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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 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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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 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.

30 review for Everything and More: A Compact History of Infinity

  1. 5 out of 5

    BlackOxford

    Thinking Impossibly It was the Greeks who discovered that numbers, and therefore mathematics, had only the most tenuous connection with the world in which we live. Numbers constitute a separate order of existence. The number 5 for example has no connection with the five apples that might be sitting on my kitchen table, or with the age of my youngest relative. The number 5 is something all on its own. It is constructed out of other numbers, which are made up of other numbers that may in turn be co Thinking Impossibly It was the Greeks who discovered that numbers, and therefore mathematics, had only the most tenuous connection with the world in which we live. Numbers constitute a separate order of existence. The number 5 for example has no connection with the five apples that might be sitting on my kitchen table, or with the age of my youngest relative. The number 5 is something all on its own. It is constructed out of other numbers, which are made up of other numbers that may in turn be constructed using the number 5. Mathematics, in other words, is a completely self-contained and isolated world we make up. No one was aware of this quite separate world before the Greeks stumbled across it. They were, rightly, in awe of its implications. The otherworldliness of mathematics suggested an unnaturalness, indeed a supernaturalness, that demanded religious veneration. Mathematics seemed to literally reveal things that were unknowable in any other way. Numbers must be divine, they thought. Numbers were perfect. What we experienced outside of mathematics were imperfect approximations or distorted reflection of numbers. Within this religion of numbers, only two heresies were recognised: zero and infinity. These were demons which had no place in either the divine or the divine ‘word’ of mathematics. The theological prejudice of the Greeks was tempered a bit in late antiquity. As mathematics inched its way from geometry to algebra, zero was recognised as a useful addition to mathematical doctrine - much like free will later became essential in strict Calvinism to motivate virtue. Zero seemed real enough since it was possible to point to an empty basket of fruit as a purported proof of its existence. But even today, there is debate about whether zero is a number or merely a digit which is useful in mathematical expression - something like a decimal point for example. Infinity, however, is a different matter altogether. Although infinity is an essential concept in modern mathematics, there is no way to throw shade about what it is. Infinity can’t be pointed to nor represented except by symbols for something that is entirely beyond anyone’s experience. As Wallace’s title so concisely says, infinity is more than everything there is - more than the number of gluons, muons, bosons, and all other elementary particles in the entire universe, for example. And the distance of infinity from any reality we know only increases when we recognise that there are many ‘orders’ of infinity - infinities that are more or less than other infinities. These higher orders of infinity weren’t discovered until the 19th century. And we appear still to have resisted the implications of these discoveries in the same way that the Pythagoreans did by keeping the indeterminacy of the infinitely long decimal expression of π, the relation between the circumference and the diameter of a circle, as a cultic secret which might undermine faith in mathematics. Infinity for them meant ‘mess.’ And infinity today, although less of a mess, is still very messy indeed about what it implies. Wallace quotes the great German mathematician, David Hilbert, approvingly: “The infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.” Infinity is an abstraction, the ultimate mathematical abstraction. But an abstraction of what? No one has ever seen an infinitely full basket of anything in order to make such an abstraction. No, infinity is an abstraction from a system of numbers, which themselves are supposedly abstractions. It is at this point that the ultimate revelation of mathematics takes place: numbers are indeed abstractions but abstractions of each other not of some experience of baskets of various items. Numbers produce each other; they have no existence except in their relationship with each other. 2 + 2 = 4 is not an inductive generalisation of market experience of baskets and their contents; it is an entirely intellectual proposition/discovery/definition. Which of these you choose to describe infinity is a reflection of one’s already established metaphysical position. It fits with and confirms them all. Here’s the thing: infinity shows that the world created by mathematics has only an obscure and unreliable connection to our experience. This applies not just to the infinite in all its manifestations but also to the number 5 and its colleagues and associates. Like infinity, no one has ever experienced the number 5, or the way it interacts with other numbers to produce itself or yet further numbers. If you doubt this, just try to provide a precise statement of, say, the square root of 5. Numbers don’t cut the world at its joints. Sometimes they don’t even know their own joints. As Wallace summarises the situation: “... mathematical truths are certain and universal precisely because they have nothing to do with the world.” And the revelations generated by infinity are not limited to mathematics; they extend to that more general realm of which mathematics is a part: language. Wallace nails this too: “... the abstract math that’s banished superstition and ignorance and unreason and birthed the modern world is also the abstract math that is shot through with unreason and paradox and conundrum and has, as it were, been trying to tie its shoes on the run ever since the beginning of its status as a real language.” Mathematics is the most precise language we have. Yet, ultimately it doesn’t know what it’s talking about, except itself. None of this means that mathematics, or language in general, isn’t immensely useful. Of course it is; but for rather complex and often mysterious reasons. The revelation of infinity is simply that mathematics is not reality. Nor is any other language. Like all language, mathematics can be beautiful, and compelling, and inspirational. But it is never the way the world is. Confusion about this simple fact is something that human beings seem to have a great deal of trouble with. Language especially political language, easily reverts to religion (and vice-versa). Wallace’s little book is appropriate therapy for reducing this confusion. And by the way, Neal Stephenson’s introduction alone is worth the price of admission.

