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on February 1, 2011
The mathematician in the title of this review is of course Newton, but Penrose has a similar claim, though being modest would probably be embarassed at the comparison. Other than their profound knowledge of Mathematics and its closely allied subject Physics, Newton and Penrose were both willing to peer into other areas of science and speculate. Trespassing outside of ones own scientific territory has its perils. Newton wandered into Alchemy and the Occult and Penrose has written on the function of the brain and now in this book has stepped into the great unknown before the Universe exploded in the Big Bang. As a communicator and teacher of advanced Physics Penrose is bettered in my opinion only by Richard Feynman, but where Penrose is extraordinary is in his courage in presenting revolutionary ideas in a world of aggressive and often very unpleasant academics who defend their turf with a vigour verging on mania.

He expects a lot from his reader but much of what he is trying to explain is not understandable outside of Mathematics and any attempt to explain his arguments using language is not just an oversimplification but may indeed be wrong. Many kinds of mathematical space other than our own three dimensions require some understanding of tensors to follow the reasoning. Quantum physics is based upon complex numbers. Penrose's earlier book The Road to Reality deals with all this in some detail and is understandable with a lot of effort even by non-mathematicians such as me.

Although marginal to the subject of this book I would have liked to hear more on his views on the cosmological constant that to applied scientists sounds embarassingly like a 'fudge factor' designed to make theory fit facts. Another minor quibble is in the editing. Some sentences sound as if they were taken verbatim from a lecture (perhaps they were). An inevitable problem when a specialist is explaining a subject to a non-specialist editor is that obscurity isn't always because of the nature of the subject but may be because it is badly expressed in language. The spelling of the word discernible and a few other grammatical errors should be corrected in future editions, after all Penrose can't do everything...not quite.
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on December 17, 2010
Excellent, covers extremely well all steps leading to his conclusion. However, the said coverage heavy at time for the layman . . . Well worth plowing through to better understand the thinking of a major intellectual of our time.Cycles of Time: An Extraordinary New View of the Universe
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on January 31, 2011
The problem I have with books of this type, which I think of as attempts to popularize cosmology, is that I'm inevitably confronted with math that is way over my head, when what I'm really interested in is the idea that the author is trying to demonstrate and support with the math: so instead of marveling at the author's genius, I find myself drowning in math that makes my eyes glaze over. Admittedly, this book is also for people that will have no problem with the math, and to them it will mean something, and certainly the math is important. Nonetheless, I was hoping for something a bit more like 'Cosmos', and something a lot less like my first or second year university calculus/algebra/geometry text book.

Nonetheless, the idea of cyclical universes coming and going and coming and going... is an interesting one. The older cosmology gets, the more mystical and weird it gets.
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on June 16, 2014
your PRICE is too low! !!

PENROSE is NEAR PERFECT. No adequate word to describe the joy to read his thought.

If one can understand 10 % of it, that qualify for a Phd.
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