Field Theory) which is is a bit too qualitative - more like a "popularization" rather than a treatment at the same good level as done in the other chapters of this book – and unfortunately the important subject of re-normalization is treated only briefly and qualitatively.
- The chapters on cosmology are very interesting and nicely written.
- Chapter 29 is essentially about the measurement paradox and the various interpretations of quantum mechanics – succinctly but beautifully written.
- The next chapters are essentially about the current unification attempts to reconcile QFT with GR. Penrose's FELIX experiment proposal (essentially testing the hypothesis of automatic quantum state-reduction as an objective gravitational effect) is utterly fascinating, but I feel that I should not bet any money on this daring hypothesis.
- I must say though that I was disappointed by the second part of chapter 33 (twistor theory): in section 33.8 Penrose uses several verbose sentences to express mathematical relationships, rather than writing down the actual underlying equations - result: something quite close to incomprehensible. I also fail to get the underlying physical intuition. Pity, as the other 33 chapters and a half are mostly beautifully written, and generally very rewarding.
- The last chapter (34) is beautifully written, and it deals primarily with aspects of philosophy of science and philosophy of mathematics.
To summarize: this is an immensely rewarding, even exhilarating book - a fantastic reading and learning experience. And it has opened my eyes on many aspects and connections that I was not aware of, and new beautiful vistas in modern mathematics (for example: tensor calculus, and exterior calculus in general) that I will now pursue in more depth.
After reading this great book, I can tell you that I now feel that the majority of popular science books I have read are dull and superficial by comparison.
It is not a perfect book by any means, but overall it is a great book, unique in its approach and contents. Not exhaustive, but with a huge and ambitious scope, virtually unrivaled in its category. It is much more than a “standard” popular science book. Very highly recommended, to be bought, studied, enjoyed and kept for future reference.
4.5 stars (rounded up to 5).
UPDATE: with link to a beautiful series of online lectures about Tensor Calculus and the Calculus of Moving Surfaces: https://www.youtube.com/playlist?list... (highly recommended to anybody interested in this subject).
Finished? Well you are never finished with such a book, titled “The road to reality” but actually providing more than that: providing nothing less than a “road-map” to reality, and opening to the reader new beautiful vistas in modern mathematics and physics. I am sure that I will come back to this book in the future, as a source of inspiration and for future reference.
Before I start, I must confess that it feels slightly ridiculous for me to critique such a monumental work by a crazy genius like Penrose, who clearly lives in a higher realm of consciousness than the large majority of us common mortals. Never mind – the best I can do is to describe my personal, deeply humbling experience in reading this amazing piece of intellectual prowess. Penrose is clearly the Mozart of mathematical physics: genius, craziness, wild imagination and pure technical virtuosity all combined into a unique intellect.
Let me start by highlighting some of the peculiarities of this book (due, in my personal opinion, much to editorial/commercial choices/pressures, and only partially to personal choices by the author himself). This is also important to the proper positioning of this book within the overcrowded (and of hugely varying quality) world of popular science books:
A) this book is sold as a science “popularization” (probably with the objective to attract as wide an audience as possible): in reality this book requires a significant amount of background knowledge in mathematical physics; in fact there are some sections where the equivalent of a full maths/physics degree would be required to fully appreciate all the subtleties of some of the subjects being treated. I would personally recommend, as a prerequisite, the following minimum:
- calculus (including multivariate)
- ordinary and partial differential equations (at least at rudimentary level)
- complex analysis
- linear algebra
- basics of topology
- ideally, differential geometry at basic level
- in the physics area, some prior exposure to Maxwell's equations, the Lagrangian and Hamiltonian formalisms, the basics of quantum mechanics and relativity (at least special) would also be a great help.
If a reader tried this book with no prior exposure to any such topics, I am afraid that it all might prove a very steep learning curve indeed. I had all the above pre-reqs, and still it was, for me, an occasionally demanding if not challenging book in terms of required focus, time and intellectual stamina. But this is also a strength of this book - one of its greatly rewarding aspects is that the author does not refrain from exposing the reader to real maths (some of the exercises can be pretty hardcore), and to get into the heart of modern physical theories such as QFT and GR, if you want the real thing, you simply can't avoid getting into some real maths.
B) this book is not really a textbook, or at least not an ordinary textbook: it lacks the necessary structure and flow, and (too) many important derivations are left as exercises. The depth of mathematical analysis and rigour are uneven, and they seems also highly dependent on the occasionally whimsical personal level of the author's interest in the subject. Moreover, the formal treatment of many subjects is highly original and something that, unless you have had some previous exposure to them, might be confusing and certainly not easily reconcilable with what standard textbooks present. But this is part of the beauty of this masterpiece.
C) this book, contrarily to what stated in the title, is not a “complete” guide to the laws of the Universe. While managing to concentrate so many sophisticated and fascinating subjects into a single book, and at a serious level of detail (which is no mean feat, and something quite unique), I think that Penrose should have written two books (one on the mathematical underpinnings, and a separate one on the physical aspects) rather than trying to concentrate such a massive amount of information in one single big book.
This approach (admittedly less palatable from a commercial standpoint) would have allowed him to expand some important areas that he has unfortunately neglected in his otherwise magnificent book (such as finiteness and re-normalization issues in QFT) and which would have also allowed him to include other subject matters too – for example, the coverage of thermodynamics focuses mainly on the statistical view of the Second Law, neglecting all the other elements.
But make no mistake - this book feels like a "War and Peace" of mathematical physics – a colossal enterprise that just keeps giving and giving, a treasure trove of original insights, beautiful hidden connections, amazing stories and revelations. A fantastic and detailed exploration of quantum physics, relativity, of the current trends in the attempts to unify the two, and of cosmology. An exhilarating intellectual adventure in the company of a crazy genius.
Let me now make a few comments about the author's peculiar personal style and approach:
- Penrose's prose is beautiful, even if considered from a purely literary perspective; often very clear even if sometimes a bit too concise; it usually flows very smoothly, and it occasionally even acquires some poetical undertones in sections where aspects of philosophy of science and philosophy of mathematics are treated with insightful passion.
- Penrose relies heavily on a diagrammatical/pictorial/visual/topological representation of the concepts being treated. In doing so, many beautiful, eye-catching and highly informative hand-drawn diagrams/pictures are presented to the user. This approach generally works very well, but there are instances where (in my personal opinion) the most intuitive and simplest way to learn/teach a new concept is to present it analytically (in mathematical format), and where the purely visual approach might be quite limiting if not outright confusing. For example, the visual explanation of the concept of “covariant derivative”: while important and helpful, is in my opinion by itself not sufficient to get a real appreciation of the mathematical features of this entity: its analytical derivation, and its expression using the Christoffel symbols, would have actually better clarified its tensorial nature.
- In order to condense as many subjects as possible within the constraints of the space allowed by one single book (even one of 1050+ pages) Penrose has left the derivation of many important results as “exercises”. The exercises are therefore very important, they are a must in order to get a full appreciation of the underlying theory, and some of them are beautiful and rewarding (like exercise 22.32, which entails a beautifully elegant derivation of the Laplacian in spherical coordinates, using the curved metric and covariant derivatives). But some others should not have been left as exercises, and they seem no more than an editorial cop-out: there is one exercise that is even asking the reader to complete a significant derivation step of the GR field equations! (thankfully there is a website where many exercises have been solved by other readers (the majority of them clearly with a professional background in mathematical physics) – see https://sites.google.com/site/vascopr... ).
- I love Penrose's great intellectual honesty in not just debunking much of the hype behind String Theory and Multiverse Hypotheses in general, and in destroying the so-called “Strong Anthropic Principle”, but also in making very clear the speculative character of some of his own positions and theories. I also love his great originality and independence of mind, and his nuanced, multi-disciplinarian approach which includes aspects of philosophy of science and considerations of pure mathematical nature.
- Penrose has reached such a higher, rarefied level of proficiency in mathematical physics that he must have completely forgotten how common humans think in relation to mathematical formalism. Just as an example: after getting into pretty advanced stuff such as hyperfunctions, and treating it like if it is the simplest thing on Earth, the author then refuses to get into a detailed definition of differentiability of a many variable function (which is quite simple, really) because "it is too technical"!! So his ideas of what is complex can occasionally be significantly at variance with what the common mortal might think.
Finally, let me add here some miscellaneous notes about selected individual chapters of this majestic book (it is a very incomplete list, only a severely reduced sample, as there is simply too much stuff in this book for me to be able to analyse in just one review):
- In the first few chapters, after a fascinating introduction of overall philosophical character, Penrose briefly addresses some of the basic fundamentals of mathematics, including a short but intensely interesting discussion about the Axiom of Choice and its relationship to the Zermelo–Fraenkel set theory. A totally fascinating subject that unfortunately Penrose only touches, without developing into more detail.
There is also a fascinating treatment of hyperbolic geometry, and of the number system/s. However, when dealing with the relationship between real numbers and reality, the author does not make any reference to important aspects such as computability and irreducible complexity, as for example addressed by the excellent work done by G.Chaitin.
- The author then gets into one of the most beautiful and fascinating realms of mathematics - complex analysis. The treatment is concise but done well, and I completely share Penrose's enthusiasm and love for the aesthetically as well as functionally beautiful world of complex numbers, which he calls “magical” with good reason.
- Another subject of interest treated are the fascinating quaternions, which extend the complex numbers and provide the uncommon and interesting features of a non-commutative division algebra. There are in the book a couple of minor missing things in relation to the algebraic structure of quaternions: an algebra is a vector space that must also be equipped with a bilinear product, and a ring (being also an abelian group under addition) must be provided with an additive inverse.
Moreover, Penrose is dismissive of the utility of the quaternions in the development of physical theories – this is correct, but it must also be said that quaternions find important uses in Information technology applications, in particular for calculations involving three-dimensional rotations, computer graphics and computer vision.
- Penrose could not have forgotten the extremely important Clifford/Grassmann algebras, which are foundational to the entire architectural structure of mathematics, and he didn't; they are treated well, but a bit too succinctly in my opinion, considering their importance.
- Symmetry groups are treated really well, clearly and concisely. Very nice.
- Manifolds and calculus on manifolds: all is treated quite well, but I would have found quite helpful some more analytical detail rather than a focus almost exclusively on the visual/topological approach. I confess that here, in order to get a proper detailed handle of tensor calculus and exterior calculus, I had to consult other more traditional, “textbook-type” sources.
- Chapter 16 (Cantor's infinities, continuum hypothesis, Godel's incompleteness, Turing computability and similar) is OK and well written, and it would be utterly fascinating to a neophyte – but of course it could not have been detailed nor exhaustive, considering the complexity and width of such subjects.
- The “Physics” part proper starts with Chapter 17. Chapter 17 on spacetime, and chapter 18 on Minkowskian geometry (and special relativity of course) are succinct, but riveting and beautifully written. Just one small note: Penrose has a fetishism for non-standard, or uncommon, notational or representational choices, not always justified: for example, by using a non-standard metric tensor in page 434, Penrose gets himself into an error at the end of page 435 (c^4 should have been used rather than c^2) and I think that he would not have fallen into this typo, had he used the more standard and simple-to-use metric.
- Chapter 19 (Maxwell and Einstein) are beautiful; Maxwell equations and Einstein field equations in tensorial/differential form are mind-blowing for their mathematical conciseness and beauty, and this is where the reader can start to see the value of the mathematical apparatus described in the previous chapters: things such as manifolds, tensors, exterior derivatives and bundle connections. Einstein's fields equations of general relativity are beautiful. Very rewarding. It all seems so neat and perfect, but then, the bombshell (at least to me, who was never told of such a thing!): the energy/momentum stress tensor does not account for the energy density of the gravitational field itself, and it seems that conservation of energy/momentum is non-local !
- Chapter 20: Lagrangians and Hamiltonians: I must say that they are too hastily discussed - the derivation of the Euler–Lagrange equation (one of the most classic proofs in mathematics) is not treated, the Legrende transform to derive the Hamiltonian from the Lagrangian is not treated, the derivation of Hamilton's evolution equations is not treated either. Not very happy with this chapter.
- The subsequent chapters on quantum mechanics are beautiful, and the description of the EPR issue is really nice. The derivation of Dirac's equations is equally beautiful. I also love Penrose's discussion and perspectives about the measurement paradox. Beautiful stuff indeed. An exception to the overall masterful treatment of Quantum Physics is chapter 26 (Quantum Field Theory) which is is a bit too qualitative - more like a "popularization" rather than a treatment at the same good level as done in the other chapters of this book – and unfortunately the important subject of re-normalization is treated only briefly and qualitatively.
- The chapters on cosmology are very interesting and nicely written.
- Chapter 29 is essentially about the measurement paradox and the various interpretations of quantum mechanics – succinctly but beautifully written.
- The next chapters are essentially about the current unification attempts to reconcile QFT with GR. Penrose's FELIX experiment proposal (essentially testing the hypothesis of automatic quantum state-reduction as an objective gravitational effect) is utterly fascinating, but I feel that I should not bet any money on this daring hypothesis.
- I must say though that I was disappointed by the second part of chapter 33 (twistor theory): in section 33.8 Penrose uses several verbose sentences to express mathematical relationships, rather than writing down the actual underlying equations - result: something quite close to incomprehensible. I also fail to get the underlying physical intuition. Pity, as the other 33 chapters and a half are mostly beautifully written, and generally very rewarding.
- The last chapter (34) is beautifully written, and it deals primarily with aspects of philosophy of science and philosophy of mathematics.
To summarize: this is an immensely rewarding, even exhilarating book - a fantastic reading and learning experience. And it has opened my eyes on many aspects and connections that I was not aware of, and new beautiful vistas in modern mathematics (for example: tensor calculus, and exterior calculus in general) that I will now pursue in more depth.
After reading this great book, I can tell you that I now feel that the majority of popular science books I have read are dull and superficial by comparison.
It is not a perfect book by any means, but overall it is a great book, unique in its approach and contents. Not exhaustive, but with a huge and ambitious scope, virtually unrivaled in its category. It is much more than a “standard” popular science book. Very highly recommended, to be bought, studied, enjoyed and kept for future reference.
4.5 stars (rounded up to 5).
UPDATE: with link to a beautiful series of online lectures about Tensor Calculus and the Calculus of Moving Surfaces: https://www.youtube.com/playlist?list... (highly recommended to anybody interested in this subject).
January 21, 2023
The story begins with me in the garage with my high school sweet heart. The one who had made the playground swing problem seem rather trivial through a guileless intuition which cast my cynical calculations in a kind of hideous antimony. An actor whose relaxed demeanor and gentle earnestness, served to effortlessly unweave the kinks in those rusty chains, and in so doing, spun intractable knots in my own heart. It was a union of opposites, me with my chin in my hand, and he with a wrench in his. There were no problems we could not troubleshoot in tandem. Our separate talents had even began to cross pollinate, with me sometimes starring up at the undercarriage of a vehicle and asking for a socket while he perused whatever theoretical oddities I was currently obsessed with. I could, with some confidence, suggest to people that their alternator was having a giggle, their radiator was taking the piss, their starter motor was an asshole, or, my favorite, “Your fuel economy is gobshite, bruv.” And he could clearly identify the value of switching his choice in the Monty Hall Problem, understand that some infinities are bigger than others, and comprehend the threat that a quantum computer would present to our current encryption protocols. This reciprocal exchange of mental dexterity continued to unfold one rainy day, with me sliding under a car on a rickety creeper (which I had damaged by repeatedly using it to luge down steep driveways at high speeds, causing one wheel to catch and be ground into an irregular half moon.), and Nicolas Kim Coppola (known professionally as Nicolas Cage) (ie. Nic Cage) flipping through the book I had carried in. He asked me what The Road to Reality was about. Paraphrasing, I said the following:
Have you ever, while skidding down a vertiginous concrete pathway on a damaged creeper, felt the fixed vibrational frequency of healthy rotary friction give way to dissonant melodies which often presage the rapid, explosive disassembly of machinery under immense kinetic strain? Was all the blood in your superficial capillaries wrung out from clutching the sides of the sled in mortal terror, causing your knuckles to emerge from the dark like buds of white hibiscus and your pool-noodle arms to ripple like corded steel? Did your sweetheart, who you suspect must have reduced activity in his amygdala, (due to his performance in Ghost Rider: Spirit of Vengeance), leap from their stool and make to halt your (by now considerable) momentum using a bag of blood adumbrated by sticks of calcium (i.e. the vertebral column festooned in viscera and thinly veiled by contractile tissue that we call the human body)? During those tense moments you may have thought, in the heavily affected High English which is characteristic of all your poignant inner musings: Nicolas Cage, it is a pity that I can’t communicate with you more effectively. That our bandwidth is limited by verbal exchanges in which I must compress thoughts into packets of information and utter them as faithfully as I can in the hopes that you will receive and unpack them with minimal noise inserting itself during the transfer. Putting aside incidents in which my limbs have animated in the manner of an ecstatic Neil deGrasse Tyson, this is the extent of my ability to let you experience what it’s like to be me. I cannot understand your genius for seeing the good in every screenplay, and you cannot fathom the depths of my genius when it comes to nearly dying in bizarre ways. In those simple displays of affection where nothing is said, perhaps we say the most.
