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

Overview

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.

Time and again, where Yau has ...

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

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Overview

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.

Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

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Editorial Reviews

Publishers Weekly
The invisible shape of space can be revealed via "the sheer force of mathematics.... the surest path to the truth." What it reveals is the Calabi-Yau manifolds, or surfaces, discovered by feted Harvard mathematician Yau in his work on a concept called the Calabi conjecture. With the help of Astronomy magazine contributing editor Nadis, Yau relates the saga of this groundbreaking work, which provided the foundations of string theory. Yau confidently draws readers into a realm of abstract concepts, from multiple dimensions to the exotic spaces called "manifolds," or Calabi-Yau spaces, whose curvature gives space its shape. From here it's a hop, skip, and a jump to the geometry of space around the Big Bang, black holes, and the end of the universe. The authors labor diligently to explain the advanced mathematics behind these abstract ideas, but readers without any grounding in college-level math will be lost. For those who can follow it, this book demonstrates how mysterious physical constructs like space and gravity can yield to the "hammer of geometric analysis." B&w illus. (Sept.)
From the Publisher

AUTHORS' STATEMENT by SHING-TUNG YAU and STEVE NADIS
There is a certain irony running through this book that one of the smallest things you can possibly imagine--six-dimensional geometric spaces that may be more than a trillion times smaller than an electron--could, nevertheless, be one of the defining features of our universe, exerting a profound influence that extends to every single point in the cosmos. This book is, in many ways, the story of those spaces, which physicists have dubbed "Calabi-Yau manifolds." It tells how one of us, Yau, managed to prove the existence, mathematically, of those spaces, despite the fact that he had originally set out to prove that such spaces could not possibly exist. It then goes on to explain how this mathematical proof, which had initially been ignored by physicists (partly because it was steeped in difficult, nonlinear arguments), nevertheless made its way into the center of string theory, which now stands as the leading theory of the universe and our best hope yet of unifying all the particles and forces observed--and yet to be observed--in nature.

Of course, none of this could have been foretold more than a half century ago when a man named Eugenio Calabi--the first half of the Calabi-Yau duo--proposed that there could be multidimensional spaces with properties so special that many mathematicians, including one of this book's authors, considered them "too good to be true." Calabi had not been thinking about physics at the time, in the early 1950s, when he advanced the famous conjecture named after him. Following the proof of the Calabi conjecture, we have learned many new and wonderful things in both physics and mathematics--all of which suggest that Calabi-Yau spaces are not only too good to be true, as the skeptics used to say, but that they may be even better.

BLURBS
Brian Greene, Professor of Mathematics & Physics, Columbia University; author of The Fabric of the Cosmos and The Elegant Universe
The Shape of Inner Space provides a vibrant tour through the strange and wondrous possibility that the three spatial dimensions we see may not be the only ones that exist. Told by one of the masters of the subject, the book gives an in-depth account of one of the most exciting and controversial developments in modern theoretical physics.”

Joe Polchinski, Professor of Physics, University of California - Santa Barbara; author of String Theory, Vols. 1 & 2
“Einstein’s vision of physical laws emerging from the shape of space has been expanded by the higher dimensions of string theory. This vision has transformed not only modern physics, but also modern mathematics. Shing-Tung Yau has been at the center of these developments. In this ambitious book, written

Newsletter of the European Mathematical Society
"An interested reader, even one with little background in mathematics, will be able to gather much new knowledge of, and appreciation for, both mathematics and physics from the elegant analogies and beautiful illustrations in this book...  The book gives insight into the mind of one of the world’s greatest mathematicians and will provide intellectual stimulation to interested readers with any kind of background." 

Simon Donaldson, Royal Society Research Professor in Pure Mathematics and President of the Institute for Mathematical Science, ImperialCollegeLondon
The Shape of Inner Space has a distinctive style: in part autobiography, in part an account of developments in geometric analysis and string theory over the past 40 years, and comments on future directions. It gives a unique insight into the thoughts of one of the most important and influential mathematicians of our times.”

Edward Witten, Professor, Institute for Advanced Study
“Shing-Tung Yau and Steve Nadis take the reader on a fascinating tour of many contemporary topics in geometry and physics. Readers will find many challenging ideas to explore in this book, and even specialists will enjoy Yau’s reminiscences about his education and work.”

Steven Strogatz, New York Times Opinionator contributor and professor of mathematics, Cornell University
“A fascinating first-hand account of how the math underlying string theory was discovered. Fields medalist Yau and ace science writer Nadis have teamed up to show the rest of us the deep geometry that just might lie at the heart of the universe. It’ll twist you into knots of pleasure!”

