Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

From the best-selling author of The Emperor’s New Mind and The Road to Reality, a groundbreaking book that provides new views on three of cosmology’s most profound questions: What, if anything, came before the Big Bang? What is the source of order in our universe? What is its ultimate future?

Current understanding of our universe dictates that all matter will eventually thin out to zero density, with huge black holes finally evaporating away into massless energy. Roger Penrose—one of the most innovative mathematicians of our time—turns around this predominant picture of the universe’s “heat death,” arguing how the expected ultimate fate of our accelerating, expanding universe can actually be reinterpreted as the “Big Bang” of a new one.

Along the way to this remarkable cosmological picture, Penrose sheds new light on basic principles that underlie the behavior of our universe, describing various standard and nonstandard cosmological models, the fundamental role of the cosmic microwave background, and the key status of black holes. Ideal for both the amateur astronomer and the advanced physicist—with plenty of exciting insights for each—Cycles of Time is certain to provoke and challenge.

Intellectually thrilling and accessible, this is another essential guide to the universe from one of our preeminent thinkers.

Genres: Science, Physics, Nonfiction, Philosophy, Popular Science, Astronomy, Mathematics

320 pages, Hardcover

First published September 23, 2010

About the author

Sir 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".

Reviews

[Bradley · Rating 4 out of 5]

I like to refresh myself on my intuitive understanding of physics every once in a while since I won't ever admit to understanding more than 30%-40% of the math.

Even so, what I do understand is still more than enough to endlessly fascinate and make me sit around fantasizing and ruminating and dreaming up new ways to describe what I know and how to apply it in interesting ways.

It's the curse of reading a ton of SF, too, and I'm pretty sure I'm not alone in this weird little habit of mind games and flights of attempted non-entropic fancy.

That being said, I did understand everything in this book, at least in the broad strokes, because Mr. Penrose almost never deviated from common ground.

You know, background radiation proving the Big Bang, gravitational lensing effects to prove or disprove dark matter and/or dark energy, and a few other common steps along the way to build a standard case for our current understanding of the cosmology.

No problem. He's a good writer and his analogies are interesting even if they're ones I've heard a hundred times. You know, like the one about Einstein on a Train. Raindrops on a tarmac for mass distributions of black holes and the eventual release of their captured radiation over a grand long time until entropy has its final way.

Where the good stuff is, (in my opinion,) lies in the idea of time and its reversibility in the grand 10 to the 124 schema, or if we eventually throw this whole universe down a gravitational funnel, the 10 to the 125 manifold. Is this the reversal, the homogenous transformation of matter back into straight energy that preceded the original big bang? Is this an ongoing cycle that repeats?

Well, that was what *I* wanted to know, anyway. Let me let you in on a big spoiler: We still don't know.

Honestly, this is good, even with all the talk about the lambda, Einstein's cosmological constant, and how it still maintains a strong presence in the grand discussion, but really? I truly have a much better time trying to wrap my puny little brain around the string theories more. Holographic universes also float my boat. Still, for all that this text tried to convince me of an old theory that may or may not be quite up to date, it's still a fun read.

Maybe one of these days I'll do more than just nod my head at some of the more complex equations. :) Truly, enough exposure to these, book after book, IS doing me a lot of good. Maybe if I collect enough great analogies and get a spinal shunt with a couple hundred external parallel processors to hang my brain on, I'll be just about ready to transform a few tensors. :)

[Manny · Rating 4 out of 5]

This book introduces Conformal Cyclic Cosmology: an amazingly beautiful idea, which I would love to be true. Unfortunately, the evidence to date is far from compelling. But, even if it isn't correct, Penrose is asking such interesting questions that the book is absolutely worth reading.

So here's my understanding of what it's about. Penrose starts by explaining the basic puzzle, which was a key theme in The Road to Reality and has been tantalizing cosmologists in general for a good while. As everyone knows who was paying attention during high school physics, the Second Law of Thermodynamics says that entropy increases with time; the universe gets progressively more and more disordered. If you drop an egg off a table, it breaks. But the time-reverse of this process is so vanishingly improbable that you don't ever expect to see it happen. A mess of egg-white, yolk and shell will not magically reassemble itself into an intact egg and then bound off the floor onto a table.

The rest of this review is available elsewhere (the location cannot be given for Goodreads policy reasons)

[Cassandra Kay Silva · Rating 5 out of 5]

I read this book cover to cover, and then the appendix and then tried again. I took a tea break walked in a circle, picked back up the book and continued to stare at it trying to glean somehow the information that I obviously was not meant to be clever enough to follow. I felt like Zoolander beating up the computer to get the information out of it. I can honestly admit that I could not understand nor have any basis for figuring out the vast majority of this book. I tried. I am not stupid. I know basic physics. This is not basic. The math is way in another universe from my limited calculus background. I really tried, and I kept trying because I think the idea is flawless. I love a cyclic universe. I want a cyclic universe and frankly I don't want just anyone, I want this one. It is beautiful and well conceived. I just can't honestly say I understood the building up of it from the mathematical viewpoint. I got lost three equations in. The IDEAS that are here I love. I just can't make any comment on the checking out of these ideas at this time in my life. Luckily I bought the book, and I plan on living a while longer, maybe I will eventually get enough background to re tackle this one.

