Everything and More: A Compact History of Infinity

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Everything and More: A Compact History of Infinity

3.64 of 5 stars 3.64 · rating details · 1,567 ratings · 188 reviews

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 meanin...more

Hardcover, 336 pages

Published October 17th 2003 by W. W. Norton & Company (first published 2003)

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Jul 23, 2007 David rated it 1 of 5 stars

Shelves: mind-numbingly-boring

Love him or hate him, DFW is a prodigious talent. Except for the disturbing "Conversations with Hideous Men" I have found his previous material to be so hilariously, intelligently, on-target that I was willing to overlook a multitude of stylistic transgressions (chiefly, the overly cutesy tone, gratuitous flaunting of the author's erudition, the footnote fetish).

So I was reasonably disposed to like this book and was looking forward to reading it. Sadly, it turns out that this was a case where D...more

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Dec 28, 2011 Tiffany rated it 2 of 5 stars

Shelves: geekature, history, recommendedby-a, math-numbers

I don't know how I feel about this book. It was a math-related book, which is good (Math! Yay! Fun!), but... I just ... It wasn't as good as other math books I've read. I found myself skimming parts, and my brain glazing over at other parts.

This is the first DFW book I've ever read, which may have some impact on my reception of it (Although, come to think of it, there is a DFW article in The New Kings of Nonfiction, which I didn't really have problems with.). I had a friend once, however, (actua...more I don't know how I feel about this book. It was a math-related book, which is good (Math! Yay! Fun!), but... I just ... It wasn't as good as other math books I've read. I found myself skimming parts, and my brain glazing over at other parts.

This is the first DFW book I've ever read, which may have some impact on my reception of it (Although, come to think of it, there is a DFW article in The New Kings of Nonfiction, which I didn't really have problems with.). I had a friend once, however, (actually, the person who gave me this book) who LOVED Wallace, and subsequently wrote like him -- his style and his affinity for footnotes (in every sentence, it sometimes feels like). And at many points, I thought his [DFW's] writing style was somewhat similar to my own (which makes me now have pity for anyone who's ever read anything [e-mail, letter, article, essay, school report...Goodreads review] I've written.). And yet, I sometimes (often) had troubles following him/his style. Plus, then, often his footnotes would be something snarky like "Don't ask," implying that the history behind a certain concept (that wasn't a main focus, but merely a comment in the text) was too complex to cover. Then why bring it up?? Why do I need a footnote telling me not to ask you about a certain convoluted concept? If I wanted more information about something you didn't go in-depth on, I know how to use a library. And again, it sounds like my style of writing, but here's the one important difference: I DON'T WRITE PROFESSIONALLY. And if I did, I wouldn't put comments like those in my published writing.

But I digress. Anyway, his style, not my cup of tea, at least not in this book. I will say, though, that many (most?) of his footnotes were designated "If you're interested," so at least the reader could know to skip/skim if they aren't really all that interested in the topic at hand. But still, his writing (the footnotes, the digressions within the text, the text itself) made the book way more difficult than I think it needed to be. "Slog" is a good word to describe my time with it.

My other major problem with this book is that he says it's for the layman or someone with *some* math classes in school. Now, I know I'm not the smartest person in the world, but I do know *some* math (with it being my minor, and having been a math tutor for 12+ years), and yet I WAS LOST. A LOT. He kind of talks about the challenges of writing a piece that is simple enough for someone without a math background, and yet interesting enough for someone who does have that technical math knowledge; I just know that he lost me a lot (hence the skimming and brain glazing over), which means it was too technical for someone with even some amount of math background. Plus, he gets into REALLY technical math, and a lot of times I couldn't figure out (or forgot) how they related to infinity. (I know they do, but he was just so mired in math, and technical math, and set theory, and on and on, that I forgot that this was all supposed to come back around to the idea of infinity.)

I thought To Infinity and Beyond was a much (MUCH!) better book about infinity. (But even with that, DFW criticizes other "pop culture" math books, saying they gloss over things, or misrepresent things [like Cantor's mental issues and his study of infinity], and I kept wondering if Eli Maor's book was one of those. Damn you, DFW!)(less)

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Nov 05, 2011 Patty added it · review of another edition

Shelves: to-retry

I'm on page 109, and I think that's where I'll stop. It's not that I haven't enjoyed it, I have. In fact it's quite soothing to try to see how many layers of abstraction you can hold in your mind at once. However, I only seem to be able to read 2-5 pages at a time before the soothingness of it puts me to sleep, and my mind really is somewhat math resistant. I've gotten to a point in the book where the equations are just meaningless to me. One of my best friends loved this book intensely, and act...more

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Feb 07, 2009 Matt Evans rated it 3 of 5 stars · review of another edition

I've now read everything that David Foster Wallace published in book form, which became a goal of mine back on 09/15/08 when I heard that he'd hanged himself on 09/12/08. At that time, this book and "Signifying Rappers" were the only two I hadn't yet read. I wouldn't otherwise have read "Everything and More," given that I'm not all that strong a math student.

