Everything and More: A Compact History of Infinity

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Overview

Since the time of the ancient Greeks, when Zeno proposed his notorious paradoxes, the nature of infinity has perplexed mathematicians and philosophers. Is it a valid mathematical entity or a meaningless abstraction? Plato and Aristotle in their day, Galileo and Newton nearly two thousand years later, all grappled with it. But it was the nineteenth-century mathematicians Karl Weierstrass, Richard Dedekind, and Georg Cantor whose work established a whole new mathematics of infinity. In particular, Cantor's ...
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Overview

Since the time of the ancient Greeks, when Zeno proposed his notorious paradoxes, the nature of infinity has perplexed mathematicians and philosophers. Is it a valid mathematical entity or a meaningless abstraction? Plato and Aristotle in their day, Galileo and Newton nearly two thousand years later, all grappled with it. But it was the nineteenth-century mathematicians Karl Weierstrass, Richard Dedekind, and Georg Cantor whose work established a whole new mathematics of infinity. In particular, Cantor's counterintuitive discovery of a progression of larger and larger infinities was both enormously controversial and mind-bendingly beautiful - a glimpse of a strange landscape where the everyday rules of arithmetic are broken, and where there truly can be found everything and more.

Wallace is a splendid guide to this new territory, patiently and ingeniously taking us through the math and ideas that led to Cantor's discovery. In so doing he has created both an adept introduction to infinity and a literary masterpiece.

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Editorial Reviews

New York Times Book Review
“A gripping guide to the modern taming of the infinite.”
John Allen Paulos - The American Scholar
“[Wallace] brings to his task a refreshingly conversational style as well as a surprisingly authoritative command of mathematics....A success.”
Booklist
“Shockingly readable....A brilliant antidote both to boring math textbooks and to pop-culture math books that emphasize the discoverer over the discovery.”
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. (Oct.) FYI: This title, along with Sherwin Nuland's The Doctor's Plague, is launching James Atlas's Great Discoveries series for Norton. Copyright 2003 Reed Business Information.
Library Journal
Wallace's writing about math isn't new-his novel Infinite Jest (1996) and some of his essays include a more than superficial treatment of the subject. Here, however, he digs as deeply into it as is possible for a nonprofessional math geek faced with a page limit, and the result is classic DFW: engaging, self-conscious, playful, and often breathless. This second installment in the "Great Discoveries" series traces the history of infinity from the Greeks to the calculus, culminating in a discussion of Georg Cantor's (1845-1918) groundbreaking work with transfinite numbers. Unfortunately, context requires Wallace to bulldoze heroically through a couple thousand years of logic, geometry, and number theory, which, even with "emergency glossaries" and frequent cross-referencing tips, can make for some teeth-grindingly dense passages. In one of the 400-plus footnotes, he writes, "It's true that it would be nice if you've had some college math, but please rest assured that considerable pains have been taken and infelicities permitted to make sure it's not required." For devout Wallace fans, it won't matter either way. Readers looking to soak up some pure abstraction, however, may just need to read the book twice. Luckily, they couldn't have been blessed with a more talented or stimulating guide. Enthusiastically recommended for all libraries. [Previewed in Prepub Alert, LJ 6/15/03.]-Christopher Tinney, Brooklyn, NY Copyright 2003 Reed Business Information.
Boston Globe
Everything and More is, in nearly every way, a gift. It's a thoughtful and witty 300-page testimonial to the qualities I never fully understood that mathematics possessed: Math is astonishing and full of 'shadowlands,' and-ultimately-stunning beauty.— Anthony Doerr
Village Voice
Wallace is the perfect parachute buddy for a free fall into the mathematical and metaphysical abyss that is infinity.— Dennis Lim
American Scholar
[Wallace] brings to his task a refreshingly conversational style as well as a surprisingly authoritative command of mathematics. . . . A success.— John Allen Paulos
Anthony Doerr - Boston Globe
“ Everything and More is, in nearly every way, a gift. It's a thoughtful and witty 300-page testimonial to the qualities I never fully understood that mathematics possessed: Math is astonishing and full of 'shadowlands,' and-ultimately-stunning beauty.”
Dennis Lim - Village Voice
“Wallace is the perfect parachute buddy for a free fall into the mathematical and metaphysical abyss that is infinity.”
John Allen Paulos - American Scholar
“[Wallace] brings to his task a refreshingly conversational style as well as a surprisingly authoritative command of mathematics. . . . A success.”
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Product Details

  • ISBN-13: 9780393003383
  • Publisher: Norton, W. W. & Company, Inc.
  • Publication date: 10/1/2003
  • Series: Great Discoveries Series
  • Pages: 332
  • Sales rank: 450,094
  • Product dimensions: 5.70 (w) x 8.30 (h) x 1.10 (d)

Meet the Author

David Foster Wallace

David Foster Wallace (1962-2008) is the author of Infinite Jest, Girl with Curious Hair, Everything and More, The Broom of the System, and other fiction and nonfiction. Among his honors, he received a MacArthur Foundation Fellowship, a Lannan Literary Award, and a Whiting Writers' Award.

Biography

Born in Ithaca, NY, and raised in Champaign, IL, David Foster Wallace grew up athletically gifted and exceptionally bright, with an avid interest in tennis, literature, philosophy, and math. He attended Amherst and graduated in 1985 with a double major in English and Philosophy. His philosophy thesis (on modal logic) won the Gail Kennedy Memorial Prize. His English thesis would become his first novel, The Broom of the System. Published in 1987 during his second year of grad school at the University of Arizona, the book sold well, garnering national attention and critical praise in equal measure. Two years later, a book of short stories, Girl with Curious Hair, was published to admiring reviews.

