A book with this breath and sublty comes along a couple of times in a generation.  There have been Feynman's Lectures on Physics, Misner Thorne Wheeler Gravitation and others.  Penrose is a world class mathematician and physicist (but you already know that). I cannot begin to adequately review this book even handedly because his audience is really other stellar mathematical physicists which I certainly am not.<br><br>I had the requisite math background so I understood most of it from cover to cover. But I am under no illusion that I have mastered the material. I can say the content is superficial and tricks the lay reader into thinking he has mastered something when he has not.<br><br>We are talking about maths that are even beyond the Ph.D. level of mathematical physics here folks!  How can even Penrose condense tens of thousands of pages of textbooks that one routinely must grasp to get where he is with so much facility? The publisher must have thought (and Penrose rationalized) that they could sell more books if they touted that even a mathematically challenged reader could get something from it.  This is not the case.<br><br>True, I was thrilled at Penrose's intuitive grasp of difficult abstractions that had me puzzled from studying more pedestrian texts on these subjects.  Simply breathtaking.  I was a page turner from the get-go.  However I was under no illusions that I was learning something other than vaporware.<br><br>The most interesting idea that caught my eye was his critique of symmetry.  Animals have evolved to be pattern recognition machines.  Survival goes to the brain that can see the "tiger burning bright in the forests of the night. Who has framed thy fearful symmetry?"<br><br>Physicists and certainly mathematicians have been guided by a mystical belief that Nature must follow some beautiful elegant mathematical plan. What is the platonic world of ideas but the symmetry of our own evolved brain functions? -- Good for this time and place but not generalizable. It has worked so far but what if looking for symmetry is wrong. What if framing our equations in terms of groups is wrong.  What if Nature is chaotic, asymmetric, fractal?<br><br>Penrose entertains that the last 30 years has produced nothing which makes sense or is even observable.  Yet physicists blindly 'theory-on' capivated by their presumptions.  The point is they have lost sight of the physics, the data, the observations.<br><br>As Firesign Theatre once said "The People! Give them a light and they will follow it anywhere!" Well, we know from history where this goes. Penrose suffers from his own criticisms and wants to create something like Einstein's elegant relativity applied to quantum gravity.  Who can blame him?  What is learning but man's vain search for God?<br><br>But what if QFT's incredible accuracy is only an accident like the resonance particles.  Feynman and others fudged enough to get the answers they were looking for even though QFT is not in principle normalizable. It is not even beautiful!<br><br>What if Einstein and unitary quantum mechanics was the last hurrah of this sort of elegance in our species?  Strings are beautiful but we will never know if the theory is observable.  I'm afraid the measurement paradox is confusing what side of the experiment the measurement is taken.<br><br>It is consciousness and evolved brain structure that is the problem.  Penrose in other books has the (admittedly crack pot notion) that quantum gravity collapses the wavefunction and thereby creates consciousness.  But maybe he was looking in the right direction?<br><br>It is time to examine ourselves and our inherited prejudices as Nature is not only stranger (non-symmetric, anti commutative) than we suppose;  it is stranger than we can suppose (Arthur Eddington).  The future of physics and maths lies in understanding the limits of our own brains.  Maybe the largest symmetry group that exists (the "Monster" of 196K dimensions) is the symmetry group of the thinkers which discovered it.  And there are no groups bigger than this!