With that happy preface, let me tell you that "Everything and More: A Compact History of [insert here a lemniscate, the graphic symbol of i...more I've now read everything that David Foster Wallace published in book form, which became a goal of mine back on 09/15/08 when I heard that he'd hanged himself on 09/12/08. At that time, this book and "Signifying Rappers" were the only two I hadn't yet read. I wouldn't otherwise have read "Everything and More," given that I'm not all that strong a math student.

With that happy preface, let me tell you that "Everything and More: A Compact History of [insert here a lemniscate, the graphic symbol of infinity:]" is very technical, and its reader should ideally possess a medium to strong math background. This reader, mathematically anemic at best, did however enjoy the good old DFW rhetorical japes and games and general good times, which are also present in this work. Also, I did enjoy learning the basic rough outlines of such concepts as Zenos's Paradox, Vicious Infinite Regress, number theory, etc. ("Rough outlines" not because DFW doesn't devote considerable rhetorical- and word-count attention to the concepts, but "rough" because so much of it went over my head.)

Here's what the back of the book says, "[DFW:] brings his intellectual ambition and bravura style to the story of how mathematicians have struggled to understand the infinite, from the ancient Greeks to the nineteenth-century mathematical genius Georg Cantor's counterintuitive discovery that there was more than one kind of infinity."

Okay. Not exactly ADD medicine here, but the blurb is at least generally accurate. But not "sexy," which is DFW's operative term (that and synonyms like "eros-laden", "zaftig", etc.) for interesting or exciting concepts. Sexy is this quote from the little booklet's text (which quote will be this review's conclusion):

"The Mentally Ill Mathematician seems now in some ways to be what the Knight Errant, Mortified Saint, Tortured Artist, and Mad Scientist have been for other eras: sort of our Prometheus, the one who goes to forbidden places and returns with gifts we all can use but he alone pays for. That's probably a bit overblown, at least in most cases. (FN2: Although, so is the other, antipodal stereotype of mathematicians as nerdy little bowtied fissiparous creatures. In today's archetypology, the two stereotypes seem to play off each other in important ways.) But Cantor fits the template better than most. And the reasons for this are a lot more interesting than whatever his problems and symptoms were. (FN3: In modern medical terms, it's fairly clear that G.F.L.P. Cantor suffered from manic-depressive illness at a time when nobody knew what this was, and that his polar cycles were aggravated by professional stresses and disappointments, of which Cantor had more than his share. Of course, this makes for less interesting flap copy than Genius Driven Mad By Attempts To Grapple With [the text inserts here a lemniscate:]. The truth, though, is that Cantor's work and its context are so totally interesting and beautiful that there's no need for breathless Prometheusizing of the poor guy's life. The real irony is that the view of [lemniscate:] as some forbidden zone or road to insanity -- which view was very old and powerful and haunted math for 2000+ years -- is precisely what Cantor's own work overturned. Saying that [lemniscate:] drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting.)"

Please recall or here be informed (as wikipedia just informed me) that St. George actually first wounded then tamed and finally slew the dragon. Which of course underscores DFW's point about Georg F.L.P. Cantor first (figuratively) taming then slaying the [lemniscate:].

DFW: requiescat in pace.

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Jan 07, 2012 Miles rated it 2 of 5 stars · review of another edition

Despite Herculean efforts on Wallace's part, to get the most out of this book you really need more math (and more recently) than what I've taken. At least some calculus, probably.

Ostensibly the book's about the history of infinity, which sounds pretty interesting, but what it's really about the history of how infinity as a concept has been treated in mathematics — which is still a fairly interesting-sounding topic, except it turns out that for it to make sense you have to understand a lot of pr...more

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Apr 14, 2011 Nick Black marked it as to-read

Recommended to Nick by: Mykle

DFW's math always seemed rather suspect, and he fucked up a thing or two quite badly in Infinite Jest, but Mykle's adulatory review -- plus sitting out thus far on The Pale King (which is it just me, or is that awfully close to A Pale Fire?), and DFW's surprisingly pedestrian short story from a New Yorker last month, has me craving Wallace. ordered! somewhat distressing that the interminable bore Neal Stephenson did the introduction, but he occasionally manages to crap out something better than...more

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Mar 06, 2011 Fraser Kinnear rated it 4 of 5 stars · review of another edition

Shelves: math

I bought this book despite the strong criticism it got from mathematicians who found pretty egregious mistakes in some of the math. But I'd never read David Foster Wallace before (aside from some of his journalism) and I wanted to try him out.

