very difficult masterwork
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Many of the reviews focus on the fact that this book is difficult to read. It is. The information content is dense. Arguably not as dense as a technical math or physics book, this is a technical work, and requires a very slow process of reading and re-reading.
My opinion is that those with an understanding of calculus will get the most out of this book. If you really do not understand partial derivatives and integrals, I think you're in for a tough road.
There was math in this book that was unfamiliar to me, specifically Lie algebras, Lie derivatives, calculus on manifolds, and fiber bundles. These chapters were very slow going.
However, if you assiduously go through every sentence until you understand its meaning, if you consult outside references as necessary, if you really absorb this material- it is phenomenal. Penrose will equip you with a visual and intuitive comprehension of the advanced math necessary to really understand the big theories of physics. You won't be able to do calculations and solve problems, but the intuitive understanding is primary- and if you decide to go farther and look into really solving physics problems, you will be ready to learn quickly and easily.
In terms of the breadth and scope, I could compare this to the Feynman lectures. Feynman was far less stiff in his explanations- but if you really follow Penrose, his presentation is both elegant and thorough.
The book splits into 3 sections. The math background is followed by a very fine summary of the two big theories of modern physics- relativity and quantum mechanics. Finally, at about page 700, Penrose starts to discuss speculative ideas on the frontiers of physics. He carefully denotes where his own ideas differ from those of other theorists. By this time, having laid a full groundwork, Penrose addresses the reader as almost a technical peer. This is not dumbed down.
This is a book to live in for a long time. There is nothing else quite like it. The rewards justify the large amount of reader time and effort that will need to be committed. Five stars, absolutely.
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Fantastic Book, though not for the true layman
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This book is a real tour-de-force. My A-Level Maths of 18 Months ago was definetley a sufficient starting block for understanding almost everything in the book to an o.k. sort of standard, i plan to read it through at least twice more to make sure i really understand everything to the level that i want to. (I'm doing a MSc in Mathematics now, but plan to Do a 2nd MSc in Theoretical Physics later on, as that is where my true interests and ambitions lie) The explanations of the physics are possibly even better than those of the mathematics, although it is virtually impossible to really understand quantum mechanics without many years of proper study, this book really gives a nice intro to the wierd and wonderful world of the quantum.
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Not a book for the "popular science" market
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I'm an extremely keen reader and viewer of what is now commonly called Popular Science. I have a great amateur interest and knowledge of cosmology, quantum physics and related physics. I am also a (qualified) and pretty darn good computer programmer in languages from BASIC to 68000 assembly language and have contributed to professional games releases and written 3D engines, amongst other things.
I haven't said this to show-off how smart I am by any means, merely to illustrate just what an Everest this book is to the casual reader, including myself.
If one were to pick this book up from the shelf and note the blurb on the back which says "It assumes no particular specialist knowledge on the part of the reader" and that "the early chapters give us the vital mathematical background", you might assume that it was accessible to pretty much everyone who had the capacity to read, learn and could add up.
Not so. This blurb is seriously misleading, requiring at least- in my view- an understanding of mathematics to college level, if not university level.
It is true that the early parts of the book are largely devoted to explaining the maths involved to getting deeper into the physics of the rest of the book, but from very simple beginnings they rapidly fall into a whole host of symbols and equations most people won't understand. Including myself.
We start off with mathematical proofs, which are nicely explained, interesting and fairly straight forward for the novice to get to grips with, but are then remarkably quickly plunged into the topic of hyperbolic geometry and the terrible, mystical symbols crop up without any explanation of what they mean.
It's been said that once can fill in one's gaps of knowledge on the maths involved here by Googling the terms and studying the results, and that the book then opens up quite well to the reader- I've even seen it suggested that one can do it a page-a-day. That may be true, but I find Googling symbols rather difficult and I also think that studying a page-a-day of a 1000+ page book might require a lot more commitment than the interested amateur would be prepared to give.
From what I can ascertain, this book is- in its scope and ambition- a bit of a stunner and pretty much a definitive guide to most of the current thinking in the world of physics. For that reason, I'd dearly love to be able to read it.
However, the assertions of "no specialist knowledge" is extremely misleading. I can't help feel that, if the author had spent a dozen or so more chapters at the beginning explaining the maths and symbols behind the maths and symbols in the next dozen or so chapters, the reader would not only be much more involved but much more educated and willing to tackle the rest of the book.
As it is, I've put the book aside rather quickly until I can educate myself in the mathematics involved to even begin to get beyond the first few chapters.
A bit of a missed opportunity, in my view and this is solely why I have given it such a low star-rating- I have no doubt the book is excellent on its topic; probably worthy of a five-star; but to mislead the buyer by its blurb is rather unforgiveable. Probably the fault of the publisher rather than the author, admittedly, but the author could have offered more by way of a foundation class in the maths needed.
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For the mathematically literate only
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Sorry but you *have* to understand your maths before you can get to grips with this. As for me, I've got an MMath with Quantum Mechanics and Electromagnetic Theory under my belt, but I was *still* having trouble with it.
If anyone can explain the mathematics behind the state of play of theoretical physics, then surely Penrose can. His style is not quite as impenetrable as it was for some of his earlier works, but it's not as easy as you'd like it to be. Having said that, I wouldn't be able to do any better so fair play to him.
I struggled through to the end (and I admire anyone who managed six chapters and commiserate with those who couldn't get that far) but I still feel short-changed by my own mathematical limitations as I had to take so much of it on trust (and sorry, but life was too short to do the exercises, I've got too many other projects on the boil).
I have a dream of being able to boil this thwacking great tome down into an account that "the layman" *will* be able to appreciate, but by the time I'd have managed to do that, it would be out of date. Apparently things move faster than you'd think out on the edges of thought.
If you can't quite handle the mathematics in this, but want to, then it's worth considering whether to take a degree in the subject. If this book encourages anyone out there to embark on such a course of study, then it's more than paid for itself.
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Very hard going
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This book is supposedly for the intelligent layman. However, Penrose's cutoff point is clearly quite high, and I for one failed to make the grade. Penrose starts slowly but suddenly after a couple of chapters it gets very technical. The actually quality of the softback copy I read was terrible and started to fall apart. This meant going back to re-read sections became difficult. I also suspected that there were some typos in my edition. I found it so hard going that I gave up before I had reached halfway. It gets 2 stars rather than 1 simply because it did stimulate me to think.
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