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The Infinite Book: A Short Guide to the Boundless, Timeless and Endless

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ISBN-13: 978-1400032242
ISBN-10: 1400032245
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Editorial Reviews

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As prolific science writer and physicist Barrow regularly remarks, infinity is not merely the smallest or biggest thing, or the longest time imaginable: it's a quality that is unimaginable. It's thus a paradox that mathematicians, physicists, and philosophers have discovered quite a bit about infinity, albeit with different degrees of certitude. As also related in David Foster Wallace's Everything and More: A Compact History of Infinity (2003), Barrow recounts the career of German mathematician Georg Cantor, whose explorations of set theory resulted in fundamental proofs about infinities (some are bigger than others, for example). However joyous such discoveries are to the numbers masters, physicists' encounters with infinities are less rapturous because they hint at deficiencies in general relativity; hence their joy over string theory, which eliminates infinities that arise in calculations about the big bang and black holes. Performing with his customary fluency and accessibility, Barrow imparts for general readers a feeling for the nub of thought about the mathematical, cosmic, ethical, and theological implications of infinity. Gilbert Taylor
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Review

“Highly engaging. . . . [Barrow] brings his charm and wit to bear. . . . [He] introduces novel twists and turns, and presents [the] material in refreshing ways.”–Nature

"Eloquent. . . . Succinct. . . . Barrow [has the] remarkable ability to provide clear, concise, engaging and distinctly finite explanations–even when describing some fairly advanced concepts. . . . [An] engaging read."–San Francisco Chronicle

"Clever and insightful. . . . [A] lively history of infinity through the ages."–Entertainment Weekly

“Entertaining. . . . Remarkably lucid and not the least mind-boggling. . . . His clear, engaging style manages to illuminate abstruse matters.... This is a useful guide to an endlessly fascinating subject.” –American Scientist

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Product Details

  • Paperback: 328 pages
  • Publisher: Vintage (September 12, 2006)
  • Language: English
  • ISBN-10: 1400032245
  • ISBN-13: 978-1400032242
  • Product Dimensions: 5.2 x 0.7 x 8 inches
  • Shipping Weight: 6.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #116,529 in Books (See Top 100 in Books)

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56 of 60 people found the following review helpful By Rob Hardy HALL OF FAMETOP 500 REVIEWER on August 15, 2005
Format: Hardcover
When we get the capacity to look closer and closer into molecules, atoms, and subatomic particles, will we always be able to find something smaller? When our telescopes or probes look deeper into space, will we always find something larger? Is there a limit to the shortness of an instant, or the duration of eternity? In _The Infinite Book: A Short Guide to the Boundless, Timeless, and Endless_, John D. Barrow has invited us to look at infinities in many ways. He's competent to do so, as a professor of mathematical sciences at Cambridge, and as the author of previous books which successfully explained such concepts as nothing or impossibility. Like his previous efforts, this is highly readable stuff, but extraordinarily mysterious. The topic is something that everyone has pondered in some way; who has not, looking into the stars, wondered how far they go? It has a universal appeal, and a history within religion, philosophy, mathematics, and physics, all of which Barrow goes into here, in an entertaining summary. There are answers here, but plenty of mysteries.

Consider a universe that is infinite in space; this is a possibility, for no one knows that space is not infinite. In a universe of infinite size anything that can happen does happen, and does so infinitely often. In such a universe, not only are you here, but somewhere out there is another you doing exactly what you are doing; in fact, there are an infinite number of you. There is also somewhere out there another you who has done everything you ever did, but on the day after his sixteenth birthday, wore black socks instead of brown. This has to be the case in an infinite universe, Barrow shows; it is enough to make us uncomfortable, but discomfort is not an argument that an infinite universe cannot exist.
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32 of 34 people found the following review helpful By Joanna Daneman #1 HALL OF FAMETOP 10 REVIEWERVINE VOICE on February 3, 2006
Format: Hardcover
The value of "The Infinite Book" is definitely summed up in the chapter "The Madness of Georg Cantor." Believe it or not, "new math", that strange evolution of math teaching that stumped homework for a generation in the 60's was a direct result of Cantor's theories about sets, and the supposition that some infinite sets could be larger than others--which is the first thing you REALLY learn about infinity in mathematics.

The other great part of this book is the coupling of mathematics theory with physics. The assertion by Einstein that a singularity would be a breakdown of the laws of physics, and that any theory involving singularities would thereby have in it, the "seeds of its own destruction." Then author Barrow moves on to a very good explanation of string theory (imagine a particle that stretches like a tube in a warm enviroment, but contracts to a single point in a cool environment.) The explanations, illustrations are so clearly written in this book. It's a valuable reference for students of physics and mathematics and a great read for the curious about these subjects. Recommended.
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30 of 34 people found the following review helpful By John Matlock on August 29, 2005
Format: Hardcover
The infinite is one of those concepts that takes just a bit of understanding. Well, maybe more than just a bit. Infinity doesn't necessarily mean a bunch, it means, mathematically, that a number cannot be determined.

Infinity is not a new idea. Mathematicians have been working on them for hundreds of years. Physicists really got involved when Einstein published the Theory of Relativity in 1905. He talked about all kinds of things happening when you approached the speed of light. Then when you actually got to the speed of light his equations went to infinity. This was a bit disconcerting. One of the real reasons for the willingness of physicists to believe in string theory is that that the equations still show valid values at and above the speed of light.

But enough on infinity. If you want to know more, here's the book for you. It discusses just about everything there is to know about infinity. It would be great for the high school math/physics teacher to use for examples. Or, it's just plain fun reading to anyone that's interested.
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27 of 32 people found the following review helpful By Enrique Perez de Vargas on August 3, 2006
Format: Hardcover Verified Purchase
If you are interested in infinity and you are not familar with Cantor or Borges' "The Library of Babel", then you may be amazed by this book. Otherwise, you can find it too light. Probably good as a light summer reading.

Infinity is a fascinating subject, and I thought that this book would contain a lot of interesting information in its 300 pages. I have found many quotations, a lot of superficial theology and ethics, and little information on the concept itself. I missed more depth in handling the mathematical concepts.

Anyway, there is a very good part of the book (from my point of view) devoted to eternal inflation and simulated universes, especially for how the theories are introduced and chained. Even if it is not strictly related to infinity, it is the best part of the book. The chapter that describes Cantor's works is worth reading too.
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5 of 5 people found the following review helpful By Regnal on December 1, 2006
Format: Hardcover Verified Purchase
I have not been disappointed by any of John Barrow's book so far. He has a unique gift of writing with exceptional clarity about difficult topics. This is not a typical cosmology book, but large portion is devoted to beginning, shape and future of The Universe.
Like in his previous "Book of Nothing", author mixes philosophical and scientific musings about infinities (big and small) affecting theology, mathematics, cosmology, physics (TOE) and our existence.
I found Georg Cantor's life and his quest for understanding "absolute infinity" (God?) quite interesting and emotional. And check how Blaise Pascal argued about believing (or not) in God, because of infinite gain (or loss!!).
One truth emanates from "The Infinite Book": we are far, infinitely far from knowing the truth about everything (Immanuel Kant's rings the bell!). The more we learn the bigger infinite number of questions surface in front of us. Are we nearing the limits of knowledge? Professor John Barrow does not suggest it has come to this, but read about them and enjoy stretching your mind.
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