And what of inhabiting the mind of a true genius, and more difficult still; the mind of brilliant theoretical physicist and math prodigy? With art, something primal touches the soul, so that even if you don’t understand the creative flourishes of virtuosos, you are moved and made aware of their power. Who could read Nabokov and not be humbled by its beauty and precision? Who could hear Hangar 18 by Megadeth and not respect how a guitarist’s flanges dance across wires like the legs of camel spiders on a heroic doses of methamphetamines? Who could see the Venus of Urbino by Titian and not want to bury their face in her gorgeous tummy and blow a gentle raspberry? And finally, who could hear Anton Chigurh request a ‘screwgie’ in No Country for Old Men and not be gripped by a palpable dread? But here the scientific genius faces a problem, in elucidating the purely conceptual matters of their field to a general public, they must conceal much of their brilliance. If they were to riff like Dave Mustaine and fill pages with the lateral movements of their mutant intellects, the majority of us could but collectively shrug before these strange symbols. But imagine if there were a book that managed the impossible. One that was simultaneously accessible to the laymen audience, but omitted none of the technical jargon which made it possible to appreciate the operations of their brilliant minds? Perfectly comprehensible to curious high school freshmen. What you hold in your hands, Nicolas Cage...” Sliding out from under the car and standing next to him. “This..” I say, taking the book gently in my hands. “Is NOT that fucking book!” Throwing it viciously to the ground and jabbing my finger at it. “THIS is madness, Nicolas Cage! This is fucking popsci for math and physics PHDs! Calculus, Fourier series, hyper functions, Riemann surfaces, Riemann mapping theorem, quaternions, Clifford and Grassmann algebras, transformation groups, Lie algebras, parallel transport, geodesics, curvature, exterior derivatives, calculus of manifolds, connections, fibre bundles.. In the first third of a book which contains, in its preface, words that indicate he wrote it for his innumerate aunt. Show me the numerically deficient aunt that made it through this with even the foggiest notion of what the hell was going on and I will crawl inside myself and subsist on my own incredulity until the stars grow cold.”
Nicolas Cage, picking the book up and carefully inspecting it for damage, hands it back to me, saying, “It’s fine. You’ll understand it eventually. I know you will.”
Begrudgingly I put the book under my arm and nod. I feel an insurgent grin dismantle the severity of my countenance. I silently curse his ability to mollify my tantrums so easily. I seize this renewal of levity to suggest we take the creeper out for some limit testing.
“Wait!”
I can now appreciate a lot this book. If you’re someone with a strong background in math and physics and you’re interested, I can’t recommend it highly enough. It may be the most wide-ranging book on theoretical physics I’ve ever seen, not merely summarizing material, but offering an in-depth treatment of many of the more sophisticated ideas of the subject. The first half of the book takes you through most of the mathematical techniques that physicists use today, gradually moving through things like, Riemann surfaces and complex mapping, hypercomplex numbers, manifolds of n dimensions, symplectic groups and tensors. Equations are curated magnificently on the basis of explanatory power. And here I would add that Penrose, perhaps owing to his genius, has a level of idiosyncrasy in his presentation that I don’t think I’ve witnessed since Feynman. It is quite obvious that what goes on in his brain is an intensely visual phenomena. All of his diagrams and drawings are incredibly helpful, especially if you too think in this fashion. The second half of the book is devoted to physics and the ascent is quite dizzying as we approach the various hopeful theoretical bridges we’re constructing in order to reconcile the discontinuities between our two most successful theories (general relativity and quantum field theory) and so you have discussions (it may be more appropriate, considering the sheer rhetorical heft with which Roger slings these ideas against the wall like wet pieces of bologna, to call it evisceration.) String Theory, M Theory, Loop Quantum Gravity, and Penrose’s horse in this race: Twistor Theory. If you do not have a background in these things, and don’t pursue high level mathematics recreationally, I would not recommend it to you as a comprehensive place to start. If you just want to keep it around and flip through it to occasionally augment your understanding with some clever illustrations, or you simply wish to marvel at it as an enduring artifact of the human intellect, by all means. But if you’re planning to work through it from front to back, caveat emptor.
This is one of those rare gems that has brought me very close to experiencing the intuitive ease with which a mathematical genius operates. A beautiful work of staggering breadth and depth.
Have you ever, while skidding down a vertiginous concrete pathway on a damaged creeper, felt the fixed vibrational frequency of healthy rotary friction give way to dissonant melodies which often presage the rapid, explosive disassembly of machinery under immense kinetic strain? Was all the blood in your superficial capillaries wrung out from clutching the sides of the sled in mortal terror, causing your knuckles to emerge from the dark like buds of white hibiscus and your pool-noodle arms to ripple like corded steel? Did your sweetheart, who you suspect must have reduced activity in his amygdala, (due to his performance in Ghost Rider: Spirit of Vengeance), leap from their stool and make to halt your (by now considerable) momentum using a bag of blood adumbrated by sticks of calcium (i.e. the vertebral column festooned in viscera and thinly veiled by contractile tissue that we call the human body)? During those tense moments you may have thought, in the heavily affected High English which is characteristic of all your poignant inner musings: Nicolas Cage, it is a pity that I can’t communicate with you more effectively. That our bandwidth is limited by verbal exchanges in which I must compress thoughts into packets of information and utter them as faithfully as I can in the hopes that you will receive and unpack them with minimal noise inserting itself during the transfer. Putting aside incidents in which my limbs have animated in the manner of an ecstatic Neil deGrasse Tyson, this is the extent of my ability to let you experience what it’s like to be me. I cannot understand your genius for seeing the good in every screenplay, and you cannot fathom the depths of my genius when it comes to nearly dying in bizarre ways. In those simple displays of affection where nothing is said, perhaps we say the most.
And what of inhabiting the mind of a true genius, and more difficult still; the mind of brilliant theoretical physicist and math prodigy? With art, something primal touches the soul, so that even if you don’t understand the creative flourishes of virtuosos, you are moved and made aware of their power. Who could read Nabokov and not be humbled by its beauty and precision? Who could hear Hangar 18 by Megadeth and not respect how a guitarist’s flanges dance across wires like the legs of camel spiders on a heroic doses of methamphetamines? Who could see the Venus of Urbino by Titian and not want to bury their face in her gorgeous tummy and blow a gentle raspberry? And finally, who could hear Anton Chigurh request a ‘screwgie’ in No Country for Old Men and not be gripped by a palpable dread? But here the scientific genius faces a problem, in elucidating the purely conceptual matters of their field to a general public, they must conceal much of their brilliance. If they were to riff like Dave Mustaine and fill pages with the lateral movements of their mutant intellects, the majority of us could but collectively shrug before these strange symbols. But imagine if there were a book that managed the impossible. One that was simultaneously accessible to the laymen audience, but omitted none of the technical jargon which made it possible to appreciate the operations of their brilliant minds? Perfectly comprehensible to curious high school freshmen. What you hold in your hands, Nicolas Cage...” Sliding out from under the car and standing next to him. “This..” I say, taking the book gently in my hands. “Is NOT that fucking book!” Throwing it viciously to the ground and jabbing my finger at it. “THIS is madness, Nicolas Cage! This is fucking popsci for math and physics PHDs! Calculus, Fourier series, hyper functions, Riemann surfaces, Riemann mapping theorem, quaternions, Clifford and Grassmann algebras, transformation groups, Lie algebras, parallel transport, geodesics, curvature, exterior derivatives, calculus of manifolds, connections, fibre bundles.. In the first third of a book which contains, in its preface, words that indicate he wrote it for his innumerate aunt. Show me the numerically deficient aunt that made it through this with even the foggiest notion of what the hell was going on and I will crawl inside myself and subsist on my own incredulity until the stars grow cold.”
Nicolas Cage, picking the book up and carefully inspecting it for damage, hands it back to me, saying, “It’s fine. You’ll understand it eventually. I know you will.”
Begrudgingly I put the book under my arm and nod. I feel an insurgent grin dismantle the severity of my countenance. I silently curse his ability to mollify my tantrums so easily. I seize this renewal of levity to suggest we take the creeper out for some limit testing.
“Wait!”
I can now appreciate a lot this book. If you’re someone with a strong background in math and physics and you’re interested, I can’t recommend it highly enough. It may be the most wide-ranging book on theoretical physics I’ve ever seen, not merely summarizing material, but offering an in-depth treatment of many of the more sophisticated ideas of the subject. The first half of the book takes you through most of the mathematical techniques that physicists use today, gradually moving through things like, Riemann surfaces and complex mapping, hypercomplex numbers, manifolds of n dimensions, symplectic groups and tensors. Equations are curated magnificently on the basis of explanatory power. And here I would add that Penrose, perhaps owing to his genius, has a level of idiosyncrasy in his presentation that I don’t think I’ve witnessed since Feynman. It is quite obvious that what goes on in his brain is an intensely visual phenomena. All of his diagrams and drawings are incredibly helpful, especially if you too think in this fashion. The second half of the book is devoted to physics and the ascent is quite dizzying as we approach the various hopeful theoretical bridges we’re constructing in order to reconcile the discontinuities between our two most successful theories (general relativity and quantum field theory) and so you have discussions (it may be more appropriate, considering the sheer rhetorical heft with which Roger slings these ideas against the wall like wet pieces of bologna, to call it evisceration.) String Theory, M Theory, Loop Quantum Gravity, and Penrose’s horse in this race: Twistor Theory. If you do not have a background in these things, and don’t pursue high level mathematics recreationally, I would not recommend it to you as a comprehensive place to start. If you just want to keep it around and flip through it to occasionally augment your understanding with some clever illustrations, or you simply wish to marvel at it as an enduring artifact of the human intellect, by all means. But if you’re planning to work through it from front to back, caveat emptor.
This is one of those rare gems that has brought me very close to experiencing the intuitive ease with which a mathematical genius operates. A beautiful work of staggering breadth and depth.
February 12, 2016
Dave Langford, SF&F critic and reviewer, in his long-since defunct column for White Dwarf magazine, once said that, "There is a tendency to over-praise big books simply because one has got through them." I agree that this tendency exists but note that Langford gave no reason for it. I think the reason is more or less macho intellectual pride; look at me! I read this honking great saga! It must be great or I'd have to admit wasting my time! And I need to show off my intellectual credentials! Now imagine that the book is not only huge, but really difficult because, say, it's dense with obscure references (e.g. Ulysses) or full of mathematics and not kiddie maths, either...the temptation must be even worse.
Hence I'm going to start my review with a couple of gripes: This book, which is full of maths, much of which would make your average undergrad scientist grunt with the strain at the very least, as well as physics to post-grad level in places, has no glossary of technical terms. There is ample cross-referencing and an index but these are no substitute. When you want to know, Clifford Algebra, which one was that again? (Because you've met ordinary algebra, complex algebra, Clifford Algebras, Lie Algebras and Grassman Algebras...), going back and reading through an entire section again to find out, is a bit annoying - a list of definitions at the back would have helped enormously. Admittedly this would have made a big book even bigger but it would have made it much more user-friendly.
Gripe number two is in a similar vein; Penrose fails to supply a list of the upper and lower case Greek alphabet symbols and their names or a similar list for obscure mathematical symbols, such as del and scri. Given that nobody without training in Greek or in science is going to know these and such a list would only take up one page, its omission is egregious.
This leads neatly into a topic that has been dicussed quite a bit here on Goodreads - namely, who is this book aimed at? What is it's purpose? Firstly I would point out that the subtitle "A Complete Guide to the Laws of the Universe" is not really true: Classical Thermodynamics is barely seen as we rush straight into the statistical view of the Second Law. Of the other three Laws of Thermodynamics, Zero is never mentioned and the others barely name-checked. I doubt many physicists would consider that all the basic theories have been covered in such a circumstance. But I think this is a marketing problem; I don't believe Penrose ever intended to write such a "Complete Guide."
In the preface Penrose talks about wanting, with this book, to make cutting edge physics available to people who struggle to understand fractions. Now, this can only be taken as a joke, considering what one is up against only in chapter 2, but I would guess that Penrose genuinely wants to have the widest possible audience for his book whilst not compromising his aims.
What are those aims? In my view he wants to give his personal views on the state of cosmology and fundamental physics but to be able to do it at an advanced technical and mathematical level and additionally to give his own philosophies regarding the nature of thought, science, maths and...Nature! This means that he wanted to deliver Chapters 27 - 33 on the physics/cosmology, bracketed by Chapters 1 and 34 of philosophising. The entirety of the rest of the book is simply there in order to equip readers to understand what he says in those six technical chapters! This requires 15 Chapters of maths and ten Chapters of physics/cosmology...
Looked at this way, the book begins to reflect the genius and madness of the author: Many of the explanations in earlier stages of the book left me thinking, why do it that way? That's not the easiest way to understand this if you've never come across it before! He also goes straight to very general mathematical principles, missing out intermediate levels of abstraction that might make what comes later easier. He chooses to emphasise the geometrical/topological view of everything, which, it might surprise one to know, is not always the easiest way to understand things. Many of the choices of what to emphasise and what to ignore seem odd...that is until one gets to the late stages of the book.
Upon arrival at Chapters 27 - 33 (i.e. what I think Penrose really wants to talk about) one can see that everything that has gone before has been put together in order to provide the most efficient route to understanding - hardly a page has been wasted. All those strange choices of what to emphasise, all the peculiar, non-standard explanations when easier explanations exist, all the leaping to the most general mathematical ideas, all the things missed out, all these things are done so that the points he wants to discuss can be followed without wasting time or space in what is a 1000+p book as it stands. The necessary skill, thought and effort required to do this impress me enormously.
Inevitably this means that most of what is covered in the book of "standard" physics has been explained better (by which I mean more readily comprehensibly), even at a mathematical level, elsewhere - but not in one volume! The consequence of this is that Penrose's widest possible audience may not be all that wide: although he suggests one could read the book and ignore every equation in it, (something I often do when reading technical literature!) I suspect one would rapidly become bored and disenchanted. The unavoidable fact is that the greater your mathematical capabilities, the more you will get from this book and additionally, the more maths and physics you know before starting, the more you will gain from this book.
Further, the more you are willing to study the book the more you will gain. Manny approached it by reading 3 hours per night until done. I would suggest that the nearer to that approach you can get the better off you will be, even though I failed miserably to do so. There are numerous excercises scattered through-out, which I did not attempt, but I would suggest that if you are determined to attempt them, you should read the remainder of each chapter as soon as you hit a hard problem, then go back and look at the problems again. (And note the solutions web address given in the preface!)
So what did I gain from the unavoidable slog of this book?
The general philosophising of Chapters 1 and 34 struck me as a waste of time; I either thought what was being espoused was obviously clap-trap or obviously true - and for me the questions he raises mostly aren't interesting to me anymore. (They were back when I hadn't reached my own conclusions yet.) Others, may feel very differently, however - and many would not agree about which parts are claptrap! The remainder offered me quite a bit, however.