[David Nash · Rating 1 out of 5]

I found this completely unintelligible.

Reading this book was like being kidnapped. I had a bag over my head and kept asking where we were going. Mostly I was ignored but occasionally I was told "we're turning left" or an explanation of how the steering mechanism worked.

I have a hard time imagining who the intended audience is. It's definitely not the general population.

You need some serious background in physics and mathematics to even start to understand what he's on about. So much so that you probably don't need to read the book, you could just read a summary of the argument and understand it.

I usually don't mind skim-reading the deeply technical parts and I can still appreciate a book where the author tells you what it all means in plain english. But that just never happens.

There wasn't even a conclusion that I could discern. The title on the cover says "Cycles of Time" but it's hard for me to relate that to anything in the at all book, really.

[Bill Bowyer · Rating 5 out of 5]

"The entire fabric of life on earth requires the maintaining of a profound and subtle organization, which undoubtedly involves entropy being kept at a low level." ... "The structure of life on this planet would run rapidly down were it not for a powerful low-entropy source, upon which almost all life depends, namely the Sun."

Remember reading Penrose in college and being blown away. Favorite living theorist, turns complex ideas into digestible knowledge with simple charts and a straightforward writing style. When you pick apart the details and rearrange them in a way that makes sense, they can be rather inspirational. Big takeaway: the universe is a force of living energy balanced by entropy. Eternal harmony through a little give and take.

Pay attention to 2.2"The ubiquitous microwave background."

[Keith Davis · Rating 3 out of 5]

I'm not sure who the intended audience of this book is. It is not as technical as a scientific paper, but it is way more technical than a popular science book. Roger Penrose is clearly much more comfortable with linear algebra and tensor calculus than this reader.

[Ami Iida · Rating 5 out of 5]

The book themes are
How wide is our universe?
When does the universe start?
When does the universe finish?
How long the universe 's age?
What is the quantum gravity theory?. etc........................

[Raed · Rating 3 out of 5]

Big Bang or Steady State?
fulfilled of innovative ideas but this is a tough book to read

I had no business reading it, too much details.
i'm truly tired 🧠

[John Gribbin · Rating 3 out of 5]

A joint review of:
Cycles of Time
Roger Penrose
The Grand Design
Stephen Hawking and Leonard Mlodinow



