I didn't actually read all 1,136 pages of Roger Penrose's magnum opus. I'm only writing a review now because I know I never will. Not that the book was so atrocious or anything. I actually quite enjoyed the first 300 pages and learned a lot. Penrose, however, bit off more than most of us can chew. He wanted to give a high level, but still mathematically accurate, view of all of the laws of physics in a single volume. This is not just undergraduate physics here, but extending all the way up through general relativity, the standard model, and string theory, etc ...
A noble, but ultimately somewhat quixotic goal. Just who is the audience he is tilting at here? I know more physics than approximately 99.8998% of Americans (33.4% of people have a bachelor's degree, 0.3% of those degrees are in physics). I followed the first 250 pages reasonably well, though Penrose presents some of the things I vaguely remember learning 25 years ago in a completely different light (this is not necessarily a critique). I sorta followed the next 50 pages, but shortly after his math outran what I remember learning his explanations became too terse for me to really understand what was going on. I did enjoy the fact that the math at the beginning of the book was presented as a physicist, rather than a mathematician -- as something one wants to understand intuitively and ultimately use, not simply a bunch of definitions and arid proofs with nary a hint of why anyone would ever get interested in anything as abstract as the Riemann Sphere. In fact, this last was really the high point of the book for me. I never knew what these surfaces were, and yet they were just beyond what I'd learned, so his explanations were enough to give me some glimmer of how interesting the structure is. After that, as he moved in Grassman algebras and his own special type of tensor notation, it became pretty hard for me to follow. I guess we can conclude that he was writing for the .001002%? Talk about being an elitist!
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