I suspect the criticism is largely unwarranted - DFW provides enough forewarning that he has "dumbed down" much of the math in order to bridge the gap to the difficult and abstract math he is describing. Doing so comes with the sacrifice of some accuracy....more I bought this book despite the strong criticism it got from mathematicians who found pretty egregious mistakes in some of the math. But I'd never read David Foster Wallace before (aside from some of his journalism) and I wanted to try him out.

I suspect the criticism is largely unwarranted - DFW provides enough forewarning that he has "dumbed down" much of the math in order to bridge the gap to the difficult and abstract math he is describing. Doing so comes with the sacrifice of some accuracy. Richard Feynman once explained that there is no real substitute to getting down and dirty in the math - no amount of summarizing and translation into layman's terms will ever do. So for those who want a complete and 100% correct understanding of these ideas, well, caveat emptor.

Then again, for those who want a complete understanding, none of these kind of books will really do.

DFW keeps a very conversational tone throughout the book - peppering words like "stuff" around concepts like Fourier series and uniform convergence, which helps keep your attention without blunting the fidelity (can you blunt fidelity???) of the explanation. I also really enjoyed his extensive foot-noting, which I understand turns a lot of people off. DFW defended his footnotes in Infinite Jest on Charlie Rose, and I think the defense works very well for this book also:

"There is a way, it seems to me, that reality is fractured right now (at least the reality that I live in) and the difficulty of writing about that reality is that text is very linear, and I am constantly on the lookout for ways to fracture the text that aren't totally disorienting." http://www.charlierose.com/view/inter...

The history of our grasp of infinity from a mathematical perspective isn't linear, so why should the telling of it be? DFW's constant use of IYI (his invented acronym for "if you're interested") allows for the reader to delve deeper into the history, if they're interested.

In this way, DFW writes Everything And More mimics the way that I amble wikipedia. Or perhaps I go too far, the asides are always brief and are seldom interconnected.

I enjoyed it, and I suspect that I'll pick it up again.(less)

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Nov 20, 2010 Akiva rated it 3 of 5 stars

This book has a serious Law of the Excluded Middle problem. Not just technically - he cites LEM (these things always end up abbreviated in typical DFW style) in totally unnecessary cases - but in that the book is neither A nor not A. David Foster Wallace thinks that the development of the mathematical understanding of infinity is deeply interesting and this book is him telling you about it. He's right. It is deeply interesting. The problem is how he decides to tell you about it. And in some ways...more

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Oct 25, 2010 Ben Richmond rated it 3 of 5 stars