Once upon a time, Roger Penrose and Stephen Hawking collaborated on a seminal piece of work which proved that if the general theory of relativity is correct our Universe began from a state of infinite density – a singularity. The investigation of the implications of that work, now more than 40 years old, still reverberate, providing the basis for intense debate among cosmologists.
Since the 1960s, Penrose and Hawking have each written best-selling books introducing the lay reader to arcane areas of science. Now, they have independently produced books which address some of the implications of their early discovery about the origins of the Universe. But it would be hard to imagine two more different approaches to the subject, both in terms of content and of style.
Penrose addresses the question, “what came before the Big Bang?” But it is important to appreciate that the Big Bang was not the singularity. There is a well-established consensus that the Universe as we know it emerged from as superhot, superdense state – the evidence for this comes in particular from studies of the famous cosmic microwave background radiation. But “superdense” does not mean “infinitely dense,” and there is room to suggest, or even expect, that under the extreme conditions “before the Big Bang” the laws of physics are not quite as described by Einstein so there may not have been a singularity.
The way Penrose tackles the problem is by combining what we know about the second law of thermodynamics and the arrow of time with what we know about the Big Bang and the general theory. If that thought makes your head hurt, his book is not for you. It contains many equations and pulls few punches, an archetypal example of what an Oxford don thinks is a simple exposition of his subject. But if you do not have a maths phobia, and you can live with language like “at this point, it is appropriate to mention . . . ”, Cycles of Time can be highly recommended as an example of how cosmologists are now thinking the unthinkable in trying to look back beyond the Big Bang and forward beyond the death of our Universe.
A superficial summary of Penrose’s thesis is that as the expanding Universe thins out and all the stars die the conditions that result are just right to produce a new Big Bang, so that universes like ours follow one another in an endless chain, or perhaps in an eternal loop, reminiscent of the image of the worm Ourobouros swallowing its own tail. As a speculation, this is a very old idea; the difference is that Penrose has the mathematical and physical foundations to make what he calls “conformal cyclic cosmology” respectable. It is also an idea whose time has come. I know of at least one other recent scientific suggestion, based on the idea of inflation, which also leads to the rebirth of the Universe from what in thermodynamic terms is sometimes called the “heat death”.
Penrose has universes following each other. Stephen Hawking, writing with the American physicist Leonard Mlodinow (who suffers the indignity of having his name in much smaller type on the cover, but is no doubt crying all the way to the bank), has universes lying side by side. This idea of the “multiverse” is also familiar from science fiction and other speculations, but like the cyclic universe idea it is now firmly based on scientific fact. The trouble is, you would be hard pressed to be sure of this after reading The Grand Design.
Hawking and Mlodinow favour cartoons rather than equations, and anecdote rather than exposition. If you knew nothing at all about science, the resulting book would make for a light read on a short journey, but the story has been told many times, by many people (Paul Davies and Martin Rees spring to mind), and it’s hard to imagine that it can have take more than a month to write, whereas it’s easy to believe that Cycles of Time took years. This is born out by the failure of either of the authors, both of whom know better, to pick up the error which refers to black holes as one of the “new effects” predicted by the general theory of relativity, when they are also predicted by Newton’s theory of gravity.
All this is particularly disappointing because I have a great fondness for the multiverse idea, which I believe to be the best explanation of why the Universe we see around us is the way it is. As Hawking and Mlodinow put it, in this view “the universe appeared spontaneously, starting off in every possible way. [Universes] aren’t just different in details, such as whether Elvis really did die young or whether turnips are a dessert food, but rather they differ even in their apparent laws of nature. In fact, many universes exist with many different sets of physical laws.”
Where do those other universes exist? Penrose’s universes follow one another, in a sense separated by time. But the universes of Hawking and Mlodinow exist side by side in different dimensions, separated by space. This array of universes is what is known as the Multiverse.
Part of the attraction of this idea is that it explains the many apparent coincidences that allow the existence of life forms like ourselves in the Universe we inhabit. To take just one example, more than half a century ago the physicist Fred Hoyle pointed out that the ability of stars to manufacture elements such as carbon and oxygen, which are essential for life as we know it, depends on a particular property of the nucleus of the carbon atom. If this and other parameters were not “just right” (and there is no a priori reason why they should have the properties they have) life as we know it would not exist.
At one extreme, the existence of these cosmic coincidences suggests to some people that the Universe was designed for our benefit. But the multiverse idea says that there is a multitude of universes in which all possible combinations of the laws of physics are played out and that life forms like us will only be found in the ones where conditions are suitable, just as it is no surprise that polar bears live in the Arctic. Martin Rees, the outgoing President of the Royal Society, has used the analogy of the difference between a bespoke suit, made to measure for a particular customer, and an off-the-peg suit, chosen from as vast variety in a chain store, where one of them is bound to fit whoever walks in the door. In each case, it is no surprise that the suit fits. And this brings us back to Penrose’s conformal cyclic cosmology, since on that picture each universe in the chain, or cycle, may have a different set of physical laws. Whichever way you look at it, the multiverse explains our existence without the need to invoke a designer.

This review first appeared in the Literary Review.

[Frans Robyns · Rating 4 out of 5]

I'm not going to lie, I really struggled to get through this book. Not because of the mathematical complexity (he helpfully banishes the complex equations to the Appendices to avoid confusing laymen such as myself) but because the ideas that he expresses in this book are so fundamentally non-intuitive. I had to take several breaks from the book to try and digest what I had understood from the text, often returning to it only to discover that what I thought he was trying to say was almost the complete opposite of what he was saying. Nevertheless, perseverance eventually paid off and I was able to comprehend (mostly) a genuinely new theory about the nature and history of our universe, one of the most beguiling and fundamental questions we can ask.

However, this book is really not for the uninitiated. After struggling through the first part outlining why the second law of thermodynamics is central to an understanding of the processes of the universe, I realised that my current knowledge was not suitable to tackle this text, so I had to take a prolonged break from the book to refresh my understanding of thermodynamics in general. Once I had done this, I thought the rest of the book should now very simply and elegantly fall into place. How wrong I was. The second part of the book throws you into the strange world of relativity, conformal geometry, and black holes. I think I understand his broad point of this second part, that the Big Bang was a special moment in space-time as while it appears to breach the second law of thermodynamics it actually didn't. Why not? Well, this has all to do with the time-symmetry of matter and the nature of the universe as an inflationary body that conforms to a principle known as a null-cone. Nope, I'm not entirely sure what this means either. However, the consequence of these principles, while equally conceptionally difficult to envisage as what is laid out above, is at the very least one of the most fascinating thoughts a human can have: the Big Bang does NOT represent the start of THE universe, only of THIS universe.