For instance, a frankly embarressing mis-understanding of the EPR paradox I was labouring under was corrected! (Something of a body-blow to me as it is undergrad physics!) On the other hand, Penrose makes an astounding mistake at one point, where he gets himself horribly messed up with basic (high school) probability theory and time-reversal. (Pretty good combination to the head from me!) This is a good reminder that there is no argument from authority in science: just 'cos Penrose says it, doesn't make it right! This wrong argument is then used to go on to explain a completely freaky (and I suspect wrong) prediction about basic quantum theory. I am not clear that the example, which is definitely wrong, invalidates his whole line of reasoning, though; it may be that other examples show the general argument to be correct.
Then Penrose delivers the knock-out punch: Conservation of energy/momentum/angular momentum in General Relativity is non-local! Not only that but it has only been proved to be true at all in a subset of cases! Seriously, how could I have never known this before?! (Non-physicists may well have no clue why I am so thunder-struck by this revelation, but it is not far short of learning that there's a whole continent you'd never heard of before.) It's completely gob-smacking. And I can't see how I didn't get told as an undergrad.
Further, Penrose's main purpose was achieved; I have a much better understanding of the main approaches to tackling the outstanding problems in cosmology/fundamental physics than I did before and along the way I gained some insights I previously lacked. Two examples are the Higgs boson explanation of the origin of mass and spinors. The Higgs boson theory is barely touched upon and is one of the rare examples of something being included that is not strictly necessary later. I wish there had been more about it, whilst recognising precisely why there is not. What material there is made the theory seem much less arbitrary than it had previously.
Spinors are a mathematical concept that feature heavily in the book, mainly because they feature extremely strongly in Penrose's Twistor Theory of quantum gravitation. Penrose gives an assessment of his own theory that I respect enormously and cannot praise highly enough; he expresses clearly what it it can acheive and equally clearly and forthrightly what it cannot. Every weakness and limitation is mentioned and explained. The only time I have previously come across a scientist giving such an honest and complete assessment of the weaknesses of his own theories in a popular account is when I read Charles Darwin's Origin of Species. I cannot express how much respect Penrose earns from me by doing this. Suffice to say that most popular science books will make out that the author's ideas are obviously and unassailably correct. Further, many technical papers fail to match this level of dispassionate critical assessment.
But back to the spinors; they feature in the now well established Dirac Equation for a relativistic electron but the (non-standard) way Penrose shows this and explains their connection with the left-handedness of the Weak nuclear force and how they link to the Higgs boson ideas are fascinating. However I am not clear about them in one (crucial) regard: are they real? Penrose says they are. I am not sure (because my understanding is still muddy) and I find (somewhat to my horror!) that even though I've read all 1050p of the main text, all of Chapters 2-17 twice and many individual sections several more times, I am still not done with this book! I have to go back and see if I can make sense out of these spinors. Also, I owe Manny a discussion of Inflationary Cosmology: I'm going to have to read the relevant chapter again in order to provide it.
Wish me luck as I delve back into the very deep waters of this book!
Cosmology, Early Universe Symmetry Breaking and Inflation
So, Manny requested my views on the above topics: blame him!
I must say at the outset that I am no expert in this field and in fact Manny has read much more about modern cosmology than I have, so I’m not sure how much value should be placed on the following; it’s a pretty naïve collection of speculations and intuitions.
Early Universe Electro-weak Symmetry Breaking (EUSB)
The current theory of the weak nuclear force and the electromagnetic force relies on a “broken” symmetry. That is to say all the relevant particles and their interactions were more symmetrical when their temperature was higher; so high that one has to look back to shortly after the Big Bang to find anything with a high enough temperature. Penrose gives the (standard) analogy of a lump or iron cooling down; at some critical temperature, the atoms go through a phase change and instead of having randomly aligned magnetic fields, these fields all line up in one direction. This creates the macroscopic magnetic field but in the process reduces the symmetry of the iron. It used to look the same in every direction but now it has an obviously different look, depending on the direction the magnetic field is pointing. So the idea is something similar happened when the universe cooled down below a critical value and the weak nuclear force and the electromagnetic force now look different because of the reduction in symmetry. But the lump of iron in fact won’t spontaneously have all its atoms line up in exactly the same direction unless it is cooled very slowly. Instead, “domains” develop. Inside a domain all the atoms are lined up the same direction but each domain has its own direction, which is why any old lump of iron is in fact not a macroscopic magnet. All the fields from the microscopic domains, pointing in different directions tend to cancel each other out. Which leads to weirdness when talking about the particles and forces of the universe doing the same thing: there are equivalents of the directions of the magnetic domains that the cooling particles could drop into that are different from what we observe. So the fundamental interactions would look different in a different domain. And the universe did not cool slowly, so it is much more likely than not that such “domains” did form if the theory is true. Now the boundaries of these domains would look and behave very strangely. In fact one type of boundary predicted by the theory, Cosmic Strings, can lead to something really bizarre: time travel! That is, technically, space-like movement into the past.
Well, I just don’t believe time travel into the past is actually possible, which means I don’t believe cosmic strings exist which means I think there’s something wrong with current electro-weak theory. However all the “low” energy density tests done show electro-weak theory to do very well indeed, thanks! So I’m in a bind; the high-energy prediction of a low energy theory that works really well predicts something I don’t believe. What to do? Well, it is often possible to write a theory in more than one way, mathematically, so I would search for a different mathematical description of the low energy theory that did not rely on the EUSB idea, thus getting rid of the unwanted cosmic strings and parts of the universe that are radically different from ours altogether. I don’t know if this is possible. There has been one claim that a cosmic string has been observed but I don’t know if any corroboration of the claim exists. If they do, then electro-weak theory as it stands gets an extra-ordinary boost.
Inflation
Penrose states that the initial motivation for the idea of cosmological inflation was to “explain” why magnetic monopoles are not observed but exist anyway. Magnetic monopoles are neat as they would explain why electrical charge comes only as integer multiples of a fundamental value (though not what the value is). The trouble is, nobody has ever seen one and if they were formed at all it would have been with such concentration that they would have been easily spotted by now. Unless inflation had reduced their concentration radically by expanding the universe at a ridiculous rate…
Well, this seems to me to be only half the problem; the other half is demonstrating that monopoles must have formed and that they did so prior to inflation and not afterward.
Later, people suggested that inflation could explain homogeneity and flatness. Homogeneity is the fact that wherever we look the in the universe the matter seems to be distributed in a similar way (i.e. stars, galaxies, clusters, super-clusters…). Flatness is the idea that the universe is, over-all, expanding at a rate just high enough to prevent it collapsing again because of the gravity of all the stuff in it.
Penrose presents cogent arguments as to why inflation actually cannot explain homogeneity. They seem indisputable to me. That the universe started off in an extremely low entropy state seems an unavoidable fact. Why was it like that? I don’t know. It’s a big mystery.
Inflation cannot solve the problem of EUSB either, but hey! it’s a hypothesis and it can make predictions, so astronomers should try to see if they can prove it wrong or not. As far as I have gathered, the observational status of inflation is ambiguous. My feeling is that the whole idea is very arbitrary: a field occupying the whole universe must exist in order to provide the opportunity for inflation to occur. No hint of a carrier-boson for said field has ever been found. I don’t know if theory can predict anything at all about such a particle, apart from it must have integer spin. There is talk of a second inflation occurring because it seems that some astronomical objects are not only moving away from us but accelerating away from us. This suggests to me that whilst there may in fact have been inflation in the early universe, current theory is nowhere near adequate to explain it: why then? Why again now? What causes the transition? It could be a purely random event where the field transitions from one state to another quantum mechanically but to do so the new state must allow an immediate drop of energy in the field. How can one decide what the possible energy levels of the field are? Or if we are in the ground state now or not? The theory also has implications for the nature of the vacuum i.e. it is different before and after an inflation period starts. The vacuum in the quantum mechanical sense seems to me not to be understood at all well. I think that if inflation has ever happened it indicates that a deep theory explaining the nature of the vacuum is required.
The Anthropic Principle
This gets dragged up a lot in discussions of cosmology. It’s annoyingly persistent. It comes in a weak and a strong form. Starting with the weak form (WAP): Many adherents claim that the WAP has predictive power and is therefore in some sense “correct” i.e. some deep law of the universe. What it states is that there is sentient life therefore…X. X is a prediction of some phenomenon. The most famous example is a certain energy level of the Carbon nucleus. The argument went, we have life because we have heavy atoms so there must be a way of fusing lighter atoms to make heavier ones but to make any atom heavier than carbon, carbon itself must have this specific energy level…and it does! Triumph for the WAP! Except that is rubbish, because the argument doesn’t rely on the existence of life at all; it is easy to imaging a lot of heavy atoms floating about but no life. The real argument, stripped of inessential guff, is simply: there are atoms heavier than carbon – there must be this energy level of the carbon nucleus for that to happen. Life, let alone human sentience doesn’t feature at all. All WAP arguments fail in this manner: it turns out that life is inessential to the argument.
Then there is the strong anthropic principle (SAP): This states either the universe was fine-tuned for the existence of human sentience to be possible or there are in fact a huge number of universes that are somehow different from each other so ours is just a statistical freak. This assumes that the only possible way that sentience could occur is if physics follows the laws we see. I don’t buy this at all: are people seriously claiming that they know what all the possible emergent ramifications of some grand set of all possible sets of physical laws are and only a tiny fraction of them could sustain sentience? It seems to me we don’t even know all the ramifications of the laws of the observed universe yet, let alone any other one. But there is some sort of prediction here; there might be other universes. Maybe that is a testable proposition. I don’t know.
Spinors and Spin
I re-read the material on the Dirac Equation and spinors a while ago but I've only just got round to discussing it. The discussion is moved to the comments due to the character limit on reviews!
Hence I'm going to start my review with a couple of gripes: This book, which is full of maths, much of which would make your average undergrad scientist grunt with the strain at the very least, as well as physics to post-grad level in places, has no glossary of technical terms. There is ample cross-referencing and an index but these are no substitute. When you want to know, Clifford Algebra, which one was that again? (Because you've met ordinary algebra, complex algebra, Clifford Algebras, Lie Algebras and Grassman Algebras...), going back and reading through an entire section again to find out, is a bit annoying - a list of definitions at the back would have helped enormously. Admittedly this would have made a big book even bigger but it would have made it much more user-friendly.
Gripe number two is in a similar vein; Penrose fails to supply a list of the upper and lower case Greek alphabet symbols and their names or a similar list for obscure mathematical symbols, such as del and scri. Given that nobody without training in Greek or in science is going to know these and such a list would only take up one page, its omission is egregious.
This leads neatly into a topic that has been dicussed quite a bit here on Goodreads - namely, who is this book aimed at? What is it's purpose? Firstly I would point out that the subtitle "A Complete Guide to the Laws of the Universe" is not really true: Classical Thermodynamics is barely seen as we rush straight into the statistical view of the Second Law. Of the other three Laws of Thermodynamics, Zero is never mentioned and the others barely name-checked. I doubt many physicists would consider that all the basic theories have been covered in such a circumstance. But I think this is a marketing problem; I don't believe Penrose ever intended to write such a "Complete Guide."
In the preface Penrose talks about wanting, with this book, to make cutting edge physics available to people who struggle to understand fractions. Now, this can only be taken as a joke, considering what one is up against only in chapter 2, but I would guess that Penrose genuinely wants to have the widest possible audience for his book whilst not compromising his aims.
What are those aims? In my view he wants to give his personal views on the state of cosmology and fundamental physics but to be able to do it at an advanced technical and mathematical level and additionally to give his own philosophies regarding the nature of thought, science, maths and...Nature! This means that he wanted to deliver Chapters 27 - 33 on the physics/cosmology, bracketed by Chapters 1 and 34 of philosophising. The entirety of the rest of the book is simply there in order to equip readers to understand what he says in those six technical chapters! This requires 15 Chapters of maths and ten Chapters of physics/cosmology...
Looked at this way, the book begins to reflect the genius and madness of the author: Many of the explanations in earlier stages of the book left me thinking, why do it that way? That's not the easiest way to understand this if you've never come across it before! He also goes straight to very general mathematical principles, missing out intermediate levels of abstraction that might make what comes later easier. He chooses to emphasise the geometrical/topological view of everything, which, it might surprise one to know, is not always the easiest way to understand things. Many of the choices of what to emphasise and what to ignore seem odd...that is until one gets to the late stages of the book.
Upon arrival at Chapters 27 - 33 (i.e. what I think Penrose really wants to talk about) one can see that everything that has gone before has been put together in order to provide the most efficient route to understanding - hardly a page has been wasted. All those strange choices of what to emphasise, all the peculiar, non-standard explanations when easier explanations exist, all the leaping to the most general mathematical ideas, all the things missed out, all these things are done so that the points he wants to discuss can be followed without wasting time or space in what is a 1000+p book as it stands. The necessary skill, thought and effort required to do this impress me enormously.
Inevitably this means that most of what is covered in the book of "standard" physics has been explained better (by which I mean more readily comprehensibly), even at a mathematical level, elsewhere - but not in one volume! The consequence of this is that Penrose's widest possible audience may not be all that wide: although he suggests one could read the book and ignore every equation in it, (something I often do when reading technical literature!) I suspect one would rapidly become bored and disenchanted. The unavoidable fact is that the greater your mathematical capabilities, the more you will get from this book and additionally, the more maths and physics you know before starting, the more you will gain from this book.
Further, the more you are willing to study the book the more you will gain. Manny approached it by reading 3 hours per night until done. I would suggest that the nearer to that approach you can get the better off you will be, even though I failed miserably to do so. There are numerous excercises scattered through-out, which I did not attempt, but I would suggest that if you are determined to attempt them, you should read the remainder of each chapter as soon as you hit a hard problem, then go back and look at the problems again. (And note the solutions web address given in the preface!)
So what did I gain from the unavoidable slog of this book?
The general philosophising of Chapters 1 and 34 struck me as a waste of time; I either thought what was being espoused was obviously clap-trap or obviously true - and for me the questions he raises mostly aren't interesting to me anymore. (They were back when I hadn't reached my own conclusions yet.) Others, may feel very differently, however - and many would not agree about which parts are claptrap! The remainder offered me quite a bit, however.
For instance, a frankly embarressing mis-understanding of the EPR paradox I was labouring under was corrected! (Something of a body-blow to me as it is undergrad physics!) On the other hand, Penrose makes an astounding mistake at one point, where he gets himself horribly messed up with basic (high school) probability theory and time-reversal. (Pretty good combination to the head from me!) This is a good reminder that there is no argument from authority in science: just 'cos Penrose says it, doesn't make it right! This wrong argument is then used to go on to explain a completely freaky (and I suspect wrong) prediction about basic quantum theory. I am not clear that the example, which is definitely wrong, invalidates his whole line of reasoning, though; it may be that other examples show the general argument to be correct.
Then Penrose delivers the knock-out punch: Conservation of energy/momentum/angular momentum in General Relativity is non-local! Not only that but it has only been proved to be true at all in a subset of cases! Seriously, how could I have never known this before?! (Non-physicists may well have no clue why I am so thunder-struck by this revelation, but it is not far short of learning that there's a whole continent you'd never heard of before.) It's completely gob-smacking. And I can't see how I didn't get told as an undergrad.
Further, Penrose's main purpose was achieved; I have a much better understanding of the main approaches to tackling the outstanding problems in cosmology/fundamental physics than I did before and along the way I gained some insights I previously lacked. Two examples are the Higgs boson explanation of the origin of mass and spinors. The Higgs boson theory is barely touched upon and is one of the rare examples of something being included that is not strictly necessary later. I wish there had been more about it, whilst recognising precisely why there is not. What material there is made the theory seem much less arbitrary than it had previously.
Spinors are a mathematical concept that feature heavily in the book, mainly because they feature extremely strongly in Penrose's Twistor Theory of quantum gravitation. Penrose gives an assessment of his own theory that I respect enormously and cannot praise highly enough; he expresses clearly what it it can acheive and equally clearly and forthrightly what it cannot. Every weakness and limitation is mentioned and explained. The only time I have previously come across a scientist giving such an honest and complete assessment of the weaknesses of his own theories in a popular account is when I read Charles Darwin's Origin of Species. I cannot express how much respect Penrose earns from me by doing this. Suffice to say that most popular science books will make out that the author's ideas are obviously and unassailably correct. Further, many technical papers fail to match this level of dispassionate critical assessment.