  2. 4 out of 5

    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 ca 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.

  3. 4 out of 5

    Edward

    I never intended to read this one, given that it's almost universally panned. But I found a hardback copy for sale for a literal dollar, and sometimes a bargain of that magnitude can feel strangely like divine providence... The subject is perhaps DFW's most incongruous since Signifying Rappers, but you have to give him credit for the commitment: this is a thoroughly researched book, and the effort needed to put this together must have been immense, especially for a non-expert. But the problem he I never intended to read this one, given that it's almost universally panned. But I found a hardback copy for sale for a literal dollar, and sometimes a bargain of that magnitude can feel strangely like divine providence... The subject is perhaps DFW's most incongruous since Signifying Rappers, but you have to give him credit for the commitment: this is a thoroughly researched book, and the effort needed to put this together must have been immense, especially for a non-expert. But the problem here is that the author's writing style is totally at odds with the subject matter. DFW as a nonfiction writer is at his most compelling when exploring hidden facets of mundane things. He uses frequent digressions and footnotes to create complexity, and he uses complex language to frame simple concepts. This creates a sort of fervent energy, which (since there is no risk of losing the reader on the subject matter) allows him to generate interest on the strength of his voice alone. While this approach works well when writing about something as quotidian as a concert or sporting event, it is misapplied to the already very complex subjects tackled in Everything And More. DFW tries earnestly to explain each concept, but he constantly gets in his own way, offering branching digressions where they are not needed, and serving only to obscure the core narrative or point, making the whole thing more difficult to understand, and less enjoyable. What he needed to do is rein himself in; simplify; focus on clarity and the logical organisation of his ideas.