In the early 1990s, Wallace's short fiction began to appear regularly in publications like Playboy, The Paris Review, and The New Yorker, along with excerpts from his second novel, a complex, enormously ambitious work published in 1996 as Infinite Jest. Surpassing 1,000 pages in length, the novel was hailed as a masterpiece ("[A]n entertainment so irresistibly pleasurable it renders the viewer catatonic," raved Newsweek. "[R]esourceful, hilarious, intelligent, and unique," pronounced Atlantic Monthly), and Wallace was crowned on the spot the new heavyweight champion of literary fiction.

Hyperbole aside, Infinite Jest, with its linguistic acrobatics (challenging complex clauses, coined words, etc.) and sly, self-referential footnotes, proved to be the template for a new literary style. Subversive, hip, and teeming with postmodernist irony, the book attracted a rabid cult following and exerted an influence on up-and-coming young writers that is still felt today. The scope of Wallace's achievement can be measured by the fact that one year after the publication of Infinite Jest, he was awarded the MacArthur Foundation "Genius Grant."

Nearly as famous for his nonfiction as for his novels and stories, Wallace produced mind-boggling essays on assignment for magazines like Harper's. In contrast to his sad, dark, disturbing fiction, these essays -- subsequently collected into such bestselling anthologies as A Supposedly Fun Thing I'll Never Do Again (1997), Everything and More (2003), and Consider the Lobster (2007) -- were ridiculously exuberant, fairly bursting with humor, energy, and good cheer. Yet Wallace himself suffered from clinical depression most of his adult life. He was treated successfully with anti-depressants, until side effects from the drugs began to interfere with his productivity. At his doctor's suggestion, he stopped taking the medication.The depression returned, and he did not respond to any further treatment. In September of 2008, at the age of 46, he committed suicide.

Wallace's influence on contemporary literature cannot be overstated. Descended from post-war superstars like Thomas Pynchon and Don De Lillo, his style is clearly visible in the work of postmodernists like Jonathan Safran Foer and Dave Eggers. His untimely death was mourned by critics, writers, and millions of adoring fans. As author David Lipsky stated in a tribute that aired on NPR in September, 2008: "To read David Foster Wallace was to feel your eyelids pulled open."

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    1. Date of Birth:
      February 21, 1962
    2. Place of Birth:
      Ithaca, NY
    1. Date of Death:
      September 12, 2008
    2. Place of Death:
      Claremont, CA
    1. Education:
      B.A. in English & Philosophy, Amherst College, 1985;MFA, University of Arizona, 1987

Customer Reviews

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Sort by: Showing all of 7 Customer Reviews
  • Anonymous

    Posted April 9, 2004

    Infinity -- And More

    Readers who are interested in the subject more than in math itself and who, like myself, have only a first year college math, will want to read this book twice. But I will go a step further than the Journal in saying that readers, when they feel they are getting lost, will stop, as I did, and put in a marker. They will then return to the last place where they felt comfortable and try again to 'cross the road', confident that it is possible (because Wallace says so) but all the while mindfull of the fact that there really is no end.

    5 out of 5 people found this review helpful.

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  • Anonymous

    Posted November 6, 2003

    the bland leading the blind

    A Review of David Foster Wallace's 'Everything and More: A Compact History of {infinity}' Is this book merely an instance of the bland leading the blind? It may be more perilous than that, since readers with a genuine but uncultivated interest in the subjects which the book purports to address---roughly, the concept of 'infinity' in mathematics---may be more than merely mislead by Wallace's rambling, irreverent romp through soundbytes from the undergraduate math curriculum: they may be soured on the subjects themselves. The first---and cardinal---error committed by Wallace is his presentational style. His mistake is one that could only be committed but one who either lacked comprehension of the math behind the pop-sci summaries, or else was so contemptuous of those results that a sincere attempt to communicate the underlying ideas seemed superflous. Bluntly put, the first thing any prospective initiate into the world of mathematical thought must do is free himself from the need to accomodate one's thinking, reasoning---and indeed, presentational style---to the comfortable glibness prized in everyday discourse (and apparently, in certain long-winded works of fiction). Wallace probably believes that by adhering to a populist style, he will attract more readers to his subject. This may be true, but in so doing, he has marred the beauty of that subject so hopelessly beyond recognition that sincere readers will find little of value in his presentation. The book is not only not recommended, it is recommended to be avoided.

    3 out of 5 people found this review helpful.

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  • Posted December 10, 2010

    more from this reviewer

    A History Book For Geeks!

    While in today's world of calculus and advanced math, we may take infinity for granted, this book is a great demonstration of the difficulties and benefits of abstract thought.

    Like how it wasn't until math became more abstracted (and removed from the physical reality) that it was able to provide science with profound real-world breakthroughs.

    A fiction writer of the non-science variety, DFW is brings his unique perspective and writing style to a truly fascinating subject. While the math can get heavy at times, he still manages to spin an intriguing narrative and show the trouble, paradoxes, and controversy throughout history caused by the very concept of infinity.

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    Posted April 29, 2009

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    Posted December 24, 2008

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    Posted April 16, 2010

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    Posted May 9, 2009

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