This has to qualify as the most difficult book that I have ever read. As Francis Bacon said...."Some books are to be read with the speed of summer lightning and some are to be chewed and digested". Well I think "Fashion, Faith etc" has pretty much given me indigestion. And it's taken me months to wade my way through....a few pages at a time. As a general rule, I try to read books before I read the preface or the critiques so I can make up my own mind about it and not be prejudiced by other writers. In this case, I read the Mathematical Appendices after I had read the book. I'm still not sure if this was a mistake......because I couldn't understand a high proportion of the appendices either.
As many of the reviewers have commented; you need a very high level of mathematics to be able to follow this book...and even some of the reviewers with a high level of maths admitted to being overwhelmed. Well. I guess, Penrose is a Nobel Prize winner. And he's co-authored books with Steven Hawking, And he's made major contributions to Maths and Cosmology across fields such as Black holes and tile tessellation. So not surprising that he's going to be using maths that is well out of my league.
In fact, I found myself reading through paragraphs of equations with infinity raised to the power of 2, in turn raised to the power of 3 where Penrose says something like ...."well we can ignore this because it's vanishingly small in comparison with some other similar looking expression". To all of this I have to simply say: "Well, OK if you say so!"....I just have to take it at face value.....I have no way really of knowing if he's right but he usually reduces it all to some prose summary such as:(p116) "To sum it up, it does seem clear that the AdS.CFT correspondence [the Holographic Principle] has opened a huge new area of research, which has related many active areas of theoretical research, making unexpected connections between such disparate fields as condensed matter physics, black holes, and particle physics. On the other hand, there is a strange contrast between this great versatility and wealth of ideas, and the unreality of the immediate picture of the world that it projects. It depends upon the wrong sign for the cosmological constant; it requires 4 generators of super symmetry, whereas none has been observed; it requires a gauge symmetry group acting on infinitely many parameters instead of the 3 that particle physics requires; and it's bulk space-time has 1 too many dimensions! it will be most fascinating to see where all of this leads". In other words; a fairly damning round-up of criticisms.
I write these reviews really for my own edification and as memory joggers not for any other readers (sorry) so I'm including an extract here from another reviewer on "Goodreads", Athan Tolis......he rather nicely summarises some of the main threads of Penrose's arguments, viz:
1. Highly fashionable 26-dimension string theory, while elegant and originally promising, is likely a dead end, for example because it leads to singularities
2. Supersymmetry between Fermions and Bosons cuts down the dimensions of string theory to a more manageable 10, but makes it necessary to believe in the existence of a whole lot of particles we will never observe
3. The holographic conjecture, while beautiful, relies on supersymmetry and requires that we radically revise what we believe about the cosmological constant, the gauge symmetry group and bulk space
4. Quantum entanglement is probably ultimately only a feature of the simplified, linear orthodoxy we cling to in Quantum Mechanics, which we will one day abandon for a nonlinear model. The Quantum Mechanics of the present is useful, but requires a leap of faith you should refuse to take.
5. Inflationary Cosmology poses even more problems than it answers questions and is a convenient untruth.
Basically, Penrose is saying that a lot of what physicists are saying about cosmology is based on fashion, faith and pure fantasy and the proponents are ignoring or glossing-over the very real mathematical problems in their quests.
I found myself wondering why Penrose himself was so against something like string theory; why he was opting for a simpler view of the universe? Was it because he was taking Occam's Razor seriously? Was it because he had his own Twistor theory that hadn't really caught on? Or was it because he agreed with Einstein, and many others, that the mathematics really was reflecting some sort of reality that we should, ultimately, be able to grasp?
I recall attending a lecture by Penrose at the Australian National University where he ran through some mathematics and showed some sort of matrix which he said "was intuitively obvious......that everyone would accept it". I was not quite convinced and my doubts were compounded when my Philosophy supervisor who was sitting alongside me commented that he was not sure that Penrose understood the psychology/philosophy of mathematics all that well. Not sure who was correct but it did sow the seed of doubt that even giant intellects sometimes get it wrong.
However, I thought that Penrose showed great intellectual honesty on p392 where he says that he has both a public reason and a private reason for objecting to higher-dimensional theories. The public reason would indeed be one based largely on the problems raised by the excessive functional freedom, but the private one was that from his undergraduate days he had been smitten by the power and the magic of complex analysis and geometry and had become convinced that this magic must also lie deep in the fundamental workings of the world. And he seemed to find this in with his twistor theory and the link between 3-dimensional geometry and quantum mechanical amplitudes but also a somewhat different link between the Lorenz group and the Riemann sphere. Both these relationships demanded the particulate space-time dimensionality that we see about us. So when he heard that string theory, to which he had initially been attracted .....had moved in the direction of requiring all these extra spatial dimensions...he was horrified ....and "found it impossible to believe that nature would have rejected all those beautiful connections with Lorenzian-4 space...and still do".
So it seems to me that Penrose is here confessing that he has his own brand of faith too.
But I come away from the book mildly depressed. I had believed that the great mathematicians of our time and the great cosmologists were actually getting close to the universal theory that would explain everything. But Penrose has me, more or less, convinced that, at best, we are a very long way from that universal equation and that many of the physicists didn't understand the underpinnings and the weaknesses in much of their mathematics.
And as for Penrose, I do have some sympathy that his twistor theory has never really become fashionable. After all.....it seems that to be successful in physics as in many other professions one has to be both fashionable and have faith in the latest fantasies.
If I gave this book 5 stars, I would be kidding myself because I probably only followed about 25% of it but to give it less than 4 stars would be churlish. Clearly it is a significant work. I just wish, more people (including myself) had the education to be able to understand all of it. ( )