  4. 5 out of 5

    Mykle

    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 mathematician 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 mathematicians nuts. The designated hero of the story is Gregory Cantor, but you hardly even see him until the last chapter. The rest is foreshadowing & background material & lots and lots (lots!) of math. Lovers of DFW's prose couldn't ever find a purer source of it. I was constantly laughing at footnotes, loving the intertwine of math and history, enjoyed all the ways he bent the conventions of mathematical writing to the weird shape of his brain. If you like DFW but have been putting this one off, this really is not the one to put off. His stated goal is to make a bunch of boring math more interesting and to walk you through the hard parts. I am probably his ideal reader: an interested and smart yet lazy & unconcerned person who hasn't thought about infinity lately. My measure of a good book is how much it makes me think, and this book gets five starts for reminding me that Math is a planet and not just a multi-tool. And for succeeding in highlighting that the paradoxical nature of infinity is hiding right behind all the math-tricks I learned in high school, had anyone ever pointed them out to me or had I ever bothered to look. (I recall the opposite: we were encouraged not to go there.) The nature of the infinitely large and the infinitely small has felt, at least for a few days, like a metaphor for all sorts of other failures of logic and rationality. Likewise, the concept of a discrete set vs. a continuum is ably and interestingly highlighted here. The many ways in which it seems all of geometry and all of arithmetic are non-identical conjoined twins, even though that distinction divides math history into two warring camps, is suitably made deep. My appetite for understanding is bolstered. Infinity is fun! I have to admit my main discouragement in following the math presented here is that I can't seem to summon the sense of dread and confusion that comes from, for instance, asserting that 9.999... repeating forever is equal to 10. Maybe because I didn't have DFW's high school math teacher, I find I'm blasé about infinity in a way that I gather would appall most of the mathematicians who have grappled with the concepts. In a sense, I just don't care. And so many different ways of talking about the problems of infinity and discontinuity, from Zeno up to Cantor, as presented by DFW, really do feel like a long series of restatements of the obvious: that infinity is a paradox math can't ever straighten out, but if you don't worry too hard it's actually present everywhere and quite handy. A sad truth this book drives home, once again, is that high school Math is too often taught -- was taught to me, even in "Honors" math courses -- as Computation: come, kids, and learn about these nifty, cryptic, useful symbolic systems we found over here on this bookshelf! Do some drills, get some practice using them to solve certain kinds of problems, and just maybe (via the dreaded Word Problems) develop some intuition about which of these solutions might apply to which of your upcoming future questions. Wheras Math, as understood by mathematicians (such as DFW's amazing-sounding HS math teacher) is more like another planet -- an actual landscape, a real thing that exists and can be perceived, initially by our intuitions (i.e. that two grapes and two oranges are similar in the sense that there are two of them, and therefore "twoness" exists and can be known, as can the nesses of other integers) and then later by deducing from just those truths plus our intuitions, just as astrophysicists can know the likely orbits of habitable planets in far-off galaxies. There is this incredible detail to the mathematical landscape, and the people who discovered it were real explorers. This version of Math relates to mere Computation in about the same way that the study of physics relates to auto shop. But efforts to base grade school mathematical education in intuition of mathematical truths instead of computation drills (see: New Math) are constantly met with deep suspicion by all the parents and administrators who themselves only learned Computation and don't get the difference. So DFW lucked out there. (One thesis of Neal Stephenson's introduction is that this was a direct result of DFW growing up in a midwest college town, overpopulated with humble degreed braniacs who did things like teach high school math. Whereas I -- in defense of my own quite likable Honors Math teacher -- grew up in Silicon Valley, a society fairly fixated on Computation for Computation's sake.) Which in the end means that, to me, Cantor's diagonal proof about the rational number set & subsequent branding of the real number set as a higher order of infinity seems like much ado about nothing, just another rephrasing of the fact that the latter is continuous and the former is not, which means that the former is composed of numbers and the latter of spaces containing numbers, which really doesn't seem so "hard" to me, but i'm totally willing to accept that I'm just missing something. Perhaps this is the inevitable result of an education in Computation of math instead of Comprehension of it: I'm too quick to discount the divine & take the rest for granted. HERE IS WHY THIS BOOK SUCKS: I had a big objection to Infinite Jest based on one mathematical footnote DFW gave which convinced me his grasp of mathematics was not all he thought it was. I must look up and revisit that, because this book really thoroougly convinces me that he knew way more about Math than I ever will. Reading it, I have not just been entertained by a whole bunch of chaotic, burbling DFW-prose; I have also come to believe that I learned something. However, there are quite a few Real Mathematicians who would dispute that. This book was not well-reviewed by mathematicians, in two senses First, it seems not enough of them were asked to review the manuscript for errors before publication. Second, upon publication, many of them found the math to be full of holes. Here is probably the most charitable review in this vein; Here is one that really slides the knife in. I will not get into them. Suffice it to say that I have two warring concepts of DFW: one is True Genius, the other is Bullshitter In Genius Clothing. Reading the book, I was lured back to the Genius side. But I felt a necessity to check the facts, and when I did -- just like with Infinite Jest -- the odor of Bullshit again became detectable. Mathematicians, of course, are just the sort of fun-free jerks who would be anal enough to poke holes in a lyrical work of math fantasy that the rest of us are trying to enjoy. How you feel about that is a really important question. Please take a moment to ponder it; it is pertinent across the entire Popular Science section of your local bookstore. The math-reviewers don't hesitate to label DFW a "fiction writer" although his best work IMHO is journalism. But yes, he writes to entertain. This book is entertaining. And Popular Science, taken as a genre -- with Popular Math, its more recent sub-genre -- strives to entertain. That's how it gets Popular. Publishers put these books out to sell them, and the idea of DFW writing a treatise on the history of infinity had to sound good in the boardroom. He wrote something -- apparently something a bit more erudite and symbol-encrusted than they were hoping -- but they printed it anyway. It seemed entertaining enough. Print it! Sell it! And that's fine for fiction, but this book purports to relay mathematical and historical fact. In such a book, facts should be checked and then double-checked -- that is, if the book is really striving to educate. It would not have been hard AT ALL. But, if you believe science is a decorative art and history is "true stories", it's not much of a stretch to consider Mathematics a flexible world of witchcraft akin to that found in Harry Potter books. Can you tell how much that offends me? It really does. This book, brilliant as it is, comes across as a first draft, despite at least one mention of a previous, even more chaotic draft, and despite what undoubtedly must have been a fair amount of research. Then again, he's faulted by some for not researching better; for not having read more of the available research on Cantor, for instance -- recall that Gregory Cantor is the purported star of this book, and DFW screws up certain facts about his life. Meanwhile, an extremely mathy-looking organizational scheme is invented on the fly for the sole purpose of making the book seem more organized than it is. In a word: sloppy. DFW was a writer who's so talented at rhetoric, forming excellent sentences and entertaining voices, and also with a certain talent for bedazzling us with concepts from math, philosophy and tennis, that he could just ramble on about anything he thought was really interesting and sell the first draft to a major publisher. He was absolutely brilliant at sounding brilliant. But I keep on catching him trying to sound erudite without checking his facts, and it keeps eroding my faith in him.

