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By
Roger Penrose

- Little Secrets
- Chosen Ones
- The New Husband
- Afterlife
- Hidden Valley Road: Inside the Mind of an American Family
- The Missing Sister
- The Book of Longings
- The Southern Book Club's Guide to Slaying Vampires
- The Southern Book Club's Guide to Slaying Vampires
- The Sweeney Sisters
- Chosen Ones
- Death in Her Hands
- A Bad Day for Sunshine
- Conjure Women
- Crave

Theme: Avant by
Kaira

El libro es una maravilla, pero el comprador debe saber que no es un libro para aprender f sica sino para, ya sabiendo algo, introducirse en distintas reas La introducci n a cu ntica, por ejemplo, es maravillosa si ya sabes ALGO o te suena el formalismo Sino, dif cilmente vas a enterarte BIEN Adem s luego no profundiza demasiado Igual que con ste rea podr a decir de las dem s El libro es estupendo para un iniciado en la f sica.

and many sections require slow digestion But if you re genuinely interested in understanding something of the processes of this universe, then Penrose has some very worthwhile and interesting things to say The amount of re reading of sections I found necessary in working my way through this book were copious I probably ended up reading triple the content by the time I made it to the end.There will be a small sub set of the mathematical physics population that will find this book a breeze, perhaps even light reading But for everyone else it will be hard going Personally I found it hell at times But I stuck with it and Penrose had genuinely left me with a better understanding of the road to reality than I had before I found this a very worthwhile book to read Just don t make it your first book on the subject Take a few years and several other books first.

While this will not make you a mathematical wizard, it does try and explain calculus, complex numbers and quaternoins as well as a host of mathematical topics in laymen terms Penrose does not stop there he moves on to advanced topics such as Riemann Surfaces, Group theory lie groups , fiber bundles, twistor theory to which Penrose contributed heavily and other advanced topics He offers the reader the option of skipping the math and reading the physics applications of the math For those interested in problem solving, interesting problems accompany most chapters His treatment of complex number calculus and his chapter on Quantum Entanglement stand out as above par If you ever struggled to understand the value of complex numbers or how they simplify actual problem solving, Penrose provides simple and elegant explanations There is no doubt that a book of such grandiose breadth will attract critics, but overall, the book has goodies than negatives It is targeted towards a very large audience from high school students with some physics and calculus to the advanced undergraduate student to the layperson with some mathematical exposure looking to learn .While not an easy read, it is a great starting point for anyone looking to get back into physics by approaching it from the mathematical side Penrose is actually a mathematical physicist he holds one of the most prestigious chairs in the world of mathematics For those who are interested in the NEXT book after this one, I had compiled a list of similar self learning books

