I don't make a habit of discussing books I haven't finished reading, let alone reviewing them. I'm breaking with habit because, first, I think I've made a reasonable stab at getting into this book, and second, I'll probably die of old age somewhere around page 800 and want to have my say before then.<br><br>The dust jacket and various reviews assure us that this book is written for "the serious lay reader." That depends on how we define "serious" and "lay." For "serious" I might say "insanely obsessive," and for "lay," "without a graduate degree in physics." Penrose claims that "you can gain much from this book" while skipping over the formulae. I suppose that depends on what he means by "gain" and "much."<br><br>As I see it, this book is for the lay reader who studied and hasn't forgotten all he learned about calculus, linear algebra, and complex variables. Penrose lays out mathematical concepts in a clear and logical way, but I find that this text is detailed enough to remind me of things I once knew, not to teach me math I never had. His serious lay reader might have been trained as an engineer, but probably not as a lit. theorist.<br><br>Do I think the lit. theorist can gain much by reading this book? Not if reading means skipping over the formulae. The math in this book couldn't be relegated to an appendix; it's integral to the text. Let me repeat: I don't think this book could be re-written so that the mathematical formulae are in an appendix and remain a coherent explanation of physics. This isn't just Greene's Elegant Universe with a lot of mathematical explanation tacked on. The mathematical material is integral to understanding Penrose's explanations of physical theory and laws. (Okay, I've skipped ahead to later chapters - I wanted to see if I could understand "Quantum field theory" (Ch. 26) just reading the words. Ha!) If you haven't studied the math, this book isn't the place to learn it, and if you can't understand the math, the physics makes no sense.<br><br>I did actually study a lot of math in college, but since I rarely use more than basic calculus these days, I've gone aground on the shoals of Chapter 12, "Manifolds of n dimensions" (about page 225). Perhaps when I take a vacation I can pull down my math texts and get up to speed on this. I really am enjoying this book. It's a challenge and it's helping get some of the cobwebs out of the math regions of my brain. I like the illustrations, the notes are interesting and informative, and I think this book really can help a non-physicist understand (or at least have pretty solid delusions of understanding) the intellectual feast of modern physics. But let's be clear that the reader must have some degree of mathematical sophistication. It isn't for the mathematically innocent.