But back to the spinors; they feature in the now well established Dirac Equation for a relativistic electron but the (non-standard) way Penrose shows this and explains their connection with the left-handedness of the Weak nuclear force and how they link to the Higgs boson ideas are fascinating. However I am not clear about them in one (crucial) regard: are they real? Penrose says they are. I am not sure (because my understanding is still muddy) and I find (somewhat to my horror!) that even though I've read all 1050p of the main text, all of Chapters 2-17 twice and many individual sections several more times, I am still not done with this book! I have to go back and see if I can make sense out of these spinors. Also, I owe Manny a discussion of Inflationary Cosmology: I'm going to have to read the relevant chapter again in order to provide it.
Wish me luck as I delve back into the very deep waters of this book!
Cosmology, Early Universe Symmetry Breaking and Inflation
So, Manny requested my views on the above topics: blame him!
I must say at the outset that I am no expert in this field and in fact Manny has read much more about modern cosmology than I have, so I’m not sure how much value should be placed on the following; it’s a pretty naïve collection of speculations and intuitions.
Early Universe Electro-weak Symmetry Breaking (EUSB)
The current theory of the weak nuclear force and the electromagnetic force relies on a “broken” symmetry. That is to say all the relevant particles and their interactions were more symmetrical when their temperature was higher; so high that one has to look back to shortly after the Big Bang to find anything with a high enough temperature. Penrose gives the (standard) analogy of a lump or iron cooling down; at some critical temperature, the atoms go through a phase change and instead of having randomly aligned magnetic fields, these fields all line up in one direction. This creates the macroscopic magnetic field but in the process reduces the symmetry of the iron. It used to look the same in every direction but now it has an obviously different look, depending on the direction the magnetic field is pointing. So the idea is something similar happened when the universe cooled down below a critical value and the weak nuclear force and the electromagnetic force now look different because of the reduction in symmetry. But the lump of iron in fact won’t spontaneously have all its atoms line up in exactly the same direction unless it is cooled very slowly. Instead, “domains” develop. Inside a domain all the atoms are lined up the same direction but each domain has its own direction, which is why any old lump of iron is in fact not a macroscopic magnet. All the fields from the microscopic domains, pointing in different directions tend to cancel each other out. Which leads to weirdness when talking about the particles and forces of the universe doing the same thing: there are equivalents of the directions of the magnetic domains that the cooling particles could drop into that are different from what we observe. So the fundamental interactions would look different in a different domain. And the universe did not cool slowly, so it is much more likely than not that such “domains” did form if the theory is true. Now the boundaries of these domains would look and behave very strangely. In fact one type of boundary predicted by the theory, Cosmic Strings, can lead to something really bizarre: time travel! That is, technically, space-like movement into the past.
Well, I just don’t believe time travel into the past is actually possible, which means I don’t believe cosmic strings exist which means I think there’s something wrong with current electro-weak theory. However all the “low” energy density tests done show electro-weak theory to do very well indeed, thanks! So I’m in a bind; the high-energy prediction of a low energy theory that works really well predicts something I don’t believe. What to do? Well, it is often possible to write a theory in more than one way, mathematically, so I would search for a different mathematical description of the low energy theory that did not rely on the EUSB idea, thus getting rid of the unwanted cosmic strings and parts of the universe that are radically different from ours altogether. I don’t know if this is possible. There has been one claim that a cosmic string has been observed but I don’t know if any corroboration of the claim exists. If they do, then electro-weak theory as it stands gets an extra-ordinary boost.
Inflation
Penrose states that the initial motivation for the idea of cosmological inflation was to “explain” why magnetic monopoles are not observed but exist anyway. Magnetic monopoles are neat as they would explain why electrical charge comes only as integer multiples of a fundamental value (though not what the value is). The trouble is, nobody has ever seen one and if they were formed at all it would have been with such concentration that they would have been easily spotted by now. Unless inflation had reduced their concentration radically by expanding the universe at a ridiculous rate…
Well, this seems to me to be only half the problem; the other half is demonstrating that monopoles must have formed and that they did so prior to inflation and not afterward.
Later, people suggested that inflation could explain homogeneity and flatness. Homogeneity is the fact that wherever we look the in the universe the matter seems to be distributed in a similar way (i.e. stars, galaxies, clusters, super-clusters…). Flatness is the idea that the universe is, over-all, expanding at a rate just high enough to prevent it collapsing again because of the gravity of all the stuff in it.
Penrose presents cogent arguments as to why inflation actually cannot explain homogeneity. They seem indisputable to me. That the universe started off in an extremely low entropy state seems an unavoidable fact. Why was it like that? I don’t know. It’s a big mystery.
Inflation cannot solve the problem of EUSB either, but hey! it’s a hypothesis and it can make predictions, so astronomers should try to see if they can prove it wrong or not. As far as I have gathered, the observational status of inflation is ambiguous. My feeling is that the whole idea is very arbitrary: a field occupying the whole universe must exist in order to provide the opportunity for inflation to occur. No hint of a carrier-boson for said field has ever been found. I don’t know if theory can predict anything at all about such a particle, apart from it must have integer spin. There is talk of a second inflation occurring because it seems that some astronomical objects are not only moving away from us but accelerating away from us. This suggests to me that whilst there may in fact have been inflation in the early universe, current theory is nowhere near adequate to explain it: why then? Why again now? What causes the transition? It could be a purely random event where the field transitions from one state to another quantum mechanically but to do so the new state must allow an immediate drop of energy in the field. How can one decide what the possible energy levels of the field are? Or if we are in the ground state now or not? The theory also has implications for the nature of the vacuum i.e. it is different before and after an inflation period starts. The vacuum in the quantum mechanical sense seems to me not to be understood at all well. I think that if inflation has ever happened it indicates that a deep theory explaining the nature of the vacuum is required.
The Anthropic Principle
This gets dragged up a lot in discussions of cosmology. It’s annoyingly persistent. It comes in a weak and a strong form. Starting with the weak form (WAP): Many adherents claim that the WAP has predictive power and is therefore in some sense “correct” i.e. some deep law of the universe. What it states is that there is sentient life therefore…X. X is a prediction of some phenomenon. The most famous example is a certain energy level of the Carbon nucleus. The argument went, we have life because we have heavy atoms so there must be a way of fusing lighter atoms to make heavier ones but to make any atom heavier than carbon, carbon itself must have this specific energy level…and it does! Triumph for the WAP! Except that is rubbish, because the argument doesn’t rely on the existence of life at all; it is easy to imaging a lot of heavy atoms floating about but no life. The real argument, stripped of inessential guff, is simply: there are atoms heavier than carbon – there must be this energy level of the carbon nucleus for that to happen. Life, let alone human sentience doesn’t feature at all. All WAP arguments fail in this manner: it turns out that life is inessential to the argument.
Then there is the strong anthropic principle (SAP): This states either the universe was fine-tuned for the existence of human sentience to be possible or there are in fact a huge number of universes that are somehow different from each other so ours is just a statistical freak. This assumes that the only possible way that sentience could occur is if physics follows the laws we see. I don’t buy this at all: are people seriously claiming that they know what all the possible emergent ramifications of some grand set of all possible sets of physical laws are and only a tiny fraction of them could sustain sentience? It seems to me we don’t even know all the ramifications of the laws of the observed universe yet, let alone any other one. But there is some sort of prediction here; there might be other universes. Maybe that is a testable proposition. I don’t know.
Spinors and Spin
I re-read the material on the Dirac Equation and spinors a while ago but I've only just got round to discussing it. The discussion is moved to the comments due to the character limit on reviews!
December 27, 2018
Its the greatest science book ever written in the whole world, since the beginning of the time. Its certainly not popular science, its hardcore science and maths, written for general audience.
August 19, 2011
Penrose, Penrose, Penrose. Oh how I LONG to know thee. I am becoming minorly obsessed with you and your work. I am pacing for crying out loud. I am running myself in circles. Opening, closing, referencing, coming back, straining my eyes as if that will make me see the world that 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 in 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 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 some superficial knowledge, but some deep personal connective enlightenment. Cosmic if you will.
I pledge to re attend school. 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.
I pledge to re attend school. 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.
Want to read
November 15, 2009I have a suspicion that Penrose hasn't spoken to a undergraduate in 30 years. His notion of "introductory material" is not just wrong, its downright strange.
The famed mathematician devotes several pages to discussing the addition of fractions then breezes through holomorphic functions and Reimann spheres.
I'll return to this book in a year or two when I have the mathematical background to qualify as a "non-mathematician."
The famed mathematician devotes several pages to discussing the addition of fractions then breezes through holomorphic functions and Reimann spheres.
I'll return to this book in a year or two when I have the mathematical background to qualify as a "non-mathematician."
May 15, 2011
Penrose came to GT and gave an open lecture on cosmic parameters and cosmological arguments from the 2nd Law of Thermodynamics (chapter 27 in this book, one of the most ambitious and impressive -- if incomplete, a bit uneven, and just as taxing as you've heard -- catechisms I've ever read), and a closed lecture on twistor theory (chapter 33), and signed my copy! w00t! I shook Sir Roger's hand as trillions of neutrinos passed through us both, completely undetected, our entangled R-type state evolution leaving an indelible imprint on all our lightcones forevermore at the cost of a little more entropy, order traded for disorder in the guise of order, orderly.
March 1, 2022
UPDATE 2022:
Several years later I found this work, including Feynman's lectures, to be a much better use of time, and thanks to it (and COVID) came to understand fundamental physics. These are the "years' worth of secondary sources" mentioned in the review: I could now comprehend the book. https://www.susanrigetti.com/physics
_______________³¹⁴⁸⁸⁵⁹_______________
t me start off by saying (its relevance will soon be revealed) I have a bachelor of science in applied mathematics and a PhD-ABD in another strongly quantitative discipline* (both are top-50 schools, and I wasn't in the bottom 50% of the class), and after the first 300 or so pages (out of 1200) the math in this book (and it's at least 40% or more straight math, not text, and often without text explaining the math) is way above my head and is left often undefined in the text. The author doesn't even do the courtesy of pointing the reader to textbooks where these concepts, such as pseudo-Riemannian geometry and anti-de Sitter spaces and Seiberg-Witten manifolds, are defined and can be learned.
The book fails in its promise and purpose to be a self-contained guide to the current mathematical- or theoretical-physical understanding of the universe. It is far from accessible to the layman (I have postgraduate training in math and I was a good student and its inaccessible to me), and to grasp the concepts in this book, I'd have to spend probably a year of free time and a thousand or more dollars in secondary sources (if I bought them used and cheap). I bought this book to get a $20 overview (like Collier's 'A Most Incomprehensible Thing' for the theories of relativity [I prefer the original 'invariance'], which was technical but self-contained and comprehensible; reading that is the only thing that gave me any knowledge at all of tensors, which this book is chock full of): what I got was in essence a 1200 page bibliography without the authors being noted and without the important works being starred.
This is a very ambitious book which fails utterly in execution.
The author goes from explaining what complex and irrational numbers are and why they are useful (this is freshman high school math) in the introduction, accompanied by an apology for the necessity of using as difficult a concept as logarithms, to pseudo-Riemannian geometry (this is postgraduate pure math) 200 pages later. No joke. Penrose spends about five pages defining all of classical statics and dynamics, and then assumes that you understand classical mechanics. This same breakneck pace is kept up throughout, which is how he manages to range from logarithms and complex numbers to doctoral-level mathematics in 500 or 600 pages. Once he goes out of the pure math and back to applied math (i.e., physics proper) it gets a little easier but I'd still not recommend trying to tackle this book unless you're a graduate in maths or a self-taught prodigy in pure maths.
The book promises to be a self-contained guide to the best mathematical understanding of the universe we have, but it ends up more like the author just stuck the important theorems in with a minimum of explanation (he does hit almost all of them: one thing that struck me as unnecessarily erudite - showing off - and odd was the statement of Maxwell's field equations, which is mathematically simple and elegant, in terms of tensors, which are very, very difficult), so it's a complete guide if you already know all of the math (in which case you don't need the book): it's much more of a refresher and quick reference for people who already are familiar with and understand (or at one time understood) the concepts the author represents.
Required prerequisites: understanding of linear algebra (Lie, Poisson, Frobenius), TENSORS (and more tensors), several varieties of noneuclidean geometry (Minkowski, de Sitter, Riemann), scalars, topology and n-manifolds, group theory (Lie groups), gauge theory, etc., or the willingness to learn these from expensive secondary sources, because Penrose will not teach you them here and the arguments of the book are incomprehensible without them. Without them, one would be reduced to skimming the 20% of the book that is text (especially the final chapter, which is comprehensible to any semieducated layman) and taking the author's word for the rest of it. Just about the only thing he explains in full is twistor theory (his own invention).
I still have to award two stars for the obvious intensity and depths of erudition which Penrose funneled in to this work, but only two because it doesn't even partially fulfill its stated purpose or self-description.
*Redacted to protect the privacy of a member of Vagabond of Letters.
Several years later I found this work, including Feynman's lectures, to be a much better use of time, and thanks to it (and COVID) came to understand fundamental physics. These are the "years' worth of secondary sources" mentioned in the review: I could now comprehend the book. https://www.susanrigetti.com/physics
_______________³¹⁴⁸⁸⁵⁹_______________
t me start off by saying (its relevance will soon be revealed) I have a bachelor of science in applied mathematics and a PhD-ABD in another strongly quantitative discipline* (both are top-50 schools, and I wasn't in the bottom 50% of the class), and after the first 300 or so pages (out of 1200) the math in this book (and it's at least 40% or more straight math, not text, and often without text explaining the math) is way above my head and is left often undefined in the text. The author doesn't even do the courtesy of pointing the reader to textbooks where these concepts, such as pseudo-Riemannian geometry and anti-de Sitter spaces and Seiberg-Witten manifolds, are defined and can be learned.
The book fails in its promise and purpose to be a self-contained guide to the current mathematical- or theoretical-physical understanding of the universe. It is far from accessible to the layman (I have postgraduate training in math and I was a good student and its inaccessible to me), and to grasp the concepts in this book, I'd have to spend probably a year of free time and a thousand or more dollars in secondary sources (if I bought them used and cheap). I bought this book to get a $20 overview (like Collier's 'A Most Incomprehensible Thing' for the theories of relativity [I prefer the original 'invariance'], which was technical but self-contained and comprehensible; reading that is the only thing that gave me any knowledge at all of tensors, which this book is chock full of): what I got was in essence a 1200 page bibliography without the authors being noted and without the important works being starred.
This is a very ambitious book which fails utterly in execution.
The author goes from explaining what complex and irrational numbers are and why they are useful (this is freshman high school math) in the introduction, accompanied by an apology for the necessity of using as difficult a concept as logarithms, to pseudo-Riemannian geometry (this is postgraduate pure math) 200 pages later. No joke. Penrose spends about five pages defining all of classical statics and dynamics, and then assumes that you understand classical mechanics. This same breakneck pace is kept up throughout, which is how he manages to range from logarithms and complex numbers to doctoral-level mathematics in 500 or 600 pages. Once he goes out of the pure math and back to applied math (i.e., physics proper) it gets a little easier but I'd still not recommend trying to tackle this book unless you're a graduate in maths or a self-taught prodigy in pure maths.
The book promises to be a self-contained guide to the best mathematical understanding of the universe we have, but it ends up more like the author just stuck the important theorems in with a minimum of explanation (he does hit almost all of them: one thing that struck me as unnecessarily erudite - showing off - and odd was the statement of Maxwell's field equations, which is mathematically simple and elegant, in terms of tensors, which are very, very difficult), so it's a complete guide if you already know all of the math (in which case you don't need the book): it's much more of a refresher and quick reference for people who already are familiar with and understand (or at one time understood) the concepts the author represents.