What an extraordinary thought, and the third part of his book is devoted to explaining exactly why and how this is the case: through something that he calls 'Conformal Cyclic Cosmology', or CCC. The basic principles of CCC are easy enough to grasp - the contention is that there has been a definite number of 'universes' each started by a Big Bang and each followed by an infinite future expansion that eventually (this is where it starts getting tricky) encounters a level of entropy similar to the earliest moments of the Big Bang, thus encapsulating what he refers to as an aeon. This is simple enough to grasp: we are one of many universes that have come about according to this predictable state. But it is the consequences and implications of this concept that really sent my mind reeling.

The first has to do with the nature of the boundary between the universes. They are 'conformal' with each other in that they inhabit the same space-time (despite being separated by more than a googol years) and are attached together through a process called 'conformal rescaling', something that I really do not understand. The result of all this is a new solution to Einstein's equations that demonstrates that the Big Bang cannot have been the start of the universe. Fine. At least it's possible to try and understand this. The second and far more difficult problem is the physical implications of this for the universe; in other words exactly how the particles (the stuff) of our universe reacts to this situation and in particular the crossover point of the boundary between aeons. Here some really quite in-depth knowledge of quantum mechanics and particle physics would not go amiss. Essentially (at least what I could grasp from it) there are some particles that are able to cross the boundary without hindrance and some that are not (this all has to do with conformally invariant quantum theory, something that I do not understand in the slightest). The outcome of this is that space-time becomes curved, providing the kind of low-entropy state that is required by the second law of thermodynamics at the beginning of each aeon. This is therefore what makes the Big Bang 'special', and why it was not the beginning of the universe.

This is really not an easy book to get through and only the most brilliant physicists the world has ever known should be able to consider this 'light reading'. Nevertheless, it really is worth the effort to try your best to get through it. It really does make you think about the universe in a completely new way, which is undoubtedly the greatest strength of this book. Perhaps Penrose could have made it slightly easier to comprehend (an introductory and concluding paragraph for each chapter trying to get across just the most basic central points of the chapter would have been much appreciated), and so for that I eschew him the hallowed 5-stars reserved for those works that are both brilliant and relatively easily comprehensible. But perhaps I'm being too harsh on him. Given the nature of the subject he is tackling, there is a not-insignificant chance that this book really does represent the most straightforward way to convey these ideas. Or maybe not, and I would certainly appreciate someone far more clever and knowledgable than myself to give it a go, or else I fear that we may lose this extraordinary idea to obscurity.

[Roo Phillips · Rating 2 out of 5]

No doubt, Roger Penrose is a brilliant mathematician. Unfortunately, he is not brilliant at communicating his unorthodox ideas. Cycles of Time is a technical bomb, replete with unsupported and unfalsifiable, but curious ideas. I like that Penrose thinks persistently outside the box, but this “popular science” book definitely needed to be written by a scientist with more experience at communication. Basically, Penrose posits that in the far future all particles will lose their mass. With only massless particles like photons around, metrics (e.g. time and distance) have no meaning. This would somehow then pave the way for a new big bang (no explanation how, or I didn’t get it), perpetuating a universe cycle that is eternal. This new big bang couldn’t start until all black holes have evaporated away, something estimated to take around 10^100 years. This evaporation process, he suggests, will actually reduce entropy (violating what scientists hold to be quite a robust law of our universe). In summary, all particles must lose their mass (e.g. the fundamental electron particle, which shows no sign of this). This also means that the law of conservation of electric charge must also be abandoned (no sign of this). Then, all information must be destroyed through the process of evaporating black holes (current theory does not support this information loss), and the second law of thermodynamics must actually reverse by entropy greatly decreasing in the future (no evidence or theory supports this). Finally, none of this is realistically testable. It is interesting to hear about, so I’m glad he shares his thoughts, but Penrose is so mathematical and technical that I almost stopped reading several times.

[Matt McClure · Rating 2 out of 5]

Cycles of Time is Roger Penrose's attempt at (mostly) fleshing out his hypothesis of conformal cyclic cosmology (CCC), which is along the lines of previous cyclical cosmology proposals, suggesting that the current universe is merely a conformal ("smooth") geometric extension of universes past.

Penrose's prologue and epilogue in Cycles of Time are somewhat silly but presuppose the book's narrative. Penrose begins with the problems of the second law of thermodynamics in modern physics, specifically the role of entropy, which he accurately characterizes (though not explicitly) as microscopic degrees of freedom.

This raises the question of how highly dense, highly heated, low-entropy pre-big bang conditions can result in a universe that is getting hotter and whose entropy is increasing, irreversibly. Penrose does not explain how his CCC model shows the transition (or "crossover") from the previous universe ("aeon") to the present universe in terms of the dynamics that take place during this transition. Specifically, Penrose does not explaining how, nearing the end of the universe (some 10^100 years), a low-density, low-heat, radiation-dense universe with decreased phase space (and thus decreased degrees of freedom) gives rise to a new big bang. (The radiation, Penrose assumes, arises from massive particles eventually becoming massless and turning into electromagnetic radiation, or photons).

