The Road to Reality : A Complete Guide to the Laws of the Universe Hardcover – 2005
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The Road to Reality : A Complete Guide to the Laws of the Universe [Hardcover]
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I'm a little puzzled by the critical reviews mathematicians have written about it, because Penrose is a wonderful author, and his passion for understanding the underlying truths behind the reality that we see here on Earth, is rare and infectious. Further, he is very clear about the origins of the various approaches that he is presenting to the mathematical modelling of the universe. He describes the more mainstream approaches, areas of investigation that may be weaker than others, and always mentions whether the approach he is describing is well supported or not, and why.
Though other reviewers have criticized him for presenting his preferred theories, as well, I found it perfectly natural for him to do so after describing all of the other plausible approaches that have been taken, and which ones offer the best hope for leading us on through the current mysteries. The most challenging of these is the unification of the principles of particle physics and the classical view of the world, as best described by Einstein's relativistic approach. He introduces "twistor theory" as the one he feels has the best chance of leading us on, and why he thinks so, in a perfectly reasonable fashion.
Penrose begins with the veriest simplicity—the geometrical mapping of reality as lengths, widths and heights—and moves from there through increasing complexity, focusing, as he did in his former books, on the “magical” ways that mathematical descriptions seem to lead us deeper into the understanding of Nature. The way mathematical truths reveal themselves—actually come into being through reflection—is an important theme of the book.
As a composer builds a symphony from a simple flow of music, one instrument and one variation after another, Penrose builds the edifice of the current knowledge of the universe.
At the beginning of each chapter, he describes a basic truth, and you try to take it in. Then, he says, “Let us now extend this to … many variables… many derivatives… many dimensions...”, and you begin to see his text dotted and striped with mathematical formulae. So that's where you start skimming, after a good look at the formulae to glean what you can from how he is proceeding.
At this point it is useful to look at the pictures. Penrose liberally sprinkles his books with these, and they give you a visual representation of what the text means, so if you examine those, this will help you to keep tabs on the ideas he is trying to get across. At last, you get to the magical meaning of it all, and that's where, enchanted, you begin to read again. Thus you see every step of the development as Penrose describes how mathematicians model the universe.
At least you are finding out what he wants to say—you are hearing from the greatest, his description of the most up to date understanding on what our universe is really like. What could possibly beat that? When you consider what other authors get five stars for, its a mystery to me how anyone could give this extraordinary work less.
Penrose is a wonderful writer. For me, the great pleasure in reading his books is in the way he introduces his subjects. It is the path he takes, through the array of surrounding facts and ideas, that brings his subject to life for you, in the light of his advanced understanding. It is for this visionary journey that I love to read Penrose's books, and so I easily forgive myself for not being able to understand all of his math. I'm reading and understanding more than enough of his book to make it a great pleasure to read, and I heartily recommend it to anyone who loves such journeys, too.
There are some valid criticisms: Some will find this book too superficial in its treatment of mathematics and some will find that it is too mathematical. For example, thirty or so pages of basic calculus barely scratches the surface of that subject and many of his explanations of complex numbers, logarithms, Riemann surfaces, etc. while prosaic, could have been supported with broader explanations and some examples.
On the other side of the coin, it is to his credit that Mr Penrose does assume that some of his readers may freeze up at the thought of Mathematics or Physics. He therefore does try to make both subjects interesting for those less scientifically inclined and, in doing so, not get too rigorous. In his Preface, he recommends various ways to read and attempt to understand this book. He even suggests a way to read the book while skipping over the mathematical formulae. However, if you really want to enjoy the full essence of this book it would be better to understand the math.
A few suggestions which I think will help. The Bibliography, which incidentally occupies 35 pages, provides additional reference material. For those who want a better understanding of the math, I would recommend John Stillwell's "Mathematics and its History" (published by Springer). It will help to fill in the gaps of some of the earlier sections of Penrose's book, and provides a rich understanding of the concepts. For those who are having problems with Chapter 7, you should find that Stillwell's Chapters 14, 15 & 16 (each relating to complex numbers) quite rewarding. Another book is Tristan Needham's "Visual Complex Analysis". Penrose references this book. I have just received it and read the first few chapters. It is worth the investment.
Finally, while I do not presume to read Mr Penrose's mind, I do think he wrote this to encourage a broader understanding of scientific knowledge in the 21st. century. In this aspect I think he succeeds admirably. This book answers a lot of questions and poses a lot more. From reading the book I was encouraged to increase my own scientific knowledge, read a lot more and modify some of my own views.
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