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Everything and More: A Compact History of Infinity (Great Discoveries) [Paperback]

by David Foster Wallace
3.2 out of 5 stars  See all reviews (64 customer reviews)

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Book Description

November 17, 2004 0393326292 978-0393326291 Reprint

The best-selling author of Infinite Jest on the two-thousand-year-old quest to understand infinity.

One of the outstanding voices of his generation, David Foster Wallace has won a large and devoted following for the intellectual ambition and bravura style of his fiction and essays. Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.

Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.

Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

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Everything and More: A Compact History of Infinity (Great Discoveries) + A Supposedly Fun Thing I'll Never Do Again: Essays and Arguments + Consider the Lobster and Other Essays
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Editorial Reviews

Amazon.com Review

Before discussing the merits of David Foster Wallace's Everything and More: A Compact History of Infinity, it is essential to define what the book is not. This volume in the "Great Discoveries" series is not a history of the personalities and social conditions that led to the "discovery" of infinity. Nor is it a narrative fixated on the cultish fear of--and obsession with--the infinite that has seemingly driven mathematicians insane over the centuries. Rather, Everything and More is a surprisingly rigorous march through the 2000 plus years of mathematical research that began with Aristotle; continued through Galileo, Isaac Newton, G.W. Leibniz, Karl Weierstrass, and J.W.R. Dedekind; and culminated in Georg Cantor and his Set Theory. The task Wallace (author of the bestseller Infinite Jest and other fiction) has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining. To propel his narrative, Wallace even develops a style that mirrors the mathematical language he probes. One difficulty in his focus on concepts and not a strict human chronology, though, is that his structure is dependent on frequent digressions (especially early on). Patience is required. Wallace demands that his reader walk through the equations, study the graphs and charts, and relearn college-level concepts to follow along on the exploration. Indeed, after one wrenching dip into Zeno’s paradoxes, Wallace spouts at his imagined complaining audience: "Deal." But the book should be deemed a success. If one grants him the attention he requires, Wallace has made the trip richly rewarding. --Patrick O’Kelley --This text refers to the Hardcover edition.

From Publishers Weekly

The subject of infinity would probably strike most readers familiar with Wallace as perfectly suited to his recursive style, and this book is as weird and wonderful as you'd expect. There are footnotes galore, frequently prefaced by the acronym IYI ("If You're Interested"), which can signal either pure digression or the first hint of an idea more fully developed in later chapters. Among other textual idiosyncrasies is the constant use of the lemniscate instead of the word "infinity," emphasizing that this is "not just an incredibly, unbelievably enormous number" but an abstraction beyond what we normally conceive of when we contemplate numbers. Abstraction is one of Wallace's main themes, particularly how the mathematics of infinity goes squarely against our instinct to avoid abstract thought. The ancient Greeks couldn't handle infinity, he points out, because they loathed abstraction. Later mathematicians fared better, and though the emphasis is on Georg Cantor, all the milestones are treated in turn. Wallace appreciates that infinity can be a "skullclutcher," and though the book isn't exactly easy going, he guides readers through the math gently, including emergency glossaries when necessary. He has an obvious enthusiasm for the subject, inspired by a high school teacher whose presence is felt at irregular intervals. Had he not pursued a career in literary fiction, it's not difficult to imagine Wallace as a historian of science, producing quirky and challenging volumes such as this every few years.
Copyright 2003 Reed Business Information, Inc. --This text refers to the Hardcover edition.

Product Details

  • Series: Great Discoveries
  • Paperback: 368 pages
  • Publisher: W. W. Norton & Company; Reprint edition (November 17, 2004)
  • Language: English
  • ISBN-10: 0393326292
  • ISBN-13: 978-0393326291
  • Product Dimensions: 8 x 5.3 x 0.9 inches
  • Shipping Weight: 6.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.2 out of 5 stars  See all reviews (64 customer reviews)
  • Amazon Best Sellers Rank: #726,942 in Books (See Top 100 in Books)

More About the Author

David Foster Wallace wrote the acclaimed novels Infinite Jest and The Broom of the System and the story collections Oblivion, Brief Interviews with Hideous Men, and Girl With Curious Hair. His nonfiction includes the essay collections Consider the Lobster and A Supposedly Fun Thing I'll Never Do Again, and the full-length work Everything and More.  He died in 2008.

