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le 26 décembre 2014
I bought this book after having read somewhere that in it Penrose talked about the "reality of the Platonic world", and I wanted to get possible new insights, and because Penrose is a respected mathematician.
The book purports to cover all of mathematics (from integers, the theorem of Pythagore, to Fourier decomposition, manifolds, fibre bundles, etc.) and all of physics (Newtonian, Lagrangian, Quantum physics, big bang, supersymmetry, strings, etc.) It is over a thousand pages long.
Unfortunately Penrose is extremely verbose.
It starts with a discussion about a friend of his mother who couldn't understand how to simplify fractions, and what _is_ the fraction 3/8? It develops the "idea" that fractions may or may not exist.
The part on the Platonic world boils down to the observation that there are three worlds: that of the mind, that of pure Platonic ideas, and the physical world. We are already page 24.
There are the unavoidable Escher pictures.
Open it randomly, say at Lagrangian mechanics. After three confusing sentences which do not really introduce the subject the writings become heavy, tedious and obscure. Penrose (whose understanding of the subject is not questioned) addresses not so much the reader as himself, mostly to tell himself how smart he is. He makes complicated a beautiful subject.
I gave up reading sequentially. The book will become a reference manual when I need to look something up -- if it turns out to be useful.
With few exceptions, the best books I read are accessible, luminous and short.