“On the other hand, when we try deliberately to use the criterion of mathematical beauty in formulating our theories, we are easily led astray. General relativity is certainly a very beautiful theory, but how does one judge the elegance of physical theories generally? Different people have very different aesthetic judgments. [...] Moreover, the inherent beauty in a theory is often not obvious at first, and me revealed only later when the depths of its mathematical structure become apparent through later technical developments.”

In “Fashion, Faith, and Fantasy in the New Physics of the Universe” by Roger Penrose

Would it be logical if positive and negative charge represent two extra dynamic dimensions within our three dimensional Universe of continuous energy exchange? This is an invitation to see an interpretation of the mathematics of Quantum Mechanics as a geometrical of energy exchanges that forms what we see and feel as the passage of time! In such a theory the Planck's constant ħ= h/2π is a constant of action in the process that forms the continuum of time. Heisenberg's Uncertainty Principle ∆×∆p×≥h/4π represents the same uncertainty we have with any future event with the future unfolding photon by photon with each new photon electron coupling or dipole moment! With classical physics representing processes over a period of time as in Newton’s differential equations.

"Big Bang" expansion: Keep in mind, if the rapid expansion of the singularity is really true (and I am not saying it's not), then it would have most likely expanded in basically a 360 degree spherical shape. Assuming for the moment modern science is correct concerning how the forces of nature came about, (of which I believe them to be wrong, but that is a different discussion), then the forces of nature would have come about when the expansion reached a certain spherical dimension. Even "if" true that the universe is continually expanding and would most likely then end in a "big freeze" as the energy in this universe ceases to flow one day, I believe it might be possible that a "Goldilocks zone" of continually active forces of nature might remain eternally active along the "surface area" of where the forces of nature came into existence based upon the spherical energy "surface" tension of that zone of force of nature initiation along the dimensional interface, (different dimensions being defined as having different forces of nature that they function by). Any entity that makes it to this zone, and doesn't kill themselves off by some means, could in theory remain eternally consciously existent throughout all of future eternity, even though the rest of the universe would most probably end in a big freeze. Eternal life here I come. You snooze, you lose.

Now just to build my FTLRT (Faster Than Light Relative Travel) vehicle that generates a dimension within this dimension that we are in. If you see a spherical ball of light zoom off of this Earth, going up to a relative speed of faster than light from your perspective, don't worry, it just might be me leaving all your future frozen asses behind. Of course, if you see multiple balls of light, it's all those I am taking with me. (See also some of my pedant musings on this blog as to how artificial gravity, necessary shield protections, and FLTRT might even all be possible). And note, the universe might not end in a big freeze if my latest TOE is basically correct. The gravitational force of the photon would interlock with the electrical component of the photon at 90 degrees to each other, with the magnetic field of the photon split both inside of and outside of this shell keeping it intact. Hence also why the galactic backdrop is perceived as being black. No light photons get absorbed by or reflected from this universal shell. The remaining photons remain eternally active inside of this shell. The whole universe would be my "Goldilocks zone".

If theoretical physicists can come up with crazy ideas, so can I.

Bottom-line: It is difficult to criticise a book by such a distinguished (and charming) theoretical physicist as Roger Penrose because I have no doubt that I am reading a book by one of the greatest living scientific minds. As a physicist myself back in the day I am familiar with the difficulties faced in explaining advanced topics to a predominantly lay audience but I think he probably lost many with such a muddled and ill prepared book. Not as good as "The Emperor's New Mind." ( )

This is a physics book for the scientific minded, not quite for the lay person coming in off the street. Good stuff. ( )

A good (and important) book to spend a *long* time on provided that you don't expect to understand it all. If the brilliant but mavericky Sir Roger meant it to be a clearer version of his 2004 _Road to Reality_, I don't think he succeeded, although it is a few hundred pages shorter. With great conceptual and technical sophistication (e.g. "fibre bundles", and "functional freedom" ratings given by pseudo-numbers of the form infinity^(A x infinity^B)), he finds deep fault with string theory (affected by "fashion"?), quantum mechanics ("faith"?), and cosmology ("fantasy"?). At the end, he reiterates and updates his ideas on twistor theory, spontaneous ("objective", gravity-related) reduction of quantum wavefunctions, and conformal cyclic cosmology.