Required prerequisites: understanding of linear algebra (Lie, Poisson, Frobenius), TENSORS (and more tensors), several varieties of noneuclidean geometry (Minkowski, de Sitter, Riemann), scalars, topology and n-manifolds, group theory (Lie groups), gauge theory, etc., or the willingness to learn these from expensive secondary sources, because Penrose will not teach you them here and the arguments of the book are incomprehensible without them. Without them, one would be reduced to skimming the 20% of the book that is text (especially the final chapter, which is comprehensible to any semieducated layman) and taking the author's word for the rest of it. Just about the only thing he explains in full is twistor theory (his own invention).
I still have to award two stars for the obvious intensity and depths of erudition which Penrose funneled in to this work, but only two because it doesn't even partially fulfill its stated purpose or self-description.
*Redacted to protect the privacy of a member of Vagabond of Letters.
April 6, 2021
What is reality? How come that mathematics is so handy describing it? And often more astutely that our eyes? What are the laws governing it all? Are we getting it all right? What if we are trying for the wrong questions and answers? These and many other questions are what the 2020 Nobel Prize winner Roger Penrose's giving the reader a taste of working on: string theory, physics, the mindboggling quantum effects... - all through the prizm of mathematical apparatus.
Read
June 30, 2011So we had a physicist around to dinner the other day and thrust this at him. I can't call T---- by his real name, let's just say he rhymes with a dip made with chickpeas and tahini. The reason I can't call him by his real name is that he works at a place that starts with C and rhymes with a complete lack of humour. He likes his job, I don't want to get him sacked for reading Penrose.
He flicks through it and the first thing I note is that physicists take about 5 nanoseconds to read what it takes ordinary mortals eons to get through. He starts with the cover, of course. 'Reviewed in the Financial Times?' A disparaging snort follows. 'Ah,' he says after the third nanosecond. 'He's written this type of science book.' I like that. I have no idea what it means, but I like it.
After four nanoseconds he is up to page 1050 or thereabouts. He reads out a question from it and says 'That is a good question. I don't know the answer.' Slaps book shut. Really, I mostly get the impression that real physicists like him just wish those other ones would just stop it. Stop with all the philosophical 'should we be worried about this?' stuff. Let's just get on with it p-lease.
And he says 'You didn't say the dinner invitation came with a catch.' I say 'But I didn't say it didn't, did I?'
I am seriously thinking of reading this while skipping every page that doesn't have only words on it. Seriously.
He flicks through it and the first thing I note is that physicists take about 5 nanoseconds to read what it takes ordinary mortals eons to get through. He starts with the cover, of course. 'Reviewed in the Financial Times?' A disparaging snort follows. 'Ah,' he says after the third nanosecond. 'He's written this type of science book.' I like that. I have no idea what it means, but I like it.
After four nanoseconds he is up to page 1050 or thereabouts. He reads out a question from it and says 'That is a good question. I don't know the answer.' Slaps book shut. Really, I mostly get the impression that real physicists like him just wish those other ones would just stop it. Stop with all the philosophical 'should we be worried about this?' stuff. Let's just get on with it p-lease.
And he says 'You didn't say the dinner invitation came with a catch.' I say 'But I didn't say it didn't, did I?'
I am seriously thinking of reading this while skipping every page that doesn't have only words on it. Seriously.
June 27, 2008
this book RULES. it is a sort of primer on the mathematics required to really understand quantum physics. of course, that is a pretty huge pile of stuff, and this is a damn huge book. it moves faaast too: the entire theoretical foundations of single-variable calculus takes up one chapter. the reader is rapidly pulled through pretty heavy cram sessions in multivariable calculus, algebraic topology, real analysis... everything you need! and yet, it does not feel at all dense, because roger penrose is one of the great living stylists in mathematical writing: even a healthy dose of equations can't obstruct the fluidity of his prose, the lucidity of his explanations, or the enthusiasm of his presentation. i took classes in some of these topics and felt like penroses's single chapters did at least as much for me. other topics i was only cursorily familiar with, and this was felt like a rocket-fuel-grade introduction. there are even some really really nice excercises, mainly in the form of proofs (the fun kind of excercise). exhaustive theoretial math books are rare but they do exist; what makes this one actually work (in contrast to some dogmatic behemoth like the classic whitehead & russell) is that penrose is actually directed towards a somewhat taangible goal: educating a casually geeky, intellectually curious layperson about quantum physics, and leaving nothing out. for whatever reason, it works.
i brought this thing along as my only book on an 8-week tour, and it was perfect: a quick dose of clearly, beautifully written, brain twisting math a couple times a day. YES!
i brought this thing along as my only book on an 8-week tour, and it was perfect: a quick dose of clearly, beautifully written, brain twisting math a couple times a day. YES!
February 27, 2019
wow... I actually managed to read it, 1050 pages, every single one of them.
But can I really say that I'm done with this book? I don't think so... Although it took me a year and a half to read it, I didn't even understand a significant part of it. Since I'm a physics student I understood most of it on some very basic level, but I'm pretty sure I'll have to open this book again and again to take a peek at some of the awesome ideas put here by Penrose.
Did I say awesome? That's a huge understatement. I meant incredibly brilliant, original, profound and refreshingly sober!
Sir Roger Penrose is the reason why I came to love physics as much as I do and he's probably the main reason why I chose theoretical physics and why I'd like to be a mathematical physicist.
You, sir, are a huge inspiration... Thank you!
I don't want to write anything else because I don't think I could give this book a truly proper review, you should simply try to read it... and if you manage to do it, I hope you'll understand what I mean.
But can I really say that I'm done with this book? I don't think so... Although it took me a year and a half to read it, I didn't even understand a significant part of it. Since I'm a physics student I understood most of it on some very basic level, but I'm pretty sure I'll have to open this book again and again to take a peek at some of the awesome ideas put here by Penrose.
Did I say awesome? That's a huge understatement. I meant incredibly brilliant, original, profound and refreshingly sober!
Sir Roger Penrose is the reason why I came to love physics as much as I do and he's probably the main reason why I chose theoretical physics and why I'd like to be a mathematical physicist.
You, sir, are a huge inspiration... Thank you!
I don't want to write anything else because I don't think I could give this book a truly proper review, you should simply try to read it... and if you manage to do it, I hope you'll understand what I mean.
January 5, 2011
Amazing. While I can not exactly call Road to Reality a popularization of general relativity and quantum theory, it is a peerless introduction to and review of those topics. I have a PhD in mathematics, and studied physics and math as an undergraduate, and there was plenty for me to learn from this book. There are very few people in the world who would not learn much from reading it.
Many years ago, I read Penrose's Emporer's New Mind which was good as far as it went, but earned my derision with doubtful, hand-waving arguments for quantum origins of consciousness. Knowing Penrose is no dummy, I permitted a friend to convince me his work deserved another chance.
I am very glad to have read RtR, even though the process took me most of 2010. I now have a far better understanding of mathematical physics than I could have achieved with any other reading list. I did not complete most of the exercises; I suspect that if I had, then (A) I would not have finished until 2012, and (B) the exercises would have been sufficient to bring me to a fairly professional level of competence. Kudos to Mr. Penrose for including them.
The book begins with quite a few chapters of mathematics, quickly progressing to advanced undergraduate topics such as calculus on manifolds. In some ways I liked Penrose's clear treatment and drawings better than, say, Michael Spivak's beautiful but sparse texts. In order to provide a foundation for his chapters on physics, more mathematics is interspersed where necessary.
Penrose introduces complex manifolds, continuous groups (Lie groups), and principal bundles. This machinery is all truly essential to the physics, and it was enlightening to see it collected in a single place, however briefly explained. It is especially useful because most graduate students in physics or math end up missing a formal introduction to one or more of these topics.
The grand themes in RtR are the two major 20th century discoveries of general relativity and quantum theory. Penrose is particularly interested in probing how the two may be made consistent. He covers some of the cosmological work that treats both (e.g. Hawking radiation from black holes), and then discusses theories that seem to join them, including various level of detail on spin foams, string theory and M-theory, loop quantum gravity and his own invention, twistors.
A great strength of this magnum opus is Penrose's ability and willingness to discuss philosophical and aesthetic issues of the physics. Four of these stand out. First, I quite like his perspective on the futility of obtaining unified theories by (more-or-less) trying to guess a tractable Lagrangian. Second, his detailed treatment of entropy, especially the universe's original low-entropy state with respect to gravity and the cosmological implications, was really fascinating.
Third, Penrose seriously considers the various interpretations available for (apparent) collapse of the quantum wavefunction. His bias is toward objective collapse (environmental collapse), rather than being spookily dependent on "observation" by a conscious observer, and I agree with him that far. He suggests that general relativity, being the only other physical theory we have of similar stature to quantum theory) may somehow provide the mechanism. This is not an assertion but merely a suspicion on his part, and personally I lend it little credence. I do agree with him that general relativity is likely to remain a permanent Newtonian-style large-scale limit of the physics, while quantum theory seems ripe for some kind of fundamental reinterpretation.
Finally, Penrose revels in the aesthetics of what he labels complex number magic. That is, he considers the interesting ways in which physical reality is so well described not just by mathematics but specifically by complex analytic structures, a simple example being the phases of quantum wavefunctions. His fascinating twistors are the coolest example of this, where he changes the physical perspective utterly. No longer are points in spacetime the essential quantities; rather the physics is on the manifold of (potential) light rays. A spacetime point is a confluence of rays, and the interesting part is how fundamentally a point can be represented by, and treated as, a Riemann sphere (a compactified 1-dimensional complex line). As an ex-complex-manifolds guy, this was wonderful stuff to me.
I will conclude by noting that Penrose even redeemed, somewhat, his handwaving arguments from New Mind. I now understand that he is essentially pointing out that our conscious observations of physical phenomena are (or appear to be) collapsing the wavefunction. Since there must be a mechanism for that collapse, Penrose is arguing that something fundamental about conscious minds (as opposed to highly sophisticated computers) is triggering it. I still don't agree, because I believe consciousness is computational and emergent from complex systems, but his point no longer seems so silly.
Many years ago, I read Penrose's Emporer's New Mind which was good as far as it went, but earned my derision with doubtful, hand-waving arguments for quantum origins of consciousness. Knowing Penrose is no dummy, I permitted a friend to convince me his work deserved another chance.
I am very glad to have read RtR, even though the process took me most of 2010. I now have a far better understanding of mathematical physics than I could have achieved with any other reading list. I did not complete most of the exercises; I suspect that if I had, then (A) I would not have finished until 2012, and (B) the exercises would have been sufficient to bring me to a fairly professional level of competence. Kudos to Mr. Penrose for including them.
The book begins with quite a few chapters of mathematics, quickly progressing to advanced undergraduate topics such as calculus on manifolds. In some ways I liked Penrose's clear treatment and drawings better than, say, Michael Spivak's beautiful but sparse texts. In order to provide a foundation for his chapters on physics, more mathematics is interspersed where necessary.
Penrose introduces complex manifolds, continuous groups (Lie groups), and principal bundles. This machinery is all truly essential to the physics, and it was enlightening to see it collected in a single place, however briefly explained. It is especially useful because most graduate students in physics or math end up missing a formal introduction to one or more of these topics.
The grand themes in RtR are the two major 20th century discoveries of general relativity and quantum theory. Penrose is particularly interested in probing how the two may be made consistent. He covers some of the cosmological work that treats both (e.g. Hawking radiation from black holes), and then discusses theories that seem to join them, including various level of detail on spin foams, string theory and M-theory, loop quantum gravity and his own invention, twistors.
A great strength of this magnum opus is Penrose's ability and willingness to discuss philosophical and aesthetic issues of the physics. Four of these stand out. First, I quite like his perspective on the futility of obtaining unified theories by (more-or-less) trying to guess a tractable Lagrangian. Second, his detailed treatment of entropy, especially the universe's original low-entropy state with respect to gravity and the cosmological implications, was really fascinating.
Third, Penrose seriously considers the various interpretations available for (apparent) collapse of the quantum wavefunction. His bias is toward objective collapse (environmental collapse), rather than being spookily dependent on "observation" by a conscious observer, and I agree with him that far. He suggests that general relativity, being the only other physical theory we have of similar stature to quantum theory) may somehow provide the mechanism. This is not an assertion but merely a suspicion on his part, and personally I lend it little credence. I do agree with him that general relativity is likely to remain a permanent Newtonian-style large-scale limit of the physics, while quantum theory seems ripe for some kind of fundamental reinterpretation.
Finally, Penrose revels in the aesthetics of what he labels complex number magic. That is, he considers the interesting ways in which physical reality is so well described not just by mathematics but specifically by complex analytic structures, a simple example being the phases of quantum wavefunctions. His fascinating twistors are the coolest example of this, where he changes the physical perspective utterly. No longer are points in spacetime the essential quantities; rather the physics is on the manifold of (potential) light rays. A spacetime point is a confluence of rays, and the interesting part is how fundamentally a point can be represented by, and treated as, a Riemann sphere (a compactified 1-dimensional complex line). As an ex-complex-manifolds guy, this was wonderful stuff to me.
I will conclude by noting that Penrose even redeemed, somewhat, his handwaving arguments from New Mind. I now understand that he is essentially pointing out that our conscious observations of physical phenomena are (or appear to be) collapsing the wavefunction. Since there must be a mechanism for that collapse, Penrose is arguing that something fundamental about conscious minds (as opposed to highly sophisticated computers) is triggering it. I still don't agree, because I believe consciousness is computational and emergent from complex systems, but his point no longer seems so silly.
January 1, 2016
For the past year and a half I have been reading heavily in popular works on physics and astronomy, at various levels ranging from the superficial gosh-wow (Michel Kaku) through total beginner level to the somewhat more sophisticated (Brian Greene, Kip Thorne, Lee Smolin); but almost always I have been frustrated in my understanding by the lack of any mathematics to support the often metaphorical discussions. At the same time, I understood that the real mathematics of relativity, let alone quantum and string theory, would be way over my head (as when I borrowed, and immediately returned, one or two books by Penrose himself, as well as books by Wald, Susskind, etc.) So when I saw the description of this book, that Penrose intended to supply the necessary mathematics to understand the physics as he went along, I thought that it would be just what I wanted -- if it were possible. I was also rather skeptical, whether in fact it was possible, in something under 1100 pages; and as it proved, rightly so. Penrose does not succeed in making the math understandable; he explains something at a very simple level and then assumes that the reader understands far more than the author has actually explained, and when he gets to something especially difficult to comprehend, that's when he gives a footnote: show why this works. At the beginning, I read this pencil in hand, but it soon exceeded my abilities to work out the problems.
I am not totally unmathematical (I say this because it is relevant to understanding the level of this book): I minored in math in college, and beyond the usual background in high school algebra and geometry, and physics (before the dumbing down of high school math and science circa 1970), I have taken two years of college calculus, a semester of calculus-based probability and statistics, several "fundamentals" courses, and a calculus-based (but entirely "classical") first-year physics course. Not a lot, really, but probably more than most non-math/science majors. And I have tutored high school and college students in math through early calculus for over ten years. So what did I understand of this book, with that background? The first six and a half chapters. Chapter six explains calculus in nineteen pages, and I'm fairly sure most of what he talks about was never included in my two years of calculus (maybe in a real analysis course?) Chapter seven was on complex analysis, and I understood about the first half. This was the model for the rest of the book -- I understood about the first half of each chapter, where he explains the basic concepts, and got lost when he tried to "make it clearer" through "the magic of complex numbers" (his favorite expression.) The same was true when he passed over into the physics of relativity, quantum theory, and the modern speculations about strings, twistors, etc. -- I understood about half of each chapter. (Actually the chapters on loop quantum gravity and twistors were totally out of my range from the beginning.) I would say that the minimum for really following him would be to already have taken at least a complex analysis course.
Was the book a total loss, then? No. If I didn't learn the various fields of math he covers (vector and tensor calculus, some projective geometry and topology, etc.) I did learn what those fields deal with; if I didn't learn what I needed to understand the physics, I did learn what I would need to study to learn it, and perhaps most important to an autodidact who will never be able to afford any more formal education, what order I would need to study the various fields in. In short, for me (and probably for most readers who don't have a strong math/science background) this was not the "Road" but more of a roadmap; I didn't make the trip, but I got a feel for where the route passes through. At the least, I was inspired to review my high school and college math, and perhaps to try to go a little beyond where I stopped. At my age (nearing retirement) I will never get all the way to an understanding of the physics, but maybe I will keep my mind working a little longer for having read this.
