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The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions [Hardcover]

Shing-Tung Yau , Steve Nadis
4.0 out of 5 stars  See all reviews (10 customer reviews)

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Book Description

23 Sep 2010
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see What if you were told that we actually live in a 10-dimensional universe-- that the leading theory of nature posits only 4 out of 10 are accessible to our everyday senses? How do we account for the other 6 dimensions? What do they look like, where are they hiding, and what, if anything at all, do they do? In The Shape of Inner Space, geometer and leading string theorist Shing- Tung Yau unpacks the widely-held belief that these undetected dimensions are tightly curled in elaborate, twisted shapes called "Calabi-Yau manifolds." Yau explains that these spaces are so miniscule that humans will probably never see any of them directly. Amazingly, however, this hidden realm may hold the answers to some of the most profound questions we have about our universe. In examining his life's work, Yau emphasises his most important finding: proof of the manifold's mathematical existence. This discovery has been critical in advancing our understanding of geometry and string theory, and, more broadly, physics and the universe. With this acquired knowledge, string theorists can go beyond the concept of the universe that Einstein left us with, and possibly expose some of nature's greatest mysteries. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we think about mathematics, cosmology, and our quest to learn the shape of the inner universe.


Product details

  • Hardcover: 400 pages
  • Publisher: Basic Books (23 Sep 2010)
  • Language: English
  • ISBN-10: 0465020232
  • ISBN-13: 978-0465020232
  • Product Dimensions: 15.6 x 3.4 x 23.6 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Bestsellers Rank: 391,525 in Books (See Top 100 in Books)

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Review

"(A)very well-written book, and one that scientifically minded laymen will find easy to follow... It is strongly recommended to those seeking a first-hand, simply explained account of one of the most fascinating evolutions in modern science, whose impact in mathematics is significant and enduring, and whose impact in physics may be forthcoming."

--The Times Higher Education Supplement

About the Author

Shing-Tung Yau has has won many awards including the Fields medal. He is the chair of the mathematics department at Harvard University, and lives in Cambridge, Massachussettes. Steve Nadis is a Contributing Editor to Astronomy Magazine. He lives in Cambridge, Massachusetts.

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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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Most Helpful Customer Reviews
27 of 28 people found the following review helpful
4.0 out of 5 stars How to think in (mostly) ten dimensions 17 Nov 2010
By Nigel Seel VINE VOICE
Format:Hardcover|Verified Purchase
This book, from a mathematician, covers the period from the first proof that Calabi-Yau spaces actually might exist to their current central place as a preferred model for String Theory's extra dimensions. Shing-Tung Yau is the Fields Medallist godfather of the eponymous manifolds and Steve Nadis had the unenviable task of writing it all down so that the rest of us could have a prayer of understanding it. He also did the interviews and fleshed out the physics side. The best way to review this book is just to explain what it says chapter by chapter.

Chapter 1: The universe is a big place, maybe infinite. Even if its overall curvature suffices to close it, observations suggest that its volume may be more than a million times the spherical volume of radius 13.7 billion light year we actually see. The unification programme of theoretical physics doesn't really work, however, if it's confined simply to three large spatial dimensions plus time. It turns out that replacing the point-like objects of particle physics with tiny one-dimensional objects called strings, moving in a 10 dimensional spacetime may permit the unification of the electromagnetic, weak and strong forces plus gravity. Well, today it almost works.

We see only four space-time dimensions. Where are the other six? The suggestion is that they are compactified: rolled up to be very small. But that's not all, to make the equations of string theory valid, the compactified six dimensional surface must conform to a very special geometry. That is the subject of the rest of the book.

Chapter 2: Yau was born in mainland China in 1949. His father was a university professor but the pay was poor and he had a wife and eight children to support.
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4 of 4 people found the following review helpful
4.0 out of 5 stars I wish I was clever 29 Jun 2011
By John Ferngrove TOP 500 REVIEWER
Format:Hardcover|Verified Purchase
As someone who did an astrophysics degree in the late seventies, I've tried over the years to stay in touch with developments in cosmology by reading the odd popular science book now and again. Inevitably, since the string theory revolution of the eighties, that has involved digesting a few of the more or less well known lay-expositions of string theory, and its associated ideas. With each such book I have been left with a dissatisfied feeling that I would like to have been given just a bit more of the relevant conceptual mathematical framework. Well, with this book I got my wish, and its fair to say that I've come away understanding about 10% of what I've read. It is apparent that my rusty undergraduate physics level maths doesn't even get you to the front door of where string theory picks up from.

