The Road to Reality by Roger Penrose

"When I noticed that there are roughly as many pages in the latest blockbuster from Roger Penrose as the number of words allocated for my review, I was tempted to give each page a single-word comment." John Gribbin reviews The Road to Reality by Roger Penrose here at The Independent.

Comments

[Mal]

John Gribben's review is fair, if rather short. You can get to other reviews from my link. I have a 20 year old MSc in Astronomy, and this book is a great way to 'shake off the rust'. Anyone with a science degree will love this book. I'm bored with popular accounts that do not use any equations -- this book does not hold back at all, hamiltonians, tensors and everything!

[giordano bruno]

I agree, I expect physicists to _explain_ what the equations mean.
I expect that Penrose is totally wrong with his "quantum-gravity-microtubule-consciousness means robot's cant think"
just like Schroedinger was wrong with his charm-bracelet-gene idea in 1947. But Hey! fascinating anyway, guys.

BTW Brian Greene's new book is OK, a sort of grand survey sans maths mostly, but not as radical as his first book, with those neat Calabi-Yau pictures.

[Reality Road Reviews]

One of the review links on my site quotes Roger Penrose as feeling "misunderstood" by consciousness theorists. In Road to Reality he appears to be attempting to be "misunderstood" only by string theorists. He specifically avoids another foray into mind science.

[winitzki]

Sir Roger Penrose? A 1,100 page book full of equations and claiming to be popular-level? My first reaction was puzzlement. I skimmed through the book. (I am a theoretical physicist...)

Here's what I have to say:

1. Penrose claims that I'll get something out of this book even if I don't know how to add fractions. Perhaps, he suggests, I should just skip all the equations and read the book just to "experience the drama." Then he proceeds to tell me *why* I can't add fractions: this is because nobody told me that a fraction is an equivalence class in a set of pairs of integers, factored by such-and-such equivalence relations.

Well, somehow I don't feel that an explanation like this would help someone who isn't already firmly at home in algebra. Especially looking at the titles of later sections, e.g. "Twistor sheaf cohomology," that look quite daunting. I have no idea what a sheaf cohomology is, anyway. (I have a general idea but I don't really remember the precise definition of a sheaf... something is a pre-sheaf if ABC, and then something is a sheaf if XYZ... oh well. Never had to use this stuff in my physicist's work.)

2. But would I be able to learn twistor sheaf cohomology from the book? I somehow doubt it. Maybe I'll get a glimpse of it though and refresh my intuition. Penrose's qualitative explanations that I looked at are very visual and generally excellent. But... I can't really follow some of his math! For instance, I didn't fully understand the reasoning behind his explanation of the Hopf fibration, S^3 -> S^2 x S^1, in relation to the Clifford bundle (Section 15.4), and I thought I *knew* this stuff! Also, I don't understand the formula in Sec. 19.6 for the "second time derivative of volume", D^2(V)=Ricci(t,t) V. I would think this should rather be the Raychaudhuri equation which has an extra term (the squared divergence of the timelike congruence). There follows a beautiful attempt to motivate the Einstein equations by qualitative arguments, and it almost works. But maybe if the problem with the extra term in the Raychaudhuri equation were fixed, the Einstein equation would appear correctly?..

3. Penrose actually included some *very* nonstandard material in this book. Most of the book is standard, but there is for example a section 9.7 ("hyperfunctions") which was a total surprise for me. Generalized functions, like the Dirac delta function, understood and defined entirely in terms of holomorphic functions in the complex plane?? It's a lot simpler and cleaner than the usual definition using spaces of integrable functions! And why aren't there books about it?

4. Penrose included some polemics about the modern physics theories that he doesn't like. I don't feel that most non-expert readers will get much by reading those parts, except that they might "experience the drama."

An amazing book, all in all. But for whom?