Customer Reviews

Most Helpful Customer Reviews
84 of 89 people found the following review helpful
5.0 out of 5 stars Great book, but not for everyone January 28, 2006
Format:Hardcover
I greatly enjoyed this book, but it's not for everyone. To appreciate it, there are two requirements: (1) You must enjoy, or at least tolerate, Wallace's quirky writing style, with its mixture of the conversationsal and the erudite, its frequent footnotes, abbreviations, and discursions. (2) You must have a certain level of mathematical sophistication. This is not one of those popularizations of math for those who never got past high school algebra. It could perhaps be described as a history of calculus, analysis, and set theory, and specifically of their attempts to come to grips with the infinite and the infinitessimal and make them mathematically valid. The focus is on theory and rigor--which maybe makes it sound dry, but it's not, if you like that sort of thing. It's not that Wallace himself gives lots of rigorous arguments, but that he talks a lot ABOUT the search for mathematical rigor.

Reading this book is a little like sitting in on a class taught by an inspiring yet quirky professor (and, indeed, Wallace makes frequent reference to an inspiring, quirky teacher of his own). Such a class would have a prerequisite--I'm not quite sure what, maybe at least a semester or two of calculus. Probably, the more you know about calculus and related subjects, the more you'll get out of this book.
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42 of 46 people found the following review helpful
Format:Paperback
A reviewer, below, cites Zeno's Paradox as a metaphor for his experience reading E&M. This is precisely how I felt. Wallace's endlessly annoying flourishes aside, the first half of E&M is very interesting and accessible. Parts of the second half are, too, but those parts are islands in a sea of mounting incomprehensibility. Too much is left unexplained ("you'll have to trust me"-type asides, generally in "IYI" footnotes, abound) and too much else is expressed, formally, in arcane mathematical notation. Granted, Wallace's subject-matter is highly abstruse, and anything remotely approaching mathematical rigor would be both impossible in a book of E&M's size and impenetrable to a popular readership. Faced with these obstacles, Wallace makes a go of writing both to lay readers and specialists. Specialist reviewers on this page criticize Wallace for making numerous errors. As a lay reader, with a deep interest in mathematics (the practice, theory, history, and foundations of), I was (and remain) very eager to read a sophisticated (incipiently rigorous) treatment of the topic of infinity. The first half of E&M delivered a moderately sophisticated (mathematically unrigorous) treatment of the metaphysics of infinity. The second half attempted something like the treatment I had hoped for, but it was pitched entirely too high. The only hope a reader realistically has of navigating the second half of E&M is if (s)he brings a high level of mathematical sophistication to it. Such a reader, however, would almost certainly gravitate towards a genuinely rigorous treatment of the subject (like Dauben's biography of Cantor, oft-cited by Wallace). I'd like to think that I -- an interested and motivated lay reader -- am part of the target audience of E&M. As such, though I credit Wallace for his efforts, I cannot applaud his results.
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54 of 62 people found the following review helpful
5.0 out of 5 stars A Little Look at Infinity January 27, 2004
Format:Hardcover
Have you thought about infinity recently? If so, it was possibly bound up in religious ideas, in some of which it is integral ("Where will YOU spend eternity?" says one local billboard). Religious infinities have lapped over into mathematical ideas in surprising ways, and if you hanker to do some serious reading about mathematical infinities and their history, you should consider _Everything and More: A Compact History of Infinity_ (Norton) by David Foster Wallace. Wallace is a novelist, author of the huge and well regarded _Infinite Jest_. He isn't a mathematician, except by avocation, but his enthusiasm for his subject is apparent on every page. It's a good thing that this is so; this is definitely not a superficial look at the subject, and Wallace calls upon some high-powered math that you may not even have done in college. The result is a penetrating book from a serious amateur on some of the most important ideas from nineteenth and twentieth century mathematics.
Wallace starts his good-humored and sympathetic tone from the beginning: His "Small But Necessary Foreword" begins, "Unfortunately, this is a Foreword you have to read." There are plenty of footnotes, but half of them are marked "IYI": "If You're Interested," as are many of the paragraphs in the main text (along with "Semi-IYI"). In a history composed of increasing mathematical rigor, Wallace jokes and uses slang. Much of the history has to do with trying to solve the paradoxes of Zeno, like the one about how you can ever get to the other side of the street when you first have to go halfway, then half of the rest of the way, then half of that, and so on.
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25 of 27 people found the following review helpful
4.0 out of 5 stars So long and thanks for all the footnotes... September 15, 2008
Format:Hardcover
Since DFW has committed suicide, we will not see an edition revised by him. In re-reading the reviews, it appears that style means a lot. I personally found the book witty. It was a little slow sometimes because of the convolutions he introduced in style, but mostly I kept plowing (and chuckling) through. The librarian who sent back the book did a disservice to some readers. Not everyone likes to learn in the same way. With that kind of attitude, many years ago I would have had Rudin's books removed as too concise to be useful. Of course, there are many mathematicians who love those books for just that reason, and I would have done them a disservice.

