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

by David Foster Wallace

Hardcover, 2003

Status

Available

Call number

511.3

Genres

Collection

Your library

Publication

W. W. Norton & Company (2003), Edition: 1st, Hardcover

Description

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.… (more)

Media reviews

Science Magazine

David Foster Wallace is a great writer, known for his stories and essays as well as the inspiring novel Infinite Jest. Wallace’s work is revelatory, funny, and post-ironic. I fully expected to enjoy Everything and More. But it’s a train wreck of a book, a disaster. Non-mathematicians will find

Everything and More unreadable, and mathematicians will view it with, at best, sardonic amusement. Crippling errors abound... The book closes in a red haze of shame. Wallace doesn’t have time to explain the transfinite ordinals after all. As a parting shot, he gives an incorrect characterization of Kurt Godel’s beliefs regarding the power of the continuum and a misleading characterization of Godel’s demise. Godel in fact believed the size of the continuum to be X 2 {4, 5), and rather than dying “in confinement,” he lived at home until the last two weeks of his life and coherently discussed mathematical philosophy until the end.

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User reviews

LibraryThing member semckibbin

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 so obvious that no one wants to argue about it anymore. But that's just bluff. As recently as 200 years ago the real

number system was an ungrounded mess, and today mathematics is still reeling from Godel's Incompleteness Theorem. Worse, math textbooks leave out the mathematicians, the humans.

Wallace gives you a sense of the mindbending toil and real genius necessary to dream up mathematical theories and proofs. His story starts with the Greeks (they dont believe infinity and irrational numbers exist), moves through the wild success of the Calculus to calculus's masochistic foundational crisis (how can we simultaneously have n = 0 and n ≠ 0?) and culminates in Cantor's invention of set theory. It's a story of great scope and allows Wallace to indulge in his metaphysical interests and explore different expository techniques.

A lot of reviewers think the book is a failure and find fault with Wallace's grasp of the subject and with his baroque style, its curlicues and flourishes. But I dig his style; and I think he does a super job explaining how the different concepts work, as well as the historical and metaphysical background. Still, if the reader has had some college math courses it would help her make it through the book without eliding great chunks of the text.

What's more, any book that has Aristotle as a villain is aight.

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15 more

LibraryThing member name99

I really don't need to read another book about infinity, but since this is
by *David Foster Wallace* who is such a big-wig in the world of literature, I thought I'd give it a shot.

The book is meant, as far as I can tell, to be an experiment, and IMHO the experiment fails. It attempts to be a

chatty math book, and it attempts to play with language and typography (in a very mild way; lots of abbreviations, a rather aggressive breakdown into sections and footnotes).

This sort of experimentation is obviously of interest to me in that I plan to be writing my own chatty physics book and playing with my own typography; obviously I certainly hope my version does not fall as flat with most readers as did this one with me.
I do think I understand Wallace's biggest flaws.
* Too much repetition of "This is all very complicated in the details" in various ways
* Far far too much back-and-forth referencing, rather than an attempt to figure out how to lay out the book in such a way that a single monotonic increasing pass through it is satisfactory

Oh, BTW, looking at the reviews of this and other DFW books on Amazon strongly suggests that this way this was written is the way DFW writes pretty much everything, which means I can cross him off the list of authors I'll bother reading in the future.

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LibraryThing member Galizur

The one mathematics book that Wallace wrote, "Everything and More: A Compact History of Infinity", was written in 2003. This is the literary equivalent of being kicked in the groin by a Martian, or an anatomically correct troll doll. Ostensibly, it shouldn't exist, but it does. Wallace attended

Amherst and majored in English and philosophy, with a focus on mathematics and logic. He was not, however, very good at mathematics, as he mentions in "Everything and More". In fact, he claims to have done poorly in every mathematics class he had ever taken, except one (which was likely the differential equations class with a Dr. Goris that he mentions). This comes across in his arguments, which are very convoluted and difficult to understand. Consequently, a person who is not good at mathematics has no chance of understanding what they are reading; a person who is good at mathematics, on the other hand, would rapidly become annoyed by what they are reading. An excellent example is his discussion on Zeno's paradox. One way of putting this is that at every given instant an arrow in flight is motionless; if it's motionless at every point in time, it must therefore be stationary. The easiest (modern) way to explain this is that classical speed is undefined at a single point in time, but only over intervals. This is the beginning down a path that leads to differential and integral calculus. Wallace takes page after page to say what I just said in one sentence, but in a highly ornate and incomprehensible way. I'm not saying that this book has no value. It's value to me lies in the odd presentation. Clearly Wallace really likes mathematics, he's just not very good at it. Enthusiasm, for me at least, goes a long way.

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LibraryThing member nostalgebraist

David Foster Wallace was a great writer of fiction. He was not a great writer of popular math exposition, as this book shows.

The main reason I read this book, besides just curiosity about one of the lesser-read Wallace books, was my interest in figuring out a certain infamous scene in Wallace's

wonderful novel Infinite Jest. In that scene, one character (Michael Pemulis) dictates to another a description of a mathematical method, based on the Mean Value Theorem, that he says will simplify the calculations involved in playing a certain complicated wargame. But Pemulis' proposed method does not actually make any mathematical sense. (He states the Mean Value Theorem correctly, but there is no useful way to apply it to the problem he wants to solve.) Ever since reading that scene, I've wondered if this was a mistake on Wallace's part or a deliberate choice intended to cast doubt on Pemulis' mathematical ability. Since Everything and More deals with some of the same sort of math that appeared in that scene (elementary calculus), it seemed like a good place to look for answers about Wallace's own grasp of that material.