Let me start off by saying its relevance will soon be revealed I have a bachelor of science in applied mathematics from Case Western and a master s in computer science from Rensselaer both are top 50 schools, and I wasn t in the bottom 50% of the class , and after the first 300 or so pages out of 1200 the math in this book and it s at least 40% or straight math, not text, and often without text explaining the math is way above my head and is left often undefined in the text The author doesn t even do the courtesy of pointing the reader to textbooks where these concepts, such as pseudo Riemannian geometry and anti de Sitter spaces and Seiberg Gromov Witten manifolds, are defined and can be learned.The book fails in its promise and purpose to be a self contained guide to the current mathematical or theoretical physical understanding of the universe Required prerequisites understanding of linear algebra Lie, Poisson, Frobenius, Ricci calculus , scalars and higher rank TENSORS and MORE tensors , several varieties of noneuclidean geometry Minkowski, de Sitter, Riemann , scalars, topology and n manifolds, group theory Lie groups , gauge theory, etc., or the willingness to learn these from expensive secondary sources, because Penrose will not teach you them here and the arguments of the book are incomprehensible without them Without them, one would be reduced to skimming the 20% of the book that is text especially the final chapter, which is comprehensible to any semieducated layman and taking the author s word for the rest of it Just about the only thing he explains in full is twistor theory his own invention.It is far from accessible to the layman I have postgraduate training in math and I was a good student and its inaccessible to me , and to grasp the concepts in this book, I d have to spend probably a year of free time and a thousand or dollars in secondary sources if I bought them used and cheap I bought this book to get a 20 overview like Collier s A Most Incomprehensible Thing for the theories of relativity I prefer the original invariance , which was technical but self contained and comprehensible reading that is the only thing that gave me any knowledge at all of tensors, which this book is chock full of what I got was in essence a 1200 page bibliography without the authors being noted and without the important works being starred.This is a very ambitious book which fails utterly in execution.The author goes from explaining what complex and irrational numbers are and why they are useful this is freshman high school math in the introduction to pseudo Riemannian geometry this is postgraduate pure math 200 pages later He spends about five pages defining all of classical mechanics, and then assumes that you understand classical mechanics This same breakneck pace is kept up throughout, which is how he manages to range from logarithms and complex numbers to doctoral level mathematics in 500 or 600 pages Once he goes out of the pure math and back to applied math i.e. physics proper it gets a little easier but I d still not recommend trying to tackle this book with less than a bachelor s degree in math if you re a math nerd and keep your knowledge up or a master s in math or physics or some other strongly quantitative discipline if you re not , or a self taught prodigy in pure maths.The book promises to be a self contained guide to the best mathematical understanding of the universe we have, but it ends up like the author just stuck the important theorems in with a minimum of explanation he does hit almost all of them one thing that struck me as unnecessarily erudite showing off and odd was the statement of Maxwell s field equations, which is mathematically simple and elegant, in terms of tensors, which are very, very difficult , so it s a complete guide if you already know all of the math in which case you don t need the book it s much of a refresher and quick reference for people who already are familiar with and understand or at one time understood the concepts the author represents.See attached pictures representative pages from 250 , and these are not nearly the most difficult of the equations No, you re not the only person going smh, wtf at that math Not to mention yet again that many of the terms are never defined in text The author goes from explaining that he ll have to use logarithms in the introduction, to this stuff which is Chinese to me as a math major, within a few hundred pages It seems Penrose let his mathematical understanding brilliance for all I can tell, I have no idea what he s saying run away with itself after writing the preface for a book where he s apologetic about using logs and then sticking that preface on this work I still have to award two stars for the obvious intensity and depths of erudition which Penrose funneled in to this work, but only two because it doesn t even partially fulfill its stated purpose or self description I have familiarized myself additionally with pure math concepts like number theory, group theory, field and Galois theory and combinatorics, along with stochastic calculus and linear algebra to a degree I am even partially comprehending of tensors after reading A Most Incomprehensible Thing , a lay mathematicians introduction to relativity In other words, I m an educated lay mathematician, and the stated target audience for this book is educated laymen with AP high school or gen ed college math in general.

Oh what hopes were dashed with this book Even reviewers with years of mathematics and physics training seem to have been disappointed This is an extremely difficult and obscure text, at least in the opinion of an educated non mathematician and lay citizen theoretician, and there will never be any kind of reward for all the torturous eyestrain and wasted time trying to build an edifice out of insubstantial and unclarified blocks of inadequately explained mathematics In fact, sometimes the supposed mathematics seems like idiosyncratic opinions attempting to justify some agenda which is never explicitly revealed.Yeah, I guess I m an idiot, and I gave up Reading crap that stops making sense because I really really wish I could understand it is a futile exercise But I m probably not going to discard the book, I ll keep it along with Whiteheads Process and Reality and Hermes Trismegistus s Divine Pymander and Gurdjieff s Beelzebub s Tales to His Grandson and other similarly unpenetratable writings to impress people with my book collection without admitting I couldn t manage to get past the first quarter of many books Perhaps in my old age I am learning to appreciate neo Luddite perspectives, and I m beginning to suspect that books, along with technology, and other people s ideas and philosophies in general, are overrated and distracting, from a certain worldview, to the individual s path of discovery and self realization I agree with Penrose about the magic and elegance of the non Euclidian geometries and logarithms and complex numbers and e, and it is love and wonder for just that kind of knowledge that motivated me to buy this book and attempt reading it But I cannot justify paying for a book just because it mentions and recommends learning about fascinating concepts without explaining those concepts in terms a lay person could vaguely understand.