Yet, despite all this, I found the book to be compelling, and I found a way of reading it that allowed me to take much of what passed on faith, and just enjoy the handful of concepts and images that I did manage to abstract from the flow. Somewhat like watching for patterns in clouds or fire. There is a surface level story of extraordinarily gifted people, mathematicians and physicists, all attending conferences, then beavering away at impossibly difficult proofs and calculations. The history of who proved or calculated what, when, thus enabling whoever else, to prove or calculate whatever came next is, to someone like me, a plausible human interest story with a certain level of excitement. But with regard to the maths, then, if I am honest, it was really just a question of hanging on by the coattails.
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3 of 3 people found the following review helpful
Format:Hardcover
This is a fascinating story about the development of the mathematical concept of extra spatial dimensions known as Calabi-Yau spaces and its application in the string theory. The author speaks candidly, and describes his excitement at emerging new ideas in physics and mathematics, and how it progressed in string theory, and in the process changed his perspectives. Over the last 35 years this idea has shaped our thought on the nature of physical reality and involved an entire generation of theoretical physicists in research. This is partly autobiographical and hence makes it very interesting to read as he explains his odyssey. We get to read the contributions of leading physicists in this adventure; the growth of string theory as major force in theoretical physics. This is an outstanding book to read, but requires undergraduate level physics and strong interest in geometry.

A summary of this book is as follows: In string theory, the myriad of fundamental particle types is replaced by a single fundamental building block, a string. As the string moves through time it traces out a tube or a sheet (the two-dimensional string worldsheet), and different vibrational modes of the string represent the different particle types. The particles known in nature are bosons (integer spin) or fermions (half integer spin). By introducing supersymmetry to string theory both bosons and fermions could be accounted for, and with ten-dimensions, the mathematical requirements of string theory are completely satisfied. In addition, the anomalies and inconsistencies that plagued string theory are vanished. Until superstring theory came into existence, any predictions and calculations yielded nonsensical results, and were incompatible with quantum physics.
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Most Recent Customer Reviews
5.0 out of 5 stars What an Excellent Read!
Having read a couple of String Theory pro and con books by physicists, I thought this might provide me with a less partisan perspective, though I was a bit worried I might have to... Read more
Published on 12 Aug 2011 by David E. Perkins
5.0 out of 5 stars THE PERFECT SHAPE
Although this book emanates from a mathematical context, it has been co-authored by Shing-Tung Yau and Steve Nadis and impeccably offers two complementary perspectives. Read more
Published on 9 July 2011 by C. S. Ebrey
1.0 out of 5 stars Post docs only
I also gave up - less than half way through. I am near the end of a maths degree which has included quantum theory and relativity and other than the historical side of how the... Read more
Published on 28 Jan 2011 by CMN
1.0 out of 5 stars Not for the Lay Reader
As one who received a scientific training, and has attempted to keep abreast of developments in fundamental science, even though my career did not take that path, I had hoped that... Read more
Published on 12 Jan 2011 by TR
5.0 out of 5 stars AN EXHILIRATING AND CHALLENGING BOOK!
Simply put, this is a sensational book. The authors expertly guide readers through some really difficult terrain concerning "extra" dimensions, string theory, geometry, and... Read more
Published on 25 Dec 2010 by Martin H. Court
5.0 out of 5 stars AN AMAZING, INTELLECTUAL TOUR DE FORCE!
THE SHAPE OF INNER SPACE is guaranteed to take readers places they've never been before, nor thought about before. That was certainly the case for me. Read more
Published on 11 Dec 2010 by MJB
5.0 out of 5 stars Fabulous
I love this book. It is rare that somebody dares to try to popularize such an esoteric topic. I enjoyed it greatly. Read more
Published on 2 Dec 2010 by Oskar Axelsson
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