Shelves: real-life-man

I’m going to describe the one person I can possibly imagine whom I would recommend this book to. His name is Andy; he was a contemporary of mine during my undergraduate days. Andy was a math major who at one point scheduled (or maybe just invited a bunch of people to?) a talk in a library conference room about how he found math to be beautiful, and in fact in some way divine.
Andy left the study of mathematics after several months teaching remedial algebra in a public school on Chicago’s South...more I’m going to describe the one person I can possibly imagine whom I would recommend this book to. His name is Andy; he was a contemporary of mine during my undergraduate days. Andy was a math major who at one point scheduled (or maybe just invited a bunch of people to?) a talk in a library conference room about how he found math to be beautiful, and in fact in some way divine.
Andy left the study of mathematics after several months teaching remedial algebra in a public school on Chicago’s South Side. I suppose the episode, the most memorable aspect of which revolved around the nickname “Mr. Mayo” (which oddly was bestowed upon him by a student in the hallway who wasn’t in any of his classes), taught him that what he lacked was not mathematical acumen, but rather patience and possibly quite a bit of compassion. As I write this Andy is in seminary.
Which is all to say as I read David Foster Wallace’s Everything And More, I was able to vividly imagine the ideal audience for the work. Conspicuously I was not part of this ideal audience.
The point of this digression, if there is one, is to answer the only “big question” that I really understood as I read Everything, which is: who is this for?
It is a work that, perhaps quixotically and much like Andy in the library conference room, seems to be trying to bring the complex tangle of math’s centuries-long tangle with the concept of infinity out of the dry math classroom environment and into a broader philosophical and historically placed context, for the public good/enjoyment. A celebration of mathematics for all to join. This is a quick and messy definition, that I wouldn’t advise adhering to too closely, lest the book too swiftly be dismissed as an utter and total failure. Because as I tried to convey with my Andy-anecdote, this might be a bit of niche thing. I imagine most people’s interest in and knowledge of calculus won’t be adequate to make this book reach the status of “page-turner.”
Wallace begins in ancient Greece, where the questions are raised, and in his narrative, placed aside until the Renaissance, and not really grasped for another 300 years give or take. The hero of the story is Georg Cantor who lurks in the background until the late 19th century, who eventually comes along, resolves things in a way that confused me (though by this point the dilemma posed by infinity was too obscured by hundreds of years of dramatic advances), and ultimately led to more questions for mathematicians. By all accounts Cantor is a big deal and I believe it, but I couldn’t begin to explain why, or even quote why, due to not really knowing where to find Greek letters on my keyboard.
Is this due to my math background, or is this due to the author? Did this inability to really grasp the material impair my ability to enjoy myself?
Well, as must be obvious at this point, the attraction leading me to this book was to the author, not to the subject, per say. DFW casts a long shadow in the contemporary literature world. His massive masterwork, Infinite Jest, is regarded as one of the most important pieces of (at least) American literature of the last twenty years. He committed suicide in 2008, and his death was probably the first celebrity passing that actually affected me.
His work revolves around a profound unironic enthusiasm, and often characters digress and discuss philosophy for pages. Not that he is ever too dense, often times those very philosophical discussions are followed by a gag, or punctuated with a joke.
Those looking for the same in Everything and More, should be warned that while the book is unmistakably DFW, it is on the subject of infinity viewed through the lens of math. Pure and simple. Conspicuously, while DFW got a degree in modal logic (!), “mathematician” is not on his resume.
So clearly affection for the author may be causing me to spare him the rod of having written a book on a subject that he may not grasp-- at least not well enough to find the terms to explain it to a layman. A colleague of mine found out what I was reading and said that a few legitimate mathematicians had come forward to critique DFW’s work, to point out holes in his retelling of the grand old tale.
Indeed DFW admits that the legitimate mathematician is going to find his explanations either too swift, or too fraught with his idiomatic prose. So he’s painted himself into a corner. “How can the discussion be pitched so that it’s accessible to the neophyte without being dull or annoying to someone who has had a lot of college math?” he asks at the end of the foreword.
Apparently the answer wasn’t giving a lot of biographical or historical context to the mathematicians in question, though each time he did, it was riveting.
Neal Stephenson wrote a foreword for my copy of the book (which supplemented the DFW foreword nicely), and he noted that one could interpret the entire effort of Everything as sort of ostentatious. But Stephenson asked for our charity in reading “one of the other smart kids trying to explain some cool stuff.”
So the book is probably bad journalism. It pains me to say it, but if journalism writes with an audience in mind, and if the author, the author of the foreword, and the reviewer all sort of wonder who could like this book, the odds are it needed a good hard look at the concept (of the book) before proceeding, or at the very least a good stiff edit.
Yet herein lies the lesson. At no point did it feel like DFW was taking a page or section off. His profound love of the subject is catching, even if his comprehension isn’t. It would be easy to dismiss this whole effort as too insular, but DFW’s tone is always to catching, too inviting. I read 300 pages and was enthusiastic whenever I thought the narrator was.
As journalism starts to structure itself to more and more specific audiences, it will become easier and easier to say, “That really doesn’t apply to me,” and go about your day. Already RSS feeds, customizable news aggregators like Google News, and other technologies are making it easier to block out that which we know doesn’t interest us (like 300 page books about not only calculus, but the history of calculus), in favor of that which does.
But the journalist and the science writers who can make you believe you do care, even when you can’t really grasp the point because they show such utter care and diligence are the ones who can buck this trend. Journalism that has the power to wake you up to the complexity of the world, to shake your suppositions, is worth the effort to make, and worth the effort to read.
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Jul 01, 2010 David rated it 3 of 5 stars · review of another edition

I never thought I would find myself engrossed in a book about math, but David Foster Wallace actually makes this history of the philosophy and mechanics of math accessible - and I surround that word with heavy quotation marks - to anyone who can at least engage in, and enjoy, intellectual pretzel twisting. While I glazed over at the parts where equations came into play, there really was enough that didn't depend on them - enough of a tether to history or something I could actually understand - t...more

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May 21, 2010 Jon Stout rated it 4 of 5 stars Recommends it for: technocrats and literary critics

Shelves: philosophy

David Foster Wallace fascinates me as someone who had a philosophical and mathematical education and who in his spare time developed a reputation as a radically innovative fiction writer. That he committed suicide is unbelievably tragic, considering the philosophical and literary insight of which he was capable. In Everything and More, a kind of popular science version of mathematical history, he comes across as a kind of brash, friendly, wise-acreish grad student, with a whiplike genius mind, w...more David Foster Wallace fascinates me as someone who had a philosophical and mathematical education and who in his spare time developed a reputation as a radically innovative fiction writer. That he committed suicide is unbelievably tragic, considering the philosophical and literary insight of which he was capable. In Everything and More, a kind of popular science version of mathematical history, he comes across as a kind of brash, friendly, wise-acreish grad student, with a whiplike genius mind, who is nonetheless patient enough to explain everything.

