Cycles of Time: An Extraordinary New View of the Universe

Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, has written another marvellous book. Once again, he manages to discuss topics in modern physics in a way that will educate and enthuse the intelligent layman while retaining enough substance to engage the more sophisticated reader. This time, the topic is (in Penrose's words) "an extraordinary new view of the universe," a theory that he calls "Conformal Cyclic Cosmology (CCC)."As in his previous efforts, Penrose's success derives from his ability to actually teach some fundamental concepts before entering the more speculative domains. Hence, the first third of the book is devoted to an informative explanation of entropy and the second law of thermodynamics, and their place in describing the evolution of the universe. In the second third, Penrose emphasises the unique character of the low entropy state of the early universe before gravitational degrees of freedom had been activated. In this part, he also introduces the notion of "strict conformal diagrams" that provide a graphical description of the rather involved maths.The final portion of the book is devoted to an intriguing summary of CCC. This is based largely on Penrose's earlier introduction of the Weyl Curvature Hypothesis that requires the Weyl curvature tensor to vanish at the conformal hypersurface of the Big Bang. CCC proposes that beyond the distant future of the current universe lies another Big Bang and, conversely, before the Big Bang of the current universe lies the future infinity of a previous one, with space-time being merged at the boundary of each "aeon" by a conformal rescaling of the metric tensor. How this is reconciled with the continuing increase in entropy, consistent with the second law, is quite interesting and I won't spoil the surprise by revealing it here. The book concludes with a mathematical appendix that more fully describes some of the basic notions. This, in conjunction with the notes and cited references, will help the student on his way.To be sure, this book will challenge even the brightest and most motivated layman. Understanding just the elementary exposition of the basic ideas requires some serious thinking. And Penrose cannot help dropping terms like "tensor field" and "tangent space" that will baffle the novice. There are even a few equations. In addition to thinking, one should be prepared to consult additional references and ask many questions. But, after all, that is what learning is all about.Enthusiastically recommended!

As a retired surveying scientist and inventor of the loop inverse theory of estimators and matrix (and tensor) inverses, I was curious to see if Penrose is applying the inverse theory to validate his conformal math model of Bing Bang theory. My motivation to buy this book was a newspaper book review about Penrose idea of a continual or repeated Bing Bangs using a math model that is invariant on distances (such as the speed of light). In my work some 40 years ago I expanded the Moore-Penrose and Bjerhammar-Rao general inverses in the loop inverse theory of array algebra that shares this repeat or looping structure. It resulted in an expansion of the very definition of estimability in mathematical statistics with some common sense examples such as estimating the "angular" or scale invariant shape of a triangle where all sides are measured with both random and unknown systematic scale error.Two additional generalization steps of this estimation theory have made it even more closely related to the Penrose and Hawkin application in cosmology by: 1)multi-linear array algebra expansion of tensor calculus using short-hand (matrix-like) notations and concepts of the Einstein summation convention and 2)nonlinear array algebra expansion of loop inverse estimators using math models of more than four variables in the global inter-galactic( vs. local Earth or Solar system) network adjustment. This is a book that needs to be read several times in small bites to digest with some specific goal of understanding. So far I have not found any evidence that could prevent the additional loop inverse expansion of "hyper conformal" Penrose math model for repeated Bing Bang cycles. Like in any inverse theory, the validity of the postulated math model can only be confirmed when a sufficient number (and implicit space domain rank) of inter-connecting observables with proper weights can be made like in a network survey of the Earth. It may take some time before the "universal mankind" masters and shares such technologies of observables for connecting different solar or galaxy systems even when allowing scale and other bias in the observables. The earth based observables E1,E2 need often be complemented by independent observables between targets 1 and 2 to get a unique estimator for the relative geometric location of points E,1 and 2.

This book reads in many ways like a textbook without the explicit math in the main section(it is in the appendix). It presents a very unique concept of the Universe as a series of aeons that began with a Big Bang and end at10 to the 100th power years when all the Black holes have evaporated through Hawking radiation. He links the transition between aeons through the use of Conformal geometry.He does an excellent job of dealing with the issues presented by the second law of Thermodynamics and presents many thought provoking concepts.I do believe this. Book would be tough going for an individual without a fairly strong science and math background . I have a PhD in Physical Chemistry with a minor in Physics and a strong interest in Quantum mechanics and I had to approach this book as I would a textbook, but it was well worth the effort.

I read quite a lot. Most books I read are about history, philosophy, theology and the occasional science book. That being said, I could not even understand the introduction to this book. There is quite a bit of advanced mathematical concepts here and it's not for the lay reader. That being said, I gave it 5 stars since it seems like a well thought out thesis and it's not the author's fault that it was over my head.If you don't understand complex math then you probably will struggle to understand the book.

I liked the book but it struggles to keep your attention or understanding. It's not the most enjoyable science literature out there, but what I did thoroughly enjoy is his beautiful theory of cyclic conformal cosmology. I hope we find proof for that!

The chapter on the 2nd Law of Thermodynamics is likely one of the greatest science reads I have ever had. It's not particularly easy, but all scientifically trained person will be able to understand what Penrose is trying to convey with it. If you thought that you had understood it from your basic Thermodynamics course in college, be prepared to be challenged, and that's a great accomplishment for such a book. Of course, specialists will have a lot to say about Penrose's views, but I think, and the Nobel prize he has just been awarded with is likely to help with it, he may well be perceived in the future as one of the great scientific minds of the second half of the 20th century. Highly recommended!

Sir penrose shows theoretical possibility of how time can be reversible/cyclic..... A model of cyclic universe which was also mentioned in several ancient Indian scriptures...

Penrose is one the greatest researcher of the physics actually. His analysis of the questions and his definition of terms are never obvious. The approach of Penrose is able to make sense about many problems. The author considers events as Big-bang or objects of the Blak-hole and he tries to explicate certain deep reallities of the universe.

your PRICE is too low! !!PENROSE is NEAR PERFECT. No adequate word to describe the joy to read his thought.If one can understand 10 % of it, that qualify for a Phd.