CCC views the state of the universe in classical terms. Penrose dismisses modern cosmological models distinguished from CCC, such as string theory and loop quantum cosmology. CCC dismisses the necessity of discovering the nitty-gritty physics of space-time singularities in classical general relativity. In Penrose's view, non-classical (quantum) physics must be introduced at the Planck scale, which is the scale at which singularities must be dealt in order to avoid the problem, among many others, of infinite curvature. But Penrose dismisses the notion of infinity and the necessity of discovering new physics to explain spacetime singularities. Rather than working to explain them, we should merely walk around them.

Penrose's CCC relies heavily on local conformity within Riemannian differential geometry. The mathematics he presents is not difficult to follow; he barely shows any math, save for his work in the appendices. Nevertheless, it is crucial for the reader to follow ith his definitions and to keep a reference of his notes, because they help to clarify or expound certain points.

Penrose goes from a dab of statistical physics at the beginning of the book to general relativity. His arguments for CCC against other cosmological models with the aid of general relativity are relatively easy to follow, but he doesn't actually mention any dynamics of how transitions occur. Many of his explanations in these manners are hand-wavy.

Cycles of Time is worth picking up, and although a narrative is present, it doesn't bring tie everything together very neatly, because it doesn't answer every question it poses. Chapter 1 poses great questions, and Penrose's attention to detail with how entropy operates in our universe is very refreshing. In addition, Chapter 2 is wonderful crash-course in special and general relativity. Chapter 3, however, leaves much to be desired. Overall, CCC deserves a formal exposition so as to cover as many loose ends as possible to a specific audience. Penrose should have added another chapter devoted to explaining how CCC, in conjunction with other cherry-picked GR cosmological models, might work during crossover, and not just how it works or looks geometrically.

[Hal Taylor · Rating 5 out of 5]

The explanation of what happens before the big bang is laid out nicely in Roger Penrose’s book “Cycles of Time”. This book, like all Penrose, is not for wimps but at least this time he puts the Riemann geometry and manifold calculus in the appendix. According to Penrose the big bang is merely the remnants of the previous Universe which at the end of time has been cleansed of all its matter by black holes and Hawking radiation. As the boundaries of any Universe approach infinity space-time is re-scaled by a factor K as matter disappears (S=KT). When all the black holes have evaporated and there is nothing left but circulating electromagnetic radiation K approaches zero. The fascinating logic behind this is that time cannot exist without a means to measure it or be aware of it. And since photons do not experience time (they travel on the surface of the light cone after all) there’s nothing left to experience time and space so it shrinks down to the point where all the energy of the Universe now in the form of photons and background radiation can no longer be confined and a big bang occurs.

A personal note to Roger Penrose:
Dear Sir:
You finally gave me an answer for what really happens at the end of time. The notion that all the space and mass in the universe can shrink down to a microscopic point to begin anew with another Big Bang was so counter-intuitive that I, like most laymen listening to TV cosmologists on public television, was not convinced that this could happen in real life. But then I read your book “Cycles of Time”. At last someone has laid out a physical and mathematical rationale for what happens to all that space and mass. The idea of putting your friend Steven Hawking’s discovery of black hole radiation to work was brilliant. As black holes vacuum up all the mass in the universe and the boundaries of the Universe approach infinity space-time gets re-scaled by the scaling factor K. S = K T. I was even able to conceptualize the Big Bang event in my own original way by observing that since time is defined as the interval between events then when time ceases to exist all events occur at once making all the left over energy in the Universe, now just in the form of circulating electromagnetic radiation, do an instantaneous flash-bang. In fact I would be flattered if you used that idea in your next book. Yep. I got it all figured out now, Dr. Penrose.
Thank you.
Hal Taylor

[Bettie]

Unabridged. Read by Bruce Mann. 7hrs 22 min

Big Bang or Steady State? Big Bang! however an organised Big Bang.

The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium—the state of maximum entropy. Equivalently, perpetual motion machines of the second kind are impossible.

From Wiki: Sir Roger Penrose OM FRS (born 8 August 1931), is an English mathematical physicist, recreational mathematician and philosopher. He is the Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, as well as an Emeritus Fellow of Wadham College.

Penrose is internationally renowned for his scientific work in mathematical physics, in particular for his contributions to general relativity and cosmology. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics, which he shared with Stephen Hawking for their contribution to our understanding of the universe.

"impossibility in its purest form"

The Penrose Triangle

Thrown in the towel - too much for my poor noddle and I'd be better off sticking to the popular science publications.