Infinity is a broad enough topic to pull in the history of mathematics back to Pythagoras and the paradoxes of Zeno, the history of philosophy behind the mathematics, as well as the crisis in the foundations of mathematics in the twentieth century (problems of self-reference, Godel on incompleteness). He ties this together in a narrative which not only pulls in a lot historically, but also makes it clear mathematically.

His math discussions were patient and understandable, even though they stretched me to recall the differential equations and number theory on which I maxed out (and overdrew) in college. There were places where I was swamped, such as the discussion of infinite series. Wallace says numbers (such as Pi and the square root of 2) can be defined in terms of infinite series, but I thought that number was a far more primitive concept than infinite series.

I learned something about infinity, such as that there are different kinds of infinity. There is Aleph Null, which is the infinity of the countable numbers (1, 2, 3, …), which is strangely enough the same when rational numbers are added in (ratios of integers, or numbers with repeating decimals). Aleph Null is also the same infinity as odd numbers, or as primes, which you would think would be fewer than countable numbers.

But there are also infinities infinitely larger than Aleph Null, such as when one adds to the countable numbers the irrational numbers (non-repeating decimals) such as Pi and the square root of 2. And one can prove all sorts of things about these distinct kinds of infinity.

The moral of the story is that one can learn to deal with things that boggle the mind. Just as in geometry we can deal with lines which stretch out to an infinity we cannot imagine, similarly we can learn to handle other kinds of infinity. And we can also learn how to handle the paradoxes that the world presents to us, such as that there are truths we cannot prove.
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Feb 28, 2010 Mark rated it 3 of 5 stars

I am daunted by this book.

First of all, the beautiful beautiful words! I have just finished something (else: Chomsky) where I crossed out acres of text to chop it down to syntactic ligaments, only. You can't do that with THIS book! Every Word Matters; it is a thing of beauty.

However, now half way through the book, I am unable to appreciate a big part of the thesis, which has to do with the Fundamental Theorem of Calculus which takes an integral by limiting a little slice of incremental area do...more I am daunted by this book.

First of all, the beautiful beautiful words! I have just finished something (else: Chomsky) where I crossed out acres of text to chop it down to syntactic ligaments, only. You can't do that with THIS book! Every Word Matters; it is a thing of beauty.

However, now half way through the book, I am unable to appreciate a big part of the thesis, which has to do with the Fundamental Theorem of Calculus which takes an integral by limiting a little slice of incremental area down smaller and smaller as the d(x) approaches zero. The problem is that DFW advertises this as a very big paradox, that for some time (until our hero Cantor saves the day by slaying infinity) calculus was simultaneously kicking ass, and built upon a foundation of sand. (There's a beautiful passage wherein he chronicles the gleeful religious response to this. You'll well imagine that finding that Holy Mathematics is founded on Mere Faith is quite a hoot if you're in divinity school! I cannot begin to do this part justice; you must imagine yourselves enraptured (by the writing.))

But, as I said, I'm not getting it. Either I am too much the engineer, and not bothered at the distinction between the values of (~0) and (0,dammit), or maybe I have too LITTLE math to appreciate the beauty of the dilemma.

In any event, DFW is a hero of mine, and I am distraught to begin to worry that I will lose a bit of adoration for him as this book goes down.

Well, now I'm done. I put in some effort to ensure I "got" parts of it. Lots of work with not too much reward. Areas of special interest: Dedekind's proof of irrational numbers, and Cantor's argument that # rationals >> # reals. These were ok, and good to challenge my brain, but it's still the language I love. Here's an example:

"Here I perceive the reason why one has to regard the rational, irrational and complex numbers as being just as thoroughly existent as the finite complex integers.

This last and clearest sentence is a tiny blown kiss to L. Kronecker."

...how sweet! Those cute mathematicians, with their little trysts! The beauty of DFW is that he can extract the humanity from a footnote in a proof in a math text. Way to go, David.(less)

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Dec 10, 2009 Patdmac7 rated it 5 of 5 stars

'Poets do not go mad; but chess players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not attacking logic: I only sy that this danger does lie in logic, not in imagination.' - G.K. Chesterton, 6

The Mentally Ill Mathematician seems now in some ways to be what the Knight Errant, Mortified Saint, Tortured Artist, and Mad Scientist have been for other eras: sort of our Prometheus, the one who goes to forbidden places and returns with gifts we all can use but he alon...more

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Jan 15, 2011 Shannon marked it as to-read · review of another edition

Shelves: want-to-own, non-fiction, dfw

I think I'm going to have to return this to the library and try to read it at another time. I can't read any of Wallace's work right now, it makes me really sad. Because when I've read it in the past I've always been like: THIS IS SO BRILLIANT and I think of how amazing it is that someone so genius is alive. But.. he's not. Anymore. I realize whining about his death is not a review. This is a review placeholder.