I should give a brief summary of what he is saying about the questions I have been reading about in other books: he is very skeptical of string theory, because of the higher dimensions (the problem of degrees of freedom, especially); he is somewhat more friendly to quantum loops and other alternatives; he is naturally most interested in his own theory of twistors, but admits that at present it doesn't have the solution either. He argues that to be consistent with general relativity, there must be significant modifications to standard quantum theory. I'm obviously not sufficiently informed to evaluate any of this.
I would recommend the book for what it is, but not for what it claims to be, unless the reader has a real background in mathematics and physics.
I am not totally unmathematical (I say this because it is relevant to understanding the level of this book): I minored in math in college, and beyond the usual background in high school algebra and geometry, and physics (before the dumbing down of high school math and science circa 1970), I have taken two years of college calculus, a semester of calculus-based probability and statistics, several "fundamentals" courses, and a calculus-based (but entirely "classical") first-year physics course. Not a lot, really, but probably more than most non-math/science majors. And I have tutored high school and college students in math through early calculus for over ten years. So what did I understand of this book, with that background? The first six and a half chapters. Chapter six explains calculus in nineteen pages, and I'm fairly sure most of what he talks about was never included in my two years of calculus (maybe in a real analysis course?) Chapter seven was on complex analysis, and I understood about the first half. This was the model for the rest of the book -- I understood about the first half of each chapter, where he explains the basic concepts, and got lost when he tried to "make it clearer" through "the magic of complex numbers" (his favorite expression.) The same was true when he passed over into the physics of relativity, quantum theory, and the modern speculations about strings, twistors, etc. -- I understood about half of each chapter. (Actually the chapters on loop quantum gravity and twistors were totally out of my range from the beginning.) I would say that the minimum for really following him would be to already have taken at least a complex analysis course.
Was the book a total loss, then? No. If I didn't learn the various fields of math he covers (vector and tensor calculus, some projective geometry and topology, etc.) I did learn what those fields deal with; if I didn't learn what I needed to understand the physics, I did learn what I would need to study to learn it, and perhaps most important to an autodidact who will never be able to afford any more formal education, what order I would need to study the various fields in. In short, for me (and probably for most readers who don't have a strong math/science background) this was not the "Road" but more of a roadmap; I didn't make the trip, but I got a feel for where the route passes through. At the least, I was inspired to review my high school and college math, and perhaps to try to go a little beyond where I stopped. At my age (nearing retirement) I will never get all the way to an understanding of the physics, but maybe I will keep my mind working a little longer for having read this.
I should give a brief summary of what he is saying about the questions I have been reading about in other books: he is very skeptical of string theory, because of the higher dimensions (the problem of degrees of freedom, especially); he is somewhat more friendly to quantum loops and other alternatives; he is naturally most interested in his own theory of twistors, but admits that at present it doesn't have the solution either. He argues that to be consistent with general relativity, there must be significant modifications to standard quantum theory. I'm obviously not sufficiently informed to evaluate any of this.
I would recommend the book for what it is, but not for what it claims to be, unless the reader has a real background in mathematics and physics.
April 6, 2023
This book addresses an extensive variety of topics, from Euclid’s postulates to Schrodinger’s cat. It appeals to me in particular since it delivers scientific principles in chronological sequence. It enables readers to perceive the evolution of knowledge. Also, a sip of historical facts on scientists might assist the audience to swallow these challenging concepts. Having said that, his fascinating narrative had a drawback: learning science concepts chronologically isn't necessarily the best approach. In some cases, it's tougher to understand an older concept. Sometimes it's preferable for a beginner to become comfortable with more modern techniques before navigating more traditional ones. Also, the required subject continuity may not be present in timely consecutive items. However, if you are already familiar with these principles it's incredible fun seeing them all over a broad timeline and getting the big picture.
Road to Reality is comparable to Stephen Hawking’s A Brief History of Time but unlike that, it's by no means a brief history and Hawkin is indeed a better tutor. If you find some chapters a little intimidating I guarantee you could find alternative sources with simpler explanations. In particular, I had a hard time understanding several chapters in the math section. The same material is addressed with more clarity and accessibility in Thomas' Calculus or Kreyzig's Advance Engineering Mathematics.
There is one more thing I should say, but I really 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 maths. See them as tools, and familiarise yourself with their capabilities in case you ever need to use them. The real fun begins after chapter 17 when physics, astrophysics, and quantum are covered.
Road to Reality is comparable to Stephen Hawking’s A Brief History of Time but unlike that, it's by no means a brief history and Hawkin is indeed a better tutor. If you find some chapters a little intimidating I guarantee you could find alternative sources with simpler explanations. In particular, I had a hard time understanding several chapters in the math section. The same material is addressed with more clarity and accessibility in Thomas' Calculus or Kreyzig's Advance Engineering Mathematics.
There is one more thing I should say, but I really 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 maths. See them as tools, and familiarise yourself with their capabilities in case you ever need to use them. The real fun begins after chapter 17 when physics, astrophysics, and quantum are covered.
May 22, 2023
The Road to Reality: A Complete Guide to the Laws of the Universe, Roger Penrose (1931- ), 2004, 1099 pages, ISBN 0679454438, Dewey 530.1, Library-of-Congress QC20.P366 2005
Presents the math of modern physics to nonmathematicians. In a way:
Spells out the simplest; expects us to know the most complex.
So, much of the material that's new to the reader can't be followed in detail. He takes us into thickets of (a surprisingly-large number of distinct) esoteric algebras with minimal motivation or explanation. The tone, after he walks us through simple arithmetic, is, "recall all the following results from our doctoral work in pure math and in mathematical modern physics …"
The book can give a less-than-Ph.D. mathematician only a very hazy idea of what physicists have been up to since Planck in 1900 realized that the finiteness of blackbody radiant energy means that light comes in quantized lumps.
He shows where he's coming from, citing hundreds of texts, pp. 1050-1085.
Penrose gives us only abstract mathematical formalism, as distinct from quantum mechanics for /chemists/, which would compute the structure and behavior of actual atoms.
There's an excellent very brief description of the contents of (math) chapters 2 through 8 here: https://www.nicolas-pott.de/rtr/rtrSt... by Nicholas Pott.
A few of the simplest ideas:
BLACK HOLE
A black hole is a mass M within a sphere of radius r, where
r < 2 M G/c^2
whose escape velocity exceeds the speed of light, c.
G is Newton's gravitational constant.
p. 710.
USABLE ENERGY
If the sky were uniformly bright, Earth would be at thermal equilibrium with it, and its energy would be unusable. It's because the Sun is a hot spot in a cold sky that we can use its energy. We receive low-entropy yellow sunlight, and radiate high-entropy heat back into space. This lets us assemble low-entropy plants and animals, while obeying the law of increasing entropy. p. 705.
CLASSICAL MECHANICS
"Force equals mass times acceleration leads to mathematical structures of imposing splendour (Lagrangians and Hamiltonians). p. 471.
QUANTUM MECHANICS
The (time-dependent) Schrödinger equation is the Hamiltonian equation with energy expressed in terms of a time-rate-of-change, and momentum as a position-rate-of-change, of a wave function. pp. 499, 505.
BLACK-BODY RADIATION
Light energy is quantized. p. 502.
http://hyperphysics.phy-astr.gsu.edu/...
Degrees of Freedom confusion
Hyperbolic Geometry
Musical Harmony
Fermat's Last Theorem
Solutions are online https://www.google.com/search?q=road+... but not at the URL shown on page xx.
ERRATA
Penrose's Wikipedia page: https://en.m.wikipedia.org/wiki/Roger...
Books
Elementary particles and the laws of physics, R.P. Feynman, 1987, QC793.28 F49 1987 AMP Library
An Imaginary Tale: The Story of Sqrt(-1), P.J. Nahin, 1998
Visual Complex Analysis, T. Needham, 1997
The Principles of Quantum Mechanics, P.A.M. Dirac, 1930
arxiv.org
And here's a good list of the current crop of physics texts:
https://www.susanrigetti.com/physics
Presents the math of modern physics to nonmathematicians. In a way:
Spells out the simplest; expects us to know the most complex.
So, much of the material that's new to the reader can't be followed in detail. He takes us into thickets of (a surprisingly-large number of distinct) esoteric algebras with minimal motivation or explanation. The tone, after he walks us through simple arithmetic, is, "recall all the following results from our doctoral work in pure math and in mathematical modern physics …"
The book can give a less-than-Ph.D. mathematician only a very hazy idea of what physicists have been up to since Planck in 1900 realized that the finiteness of blackbody radiant energy means that light comes in quantized lumps.
He shows where he's coming from, citing hundreds of texts, pp. 1050-1085.
Penrose gives us only abstract mathematical formalism, as distinct from quantum mechanics for /chemists/, which would compute the structure and behavior of actual atoms.
There's an excellent very brief description of the contents of (math) chapters 2 through 8 here: https://www.nicolas-pott.de/rtr/rtrSt... by Nicholas Pott.
A few of the simplest ideas:
BLACK HOLE
A black hole is a mass M within a sphere of radius r, where
r < 2 M G/c^2
whose escape velocity exceeds the speed of light, c.
G is Newton's gravitational constant.
p. 710.
USABLE ENERGY
If the sky were uniformly bright, Earth would be at thermal equilibrium with it, and its energy would be unusable. It's because the Sun is a hot spot in a cold sky that we can use its energy. We receive low-entropy yellow sunlight, and radiate high-entropy heat back into space. This lets us assemble low-entropy plants and animals, while obeying the law of increasing entropy. p. 705.
CLASSICAL MECHANICS
"Force equals mass times acceleration leads to mathematical structures of imposing splendour (Lagrangians and Hamiltonians). p. 471.
QUANTUM MECHANICS
The (time-dependent) Schrödinger equation is the Hamiltonian equation with energy expressed in terms of a time-rate-of-change, and momentum as a position-rate-of-change, of a wave function. pp. 499, 505.
BLACK-BODY RADIATION
Light energy is quantized. p. 502.
http://hyperphysics.phy-astr.gsu.edu/...
Degrees of Freedom confusion
Hyperbolic Geometry
Musical Harmony
Fermat's Last Theorem
Solutions are online https://www.google.com/search?q=road+... but not at the URL shown on page xx.
ERRATA
Penrose's Wikipedia page: https://en.m.wikipedia.org/wiki/Roger...
Books
Elementary particles and the laws of physics, R.P. Feynman, 1987, QC793.28 F49 1987 AMP Library
An Imaginary Tale: The Story of Sqrt(-1), P.J. Nahin, 1998
Visual Complex Analysis, T. Needham, 1997
The Principles of Quantum Mechanics, P.A.M. Dirac, 1930
arxiv.org
And here's a good list of the current crop of physics texts:
https://www.susanrigetti.com/physics
July 8, 2011
This book is too sprawling to wait and review all at once at the end, so I've decided to do it little by little as I go along.
I thought the prologue sucked, but immediately after that it became deeply fascinating, so don't get discouraged. I guess I should say why I hated it, though. It seemed as though he was judging former times and societies through a "presentist" lens, as though all people have always and only been scientists since the start of time, only they were really bad at it back then. It's kind of a scientist's way of ignoring everything else about reality besides science, and made me a bit nauseated, thinking "oh no I hope he's not going to be this dumb all the way through." Luckily, he quickly transitioned to extreme brilliance, in which he's jaw-droppingly continued since then. Even though he's talking so far about seemingly simple stuff, he keeps knocking me for a loop with his deep insights which I've never considered before.
Only in chapter 3 so far, and discussing integers, irrational numbers, and the real numbers. I keep having to stop and think hard about the things he's saying. He asks the question if we lived in a universe where things were an amorphous soup would the integers exist there. He also points out that calculus (and stuff like momentum, velocity, and many of our physical concepts depend on calculus) is defined on the real numbers. If it turns out that the universe is discrete at the tiniest level, this math won't apply anymore (except as an approximation). However, he also observes that the real numbers first invented in Euclid's day when we had physical evidence spanning only some 15 orders of magnitudes (the smallest to largest distances known) are still going strong now when our knowledge spans something like 150 orders of magnitude, so they aren't doing too badly! These are the notions of someone who has thought deeply about how math and physics are intertwined. I keep being dumbstruck with things he casually asks about things that are ostensibly simple which I've known forever but never thought to ask that. Really important stuff. He is breathtakingly brilliant! I'm so glad I'm reading this book!
Aside: The more I read the more sure I am that Platonic essences exist independent of the nature of physical reality, and independent of their instantiation in some physical reality.
Spent some time going over familiar ground in the complex plane. It's been long enough since I studied or used this stuff that it's quite enjoyable and satisfying to do that. I think I've settled on the slow savoring method of reading this book rather than the quick devour. This review's going to be very long, but I hope it'll admit of savoring a bit as well. =)
In Chapter 5 now, and talking about e and logarithms, I wondered why it is again that 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 materializing 2.7182.... so I believe that much. =) Next I'm reading again how e originally came up in playing around with logs and powers. This book has that effect that it makes me think again about stuff that I haven't thought about since I was young. I would really like to feel I understood 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 on up to the standard model and beyond. It's always been an obsession of mine just to understand how things freaking work, what the universe is like, what nature is based on, and I have this feeling I could get much closer by going through this volume carefully. 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've 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 way, 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 pet him, I kept saying "beauty and miracles" affectionately.
I thought the prologue sucked, but immediately after that it became deeply fascinating, so don't get discouraged. I guess I should say why I hated it, though. It seemed as though he was judging former times and societies through a "presentist" lens, as though all people have always and only been scientists since the start of time, only they were really bad at it back then. It's kind of a scientist's way of ignoring everything else about reality besides science, and made me a bit nauseated, thinking "oh no I hope he's not going to be this dumb all the way through." Luckily, he quickly transitioned to extreme brilliance, in which he's jaw-droppingly continued since then. Even though he's talking so far about seemingly simple stuff, he keeps knocking me for a loop with his deep insights which I've never considered before.
Only in chapter 3 so far, and discussing integers, irrational numbers, and the real numbers. I keep having to stop and think hard about the things he's saying. He asks the question if we lived in a universe where things were an amorphous soup would the integers exist there. He also points out that calculus (and stuff like momentum, velocity, and many of our physical concepts depend on calculus) is defined on the real numbers. If it turns out that the universe is discrete at the tiniest level, this math won't apply anymore (except as an approximation). However, he also observes that the real numbers first invented in Euclid's day when we had physical evidence spanning only some 15 orders of magnitudes (the smallest to largest distances known) are still going strong now when our knowledge spans something like 150 orders of magnitude, so they aren't doing too badly! These are the notions of someone who has thought deeply about how math and physics are intertwined. I keep being dumbstruck with things he casually asks about things that are ostensibly simple which I've known forever but never thought to ask that. Really important stuff. He is breathtakingly brilliant! I'm so glad I'm reading this book!
Aside: The more I read the more sure I am that Platonic essences exist independent of the nature of physical reality, and independent of their instantiation in some physical reality.
Spent some time going over familiar ground in the complex plane. It's been long enough since I studied or used this stuff that it's quite enjoyable and satisfying to do that. I think I've settled on the slow savoring method of reading this book rather than the quick devour. This review's going to be very long, but I hope it'll admit of savoring a bit as well. =)
In Chapter 5 now, and talking about e and logarithms, I wondered why it is again that 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 materializing 2.7182.... so I believe that much. =) Next I'm reading again how e originally came up in playing around with logs and powers. This book has that effect that it makes me think again about stuff that I haven't thought about since I was young. I would really like to feel I understood 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 on up to the standard model and beyond. It's always been an obsession of mine just to understand how things freaking work, what the universe is like, what nature is based on, and I have this feeling I could get much closer by going through this volume carefully. 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've 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 way, 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 pet him, I kept saying "beauty and miracles" affectionately.
September 17, 2015
In this amazing book, Roger Penrose looks for a very fundamental issue.
He is looking for a single metric to describe everything.
This is not a unit of reality, however, although this is how he poses the issue.