Unfortunately, it was. This book is full of errors. A lot of them are just terminological solecisms that general readers won't notice or care about, but there are also some mathematical arguments in the book that are seriously flawed -- some of them much worse, in fact, than Pemulis' argument. (Some of them are wrong in an utterly weird, "only a stoned undergrad at 3 AM could think like this" way, which makes me wonder how on earth they got found their way into the book -- extreme time pressure, maybe?) I'm now forced to conclude that the Mean Value Theorem thing in IJ is not a sly bit of characterization, but simple authorial incompetence.

Everything and More is also very poorly written and organized. There's very little of the usual Wallace charm and cleverness, and a lot of aimless rambling, needless distinctions and clarifications-that-don't-really-clarify. Anyone who reads this book without no knowledge of the relevant math will come out of the experience with the impression that it is incredibly thorny and complicated and that Wallace has done his heroic best to shape it into some popularly presentable form. As it happens, most of the math is actually quite simple, and most of the appearance of complexity here is an artifact of Wallace's style -- the result of inconsequential (or incorrect!) nitpicking and a dizzying, needlessly scattered order of presentation.

It makes me sad to think that there are people out there whose first impression of Wallace will come from this book.

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LibraryThing member fpagan

Weird pure-math "booklet" (of 319 pages!) with no index, no table of contents, no chapter divisions, no section headings, jaunty writing. Yet it's very meaty and absorbing. I wouldn't recommend the culminating account of Cantor's work as the clearest intro to that subject.

LibraryThing member jezzaboogie

A history of infinity, leading through Cantor to Weierstrass' robust definition of functional continuity. (Well I think so anyhow: only a third of the way there so far and this book doesn't feature big on inside sleeve summary or back cover testimonials, thank dog.)

It is absolutely brilliant. This

is isn't pop-science(math) is the usual sense where difficult science(math) is made accessible and interesting to the layman by watered-down analogy. This is a serious dude (English Professor?) turning abstract maths into hardcore language-fun (word plays, conceptual meta-jumps, self-referential statements) without the merest hint of watering anything down. He does it so fluently that one intermittently forgets how amazing it is that he can do this with material that is fucking hard to pin down at the best of times using precise mathematical notation.

Featuring the word "shit" twice so far.
Worth it just for opening chapter's discussion of "abstraction".

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LibraryThing member jjmcgaffey

Magnificent. If you're phobic about mathematics, don't even try - but if you're even mildly interested in the subject, this is a fascinating book. Lots of equations, a lot of acronyms and shorthand expressions (which he does explicitly identify, in glossaries within the text). I suspect the book

would have been half again as long if he hadn't done all the shortening. And - I do enjoy mathematics, and have studied at least some of what he's explaining here (things like Zeno's Paradox) - but I really didn't expect to be laughing as much as I did. One example - a highly convoluted, 11-line sentence, followed by a footnote: "There is really nothing to be done about the preceding sentence except to apologize." He knows his math, and his math history - the concept (or concepts) of infinity is traced from its first appearance among the Greeks up to more or less current thought and applications. He also knows, and enjoys playing with, English. I now want to read Infinite Jest and his essays to see if they're all up to this level. Loved it, will read it again (though probably not soon), want more.

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LibraryThing member andypurshottam

Historical intro to set theory by essayist/novelist is written in idiosyncratic style to appeal to math phobics. Shows set theory created to formalize infinite reasoning needs of analysis. Has an introduction to diagonalization proofs, using |S|

LibraryThing member glowing-fish

Well, David Foster Wallace has an excuse for not making much sense this time.

LibraryThing member br77rino

I fell in love with DFW's writing when I read his preface to some book of collected shorts not by him. I went on and read more, including the first tenth or so of "Infinite Jest." I hadn't realized he was so knowledgeable about math when I came across this book.

He reviews the history of

mathematicians coming to terms with and then embracing infinity. In his own wonderful style.

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LibraryThing member rivkat

This is Wallace at his most far-out, which is far indeed. What you need to know is that Wallace repeatedly refers to this 305-page (not counting endnotes) text as a “booklet,” and that the only chapter heading in the book is labeled “Small But Necessary Forward.” While my ancient math

background wasn’t enough for me to follow very far, I am going to give a copy to my math-geek dad.

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LibraryThing member MathMaverick

An excellent book packed with tons on "Modern Math". I'm not sure this book is for everyone. The material is very deep and requires a good understanding of math as well as the ability to imagine.

LibraryThing member contriver

Meh. An acceptable overview / history of the subject. Only limited amounts of the DFW uniqueness shine through. If you both like DFW and are interested in the math, it's pretty good. If you only like one or neither of those, this will likely not change your mind.

LibraryThing member zzelinski

Couldn't finish it -- the math got too complex. What I did read, though, was awesome! Very well explained and wonderfully staged, each scene led me directly down the path towards infinity.

LibraryThing member tgraettinger

I found it interesting, but hard to read - not just because the content was difficult, but more due to the too-numerous asides made by the author. This was likely a stylistic choice of the author, but I felt it was laziness. With more effort spent trying to craft a readable narrative, the author

would have done a real service to the reader.

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LibraryThing member Eoin

High-wire all the way. More DFW or math in either direction and the thing falls to it's death. If you would like a glimpse of what Real math is like and don't hate Mr. Wallace, this is worth it.

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