[Jesús · Rating 3 out of 5]

A brief but unnecessarily technical account by Nobel Laureate Roger Penrose of his geometric take on the end/beginning of the universe (Conformal Cyclic Cosmology, or CCC). It’s a very cool idea, and seeing it play out in his diagrams is jaw-dropping. At its simplest, the claim is that the geometry at the end of the universe is indistinguishable from the geometry at the very beginning; thus, his claim is that there is no “beginning” or “end” to our universe, but rather simply a transition from one “eon” to another.

In some ways, his references to the visual work of M.C. Escher do much more of the explaining than any of the prose that Penrose writes. The logical leaps and gaps are so large that they can only be filled with complex mathematical proofs. I’m no physicist or mathematician, but even I can tell when someone is just filling empty space with a bunch of hot nonsense.

Penrose is absolutely brilliant, and I love how visual his imagination is. But he is by disposition incapable of translating his ideas into formats that non-specialists can follow (just watch an interview or lecture or something of his, and you’ll see what I mean). I can appreciate his resistance to using patronizing analogies in place of mathematical proofs, but I would appreciate maybe a few analogies here and there just so I know *something* about the method he’s using.

[Fredrik · Rating 4 out of 5]

I klassisk Penrose-stil starter boken som utrolig lesbar og interessant og lærerik. Elsker hvordan man kan resonnere om kosmologi. Etterhvert blir den vanskeligere og vanskeligere, og jeg må innrømme jeg falt av de to siste kapitlene (som ble skumlest).

Men hovedinntrykket var veldig bra.

[Andrew Noselli · Rating 3 out of 5]

I recently read Roger Penrose's "Cycles of Time" and I discovered that I was profoundly and scientifically moved by this book, which advocates for a revision of the well-known scientific definition of the second law of thermodynamics, specifically in terms of whether the origin of the universe developed from a time of low entropy and whether or not it can be stated that the universe's continued expansion should be considered as demonstrating a furtherance of an entropy-based process. While engaged in reading this book, I felt it was something that I am not used to dealing with and at times I struggled to keep my head above the rising waters of the author's masterful tides of discourse. I recommend it to you as a crucial and thoughtful follow-up to Wolfram's book on the much celebrated second law.

Penrose's book is an intriguing textbook that appears to be a patchwork of essentially three separate works rolled together. Probably the most intriguing portion of the work is that it is addressed to readers, who are not computational physical scientists, but are trying to learn about the second law of thermodynamics. It is essentially an autobiography, albeit delivered in a visual and historical style. Primary documents and pictures are leveraged to do most of the story telling rather than narration. This visuals forward style is held throughout the work, where the figures and equations appear to be doing most of the work while Wolfram keeps his commentary pithy and casual.

Admittedly, some of this work is beyond my ken or at least I cannot justify the investment necessary to make it my ken. However, Penrose's textbook on the second law is quite clearly preoccupied with extremely important questions and is eager to drive to the bedrock on these slippery ideas. I loved that Penrose has refused to accept the pat answers of prior science and work assiduously to flesh out these ideas. Three stars.

[William Schram · Rating 2 out of 5]

"Cycles of Time" is a book on Cosmology. There are open questions in the field even today, and the author hopes to clear these up. First off, did anything happen before the Big Bang? Secondly, how did the Universe gain order? Finally, how will the Universe end?

Roger Penrose goes over the consequences of the Big Bang from the perspective of the Second Law of Thermodynamics. He argues that the eventual "heat death" of the Universe is not the only possibility.

Equations don't have a preference in time. If you film a ball being thrown and show it in reverse, most people can't distinguish between them. Some events are irreversible, though. The example that Penrose uses is an egg falling to the ground from a tabletop. While the shattered egg can reconstitute itself and fly back to the tabletop, it is remarkably improbable for this event to happen.

"Cycles of Time" is confusing. I wasn't sure if it was my problem or the book. Penrose knows his Mathematical Physics well enough, but he is not a communicator of ideas. I read the words but lose the gist. From what I gather, Penrose doesn't like the idea of the Early Inflation of the Universe. He invented Conformal Cyclic Cosmology to counter that idea.

The book contains equations. Most of them are in the appendix, but Penrose sprinkles the Einstein Field Equations in some places.

[Sarah · Rating 3 out of 5]

Picked this off the 'in' shelf at the library. I can see from the date stamps that loads of people have been reading this.... Technically it lost me very soon. While I have previously encountered null cones and think I get the drift - I have also previously encountered strict conformal diagrams - and they are still complete mysteries. Maybe next time. Because that is what I love - I might not understand very much but each time I read a book like this I do understand a little more. And I just love to know that so many people are borrowing this book!

[Luca Campobasso · Rating 4 out of 5]

I think is a book fulfilled of innovative ideas and surronded by a fresh phylosophy, it's what I wanted from such a book. I will re-read it soon because of some parts I didn't understand very well.
Probably I would like to see more concepts explained in the appendices, that's it.

[Roger Blakesley · Rating 1 out of 5]

Pointless speculation.

