This book is not for the faint of heart or for those lacking a scientific background, despite the introduction.

It took me three attempts to read the entire book before I felt that I might have understood most of it. And mind you, I have a degree in theoretical physics and an astrophysics PhD from Cambridge.

The book presents a particular view of physics, which is very much the Penrose view. It is quite mathematical and abstract, and at a level of sophistication far beyond any of the other physics popularizations on the market.

It requires hard work to understand, but ultimately it is rewarding. The detailed and in-depth exploration of physical concepts provides a unique perspective that can expand one's understanding of the subject.

Although it may be challenging, for those with a passion for physics and a willingness to engage with complex ideas, this book is well worth the effort.

Well, I've delved into a plethora of science history books. Starting with Carl Sagan, and more recently exploring the works of Susan Wise Bauer and Steven Weinberg. I must admit, they all present the story in a more engaging way than what we have here.

There's nothing really wrong with this book, mind you. It's just overly long and detailed, with an encyclopedic scope. It's presented in a rather dispassionate tone and is filled to the brim with advanced mathematical formulae.

I'm truly at a loss when it comes to imagining the potential audience for this. It doesn't quite cut it as a textbook, and it makes no effort to make the subject matter appealing to the average reader. I guess it could serve as a useful reference, seeing as the topics are neatly arranged into 34 chapters, each with numerous subdivisions. I'll confess that I skipped a few chapters on topics that didn't pique my interest, but that still left an enormous amount of reading (and required many cups of coffee!).

Aside from the lack of a narrative voice, which makes this read like an encyclopedia, I have to say that I don't think Sir Roger Penrose is as effective as others in communicating complex ideas. For instance, Lagrangian mechanics is an area that interests me, so I read that chapter carefully. But feeling dissatisfied, I then went back to Sean Carroll's The Biggest Ideas in the Universe, which I'd just recently read. And I was reaffirmed that Carroll explains with much more clarity in three pages what Penrose takes twenty-two pages to do! Yes, Penrose is meticulous in crossing every "t" and dotting every "i," but this level of detail will only appeal to those who have dedicated their careers to advanced math or science.

Hats off to anyone who has actually read every word, studied every formula, and emerged with a beaming smile, feeling enriched. My reaction, on the other hand, was one of exhaustion and a bruised grey matter!

How Would a Physicist Think About the Quantum World?

I am an avid reader who usually breezes through books with ease. However, this particular book presented a significant challenge. It took me over a year, since I first opened it, to finally complete. I am truly in awe of the rigor and depth of this work. In fact, I can now claim that I have a "sort of" understanding of the major concepts of quantum mechanics, similar to how a physicist might approach it.

Most popular accounts of quantum physics tend to simplify the subject, often omitting the crucial mathematical aspects. Even more concerning is when the concepts of quantum mechanics are misused to "justify" some scientifically unfounded new-age claims. This book, on the other hand, takes an intellectually honest approach and forces you to think mathematically. It's quite a feat to imagine, and needless to say, it's not an easy task. This is especially true when Penrose delves into calculus in the complex number plane.

I do have some reservations regarding Penrose's assertions. He argues that mathematics is a reflection of the platonic world of forms, and this reflection reveals the precision of the world. He also claims that our "pure, mathematical minds" are structured to mirror this reality. If we accept this view, then reality would be seen as a mathematical system, and understanding math would be the key to understanding reality.

To me, it seems that math is simply a tool that science employs to describe reality. Science, in its truest sense, merely investigates reality and constructs a plausible model. As more data becomes available, the model is refined. Conflicting data, such as the late 19th-century conundrum of the speed of light being constant regardless of the frame of reference, can often lead to a paradigm shift, as was the case with Einstein's theory of relativity. In fact, mathematical science appears to be more like a map, rather than the messy and complex territory of reality itself.

Nevertheless, this book is highly rewarding if you are willing to persevere. Despite my philosophical differences with Penrose, I must admit that he is far more intelligent than I am. He manages to make even the most opaque concepts at least somewhat understandable. Modern physics is an exciting, yet confusing and complex field. This book does an excellent job of illuminating significant portions of it for the lay reader. However, I would highly recommend brushing up on your calculus, imaginary/complex numbers, and geometry before embarking on this journey.

It will surely enhance your understanding and make the reading experience all the more enjoyable.

All you ever need to know is a vast and comprehensive topic.