  5. 5 out of 5

    ☘Misericordia☘ ⚡ϟ⚡⛈⚡☁ ❇️❤❣

    Q: To me Everything and More reads, rather, as a discourse from a green, gridded prairie heaven, where irony-free people who’ve been educated to a turn in those prairie schoolhouses and great-but-unpretentious universities sit around their dinner tables buttering sweet corn, drinking iced tea, and patiently trying to explain even the most recondite mysteries of the universe, out of a conviction that the world must be amenable to human understanding and that if you can understand something, you ca Q: To me Everything and More reads, rather, as a discourse from a green, gridded prairie heaven, where irony-free people who’ve been educated to a turn in those prairie schoolhouses and great-but-unpretentious universities sit around their dinner tables buttering sweet corn, drinking iced tea, and patiently trying to explain even the most recondite mysteries of the universe, out of a conviction that the world must be amenable to human understanding and that if you can understand something, you can explain it in words: fancy words if that helps, plain words if possible. But in any case you can reach out to other minds through that medium of words and make a connection. (c) Q: Here is a quotation from G. K. Chesterton: “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 say that this danger does lie in logic, not in imagination.” Here also is a snippet from the flap copy for a recent pop bio of Cantor: “In the late nineteenth century, an extraordinary mathematician languished in an asylum. . . . The closer he came to the answers he sought, the further away they seemed. Eventually it drove him mad, as it had mathematicians before him.” (c) Well, this doesn't seem to be 100% true. Even though mathematicians do often get a tad odd... Q: 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. (c) Q: And of course since mathematics is a totally abstract language, one whose lack of specific real-world referents is supposed to yield maximal hygiene, its paradoxes and conundra are much more of a problem. Meaning math has to really deal with them instead of just putting them in the back of its mind once the alarm goes off. Some dilemmas can be handled legalistically, so to speak, by definition and stipulation. (c) Q: The real irony is that the view of ∞ 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. (c) Oh, boy! The dictionary was here: Q: ...the other, antipodal stereotype of mathematicians as nerdy little bowtied fissiparous creatures.(с) Q: And at what point do the questions get so abstract and the distinctions so fine and the cephalalgia so bad that we simply can’t handle thinking about any of it anymore? (c) Q: The source of this pernicious myth is Aristotle, who is in certain respects the villain of our whole Story (c)

  6. 4 out of 5

    Usha

    I love David Foster Wallace, however this book was a flop. The writing is good but it fails in delivery. It was not an enjoyable read.

  7. 5 out of 5

    Matt Evans

    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 ∞" is very technical, and its reader should ideall 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 ∞" 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 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 ∞ 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 ∞ 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 ∞. DFW: requiescat in pace.

  8. 4 out of 5

    Steev Hise

    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 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 will be my favorite DFW book ( so far Infinite Jest is the only other one I've read - I like it much more). It's just lots of slogging through a subject that has no real bearing on anything in my life and is also not that entertaining other than the 5% of it that is Wallace saying hilarious little things in footnotes, for instance that Kurt Gödel is the Dark Prince of math. It's alluring in a geeky way but that's about the extent of it. It doesn't make me wiser about life, or help me be a better person, or a better anything else that I am, and it wasn't a whole lot of fun. Those are my criteria for reading a book. But I will give this one 4 stars because I think Wallace did probably about the best job possible of doing what he set out to do. But you can pretty much summarize the book thus: "Mathematicians and philosophers kept putting off dealing with the concept of infinity for centuries. Finally some guys in Germany dealt with it. They showed that there are different kinds of greater and lesser infinities. This created more paradoxes and problems for the field, some of which still never got solved. David Foster Wallace was a really smart guy and really geeky (even though he may have screwed up some of the finer points of the math)."