[Ramnath · Rating 2 out of 5]

This is an extremely dense book that is difficult to read unless you're already an expert in the subject matter and the mathematics associated with it.

The gist of it, I think, is that Sir Roger Penrose presents a theory based on the idea that the Universe as we know it has a cyclical character to it. He suggests that very many years from now, the Universe would have reached a state where all massive objects would have decayed into massless photons and gravitons. Black holes would have swallowed up all "information" in the Universe and transformed it back into a low entropy configuration (then evaporated away themselves). And most importantly, this state would be, for all intents and purposes, indistinguishable from the early low entropy state of the Universe, ready for a new Big Bang. And so the cycle would continue, perhaps with some tweaks to our fundamental constants (or not).

The problem with this book is that while Penrose begins this journey determined to explain things to a lay audience (even going to the trouble of explaining the difference between natural and common logarithms), he forgets all about this goal somewhere in the first few chapters, and instead starts chatting exclusively with a couple of metaphorical PhD students sitting in the first row. He then muses about conformal geometries, Weyl curvatures, de Sitter space, Unruh effect, and what not, with casual references to an assortment of equations. The PhD students of course have no idea what he's talking about, but they do find it exciting and have enough of a background in the subject to ask some seemingly intelligent questions that Penrose cheerfully answers with his typical humility. Meanwhile, the rest of the class has wandered off looking for the free pizza that they were promised...

[Andrés Astudillo · Rating 5 out of 5]

No es solo cosmología, ni tampoco astrofísica, es más que todo -matemática-, pero es esa matemática que ves en las películas, en donde los pizarrones de tiza son llenados ya no con números, sino con conectores, tensores, métricas, representaciones, herramientas, conjeturas y etc, y luego números. Por tanto, este libro no es como esos libros al estilo de Carl Sagan que explican la astrofísica como que si se tratase de la Ilíada o la Odisea; este libro es la explicación de la CCC (Cosmología Cíclica Conforme) de acuerdo a lo que se obtiene del resultado de diversos cálculos, y su posterior representación en diagramas geométricos conformes. Nada fácil de digerir, por lo que si lo van a comprar, van a ver mucha matemática extremadamente pesada, por lo que no recomendaría a nadie salvo que seas un físico y que pueda entender o -debatir- con la propuesta del autor. Muy aparte de eso, las partes que no son matemática, requieren de conocimiento previo de este tema; sobre la relatividad general, relatividad espacial, física de partículas elementales, mecánica cuántica, teoremas y singularidades, y mucho, pero mucho sobre la física de los agujeros negros.

No seré como los ratings que veo aquí, que como no les "parece" les ponen 1 estrella. El autor es uno de esos físicos que se especializan en cálculo, así que, zapatero a su zapato, ¿Quién soy yo para objetarle?

[El Rato Pequeño · Rating 3 out of 5]

First part was easy to understand even for a layman, second part was difficult at spots but generally agreeable (and helped me understand quite a few concepts of general relativity in a more rational, practical light), and the third part is where it goes over my head completely, as the theory starts pulling dozens of eponymous formulas, definitions, tensors and constants as if out of thin air, just to rig the model to be even narrowly possible. And it gets quite farfetched at times with it - one of the ideas speculated on late in the book is that of a potential to study past and future "aeons" (past/future "iterations" of the universe separated by big bangs) even from our current vantage point, essentially peering into another universe. There's a fine line between theoretical physics and sci-fi mythmaking, and to me this ends up feeling more like the latter. Still, the ideas are nice, eh?

[Serdar · Rating 4 out of 5]

As many other people have noted, this is a tough book to read (hence my docking one star), but also a rewarding one if you can wrap your head around its central premise. As best I understand it: Go far enough into the future, and we lose the ability to measure time, because every way we could do that no longer exists. If that's the case, the far future of the universe may well look like the first few billion-billionths of a second of this one. If that doesn't bake your noodle, nothing will.

(If this is the shot, your chaser should be Carlo Rovelli's "The Order Of Time".)

[Mack · Rating 5 out of 5]

I thoroughly enjoyed this one. Rather than start with half a book of the history of physics, Roger Penrose jumps right in and discusses what he thinks. He knows all of the material so well that he can seemingly discuss anything about Cosmology. The mathematics are beyond me now, but I love the breadth of the ideas, and I'm going to study this book and learn all I can about every aspect. Penrose is so well established that he can talk about theories and conjectures with a freedom that most physicists I have read completely avoid. It's not that I agree with Penrose, or that I know enough to agree or disagree, but I greatly admire his courage and erudition. I highly recommend this book.

[Jason Keisling · Rating 3 out of 5]

Conformal Cyclic Cosmology (CCC) is a theory that I’ve found appealing for a while now so I’ve been interested in reading Penrose for years.