The problem with selecting a metric, as he shows us over and over, lies in how different metrics arise from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics will threaten to buckle. In many instances, the metrics (and their attendant relationships) will no longer be applicable. What this means, in the Kantian (and Badiouian sense) is that these relationships's applicability will become "undecidable". In some extreme cases, the relationships may even break down. For instance, black holes are a problem because the expressed relationships that emerge from physics experiments prove to be untenable in black holes (and the big bang) as these relationships decohere and infinities and zeros pop out everywhere.
This search for a metric leads Penrose to reject string theory as a viable relationship form. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, 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, proves to be too illusionary. As with post-structural critiques of modernism, Penrose points out that the consistency of string theory relies on theoretical supplements/signs that are attached onto the positions of various types in order to maintain coherency. For instance, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions as well as its immanent affects proves to be unweldly to Penrose because the coherence of the relationships are maintained by theoretical enforcement rather than any direct correlation of math and physical experimentation.
If Penrose was familiar with Badiou, Kant and Derrida, he would be able to recognize that the undecideability of supersymmetry and string theory result from these theoretical supplements. The supplements provide the missing pieces to cohere the theory, so physical experiments prove to be incomplete in their testing. As Penrose points out, string theorists in failing to find superpartners can always push the calibration of their theory to include these partners, just at higher energy levels, which can always lie beyond the ability of technology to generate.
In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose falls fault to this when he theorizes that Quantum Field Theory can be modified (rather than the Einstein's general relativity) by changing the cut off metric. This is in line with all his discussions to "renormalize" the math so as to remove the variance accumulated by extending localized relations from beyond the area of origin on the manifold. We can always enforce a consistency of a given domain in two ways.
1. To provide a "superpartner" to supplement the terms, to keep phenomenon visible to one another within the domain, as a motion 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 with Moffe & Laulau with their Hegemony or as with Badiou with a basic atomic "cut" to center the domain as with Being and Event II.
Both of these strategies amount to the same kind of forced coherency by mapping a domain rigidly.
Penrose does offer his own favorite solution; his Twistor theory, which removes the need for extra dimensions beyond 3 + 1. Additionally, he considers 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 meant to express. Both theories are incompatible in this regard because of their huge 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 look at how these different views are constructed, you'll see the 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 enough views. So we supplement the one we have in an attempt to normalize them.
Curiousier still is Penrose's tiny 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 seat of consciousness's ability to complexly surject different sensory views into coherency. This suggestion is of the same kind as his forced synthesis of twistor theory. The satisfaction of trying 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 chess board recognizing the orthogonal formation of board, or as in Futurama the Professor discovering the smallest unit that constitutes the universe is the pixel.
In a real way, Penrose seeks to calibrate physics to the mathematical domain. He doesn't want beautiful math that doesn't apply, that is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth of which the entirety of the physical is mapped; although mentality is generated from the physical and mathematical/Truth is generated from that.
The Platonic ideologue he insists on lies on 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 find today are largely generated from artificial means. Penrose would assume as sameness of process that forces a universalization, but that is the way metaphysics and science both work, to equate different phenomenon as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we see, all relations are born locally, within a limited scope. Their extension cosmically creates the basis for which we start to see a degradation of relation qua 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 audience is, for he approaches much mathematical complexity in such a short time, talking about basic principles like polynomials and trigonometry before jumping into Lagrangian manifolds and so on. Still, if you hunger for complexity and abstraction, here it is. Much of his explanations of very complex concepts are very clear, although at times we could use more handholding. His pictures are also very interesting and complement his point nicely.
Well worth the effort to read.
He is looking for a single metric to describe everything.
This is not a unit of reality, however, although this is how he poses the issue.
The problem with selecting a metric, as he shows us over and over, lies in how different metrics arise from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics will threaten to buckle. In many instances, the metrics (and their attendant relationships) will no longer be applicable. What this means, in the Kantian (and Badiouian sense) is that these relationships's applicability will become "undecidable". In some extreme cases, the relationships may even break down. For instance, black holes are a problem because the expressed relationships that emerge from physics experiments prove to be untenable in black holes (and the big bang) as these relationships decohere and infinities and zeros pop out everywhere.
This search for a metric leads Penrose to reject string theory as a viable relationship form. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, 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, proves to be too illusionary. As with post-structural critiques of modernism, Penrose points out that the consistency of string theory relies on theoretical supplements/signs that are attached onto the positions of various types in order to maintain coherency. For instance, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions as well as its immanent affects proves to be unweldly to Penrose because the coherence of the relationships are maintained by theoretical enforcement rather than any direct correlation of math and physical experimentation.
If Penrose was familiar with Badiou, Kant and Derrida, he would be able to recognize that the undecideability of supersymmetry and string theory result from these theoretical supplements. The supplements provide the missing pieces to cohere the theory, so physical experiments prove to be incomplete in their testing. As Penrose points out, string theorists in failing to find superpartners can always push the calibration of their theory to include these partners, just at higher energy levels, which can always lie beyond the ability of technology to generate.
In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose falls fault to this when he theorizes that Quantum Field Theory can be modified (rather than the Einstein's general relativity) by changing the cut off metric. This is in line with all his discussions to "renormalize" the math so as to remove the variance accumulated by extending localized relations from beyond the area of origin on the manifold. We can always enforce a consistency of a given domain in two ways.
1. To provide a "superpartner" to supplement the terms, to keep phenomenon visible to one another within the domain, as a motion 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 with Moffe & Laulau with their Hegemony or as with Badiou with a basic atomic "cut" to center the domain as with Being and Event II.
Both of these strategies amount to the same kind of forced coherency by mapping a domain rigidly.
Penrose does offer his own favorite solution; his Twistor theory, which removes the need for extra dimensions beyond 3 + 1. Additionally, he considers 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 meant to express. Both theories are incompatible in this regard because of their huge 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 look at how these different views are constructed, you'll see the 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 enough views. So we supplement the one we have in an attempt to normalize them.
Curiousier still is Penrose's tiny 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 seat of consciousness's ability to complexly surject different sensory views into coherency. This suggestion is of the same kind as his forced synthesis of twistor theory. The satisfaction of trying 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 chess board recognizing the orthogonal formation of board, or as in Futurama the Professor discovering the smallest unit that constitutes the universe is the pixel.
In a real way, Penrose seeks to calibrate physics to the mathematical domain. He doesn't want beautiful math that doesn't apply, that is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth of which the entirety of the physical is mapped; although mentality is generated from the physical and mathematical/Truth is generated from that.
The Platonic ideologue he insists on lies on 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 find today are largely generated from artificial means. Penrose would assume as sameness of process that forces a universalization, but that is the way metaphysics and science both work, to equate different phenomenon as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we see, all relations are born locally, within a limited scope. Their extension cosmically creates the basis for which we start to see a degradation of relation qua 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 audience is, for he approaches much mathematical complexity in such a short time, talking about basic principles like polynomials and trigonometry before jumping into Lagrangian manifolds and so on. Still, if you hunger for complexity and abstraction, here it is. Much of his explanations of very complex concepts are very clear, although at times we could use more handholding. His pictures are also very interesting and complement his point nicely.
Well worth the effort to read.
January 30, 2023
3.5 stars
This is a mathematical and physics tome of more than a thousand pages. It is essentially everything you should know about the universe by the Nobel Prize winner himself, Roger Penrose.
Heavily formula based. Many of the later chapters were beyond my depth, unfortunately.
Writing was okay. Would have liked to heard more narrative but I suspect Penrose's open mindedness kept him from deviating from established theory.
3.5 stars
This is a mathematical and physics tome of more than a thousand pages. It is essentially everything you should know about the universe by the Nobel Prize winner himself, Roger Penrose.
Heavily formula based. Many of the later chapters were beyond my depth, unfortunately.
Writing was okay. Would have liked to heard more narrative but I suspect Penrose's open mindedness kept him from deviating from established theory.
3.5 stars
February 23, 2012
As accurate a title as can be for this tremendously ambitious behemoth. I very much enjoyed the masterful laying of a mathematical framework when first I came across it (the first dozen or so chapters if memory serves; hence the rating, as well as for the aforementioned ambition in the task- I think this is a right way to go, though popular expositors seldom venture down this route), as Penrose does it so efficiently (and naturally too, so that the layman wouldn't shove it aside in disgust after hardly a half dozen pages, and for the price even that handful of beginning chapters are worthwhile). Something of an idiosyncratic emphasis might be noted in these chapters, but it doesn't take away from the breadth of the account and can't really be faulted because it's setting things up for what follows.
I never actually got to much of the 'meat' of it- which is the physics (and so unfortunately can't remark on it). I'd hoped to, but then I realised I was just putting it off out of apprehension that I'd find myself feeling the lack of formal first year physics at university (something I gleefully escaped as early as I could in favour of my chosen field- pure mathematics). This is probably an unfounded concern, since skipping ahead to chapter 17 on spacetime, I was able to follow the account, but nonetheless I closed the book at this point.
Perhaps I'll revisit it sometime with a few other references handy should I need rescue. This would certainly be worthwhile if you can give this the time and energy required; you're sure to come out richer in knowledge, in a way almost no other popular account of science can impart.
I never actually got to much of the 'meat' of it- which is the physics (and so unfortunately can't remark on it). I'd hoped to, but then I realised I was just putting it off out of apprehension that I'd find myself feeling the lack of formal first year physics at university (something I gleefully escaped as early as I could in favour of my chosen field- pure mathematics). This is probably an unfounded concern, since skipping ahead to chapter 17 on spacetime, I was able to follow the account, but nonetheless I closed the book at this point.
Perhaps I'll revisit it sometime with a few other references handy should I need rescue. This would certainly be worthwhile if you can give this the time and energy required; you're sure to come out richer in knowledge, in a way almost no other popular account of science can impart.
December 5, 2020
Un libro con un objetivo tan ambicioso como describir el estado del conocimiento científico que poseemos sobre la realidad profunda de la naturaleza y los caminos para avanzar en lo que nos falta por descubrir es realmente difícil de valorar.
Este es el único libro científico que aparece entre los 100 primeros libros de la lista de Goodreads "Libros que te llevarías a una isla desierta". Creo que está ahí con todo merecimiento. Es un libro que admite muchas relecturas- Durante los casi dos meses que me ha llevado su lectura las cosas que leía me venían a la mente continuamente. Todo lo que plantea es interesante, estimulante y te expande la mente.
El único problema con este libro es que en una isla desierta no hay Internet. Me explico: a pesar de sus más de 1.400 páginas, el libro es casi imposible de seguir solo con la información que en él aparece. He tenido que recurrir en muchísimas ocasiones a la web a buscar la información necesaria para "rellenar los huecos" de lo que estaba leyendo. El autor te lleva de la mano durante la exposición pero frecuentemente te suelta y te obliga a hacer un acto de fe en la argumentación o da por sentada la evidencia de un razonamiento matemático. He echado de menos enormemente enlaces a recursos en Internet donde se explique el detalle de las ideas expuestas o aparezcan resueltos los ejercicios que propone. En mi caso, solo cuando he podido seguir la línea argumental en detalle he tenido una imagen clara de lo que está leyendo.
En cualquier caso, el esfuerzo de enfrentarse a la lectura de este libro es ampliamente recompensado por la ampliación de tus horizontes mentales.
Resulta también fascinante el vislumbrar cómo funciona la mente de un científico como Roger Penrose, para mí, uno de los más grandes pensadores vivos.
Este es el único libro científico que aparece entre los 100 primeros libros de la lista de Goodreads "Libros que te llevarías a una isla desierta". Creo que está ahí con todo merecimiento. Es un libro que admite muchas relecturas- Durante los casi dos meses que me ha llevado su lectura las cosas que leía me venían a la mente continuamente. Todo lo que plantea es interesante, estimulante y te expande la mente.
El único problema con este libro es que en una isla desierta no hay Internet. Me explico: a pesar de sus más de 1.400 páginas, el libro es casi imposible de seguir solo con la información que en él aparece. He tenido que recurrir en muchísimas ocasiones a la web a buscar la información necesaria para "rellenar los huecos" de lo que estaba leyendo. El autor te lleva de la mano durante la exposición pero frecuentemente te suelta y te obliga a hacer un acto de fe en la argumentación o da por sentada la evidencia de un razonamiento matemático. He echado de menos enormemente enlaces a recursos en Internet donde se explique el detalle de las ideas expuestas o aparezcan resueltos los ejercicios que propone. En mi caso, solo cuando he podido seguir la línea argumental en detalle he tenido una imagen clara de lo que está leyendo.
En cualquier caso, el esfuerzo de enfrentarse a la lectura de este libro es ampliamente recompensado por la ampliación de tus horizontes mentales.
Resulta también fascinante el vislumbrar cómo funciona la mente de un científico como Roger Penrose, para mí, uno de los más grandes pensadores vivos.
February 8, 2023
By his own admission in the preface, this is Penrose' attempt to popularize the current thinking in theoretical physics, including quantum mechanics, relativity, and unification theories such as string theories and quantum gravity. In the introduction he says (paraphrased) that he has intentionally gone for the more mathematical route, in spite of advice to the contrary, but he hopes that those without a mathematical bent can just skip the equations and get the gist of the concepts anyway.
With due respect to the author, his attempt at “popularization” is a failure. I wonder who he thinks his target audience is when he goes to great pains to explain basic concepts such as imaginary numbers and why they aren't so mysterious and yet throws out higher level abstractions that take time even for a college graduate to feel comfortable with. His target audience seems to drift from the lay person on the street up to professional mathematicians and physicists.
In my opinion this book of over 1000 pages replete with equations and complex diagrams would be good fodder for several graduate courses in mathematical physics. He introduces such abstractions as complex analysis, abstract algebra, manifolds, bundles on manifolds, tensor fields, Lie groups, Hilbert spaces, etc with just a few words of explanation and a lot of hairy equations, after which he marches on with advanced theoretical concepts and applications to physics. I studied most of those topics in graduate school to some degree, but I was especially comfortable with Hilbert spaces and complex analysis. And yet, it was all I could do to keep up with him. Perhaps it's the fact that I was in my early thirties then and had more functioning neurons, but this 63 year old brain found it hard to track his descriptions, let alone the equations. I confess that (in spite of considering myself an erstwhile mathematician) I often attempted to take the route he had advised for the non-mathematically inclined: just gloss over the equations and get the general concept. But his descriptions are mostly so down in the details that I found it difficult to get to the general concepts from the text alone.
I also decided that I don't like his writing style much. It varies from overly verbose and redundant to cryptic and abstract in the extreme. And the edition I have was poorly edited: there were many mistakes such as unclosed parentheses, repeated words, missing words, and grammar mistakes. Given how turgid his prose is I don't envy the job of the editors, but it's still their job to find those kinds of obvious errors.
The one good thing from all this is that I think I finally (kind of) understand tensors and tensor fields. For whatever reason I didn’t get into tensors when I studied differential geometry in the early 80's and I’ve found this to be a deficiency in my education over the years (e.g. understanding the field equations of general relativity). His description prompted me to study up on tensors and I found a couple of good websites with detailed descriptions and examples.
In any case, I DO recommend the book if you have a knack for or interest in advance mathematics and theoretical physics. I DON’T recommend it if you want an easy read in popular science to make you feel smart :-).
With due respect to the author, his attempt at “popularization” is a failure. I wonder who he thinks his target audience is when he goes to great pains to explain basic concepts such as imaginary numbers and why they aren't so mysterious and yet throws out higher level abstractions that take time even for a college graduate to feel comfortable with. His target audience seems to drift from the lay person on the street up to professional mathematicians and physicists.
In my opinion this book of over 1000 pages replete with equations and complex diagrams would be good fodder for several graduate courses in mathematical physics. He introduces such abstractions as complex analysis, abstract algebra, manifolds, bundles on manifolds, tensor fields, Lie groups, Hilbert spaces, etc with just a few words of explanation and a lot of hairy equations, after which he marches on with advanced theoretical concepts and applications to physics. I studied most of those topics in graduate school to some degree, but I was especially comfortable with Hilbert spaces and complex analysis. And yet, it was all I could do to keep up with him. Perhaps it's the fact that I was in my early thirties then and had more functioning neurons, but this 63 year old brain found it hard to track his descriptions, let alone the equations. I confess that (in spite of considering myself an erstwhile mathematician) I often attempted to take the route he had advised for the non-mathematically inclined: just gloss over the equations and get the general concept. But his descriptions are mostly so down in the details that I found it difficult to get to the general concepts from the text alone.