  9. 5 out of 5

    Suman

    Reading other goodreads reviews, I decided I should write something because it seems that the other reviewers are either lazy or illiterate. "Everything and More" is unlike any other "pop" math book I've ever read. Most math books involve the personalities of these mythical math beings with some horrible math analogies sprinkled in to deceive the reader into thinking she is reading a math book rather than a poor biography. DFW does something completely different, actually writing about the intri Reading other goodreads reviews, I decided I should write something because it seems that the other reviewers are either lazy or illiterate. "Everything and More" is unlike any other "pop" math book I've ever read. Most math books involve the personalities of these mythical math beings with some horrible math analogies sprinkled in to deceive the reader into thinking she is reading a math book rather than a poor biography. DFW does something completely different, actually writing about the intricacies of a math concept (that of infinity), while trying to break down the Hollywood notions of the mathematicians behind the work. Yes, the book is tough to read, and this is probably why it has received mixed reviews. The problem, however, is the underlying math is much harder to understand/enjoy if one decided to take a real analysis course (which is all about these type problems) instead of reading this book.* The book is not perfect (sometimes the frenetic style is a bit much, even for me), but it will be the most rewarding math book you have read. * IYI(If you're interested) - I suffered through a real analysis course for a while before finding it completely boring and useless. After reading this work, I've decided that these questions are deep and beautiful and I will take another shot at learning this material

  10. 5 out of 5

    Fraser Kinnear

    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. 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.

  11. 4 out of 5

    Tara

    Engaging material, sloppy presentation.

  12. 5 out of 5

    Tanya

    Blake told me to read this book because it was one of his favorites from last year and funny. I have to disagree, I have been trying to finish it for 9 months and it was quite literally a book about math and the only reason it’s 2 stars is the part about the concept of zero was pretty interesting except I read that part in April and can no longer recall so maybe it wasn’t as interesting as I thought.

  13. 5 out of 5

    Kaila

    I DID IT. I FINISHED IT. Phew, the last half was a slog. This was basically a history of math, with the bent of focusing on how/why we got to certain calculations about infinity. I can easily recommend the first 100 pages to everybody who has a passing interest in philosophy or David Foster Wallace. I have read exactly two things by him (now three): Infinite Jest and This is Water, both things I bend over backward to recommend to people. The first 100 pages of Everything and More were like a conf I DID IT. I FINISHED IT. Phew, the last half was a slog. This was basically a history of math, with the bent of focusing on how/why we got to certain calculations about infinity. I can easily recommend the first 100 pages to everybody who has a passing interest in philosophy or David Foster Wallace. I have read exactly two things by him (now three): Infinite Jest and This is Water, both things I bend over backward to recommend to people. The first 100 pages of Everything and More were like a confluence of everything I love about those two pieces and it was seriously blowing my mind. Then it got into math, and my eyes started to glaze over. Math has never been a strong suit of mine, and there are some page-long proofs that I straight up skipped. It got harder and harder to understand what was happening because I didn't really understand the formative/underlying principles, so when he started to build on them, I really didn't get it. Loved the first part though and I can recommend that with abandon.

  14. 5 out of 5

    Ben Richmond

    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 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.

  15. 4 out of 5

    Isabelle Leo

    Very fun and occasionally existentially terrifying. I appreciate Dave's confidence in my mathematical/logical acuity but I would not have been insulted if he had dumbed it down just a little bit more. Very fun and occasionally existentially terrifying. I appreciate Dave's confidence in my mathematical/logical acuity but I would not have been insulted if he had dumbed it down just a little bit more.

  16. 4 out of 5

    David

    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 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 DFW's various idiosyncrasies combine to produce a book which is fundamentally unreadable. Normally, once I start a book, I feel enormous guilt if I don't finish. No guilt here - just exasperation. One can reasonably argue that DFW's enormous talent might justify certain peculiarities of style, but every author needs the discipline of a good editor. W.W. Norton seems to have dispensed with editors altogether, certainly with the sentient kind. A pity, because somebody should have explained to DFW that prefacing any section of text with the title "Soft-news interpolation, placed here ante rem because this is the last place to do it without disrupting the juggernaut-like momentum of the pre-Cantor mathematical context" is not just completely unhelpful. It is an irritating distraction, the sorry result of the inability of this talented writer to vanquish the demons which continue to plague his undisciplined style. Unfortunately, this kind of self-indulgent stylistic mannerism recurs with infuriating frequncy. As a result, this book is a complete train wreck.