It涵盖了生活的各个方面，从基本的生存技能到高深的知识领域。

In daily life, we need to know how to communicate effectively, manage our time, and take care of our physical and mental health.

In the professional field, we need to master specific skills and knowledge related to our work.

Moreover, understanding different cultures, values, and beliefs can also broaden our horizons and enhance our interpersonal skills.

In short, all you ever need to know is an ever-evolving and expanding body of knowledge that requires continuous learning and exploration.

Only by constantly updating our knowledge and skills can we adapt to the changing world and achieve our goals.

This book presents a great pasticcio of modern physics from a mathematical (platonist) standpoint. It is definitely the work of a genius, but it contains quite some difficult and hard to digest stuff. How someone might call this a piece of popular science remains a mystery. So, it may not be for everyone.

However, some chapters and subjects offer a less exhausting treatment. They serve rather as a starting point and an invitation to dive deeper. The extensive reference list, which includes many publicly available resources, can be one's guide.

This book is not an easy read, but for those who are willing to put in the effort, it can provide a wealth of knowledge and insights into the fascinating world of modern physics. It challenges the reader to think deeply and expand their understanding of the subject. Whether you are a student, a researcher, or simply someone with an interest in physics, this book is worth exploring.

At 1049 pages of text, filled with mathematical formulas, the book is about as heavy as they get.

Penrose argues that mathematical formulas capture the laws underlying everything we know about the universe. This is straightforward, yet the way he presents it is profound. He acknowledges his Platonic (Pythagorean) perspective, suggesting that these mathematical constructs have an external, independent standing that explains and governs cosmic reality.

Sometimes, he is less certain and seems to imply that the cosmos operates in accordance with these laws that mathematical formulas then describe. This has a completely different connotation, as it omits the creator factor in the Platonic worldview. It could be a chicken and egg situation for Penrose – do mathematical truths create cosmic laws or merely describe their operation? – were it not for his suggestion that aesthetics and morality might also have external standing, thus completing Plato’s triad of the Good (truth, beauty, morals).

Penrose refers to mathematical truths as things of beauty (aesthetic elegance). For someone with his skills, this makes sense, but it is a big step to then place aesthetic beauty in an independent realm. Instead of jumping into the mystical, why not seek a simpler solution? Our very essence is about matching internal understanding with external reality. When this happens, there is consonance, a state of equilibrium and pleasure, and mathematical truth is likely at the peak of such. With moral truths, universals may be internal, inherent to our biological nature, and not “out there” as Penrose believes. We are driven to serve our self-interest, with or without considering the interests of others. These interests, ours or others’, distort our relationship with the external world, creating conflict (dissonance) and the need for resolution. There is nothing here to suggest an independent moral realm. Doubtless, Penrose’s attraction to an objectified Good would mentally assist the pursuit of harmony, but that doesn’t make it so in practice.

Penrose seems overly influenced by Plato and the Pythagorean tradition, ignoring that Plato – in the context of his overall body of work (the Dialogues, especially regarding the moral realm) – discounted the material world in favor of an ascent to the Isles of the Blest. Plato was about that, not objective truth. Asserting doesn’t make “heaven” real. As Spencer noted, it could be true, or not, but we cannot know.

Penrose questions a significant part of the prevailing thinking that various truths are asserted without experimental verification, as if beauty and elegance alone (e.g. string theory) are sufficient. But when it comes to beauty and morality, Penrose is no longer cautious.

* Einstein also had similar attractions towards a god-like initiator of beauty and harmony, but his focus was on the truth of the mathematical kind, and perhaps on beauty as well. But regarding morality, the third component of Penrose’s Triad, I think Einstein was agnostic.

One of the most wonderful and magical books that could exist. A book that goes beyond, it is truly a bible of the sciences, starting from the basic concepts of physics and mathematics. From Ptolemy, the Greek thinkers, Galileo, Kepler, to the modern era that begins with Newton's theory of gravity. In this book, the topics of Einstein's general theory of relativity are touched upon. Quantum theories, curved spaces, non-Euclidean geometries, antimatter, particles and above all... Reality, among many other topics. This book is not an ordinary book, it is a reference manual, a bible that you can consult. If you are interested in knowing the world from a physico-mathematical perspective, this book is for you.