I am a physicist with a math minor. To me, the best part of this book was his explanation of why mathematicians insist on the epsilon-deltas of mathematical rigor. No one ever did that before. If I could have read this in high school, I probably would have finished my math major as well as my physics major. Instead, the whole epsilon-delta thing seemed ad-hoc and inexplicable in purpose. I could never accept the need for rigor demanded in advanced analysis.(a drunken prof and Rudin's book didn't help either) DFW showed how a crisis in dealing with the infinite and with infinitesmals led to the development of the what we call the foundations of analysis. Just excellent.

I envied him his high school math teacher, who seems responsible for much of the really good parts of this book. No, DFW wasn't a mathematician and he (in spite of what some reviewers seem to think) knew it. He made clear that he wouldn't be able to do justice to Godel. But incompleteness is moderate difficult. DFW didn't know much about Fourier series, but did know they were important enough to mention.
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Most Recent Customer Reviews
5.0 out of 5 stars Infinitley great for U
From the cover to the Intro and foreword to the list of commonly used signs symbols and abbreviations, this book is genius. Read more
Published 1 month ago by Rex Waide
3.0 out of 5 stars Not as horrible as some reviewers say, but Rudy Rucker's "Infinity and...
This book is not really quite as lousy as some of the reviewers here claim. It is, however, thoroughly mediocre and also seems far too dependent -- quite embarrassingly so -- upon... Read more
Published 2 months ago by William D. Fusfield
4.0 out of 5 stars Very very funny
I read math only when I can enjoy it; this book is enjoyable. Wallace is funny, iconoclastic, and over-the-top. Read more
Published 6 months ago by Stephen Armstrong
2.0 out of 5 stars A Quirky Introduction to Mathematical Abstraction and the World of the...
During the first part of this book, the author's quirkiness, although quaint and fanciful, remained entertaining and didactic - even if the arbitrary notational schemes he kept... Read more
Published 6 months ago by Herbert L Calhoun
5.0 out of 5 stars Brilliant, entertaining, difficult but accessible to the untutored...
I bought and read this almost ten years ago, but the Kindle version was irresistible. Read it. Slowly. When you're alert.
Published 6 months ago by Peter W. Birkett
5.0 out of 5 stars Nothing less than promised.
This is math for the serious layman, written in a conversational style, but no less rigorous for that. His footnotes are copious and intense. Read more
Published 11 months ago by Wisefool
4.0 out of 5 stars Confusing at times but enightening and worth it...
David Foster Wallace shows his brilliance in this book that explains math in non- math terms, using math terms. Confusing? Read more
Published 15 months ago by Liz Campbell
3.0 out of 5 stars David Foster Wallace Takes on Aristotle
Well, that's the most that I could really garner from this book, anyway. I'm a huge David Foster Wallace fan, as in David-Foster-Wallace-Changed-My-Life-kind of huge, but, I simply... Read more
Published 15 months ago by Maggie's Bro
4.0 out of 5 stars my review for this book
frankly speak, it is a very nice book and I am very enjoying reading this book. It not only offer me the history of the infinite, but also gave me a large amount of new knowledge... Read more
Published 16 months ago by michael
4.0 out of 5 stars Aristotle, the villain; Cantor, the hero
I wish my calculus teachers had covered the material the way Wallace does. Science and math textbooks authoritatively present the material as if it had descended from heaven and is... Read more
Published 16 months ago by Stuart Mckibbin
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