I also decided that I don't like his writing style much. It varies from overly verbose and redundant to cryptic and abstract in the extreme. And the edition I have was poorly edited: there were many mistakes such as unclosed parentheses, repeated words, missing words, and grammar mistakes. Given how turgid his prose is I don't envy the job of the editors, but it's still their job to find those kinds of obvious errors.
The one good thing from all this is that I think I finally (kind of) understand tensors and tensor fields. For whatever reason I didn’t get into tensors when I studied differential geometry in the early 80's and I’ve found this to be a deficiency in my education over the years (e.g. understanding the field equations of general relativity). His description prompted me to study up on tensors and I found a couple of good websites with detailed descriptions and examples.
In any case, I DO recommend the book if you have a knack for or interest in advance mathematics and theoretical physics. I DON’T recommend it if you want an easy read in popular science to make you feel smart :-).
Shelved as 'half-read'
April 14, 2016This book is not for those with no strong background in mathematics and physics and it is definitely not for lay readers.
Except for the first 40 pages or so the book material was very sophisticated and hard to understand for me. Today I decided to stop as for the past 30 or so oages I could only understand little of what I was reading.
I'm putting it on hold now and I may return to it later after establishing a strong base in mathematics and physics.
Except for the first 40 pages or so the book material was very sophisticated and hard to understand for me. Today I decided to stop as for the past 30 or so oages I could only understand little of what I was reading.
I'm putting it on hold now and I may return to it later after establishing a strong base in mathematics and physics.
April 10, 2019
Wow, this book covers so much material I don't even know where to start. Nor am I exactly qualified to review a few of the more advanced topics. This is not a textbook per se, and it reads much more smoothly and purposefully than a boring theorem, proof type structure. Just an fyi though, the first third or so is essentially a survey/seminar on modern math. It begins benignly with philosophy, euclidean geometry, and intro to hyperbolic geometry, and some fairly elementary number theory. However, rather suddenly, Penrose starts running you through a gauntlet of advanced topics in various fields ranging from real and complex analysis, advanced number theory, differential geometry, fourier analysis, riemann surfaces, group/symmetry theory, advanced linear algebra, representation theory, lie algebras, tensors, n-manifolds, gauge theory, calculus of variations...I think you get the picture. That's all covered in under 400 pages, and then the physics begins. As I said, some of this math is extreme, ie phd-level. The physics appears to cover the standard model of particle theory and quantum mechanics/QFT, general relativity, and then grand unification. Then it ends with some topics in supersymmetry and string theory, but you can skip those if you want because you would never need to know it unless you want a phd in theoretical physics.
Long story short: this is one massive undertaking, and Penrose doesn't go easy on you, so ensure that you want to study these topics in some depth, and then go for it cause it's brilliant.
Long story short: this is one massive undertaking, and Penrose doesn't go easy on you, so ensure that you want to study these topics in some depth, and then go for it cause it's brilliant.
September 23, 2012
Penrose examines the turn modern theoretical physics has taken in pursuit of multi-dimensional mathematical models to develop a unified model of the sub-atomic realm. His argument is not entirely mathematical, though he does have good arguments against unnecessary complexity from the point of view of the straightforward progress made by theoretical physics in discovering the mathematical elegance of relationships among various observed constants. His most profound argument against String Theory is a failure to make any predictions which could be tested by observation. He makes an eloquent argument for pursuing alternate models instead of mathematical physics being caught in what may ultimately prove to be a dead end. He proposes several ways forward, including his own twistor theory.
Penrose reminds me of Feynman in his fresh thinking. Feynman's development of quantum-electrodynamics required thinking of observed phenomena in a new way. For those willing to scratch the surface of modern physics, Penrose provides a lucid primer. He even devotes nearly a third of the book to laying out the math so the reader can begin to understand what follows. At more than a thousand pages, this is a serious primer.
I thank the friend who loaned me this book a few years ago and allowed me ample time to digest what I could. Yes, I did return it, but I may need to acquire my own copy.
Penrose reminds me of Feynman in his fresh thinking. Feynman's development of quantum-electrodynamics required thinking of observed phenomena in a new way. For those willing to scratch the surface of modern physics, Penrose provides a lucid primer. He even devotes nearly a third of the book to laying out the math so the reader can begin to understand what follows. At more than a thousand pages, this is a serious primer.
I thank the friend who loaned me this book a few years ago and allowed me ample time to digest what I could. Yes, I did return it, but I may need to acquire my own copy.
July 20, 2010
Not an easy read because of all of the math, but well worth the effort for those who can make it.
Read
June 7, 2017Най-накрая приключи.
И само това да бях коригирала, щях да се гордея със себе си.
И само това да бях коригирала, щях да се гордея със себе си.
September 6, 2019
The story goes that Stephen Hawking was once told by a book publisher that every formula in his book would halve the amount of readers (or sales, almost the same thing, but not to a publisher). He was , of course, totally and utterly wrong. The Road to Reality contains about 1100 pages and, on average, there's about 9 formulas per page. That makes roughly 10,000 formulas. According to this publisher's law, that would halve the sales ten thousand times (2^(-10000)), so a rough estimate of the amount of readers left is around 5x10^(-3001), which is a number so absurdly and unimaginably small, you have to be a Belgian surrealist painter to be able to imagine it. Roger Penrose would be left with much, much less than a single quark of a reader. Judging by the amount of readers here, this is obviously not the case.
What this publisher was pointing out, however, was that, in order to attract a lay public, you have to shun formulas, because they might chase them away and you wouldn't be able to teach anybody anything because there wouldn't be anyone left. Hawking followed the advice, wrote a book for the layman and, in my humble opinion, failed miserably. The layman didn't understand anything from his cryptic text, because they were missing several dozens of books of background information needed to understand most of the concepts. The more informed readers were chased away because of the lack of depth, the haphazard and disconnected way the concepts were presented and the absence of the mathematical beauty. It did sell well, so from this perspective, the publisher was undoubtedly right (and this was probably the only perspective he was interested in).
This fiasco teaches us something very important: writing and reading about present-day physics is no small feat. Lots of background is needed (yes, mathematical as well). However, unfortunately, most writers listen to publishers and omit the formulas and lots of the difficult bits as well, so the task for the physics reader is greatly hindered.
Luckily, Penrose is a kind old British gentleman, not afraid to take up the glove and rise to the challenge. The Road to Reality is his magnum opus, introducing the reader to modern physics (mostly cosmology and to a lesser degree quantum mechanics) , without oversimplification or the omission of essential formulas. He doesn't muck about either. If mathematics is what you need to understand it, mathematics is what you'll get. No less than 16 of the 33 chapters are devoted solely to mathematical foundations. After that, Penrose gives an overview of the established physics (mostly special and general relativity, quantum mechanics and some thermodynamics. The last few chapters are concerned with the more controversial topics, like string theory.
The mathematical part is, to the best of my knowledge, quite complete. The established physics is concise and omits most things that aren't related to the aim of the book: present-day speculative cosmology. For the last part, Penrose focuses on string theory (currently still the most popular group of theories), loop quantum gravity (the most interesting contender) and twistor theory (Penrose's own field of research). His account of these theories is very honest, making no secret of his critiques on certain fields of research and warning the reader to take his interpretations with a pinch of salt and often pointing the reader towards books containing views conflicting with his own.
Does this make The Road to Reality the ultimate physics book for the dauntless layman? Of course not. The task Penrose set himself is neigh impossible. One cannot replace several dozen textbooks by one, albeit bulky, volume, even if it is written by someone as erudite as him. A lot of his explanations are just too brief. He would need another two to three thousand pages to be able to explain everything thoroughly. Furthermore, the splitting of the maths and physics is different chapters is probably necessary, but it means Penrose refers a lot to previous chapters. Since I have a hard time exactly remembering some subtle mathematical notion from 400 pages ago, I needed to skip backwards and forwards a lot, making for quite a laborious read (not something to do while commuting by bus, for example). The subject itself is very slippery too. Current theories cannot be verified (yet) by experiments, so theoreticians are only guided by very abstract notions, such as mathematical beauty, or instincts honed by years of hard work. Such things are often very hard to convey to anyone not a specialist in that particular field, although Penrose does a good job, nonetheless.
It is probably the closest you'll get to a textbook without actually reading a textbook. The Road to Reality trumps A Brief History of Time in many ways, but ultimately it cannot be avoided that one needs to read a lot more to truly understand physics, but that's not necessarily a bad thing (publishers will agree).
What this publisher was pointing out, however, was that, in order to attract a lay public, you have to shun formulas, because they might chase them away and you wouldn't be able to teach anybody anything because there wouldn't be anyone left. Hawking followed the advice, wrote a book for the layman and, in my humble opinion, failed miserably. The layman didn't understand anything from his cryptic text, because they were missing several dozens of books of background information needed to understand most of the concepts. The more informed readers were chased away because of the lack of depth, the haphazard and disconnected way the concepts were presented and the absence of the mathematical beauty. It did sell well, so from this perspective, the publisher was undoubtedly right (and this was probably the only perspective he was interested in).
This fiasco teaches us something very important: writing and reading about present-day physics is no small feat. Lots of background is needed (yes, mathematical as well). However, unfortunately, most writers listen to publishers and omit the formulas and lots of the difficult bits as well, so the task for the physics reader is greatly hindered.
Luckily, Penrose is a kind old British gentleman, not afraid to take up the glove and rise to the challenge. The Road to Reality is his magnum opus, introducing the reader to modern physics (mostly cosmology and to a lesser degree quantum mechanics) , without oversimplification or the omission of essential formulas. He doesn't muck about either. If mathematics is what you need to understand it, mathematics is what you'll get. No less than 16 of the 33 chapters are devoted solely to mathematical foundations. After that, Penrose gives an overview of the established physics (mostly special and general relativity, quantum mechanics and some thermodynamics. The last few chapters are concerned with the more controversial topics, like string theory.
The mathematical part is, to the best of my knowledge, quite complete. The established physics is concise and omits most things that aren't related to the aim of the book: present-day speculative cosmology. For the last part, Penrose focuses on string theory (currently still the most popular group of theories), loop quantum gravity (the most interesting contender) and twistor theory (Penrose's own field of research). His account of these theories is very honest, making no secret of his critiques on certain fields of research and warning the reader to take his interpretations with a pinch of salt and often pointing the reader towards books containing views conflicting with his own.
Does this make The Road to Reality the ultimate physics book for the dauntless layman? Of course not. The task Penrose set himself is neigh impossible. One cannot replace several dozen textbooks by one, albeit bulky, volume, even if it is written by someone as erudite as him. A lot of his explanations are just too brief. He would need another two to three thousand pages to be able to explain everything thoroughly. Furthermore, the splitting of the maths and physics is different chapters is probably necessary, but it means Penrose refers a lot to previous chapters. Since I have a hard time exactly remembering some subtle mathematical notion from 400 pages ago, I needed to skip backwards and forwards a lot, making for quite a laborious read (not something to do while commuting by bus, for example). The subject itself is very slippery too. Current theories cannot be verified (yet) by experiments, so theoreticians are only guided by very abstract notions, such as mathematical beauty, or instincts honed by years of hard work. Such things are often very hard to convey to anyone not a specialist in that particular field, although Penrose does a good job, nonetheless.
It is probably the closest you'll get to a textbook without actually reading a textbook. The Road to Reality trumps A Brief History of Time in many ways, but ultimately it cannot be avoided that one needs to read a lot more to truly understand physics, but that's not necessarily a bad thing (publishers will agree).
February 20, 2014
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 significant emphasis on the mathematical component. The author is an outstanding mathematical physicist of our times, and in this book of 1100 pages, he 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 in terms of the action of a force; a vector quantity, which has both magnitude and direction. The force acts on a matter and produces a causative action that results in an effect. The cause - effect is one of the fundamental aspects of classical reality, but it gets fuzzy and uncertain at submicroscopic levels (quantum physical reality.) The main object of physical law is to describe the reality we observe. Our observation includes this universe that is made of space, time, matter, and energy. All objects are made of matter, which exists as complex structures composed of molecules, atoms and fundamental particles. Matter is also a form of energy and the two forms can interconvert as described by the Einstein's famous equation. The fundamental particles has certain physical properties and the manner in which energy (and force) is expressed is though their association with the so called force particles that are responsible for four fundamental forces that operate in nature, they are; electromagnetism, gravity, strong and weak nuclear forces. The four forces mediate matter-matter interaction and facilitate matter-energy conversions in spacetime and thus explain physical reality. The key to the understanding of nature and physical reality is to discover a theory that satisfactorily explains all the four forces and this theory must be experimentally verifiable. Unfortunately, this has not been achieved so far, but we have theories that can be verified but explains only three forces. One single physical theory that explains both quantum and classical realities have not been successful mainly because the nature of gravitational force (curved spacetime) is difficult to describe in a unified situation, since space and time at the most fundamental level are also quantized (exist in discrete quanta) and are they dynamic (not static background).
To understand this book the reader is required to have undergraduate level physics and mathematics; the author explains in the introductory part of the book why he chose to include mathematics despite its negative impact on the book's marketing potential. It would suffice 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 in being attracted aesthetically to a particular idea. You can skip chapters 1-16, and from chapters 17-30, general discussion about 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 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, but with some ingenuity, the infinity problem was circumvented leading to 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 renormalizability or finiteness as the primary goal, but the former group likes to solve the conceptual difficulties between the two theories. The combination of two theories of particles physics into one framework to describe all interactions of subatomic particles, except due to gravity, is called standard model. These two theories are electroweak theory and quantum chromodynamics. They describe force interactions between particles in terms of exchange of intermediary particles. The author also engages the reader in an insightful discussion of many other theories.
This is an exhaustive review of the laws of physics as related to physical reality with significant emphasis on the mathematical component. The author is an outstanding mathematical physicist of our times, and in this book of 1100 pages, he 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 in terms of the action of a force; a vector quantity, which has both magnitude and direction. The force acts on a matter and produces a causative action that results in an effect. The cause - effect is one of the fundamental aspects of classical reality, but it gets fuzzy and uncertain at submicroscopic levels (quantum physical reality.) The main object of physical law is to describe the reality we observe. Our observation includes this universe that is made of space, time, matter, and energy. All objects are made of matter, which exists as complex structures composed of molecules, atoms and fundamental particles. Matter is also a form of energy and the two forms can interconvert as described by the Einstein's famous equation. The fundamental particles has certain physical properties and the manner in which energy (and force) is expressed is though their association with the so called force particles that are responsible for four fundamental forces that operate in nature, they are; electromagnetism, gravity, strong and weak nuclear forces. The four forces mediate matter-matter interaction and facilitate matter-energy conversions in spacetime and thus explain physical reality. The key to the understanding of nature and physical reality is to discover a theory that satisfactorily explains all the four forces and this theory must be experimentally verifiable. Unfortunately, this has not been achieved so far, but we have theories that can be verified but explains only three forces. One single physical theory that explains both quantum and classical realities have not been successful mainly because the nature of gravitational force (curved spacetime) is difficult to describe in a unified situation, since space and time at the most fundamental level are also quantized (exist in discrete quanta) and are they dynamic (not static background).
To understand this book the reader is required to have undergraduate level physics and mathematics; the author explains in the introductory part of the book why he chose to include mathematics despite its negative impact on the book's marketing potential. It would suffice 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 in being attracted aesthetically to a particular idea. You can skip chapters 1-16, and from chapters 17-30, general discussion about 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 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, but with some ingenuity, the infinity problem was circumvented leading to 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 renormalizability or finiteness as the primary goal, but the former group likes to solve the conceptual difficulties between the two theories. The combination of two theories of particles physics into one framework to describe all interactions of subatomic particles, except due to gravity, is called standard model. These two theories are electroweak theory and quantum chromodynamics. They describe force interactions between particles in terms of exchange of intermediary particles. The author also engages the reader in an insightful discussion of many other theories.
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