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Dec 15, 2010 dead letter office rated it 2 of 5 stars

I really wanted to like this, since I like the idea of it so much: a preternaturally fearless and curious outsider explaining the world of mathematics and mathematical philosophy to other outsiders.

DFW's at his best when he's talking about the philosophy (or is it that I'm out of my depth there...), but his mathematics is in places disconcertingly shaky, and he seems too ready to abandon mathematical carefulness for the sake of literary fireworks. And yes, I find his so-called "conversational"...more

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Oct 12, 2012 Vanessa rated it 3 of 5 stars

Shelves: physics-for-laypeople

First, a warning: For the love of god, if your interest in Everything and More is primarily as a fan of the writing of David Foster Wallace then you should NOT read this book. If you are, like I was, a fan of the writing of David Foster Wallace with a quite strong interest in things like science, physics, mathematics, and the history of ideas, even you should really think hard about your grounding in mathematics before reading this book.

Did I learn stuff? Yes. Did I understand everything I read...more

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Sep 17, 2011 the review man rated it 3 of 5 stars

Shelves: math-and-stats

Everything and More was a strange book. Strange in its ambitions (to provide a brief history of infinity up to and including Georg Cantor), strange in its writing style (David Foster Wallace isn't exactly the Hemingway of the 21st century), strange in its prerequisites (i.e., the book seems to be designed for people who already know the math he explains).

I didn't enjoy Everything and More. Sure, it was an ambitious project, but I really didn't see the point. The book can't make up its mind: is i...more

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Jan 12, 2013 Prachi Gauriar rated it 2 of 5 stars

This is a book that couldn't decide who its audience was. The explanations are too detailed for the pop-math crowd, but too lacking in rigor for hardcore math folks. I'm somewhere in the middle; I have a pretty strong math background (lots of calculus, number theory, abstract algebra, set theory, etc. in college), but I'm also willing to let things go for a better narrative. This book's narrative is pretty weak. DFW's stylistic idiosyncrasies—copious footnotes and non-standard abbreviations, ult...more

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Dec 08, 2009 Isa rated it 4 of 5 stars

I read a german translation which is marketed as a a biography of Cantor, and that really does not do justice to the book -it really is more of a biography of the modern idea of the mathematical infinite, with a good deal of tangential mathematical history thrown into the package. If you actually are a mathematician and have not heard much math history definitely a recommended read, as it gives some insight into how the notions we learned to take for granted actually could have developped in oth...more

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Jun 15, 2010 Rob rated it 3 of 5 stars

A fun experiment. The noted author DFW attempted to write a treatise on a highly technical subject (the development of Cantor's mathematics of transfinite numbers and abstract set theory) and popularize it. While initially propelled along with DFW's arsenal of post-modern tools and tricks, it seemed to lose some of this steam, and in fact become somewhat rushed toward the end in a case of what seemed (and in fact was confirmed in a footnoted aside to the reader) that DFW had let the pacing of th...more

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Apr 13, 2011 Mykle rated it 5 of 5 stars

HERE IS WHY THIS BOOK IS AWESOME:

This book addresses three related enthusiasms: for mathematics itself, for math history (the lives of the mathematicians & the historical chain of deduction that gave us the math of today) and for DFW's high school math teacher (who sounds totally amazing). A book about any one of these might be more straightforward but DFW conflates the three in a breezy, entertaining mess. The operating concept is the history of infinity as a topic that has driven mathemati...more

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Feb 08, 2011 Rob rated it 3 of 5 stars

Shelves: math-and-stats, library-books, 2011

Quick summary: Navigating Wallace's tortuous prose is like eating a glass jawbreaker with a wisdom center: if you can tough it out through the pain, not to mention considerable loss of blood, you will discover something beautiful and profound. If you enjoy beauty and profundity in mathematics, at least. If you aren’t, but are still curious about Georg Cantor’s work showing that not all infinities are created equal, the essentials of Everything and More are summarized far more succinctly and acce...more

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Aug 22, 2012 Albert rated it 4 of 5 stars

Shelves: nonfiction, math, history

Frankly, I'm surprised I finished this book. I sort of saw it as part of my current project to work my way up to reading Infinite Jest . (Which is currently sitting on my dining room table. I'm afraid to shelve it lest the lack of a visual reminder will make me forget that I have it. It is also my hope that visitors will be impressed by the sight of the thing.)

Anyway, I figured I would read a bit of Everything and More, see what it's like, and skim through the rest when the math got too hairy....more Frankly, I'm surprised I finished this book. I sort of saw it as part of my current project to work my way up to reading Infinite Jest . (Which is currently sitting on my dining room table. I'm afraid to shelve it lest the lack of a visual reminder will make me forget that I have it. It is also my hope that visitors will be impressed by the sight of the thing.)