John Coates, Sadleirian Professor of Pure Mathematics, University of Cambridge
"This extraordinary book by Shing-Tung Yau and Steve Nadis gives the layman a remarkable glimpse into the mysterious inner world of one of the most beautiful and important parts of mathematics."

Andrew Strominger, Professor of Physics, Harvard University
“This book tells an inspiring story about how progress in science is made by breaking traditional boundaries in disciplines. It's really the only book of its kind—and, of course, written by someone who not only witnessed but also inspired and produced many of the major developments in this field over an exhilarating period of four decades.”

David Gross, Frederick W. Gluck Professor of Theoretical Physics, University of California – Santa Barbara; Nobel Prize-winning physicist
The Shape of Inner Space takes one on a marvelous journey that explores many beautiful areas of modern geometry and physics, and the people behind recent discoveries. It is a journey that I highly recommend to the intellectually curious.”

Michael D. Smith, Dean of the Faculty of Arts and Sciences, John H. Finley, Jr. Professor of Engineering and Applied Sciences, Harvard University
“Though this wonderful new book helped me to better understand the discoveries underpinning string theory, what I enjoyed most was what it reveals about the beauty of mathematical inquiry. This book shares a very human process of thought, discussion, and wonder that is enormously appealing, in addition to being quite obviously fertile ground for discovery. Words from Yau’s poem from the front pages—‘Inexhaustible, lovely in every detail’—provide an apt description of the book itself. Well done!”

REVIEWS
Publishers Weekly
“With the help of Astronomy magazine contributing editor Nadis, Yau relates the saga of [his] groundbreaking work which provided the foundations of string theory. Yau confidently draws readers into a realm of abstract concepts, from multiple dimensions to the exotic spaces called ‘manifolds,’ or Calabi-Yau spaces, whose curvature gives space its shape. From here it’s a hop, skip, and a jump to the geometry of space around the Big Bang, black holes, and the end of the universe.”

New Scientist
“It is a testimony to [Yau’s] careful prose (and no doubt to the skills of co-author Steve Nadis) that this book so compellingly captures the essence of what pushes string theorists forward in the face of formidable obstacles. It gives us a rare glimpse into a world as alien as the moons of Jupiter, and just as fascinating…. Yau and Nadis have produced a strangely mesmerizing account of geometry’s role in the universe.”

Nature
“Physicists investigate one cosmos, but mathematicians can explore all possible worlds. So marvels Fields medalist Shing-Tung Yau…. Relating how he solved a major theoretical problem in string theory in the 1970s, Yau explains how the geometries of the vibrating multidimensional strings that may characterize the Universe have implications across physics.”

Science Books & Films
“Concepts are introduced in a clear way, preceding more detailed discussions. The subjects examined include topology, geometries, general relativity, quantum physics, the standard model of particles, and other topics relevant to the pursuit of the understanding of extra dimensions in our universe. Among the volume’s especially interesting discussions are the possible experimental tests of the theory, the potential semistability of our universe, the five candidate string theories, and black-hole entropy.”

David Eicher, Astronomy.com
“[A] masterwork on its subject…. The book is an entertaining read, written with the absorbing style that characterizes Nadis’ feature stories in Astronomy…. Those interested in cosmology and nature as a whole will be delighted with this new work!”

New York Journal of Books
The Shape of Inner Space provides the opportunity to look over the shoulder of a giant in mathematics.”

MAA Reviews
“This fascinating book may well have a similar impact to Stephen Hawking’s A Brief History of Time…. I found this introduction to string theory totally absorbing, and well worth re-reading.”

Nature Physics
“An engaging exposition of elegant relations between geometry, topology, fields and strings, the book is also part memoir and part speculation about connections to physics…. Written with an easygoing sense of humour, and conscious of the distance between its subject and the daily concerns of the ‘average citizen’, the book in the end offers cautious optimism about the future of this ambitious programme of theoretical research. Altogether, Yau and Nadis’s effort covers some central developments in mathematical physics, and is well worth perusal by widely interested scientists as well as lay readers.”

The London Mathematical Society Newsletter                                                                                                                                         “This book tells the fascinating story of strange geometric objects that have achieved some fame outside of [mathematics] called Calabi-Yau manifolds... The collaboration between a mathematician and a science writer has worked wonders in this book. It's crowded with beautiful metaphors that clarify complex ideas and provide a peek into higher-dimensional worlds... One thing that comes through on every page of this book is the beauty of the [mathematics] and its power to shed light on the secrets of our Universe. If this is the kind of thing that fascinates you, then this is a great book to while away those dark winter evenings.”

PhysicsWorld.com
"It is fascinating to see the story of string theory told from a mathematician's point of view rather than that of a physicist... By bravely attempting to explain areas of mathematics that no one has ever tried to relate to the public before, The Shape of Inner Space takes a huge step forward... It will undoubtedly influence how string theory is taught and written about in the future."

