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

David Foster Wallace (Author)

Book Description

Publication Date: November 17, 2004 | ISBN-10: 0393326292 | ISBN-13: 978-0393326291 | Edition: First Edition

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.

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.

See all Editorial Reviews

Product Details

• Paperback: 368 pages
• Publisher: W. W. Norton & Company; First Edition edition (November 17, 2004)
• Language: English
• ISBN-10: 0393326292
• ISBN-13: 978-0393326291
• Product Dimensions: 5.5 x 0.9 x 8 inches
• Shipping Weight: 6.4 ounces (View shipping rates and policies)
• Average Customer Review: 3.1 out of 5 stars  See all reviews (60 customer reviews)
• Amazon Best Sellers Rank: #405,948 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.

Amazon Author Rankbeta 

(What's this?)

#50 in Books > Literature & Fiction > Literary

#71 in Books > Literature & Fiction > Contemporary

#50 in Books > Literature & Fiction > Literary

#71 in Books > Literature & Fiction > Contemporary

Most Helpful Customer Reviews

71 of 76 people found the following review helpful

5.0 out of 5 stars Great book, but not for everyone January 28, 2006

By Steve Stowers

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.

52 of 59 people found the following review helpful

5.0 out of 5 stars A Little Look at Infinity January 27, 2004

By R. Hardy HALL OF FAMETOP 500 REVIEWER

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. The paradoxes were curious, but when supremely useful calculus came along, the infinitesimals used had never been rigorously defined. It was not until Georg Cantor showed how to deal with infinities as real mathematical entities that calculus had a mathematical foundation. He showed that infinities could be compared, and some infinities were larger than others. The proofs of these ideas (about one of which a mathematician said, "I see it, but I don't believe it!") gave calculus roots, but also gave rise to questions that eventually shook all of mathematics to its foundations.

Wallace doesn't get much into Gödel and his eventual Incompleteness Theorem, and it is just as well. There is enough excitement here, at least exciting for anyone who finds paradoxes a charming way to make the neurons spin. Admittedly, he has included equations and propositions full of Greek letters and advanced functions that only math buffs will absorb. He says of Weierstrass's demonstration of continuity, for instance: "There's a reason this all looks so hideously abstract: it _is_ hideously abstract." The substance is tough going, but there is enough style here, in jokes, curious illustrations, and piquant asides, to make this a fascinating show of intellectual prowess.

35 of 39 people found the following review helpful

3.0 out of 5 stars Challenging, thought-provoking, entertaining, and disappointing September 5, 2006

By Librum VINE™ VOICE

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.