It offers a comprehensive exploration of the fundamental principles and theories that underlie our understanding of the universe. It takes you on a journey through the history of science, showing how our knowledge has evolved over time. You will learn about the great minds who have contributed to this field and the revolutionary ideas they have proposed. Whether you are a student, a scientist, or simply someone with a curious mind, this book will provide you with a wealth of information and inspiration.

So, if you want to expand your knowledge and gain a deeper understanding of the world around us, pick up this book and embark on an exciting adventure of discovery.

Peculiar fusion of a pop science book and a graduate level text. Penrose is extremely enthusiastic and has a remarkable knack for invoking geometric intuitions to assist the reader in reasoning about highly abstract mathematics. The book manages to cover an extensive amount of ground within a limited space. Indeed, it is still enormous, but the first 350 pages take us from basic algebra and geometry to a detailed treatment of Ricci calculus and beyond. Moreover, it often does so in an unfamiliar and unconventional manner.

For example, instead of looking at Stoke's theorem, we skip straight to the n-dimensional fundamental theorem of exterior calculus. Similarly, Maxwell's equations are introduced in their tensor calculus form, and the familiar system of 4 PDEs is never written out. However, we do get to see them shown in Penrose's own hieroglyphic notation. True, these are more elegant and fundamental ways of defining the above concepts. Given the vast amount of material to cover, perhaps it is necessary not to waste time on simplified versions of the problems he wants to discuss. But at times, it can feel like he is massively overcomplicating things that I thought I was already familiar with.

Nevertheless, when it works, it is highly elucidating and makes me feel like I understand the concept at a deeper level and better understand how it relates to the rest of mathematics and physics. Therefore, approach this book with caution.

It truly hinges on your mathematical proficiency.

If you pursued mathematical studies at a premier school or university a decade ago. Undoubtedly, I have forgotten some, but I am still far from possessing the technical skills to fully relish this book.

By the midpoint of the book, the concepts were far too intricate and numerous for me to keep tabs on all of them.

However, if you are engaged in the fields of physics or mathematics, this book can prove to be extremely fascinating as R. Penrose will reveal to you the interactions and historical background behind all the notions.

This excellent and definitive work is not for those with a faint heart or a weakness in mathematics.

By the time you have worked your way through this book, you will have completed most of the material for an undergraduate degree in math. The first half of the book begins with Pythagorean number theory, complex number calculus, Riemann surfaces, Fourier decomposition, n-dimensional manifolds, and Lie symmetry groups, and then builds on from there.

However, the real richness is reaped in the second half of the book. It delves deep into the physics of current cosmological thinking, such as relativity, quantum mechanics, and string theory, in a way that demands a solid mathematical foundation.

The book is well worth picking up, even if you don't progress beyond the first couple of chapters. In the first chapter, Penrose waxes rhapsodic on Platonism and the mysteries of human understanding. Highly recommended for those with an interest in mathematics and physics.

The book is truly frustrating.

It commences at an extremely slow pace, presenting ideas that are relatively easy to understand. However, just a few pages later, the concepts begin to accumulate haphazardly, lacking any semblance of order. This chaos confounds even those readers who are most inclined towards mathematics.

Seriously, I highly doubt that a significant number of people have managed to read the entire thing.

I, for one, did attempt to do so, hoping to glean the main ideas without fully comprehending the math. But in all likelihood, I failed in this endeavor.

The disorganized nature of the book makes it a real challenge to follow and understand, leaving the reader feeling rather exasperated.

It seems that the author could have done a better job of structuring the content to make it more accessible and less overwhelming for the average reader.

Perhaps with some revisions and a more logical arrangement of the concepts, this book could have been a more valuable and engaging read.

As it stands now, it unfortunately falls short of expectations and leaves much to be desired.

This book is truly an impressive tour de force that delves into the major theories in physics.

It took me a whopping 3 years to read it, and I must admit, it's entirely my fault. (Although, to be fair, it's not exactly the most luggage-friendly book to carry on holiday.)

I really enjoyed the beginning, as it set the stage and piqued my interest. However, the middle part was a bit of a struggle for me. But, to my delight, it managed to return to the promise of a good ending.

The main aspect that I'll take away from this book is its elegant, argumentative, and logical narrative. It's most often a critical analysis of various theories, which is both fascinating and enlightening.

I can only aspire to reach such a level of insight into the body of science and scientific thought. This book has truly been an eye-opener and has left a lasting impression on me.

I would highly recommend it to anyone with an interest in physics or a desire to expand their knowledge of the scientific world.