  17. 4 out of 5

    Alexander Weber

    Fantastic! And I'm not even a huge DFW fan. But man do I like this non-fiction. To all the naysayers who say this is full of mistakes. Yes. Yes, of course. He's simplifying things in order to get the message across. But DFW is like an obsessive-compulsive, who is both trying to simplify but isn't happy with hand-waving... so you get a complex mess. I love it. I will say that his description of Dedekind's schnittzing to prove irrationals has me completely bamboozled. But at least after reading this Fantastic! And I'm not even a huge DFW fan. But man do I like this non-fiction. To all the naysayers who say this is full of mistakes. Yes. Yes, of course. He's simplifying things in order to get the message across. But DFW is like an obsessive-compulsive, who is both trying to simplify but isn't happy with hand-waving... so you get a complex mess. I love it. I will say that his description of Dedekind's schnittzing to prove irrationals has me completely bamboozled. But at least after reading this I am VERY interested in it. I've read about Cantor's diagonalizing before, and once again was delighted to learn about it. It is seriously delightful. I think the story that I loved the most, running through this, was the intuitionists vs the platonists (vs the formalists?) and I have no idea where I stand on this issue. Intuitionism is seriously lovely, and when you consider how all math is essentially done on computers (discrete)... then what does it matter if we don't allow transfinite math into existence? Anyways, it makes me really excited to learn more about discrete math and computability etc. etc. I now want to read What is Mathematic, Really? by some guy... I can't remember. And Ian Hacking's new book on math. Which is to say: DFW's book on infinite has given me a boner for math. A boner I have not had for a long, long time. I missed this boner. :)

  18. 4 out of 5

    Patty

    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 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 actually kept a note pad at hand so she could work out the math problems for herself, so she could follow more closely. Maybe that would have helped me, but I didn't want to! So, Dan Newton, I'll be handing this off to you!

  19. 4 out of 5

    Shannon

    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. 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.

  20. 5 out of 5

    Jeff

    This wasn't written by a mathematician; math specialists seem to notice its flaws. It was written by a literary golden boy; literati seem to like its style. Some people seem to believe these aspects roughly balance out, resulting in a somewhat pleasing and somewhat unsatisfying read. I hoped that Wallace's treatment would be at least as much about the philosophical concept as about the mathematical description of infinity. Since it wasn't and since almost all of the math was too hard for me, i co This wasn't written by a mathematician; math specialists seem to notice its flaws. It was written by a literary golden boy; literati seem to like its style. Some people seem to believe these aspects roughly balance out, resulting in a somewhat pleasing and somewhat unsatisfying read. I hoped that Wallace's treatment would be at least as much about the philosophical concept as about the mathematical description of infinity. Since it wasn't and since almost all of the math was too hard for me, i couldn't really dig it. The dude seems to know way more than the average bear about this topic ... or maybe the 1-star reviewers are on point ... i really have no way to assess. Good thing you're not looking to me for the answers. All i can say is that if calculus was a stopping point for your mathematical education then this book's math might be too much for you also.

  21. 5 out of 5

    Tiffany

    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 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!)

  22. 5 out of 5

    dead letter office

    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" 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" writing style (this description seems not quite right, unless you throw around lots of Latin abbreviations, e.g. e.g., and footnotes in your conversations) really irritating and not that illuminating*. I guess I might like the idea of David Foster Wallace more than I like reading his stuff. ... *For example, the following passage: You'll have noticed that we've run up against these sorts of questions dozens of times already and we're still 2,000+ years from G. Cantor. They are the veritable bad penny in the Story of Infinity, and there's no way around them if you don't want just a bunch of abstract math-class vomitus on transfinite set theory. Deal. Right now is the time for a sketch of Plato's One Over Many argument, which is the classic treatment of just these questions as they apply to the related issue of predication. You might recall the O.O.M., too, from school, in which case relax because this won't take long.

