Let me start off by saying (its relevance will soon be revealed) I have a bachelor of science in mathematics and a master's in computer science (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 more 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 more 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 more 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 more 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.
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Reviewed in the United States on April 24, 2018
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 more 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 more 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 more 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.
Verified Purchase
An erudite but failed effort, far from self-contained: ostensibly targeted at the 'educated layman'
By Vagabond of Letters on April 24, 2018
Let me start off by saying (its relevance will soon be revealed) I have a bachelor of science in mathematics and a master's in computer science (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 more 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.By Vagabond of Letters on April 24, 2018
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 more 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 more 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 more 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.
Images in this review
Reviewed in the United States on August 9, 2018
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Reviewed in the United States on July 10, 2015
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Top reviews from other countries
DGC
A good companion book for those studying Physics from text books.
Reviewed in the United Kingdom on May 16, 2016Verified Purchase
David Irvine
A very hard read.... But enlightening
Reviewed in the United Kingdom on September 9, 2021Verified Purchase
Aidan B
Great, but not an easy read.
Reviewed in the United Kingdom on August 23, 2019Verified Purchase
Stavros Karapanos
The quality of the received book was decent. The delay was due to Covid-19, so it was expected.
Reviewed in the United Kingdom on May 10, 2020Verified Purchase
Basque-refugee-13
I've only given this book three stars because I don't ...
Reviewed in the United Kingdom on November 22, 2015Verified Purchase
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