Times Higher Education Supplement
"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.”

Choice
"This book provides an excellent insight into the current ideas about string theory."

Philip J. Davis, SIAM News
  
                                                                                                                                                                             "My experience in reading this book may be akin to that of a kibitzer in the presence of some moment of high creativity—perhaps of an onlooker in the atelier of Titian, watching how he painted the famous equestrian portrait of Charles V."

American Journal of Physics
The Shape of Inner Space is a portrait of a beautiful branch of geometric analysis as seen through the eyes of one of its pioneers, Fields medal winner Shing-Tung Yau… After describing the sequence of events that led him to the United States and to his enamoration with geometry, Yau explains as only a master could the conjecture by Calabi and the subsequent discovery of Calabi-Yau manifolds that are the centerpiece of this book. The reader is thrown into a world of complex manifolds, geometric analysis, and differential equations, yet the book is written so that the persistent layperson could follow all of the main ideas.”

Notes of the Canadian Mathematical Society
“In the fascinating book, The Shape of Inner Space… Shing-Tung Yau, along with coauthor Steve Nadis, describes the exciting development of the theory of what are now called Calabi-Yau manifolds and their relationship to the structure of the universe.”

Philippine Daily Inquirer
“A journey into the mind of a brilliant mathematician, The Shape of Inner Space will delight readers who are not afraid to use their minds.”

College Mathematics Journal
“A worthy successor to The Elegant Universe.”
 Philippine Daily Inquirer
“A journey into the mind of a brilliant mathematician, The Shape of Inner Space will delight readers who are not afraid to use their minds.”

The Mathematical Intelligencer“What makes this book unique is that Yau has a deep insight not only into the mathematics but also into the physics governing our universe, and he uses this knowledge to build a bridge between both worlds.

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Product Details

  • ISBN-13: 9780465022663
  • Publisher: Basic Books
  • Publication date: 9/7/2010
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 400
  • Sales rank: 718,016
  • File size: 5 MB

Meet the Author

Shing-Tung Yau has won many awards, including the Fields Medal. He is the chair of the mathematics department at Harvard University, and lives in Cambridge, Massachusetts.

Steve Nadis is a contributing editor to Astronomy magazine. He lives in Cambridge, Massachusetts.

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Sort by: Showing all of 11 Customer Reviews
  • Posted October 1, 2010

    Highly Recommended

    This book is not only unique for elegantly explaining complicated concepts of geometry, and its `DNA' imprint on physics via string theory, but it is said from the vantage point of the world renowned geometer who has played a major role in all
    these developments. Through
    the collaboration of the two authors, the book is very down to earth and has
    a style which not only explains how different ideas have unfolded in the past
    couple of decades, but how beautifully natural they all fit with one another.
    Black holes, curved space, topology and a human struggle to understand the inner
    workings of nature through beautiful mathematical reasoning shines very clearly
    through the book and provides the reader with a front row seat for an exciting
    journey into the interaction of modern physics and mathematics. I strongly recommend this book to all those interested in seeing the power of elegant mathematics
    applied to the most enigmatic questions in modern physics.

    2 out of 2 people found this review helpful.

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  • Posted September 14, 2010

    A true gem of popular science!

    Written by one of the world mathematical leaders, together with a science journalist, this books will take you through some of the deepest mathematical and physical discoveries of the past forty years with an unbelievable clarity and a compelling geometric vision. One of the main themes of the book is the link between physical theories for the fundamental forces of nature and the geometry of space. For example, one of the main features of string theory is that our space-time has 6 extra dimensions which are very small and undetectable by the naked eye, and that these 6 dimensions are curled up into a geometric space called a Calabi-Yau space (in honor of the mathematician Calabi who conjectured the existence of these spaces, and of Yau himself who rigorously proved they existed). This unique book, which is written partly as Yau's autobiography, makes all these concept seem easy and natural, and kept me very much engaged throughout the whole reading. Overall a book I will recommend to everyone who has just the slightest curiosity about how our universe and what its underlying structure is, no mathematical background is assumed!

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted December 6, 2011

    a good book for lay people

    some math knowledge need for some of the terms. but a geat book for novices.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted December 6, 2011

    "Indicates topic well"

    I read this book to learn more about string theory. It was very informative, but string theory itself is a difficult concept to grasp. That is why the book can be difficult to read at times.

    1 out of 1 people found this review helpful.

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  • Posted October 19, 2010

    Highly Recommended- you must check it out

    A journey into mathematics and physics, a fascinating adventure even for laymen like me.

    1 out of 1 people found this review helpful.

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