  23. 5 out of 5

    Miles

    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 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 pretty advanced mathematical concepts. At least they seemed advanced to me. Wallace does try really hard to assume not very much math knowledge, and actually apologizes a lot throughout the text about how 'brutal' and 'eyeglazing' and 'nutcrunching' big portions of the text are. Several times the reader is invited to take deep breaths, and to read sentences multiple times to try to get their meaning. So all in all, I found the book not that enjoyable nor very edifying. I got a pretty basic sense of the accomplishments of one G. Cantor to the mathematics of infinity, and Wallace's style was as usual frequently delightful. Mostly though the book made me feel kind of dumb. :(

  24. 5 out of 5

    Ísabel

    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 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 other directions. The book has weaknesses, though, and as a mathematician I winced at some parts, but I really liked the braveness to be idiosyncratic - I have read too many popularizations of mathematics that repeated the eversame stories. Also, the first § really intrigued me very much(the book is sectioned in 7 §s). Perhaps one should take the instructions to skip parts more seriously, but who ever does that, really :-)

  25. 4 out of 5

    Kfray

    As it turns out, I would read a 400 page essay on watching paint dry, as long as it was penned by DFW. Sadly, this book is not (despite emphatic protestations from the author otherwise) for people unfamiliar with advanced math (and by advanced I mean anything more complicated that basic geometry) So, I got 200 pages in and realized that he was still talking and I still had no idea what was going on. infinity remains a mystery

  26. 4 out of 5

    Ellen

    Thinking warm thoughts about my high school calc teacher, who undoubtedly would understand this book a lot better than I do.

  27. 5 out of 5

    Baal Of

    This is the most difficult book I've read in a while. It took me 2 months, but it felt like 4 months. By the last 40 pages I was pretty much lost with the math, and found the presentation fairly confusing with the mix of footnotes, "IYI" (If Your Interested) sections, and historical digressions. Despite all that, I did come out with a couple things of value. First, Dedekind's schnitt proof, which I had to work through myself on my white board, over the course of a few days, writing it out in my o This is the most difficult book I've read in a while. It took me 2 months, but it felt like 4 months. By the last 40 pages I was pretty much lost with the math, and found the presentation fairly confusing with the mix of footnotes, "IYI" (If Your Interested) sections, and historical digressions. Despite all that, I did come out with a couple things of value. First, Dedekind's schnitt proof, which I had to work through myself on my white board, over the course of a few days, writing it out in my own words, and attempting to explain it to a couple cow-orkers who are also interested in math. After going through that process, I felt like I had at least a layman's passing understanding of the proof, and it was a new one to me which I found fascinating. It is still churning around in my head. Second, I am astounding by the brilliance of those top tier mathematicians with their ability to make some pretty amazing leaps of logic, which I know is also the result of tremendous amounts of very hard work, when figuring out how to go about proving various propositions. Over and over I kept thinking "how did you figure out to do that?" Of course the answer is complicated. I've read a few of the pretty harsh negative reviews of this book, saying their were lots of mistakes, and pointing out that the book was poorly organized and made the math more complicated than it needed to be. I don't know enough to be able to gauge the accuracy of those claims, but there was at least enough right that I (vaguely) remember from my college math courses that I feel this was on some level a worthwhile refresher.

  28. 4 out of 5

    Kurt

    I read this book due to a sense of DFW fanboy completionism, not from any sense of subject matter interest. I was then pleasantly surprised at the (very) beginning of this book, that the book was self-described as a beginner level read to a very complex subject, and that - though much of the verbiage was out in the weeds - I was able to discern some interesting points from the heavy theories presented in this book. But that all ended pretty quickly. Much of this book is the embodiment of that ni I read this book due to a sense of DFW fanboy completionism, not from any sense of subject matter interest. I was then pleasantly surprised at the (very) beginning of this book, that the book was self-described as a beginner level read to a very complex subject, and that - though much of the verbiage was out in the weeds - I was able to discern some interesting points from the heavy theories presented in this book. But that all ended pretty quickly. Much of this book is the embodiment of that nightmare of stepping midway into a class of which you've somehow managed to miss the first half of the semester. I blame myself more than the author - except for his constant preambles that what he's about to discuss should be obvious to anyone who has completed "fourth grade math," before delving immediately into Cantorian Super Set Theorems. DFW and I attended very different fourth grades.

