Cover page taken from http://press.princeton.edu/titles/10664.html

Roger Penrose is unquestionably a giant of 20th century theoretical physics. He has been enormously influential in diverse areas of both mathematics and physics, from the nature of spacetime to twistor theory, to geometrical structures and beyond. His famous, but perhaps less well-accepted theories on quantum consciousness, the collapse of the wave function, and visible imprints of cyclic cosmologies on our universe are thought-provoking, to say the least.

I will premise this review of his latest book “Faith, Fashion and Fantasy in the New Physics of the Universe” (FFaFitNPotU) with a slight detour to talk about his book “The Road to Reality” (TRtR), as there are some interesting contrasts, and similarities. TRtR, I see as a fascinating attempt to teach a large swathe of mathematics and physics from the ground up (wherever the ground really is). The book is some 1000 pages long, and goes at quite a pace through a number of very complicated topics, but it is enough, I believe, for the keen high school student to get an idea of some of the most important areas of mathematical physics. Many of the approaches are not necessarily the usual ones, but they are interesting, and insightful nonetheless. The idea is not necessarily to use the concepts explained in the book to understand the physics deeply, but really to give a good overview of some of the mathematics used in many areas of physics, particularly of a geometrical bent. This is not a perfect book, but I think that it is one of the best attempts out there to achieve an extremely difficult task.

In FFaFitNPotU, we see Penrose try something very different. In this book he is trying to take a number of cutting edge areas of physics, and break down why he believes that they are wrong. In order to do this, he jumps quickly through a huge number of different areas of mathematics, many of which are expanded upon in the lengthy appendices. He teaches us about complex numbers, manifolds, fibre bundles, projective geometry, vectors and quantum mechanics in short order.  The topics which he tackles in the book are the collapse of the wave function in quantum mechanics, string theory and big-bang cosmology, using the mathematical background introduced at lightning pace.

In TRtR, the aim is to give a foundation into the mathematical and physical topics, and this, I believe he achieves. In FFaFitNPotU, the aim is to teach these topics such that his arguments against the current trends in theoretical physics can be understand. Sadly, I believe that this is virtually impossible. I believe that depending on the level of prior knowledge of the reader, the manner in which Penrose tries to fulfill his ambitions will be frustrating for different reasons.

A reader who knows only physics and mathematics through popular science books will simply be overwhelmed. I believe that the mathematics needed to understand the arguments is far beyond what can be learnt in a couple of hundred pages. This is likely to leave the reader confused and frustrated, unable to really grasp the mathematics, or to understand the arguments which follow from them. If indeed they can understand his arguments, then the mathematical exposition is somewhat unnecessary. However, his arguments really do rely heavily on the technical ideas outlined.

A reader who already knows the mathematics in the book will be frustrated by the fact that the arguments are actually not rigorous, but general sketches. Such a reader is likely to wish that this book had been published as a series of papers.

In the end it feels that the arguments against Faith, against Fashion and against Fantasy are really arguments against a certain set of theories which Penrose is unhappy with. Faith, fashion and fantasy are just useful monikers, but I don’t believe that he really uses these perfectly valid criticisms  to actually argue against particular topics. If he wishes to argue against the ideas, then concrete, fully developed mathematical papers would be the way to do this. Sadly, using the half-way-house between pop-science and consistent, logical mathematical arguments leaves a somewhat unsatisfactory feeling.

The reader on the whole is unlikely to be persuaded that the fault is in the belief systems held by many working physicists, the current trends, or indeed the magical ideas which come out of modern theories. These are used as proxy arguments for particular ideas which Penrose is unhappy with.

Of course it is necessary to critique both the scientific theories themselves as well as the sociological settings in which they occur, but to do so in a popular science book, when the critiques are very specific seems to me to be a strange way to do it. I happen not to agree with the points that he is making about these theories, but in reading the book, I was less worried about that, and more worried about who would actually find the book to be written for them.

This book feels like Penrose started with an essay, and then realised that more and more mathematics would be needed for the lay-reader to understand it, and so the whole thing bubbled into a  rather amorphous mass of mathematics, physics and personal ideology, neither useful for the lay-person, nor the working physicist.

Penrose at his best has an amazing way of explaining complex concepts, of providing intuition into cutting-edge ideas, and of course of creating mathematical tools used by generations of scientists to come. FFaFitNPotU, sadly fails on these counts. Were it either to be cut down to a series of short essays for the working physicist, or preferably papers, or expanded to be another 700 pages or so, it might hit the mark, even if the arguments themselves are not correct. At least then it would be at a consistent level for a sizeable audience.