Anyway, I figured I would read a bit of Everything and More, see what it's like, and skim through the rest when the math got too hairy. Now, I'm not claiming that I understood all of the math and that it didn't get hairy, or that I never skimmed through any of it at all, but I did follow the general gist for most of the way, or at least enough that I never felt like slamming the book closed and hurling it across the room.

This I credit to DFW's writing style. I don't think I've ever read anything where the text was so aware of its being read. There are constantly little asides and apologies (many in Wallace's trademark footnotes) about how difficult a particular section is, how you might want to re-read this or that paragraph, how it's all going to be OK in the end. These constant conversational reassurances do a lot to encourage the reader (me, at least) to keep going, despite the difficult math.

And there is a suspense to it all too. Cantor is mentioned near the beginning and is set up to be the Hero of the Story, the one whose theories are the ultimate culmination of everything I'm reading, and I genuinely felt the urge to know what Cantor did, like wanting to find out who the killer is in a mystery novel. Wallace does a good job of reminding us how each theory through history will be relevant to Cantor's transfinite numbers, while making each theory interesting to learn about on its own. And while the actual proofs and formulae are explained well, I found the most enjoyment in the connective tissue about the like societal and cultural and historical contexts around each discovery, e.g. the geometric rigidity of the Greeks, the need to develop and accept infinitesimals in physics and science during the time of Newton and Leibniz, &c. I actually wish he had focussed on those contexts more, and I think he probably could have written a thousand-page book (it amazes me how much research must have gone into this as is). I would probably have still read it all.(less)

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Apr 19, 2011 Steev Hise rated it 4 of 5 stars · review of another edition

Shelves: own-it

Well, as you might expect, this is great writing, at least the parts of it that are plain english. I hesitated to read it because it was, well, a math book, and the 7 semesters of college math i had to take was enough to last me a lifetime. Although I must say that if I had math teachers like David Foster Wallace, I probably would have liked it more. So anyway the book was a gift but sat on my shelf for a few months but I eventually sat down and read it. It was worth reading, but... I doubt it w...more

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Jun 01, 2012 Nate rated it 3 of 5 stars

Shelves: read-2012-cycle

So I definitely learned a whole bunch that I'm still trying to absorb but its like 2am as I'm writing this so you'll have to forgive me. Very idiomatic at some points and honestly it felt very disordered. More or less it goes chronologically but even Wallace himself goes to pains to discuss how fractured and disordered the whole text tends to get. A lot of times there's a whole bunch "we're just going to skip..." kind of talk which just gives me a sense of unease even though I know my overly lit...more So I definitely learned a whole bunch that I'm still trying to absorb but its like 2am as I'm writing this so you'll have to forgive me. Very idiomatic at some points and honestly it felt very disordered. More or less it goes chronologically but even Wallace himself goes to pains to discuss how fractured and disordered the whole text tends to get. A lot of times there's a whole bunch "we're just going to skip..." kind of talk which just gives me a sense of unease even though I know my overly literary mind wouldn't be able to handle it. As he nota benes several times there are several more technical texts available but I wish this was a little more narrative and straight forward.

That said if you have a good grasp for Wallace's use of language you should be to get through it. There are definitely rough spots were I'm forgetting what some abreviation is or where things are exasperatingly unclear but usually the concepts end up making sense. I suppose if I was more concerned with the whole "rigorous proof" stuff I would be more worried about the small things making sense, but again I'm not a math person and I'm trying to get the big ideas and let my memory of the little stuff fill in from there.

The last ten or twelve pages were amazing if that's not too strong. Just the idea that there are two huge pieces (the Continuum Hypothesis and the ZFP axiomatic rules) that are largely unprovable and provide huge gaps is crazy to think about. It reminds me of something Stephen Hawking said in regards to a Unified Theory of Gravity and Quantum Mechanics saying that basically there is no unified theory and if there is it would be impossible to prove or disprove.

I want to give it four stars but it's too clunky and slow in some parts. So I'll give it three and see how long I meditate on it to potentially change that rating...

Initial Reactions about mid-way through:
From what I've read so far you need to be about as comfortable with Wallace's syntax as you do some calculus mathematics. Having taken Calculus I three times (twice in college, once in high school) and having read parts or all of a number of Wallace's book I'm very comfortable with the digressions and idiosyncratic language uses and footnote fetishes. I just finished reading "Zero: the biography of a dangerous Idea" and I would recommend this to non-math-brain type people. Very narrative and much more layman friendly. (less)

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Jun 26, 2011 Peter rated it 1 of 5 stars · review of another edition

Shelves: popular-science, history, math-general, read-in-2011

This book relates, or attempts to relate, how the topic of infinity was treated in different eras. These eras include ancient Greece (e.g., Zeno's paradoxes); the 17th century, when Newton and Leibniz developed calculus; and the period from the mid-19th to the early 20th century, when Georg Cantor and others developed new foundations for the concept of infinity (as well as for set theory and indeed for all of modern mathematics).