  29. 4 out of 5

    Basho

    I have always been a poor math student. In college I took calculus twice and comprehended not a bit of it. So why read a demanding book all about math? (As a matter of fact this reads like a math text for cool kids). Well it is simple stubbornness. I didn’t know what I was getting into and by the time I realized I wasn’t understanding anything, I refused to quit. So I don’t know if this book is any good or not. I can say DFW writes great fiction though. That at least I know.

  30. 5 out of 5

    Jean-Luc

    According to David Ulin, David Foster Wallace is "one of the most influential and innovative writers of the last 20 years". Yet, to the best of my knowledge, he didn't write about space marines, so could he have really been that good? After reading this, I can conclusively say YES. In Math, Better Explained, Kalid Azad says "Children are expected to cope with mathematics that drove educated adults insane hundreds of years ago." Amusing, true, and yet no one really explained the insanity the way D According to David Ulin, David Foster Wallace is "one of the most influential and innovative writers of the last 20 years". Yet, to the best of my knowledge, he didn't write about space marines, so could he have really been that good? After reading this, I can conclusively say YES. In Math, Better Explained, Kalid Azad says "Children are expected to cope with mathematics that drove educated adults insane hundreds of years ago." Amusing, true, and yet no one really explained the insanity the way DFW does here. Yes, yes, everyone knows the story of imaginary numbers: "Of course we can't take the square root of a negative number... but what if we could???" In essence, it was just a rule change. We also know the story of the axioms of Euclidean Geometry: 5 axioms, with the 5th (the parallel postulate) being so complicated that people wondered if it was necessary. After thousands of years, people realized you could make new geometries by not assuming this axiom. Again, this was just a rule change. Shocking, but still doable if you believe that rules can change. Now consider this: in math, the "derivative" of a function is the rate of change of that function. You can tell the rate of change of a function at a specific point by drawing the tangent line at that point. To draw the tangent line, you have zoom deep into that point. But of course, a line requires 2 points, so you need the 2nd point to be close to the point in question, but no closer. You set up your equation: f'(a) = limit (h → 0) (f(a+h) - f(a)) / h. So far, so good, right? a+h and a are right next to each other but not equal because h is as close to 0 as possible w/out being 0. That's what I learned in my first calculus course, 3 times. (I didn't pass until the 3rd time.) And in all the math courses I've taken, in all the math books I've read, it never once occured to me that the definition of the derivative is asking me to believe 2 mutually exclusive things: h is small enough that a and a+h are barely distinguishable, yet h is big enough to divide by. In logic, a proposition is either true or false, it cannot be both at the same time. So which is it? And if this equation is asking us to believe 2 things at the same time, 2 things which cannot be simultaneously true, how is it that the equation works? That question drove men mad for centuries. In fact, just trying to read that paragraph may have driven you mad, because I am not 1/10th the writer Wallace was. The idea that something could be both true and not true was repugnant, but... but... but what if... what if it could be? Infinty and insanity go hand in hand, and anyone who's stared at a wall lying on the razor's edge of asleep and awake will find this book a disturbingly familiar description of being. Knowing that Wallace killed himself makes this a different experience than if he were alive, because there's no longer any way to accurately assess whether he was foreshadowing. -- Things I either didn't know or didn't understand fully before reading this book: * Bremermann's limit is the maximum computational speed of any theoretical computer. * Eudoxus' method of exhaustion was a precursor to calculus. * We know Johannes Kepler from his laws of planetary motion, but he also worked out a method for calculating the volume of a wine barrel. * 0 and nothing are not the same. -- If no one minds me speaking ill of the dead, what the FUCK is up with the footnotes? FOOT-NOTES are supposed to come at the bottom of the page and they're supposed to be short enough to fit in the bottom of the page. The book is littered with footnotes that sometimes take the entirety of the page, and they kill the pacing of the book having to go back and forth. Of course, you have to go back and forth to enjoy the setup and payoff in various parts, but that's the way it should be! Not going back and forth because "wait, what?" There are numerous parts marked "IYI", which stands for "if you're interested", and of course we're fucking interested, that's why we're reading the book! Why is any one part of the text IYI and another a footnote? Pure whimsy, whimsy of the worst kind. Maybe an editor could've helped by saying "reading this page out loud, does this make any fucking sense?" This is a great book, well worth the effort, but make no mistake, it requires an effort. (Helen Rittelmeyer explores this question more maturely.) Speaking of editors, how on Xenu's green earth did this book get published without an index? -- If you are into math and/or science or you are looking for a challenge or you think about triangles when you're lying in bed, this is a book for you.

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