Evidence shows that the universe is expanding and cooling. When this trend is extrapolated backwards, a singularity is reached where there is infinite mass, density, and temperature. An early universe expanding from this singularity would have certain qualities observable today that were predicted and later confirmed when Bell Labs researchers independently discovered microwave background radiation consistent with radiation predicted by this expansion period. So what came before this singularity (aka the Big Bang)? According to Physicist Roger Penrose, it’s a potentially infinite cycle of universes that expand from a singularity and end in another singularity that is the beginning (next Big Bang) of the next cycle. That’s a gross oversimplification, but if you’re interested in a better one, this book is for you. CCC is an intriguing theory, but it’s also highly speculative and at the moment not well supported by evidence. So while this book is worth reading, it should be considered as more of a hypothesis than a theory.

I should mention that this was also a very difficult book to understand. I’m no scientist and have no background in physics, but I’ve read a lot of books on cosmology and physics and consider myself relatively familiar with concepts for a layman. And much of this book went over my head despite many attempts to re-read sections and make sense of them. Perhaps this is a fault or limitation of my own, but I suspect that this is a difficult concept and the book is not written in a manner that’s friendly toward readers without a strong background in these concepts.

I’d give this 3.5 stars, but after a decade of wishing for half stars, goodreads still doesn’t provide that option so I’m rounding down to 3 due to the difficulty of this book. Worth reading, but it will be a chore for many people.

[Cybermilitia · Rating 4 out of 5]

Entropi, Hawking isimasi, isik konisinin kullanimlari konularinda geleneksellesmis bilgilerin uzerine bambaska bir bakis acisi getiriyor. Bu anlamda, bazen Feynman Lecture's okurken hissedilen "Bize niye boyle ogretmediler yahu?" duygusu hissedilebilir. Karadeliklerin faz uzayinin boyutunu kuculterek entropiyi baslangictaki durumuna dusurmesi fikri gercekten cok ilginc. Bu konu uzerinde cok daha fazla okuma yapmak gerek.

Kitabin ana iddiasi CCC dusuncesi henuz eksik. Kutlecekim dalgalarinin etkilerinin bir eon'dan bir sonraki eon'a gecme oykusu fazla desteksiz. En azindan I, B gibi yuzeylerini bu kadar incelemisken, boyle hikaye anlatir gibi gecemsi hic ikna edici olmamis. Gerek kosullardan biri -entropinin sonunda dusmus olmasi gerekliligi- CCC yaklasimi icin yeterli degil. Bir de sonucta ana problem kaliyor: Neden? Ne oldu da eon basladi? Evren ne oldu da ortaya cikiverdi? Her ne kadar enflasyonu gecen eonun icine yerlestirme girisiminde bulunsa da bu da yetersiz kalmis. Neden yani? Ama zaten Penrose'da "Aha budur!" demiyor. Hawking'in "Karadeliklerde bilgi yuzeyde tutuluyor!" muphem icadindan sonra alti doldurulmamis fikirlerle ilerlemenin problemleri gorulmustur sanirim. :)

Daha sonra okuyup, ozellikle eklerindeki formul-keywordleri arastiracagim icin 4 yildiz. Ama fikirlerine oyle hemen ikna olmadim. 5 yildiz vermeyecegim.

[Gendou · Rating 4 out of 5]

This is a fun and (from the midpoint) challenging book.
The prefacing fiction story is a major groan, you can skip through it.
Penrose relies a lot on figures throughout the book.
This poses some difficulty for those listening to the audio version...

The problem CCC (Conformal Cyclic Cosmology) attempts to solve is:
Why does the universe have a low-entropy beginning?
(Specifically, why is this low entropy only in the gravitational degrees of freedom?)
As a computer programmer, I have no problem whatsoever accepting this boundary condition.
For some reason, certain physicists seem to think it a problem.
The journey to understand CCC feels like swimming out into the ocean.
The only dry land in sight is to go back to solid ground and accept the boundary conditions of the early universe without too much concern.
I mean, seriously, dissipating rest-mass, universal re-scaling, proton decay, etc.
It takes some serious suspension of disbelief... not that that's a bad thing.
Then again, if we ever do see evidence of a previous epoch in the CMBR...

[Baibhav Sharma · Rating 5 out of 5]

This has to be my favorite "popular science" book. Quotations around popular science because it isn't exactly a popular science book. I would reckon you can get the ideas Penrose is trying to convey without delving into the mathematical detours. But getting a hold of the math changes the game. The concept of uncertainty in context of Penrose's work and this book still haunts and amazes me. If you are interested in thermodynamics and don't feel like you have a hold over the second law, read this book. It will likely leave you more confused and muddled but surely more invested in understanding the concepts of entropy, uncertainty and such. A great companion to this book? A treatise on information theory or refer to the founding of information theory - Claude Shannon's "A Mathematical Theory of Communication".