The book tries to present its complex subject matter in a conversat...more

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Jan 23, 2011 Bill added it

I hadn't heard of this book until my good friend Dave (the math man) recommended it to me.

I would love to recommend this book to more people, because it's got that characteristic DFW apprehension of complexity and truth to it, plus the wide ranging references to everything. However, I knew the reals vs. the integers vs. a hole in the ground going in, and I still don't understand his description of Cantor's proof of the existence of transfinite numbers.

Anyway, I ate this book up, whereas I still...more

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Jun 08, 2010 Koz rated it 3 of 5 stars

All infinities are equal, but some infinities are more equal than others.

This "booklet" as DFW has so termed it (I suppose only he could consider a 300+ page book worthy of such a diminutive suffix) is so full of math jargon and ideas, that I did have a hard time navigating it (although I was forewarned in advance, so I have no right to complain about it). The parts of it that were most interesting to me (the non-math, historical parts) were the parts that DFW was consciously avoiding delving in...more

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Jul 25, 2009 Pat rated it 1 of 5 stars

I don't know why, maybe it's his three word name and the fact everyone seemed broken up when he died, but I figured he was some eminent figure of literature. I didn't realize he was some snarky NPR dick in the McSweeny's mold. This guy is WAY out of his league in writing a book on high level math, and from the ugly mess of footnotes, cutesy abbreviations that waste more time in the looking up than they save in the reading the non sequitur jokey jokes about people's names and how hard math is, an...more

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Feb 11, 2012 Trevor rated it 5 of 5 stars · review of another edition

If one approaches this expecting a primer on Cantor's work with cardinals and ordinals, naive set theory or the CH will surely be disappointed. Those approaching this book that way should feel slightly silly -though Wallace does have a history in propositional calculus (cf. Fate Time and Language: An Essay on Free Will)- the proposed depth of subject matter does not lend itself to elucidation by a fiction writer who self confesses his own failures in most formal mathematics courses. If instead t...more If one approaches this expecting a primer on Cantor's work with cardinals and ordinals, naive set theory or the CH will surely be disappointed. Those approaching this book that way should feel slightly silly -though Wallace does have a history in propositional calculus (cf. Fate Time and Language: An Essay on Free Will)- the proposed depth of subject matter does not lend itself to elucidation by a fiction writer who self confesses his own failures in most formal mathematics courses. If instead this book is approached as a dialogue with an incredible mind on a fascinating topic whose depth of understanding is cursory at best one will be pleasantly surprised.

Hopefully the above paragraph and my borderline inability to objectively talk about David Foster Wallace will not preclude a serious interpretation of my opining. An interesting trip through the thoughts and musings of one of our generation's most gifted writers, Everything and More is engaging and entertaining. Wallace's conversational tone creates a welcoming environment for intellectual inquiry - not lecturing at but discussing with the reader - often I felt like he was bouncing ideas off the reader. He does justice to the subject matter and provides a wide scope of mathematical inquiry dating back to Zeno's paradoxes and bringing the reader on a interesting journey up to the 20th century.

This book has issues as well. At times the focus is scattered, the prose will lag and some topics are rehashed. Those not already familiar with Wallace's writing will find the verbosity unnecessary and borderline pretentious. There are too many mathematical fiddly bits as Wallace overcomplicates simple issues (e.g. "The Dreaded Constant of Integration") which often just reflect a bumpy ride through Introductory Calculus in college while quickly glossing over more advanced concepts with little or no justification (i.e. the nonlinear aspect of Cantor's mapping), forcing readers to take his word not follow his progression. However if one understands this is a mathematical dilettante's inspired inquires into infinity this will be a great read.(less)

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About David Foster Wallace

David Foster Wallace worked surprising turns on nearly everything: novels, journalism, vacation. His life was an information hunt, collecting hows and whys. "I received 500,000 discrete bits of information today," he once said, "of which maybe 25 are important. My job is to make some sense of it." He wanted to write "stuff about what it feels like to live. Instead of being a relief from what it fe...more

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“Maybe even more important than the D.B.P. [Divine Brotherhood of Pythagoras], ∞-wise is the protomystic Parmenides of Elea (c.515-? BCE), not only because of his distinction between the 'Way of Truth' and 'Way of Seeing' framed the terms of Greek metaphysics and (again) influenced Plato, but because Parmenides' #1 student and defender was the aforementioned Zeno, the most fiendishly clever and upsetting philosopher ever (who can be seen actually kicking Socrates' ass, argumentatively speaking, in Plato's Parmenides).” — 1 person liked it

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