Penrose certainly has a generous idea of his readers' mathematical ability. It's a kind of running joke among Penrose-fans: he always starts his books by saying you'll find it tough going if you haven't got a 12th Year (in Portugal)/GCSE (in the UK) in math, but that he'll explain it as he goes if you haven't. Twenty pages later you're on Gödel and conformable geometry. He doesn't do it deliberately; he really does believe his books are popular science. How can you not love him? I purchased an on-line kindle edition of this book back last year via Amazon and it was more about bringing myself up to date (I read it for the first time in 1991 when the book came out), although such things are never truly current due to Theories being debated and tested for very many years within Scientific Realms. Roger Penrose's books are as stated often inclusive of more mathematical devises than many books aimed at more laymen realms, so I often regard them as perhaps Bridging that gap between Solid Science Headaches and Laymen 'I read an article and am a common law know-all expert'.
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