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Tutto, e di più: storia compatta dell'infinito
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Tutto, e di più: storia compatta dell'infinito (Great Discoveries)

3.67 of 5 stars 3.67  ·  rating details  ·  2,073 ratings  ·  222 reviews
“Il vostro autore è un tizio con un interesse amatoriale di livello medio-alto per la matematica e i sistemi formali. Ha sempre detestato (con gli scarsi risultati che ne conseguono) qualsiasi corso di matematica seguito nel corso della sua vita, con una sola eccezione, peraltro estranea al suo curriculum universitario: un corso tenuto da uno di quei rari specialisti che s ...more
Paperback, 262 pages
Published January 1st 2005 by Codice (first published 2003)
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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
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
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
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
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 ...more
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
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
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
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"
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 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 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
Jan 15, 2011 Shannon marked it as to-read  ·  review of another edition
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.
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
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
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
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 ...more
Apr 15, 2007 Justin rated it 4 of 5 stars  ·  review of another edition
Recommends it for: Wallace Fans/Math Nerds/Infinity Nerds
The reason this book works so well is that Wallace writes about the history of grappling with possibly the most slippery and forbidding concept (infinity) in a very conversant tone. While at times, I did feel like he went overboard a bit so that it went from "conversant" to "patronizing," I generally like DF Wallace a lot and appreciated what he was trying to do with this book (i.e. write a book that "anyone can read" about a "very complicated subject").

This is one in a number of books written o
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
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
A fascinating and deeply-flawed book. I don't see how anyone with less college math than I had (a considerable amount of analysis and formal logic courses) could find their way through this thing with any kind of coherent understanding.

It's interesting as a math history, but often spinningly complex as a math book proper. I think the approach that Wallace took of trying to outline mathematical concepts and proofs as he goes along, describing things to his greatest capacity in natural language, a
Mathematics has been in a technical and metaphysical turmoil from the beginning, but human beings are very good at managing contradictory ideas, or at the least, pretending they don't exist. In this brief volume, which DFW prefers to call a "booklet" in all self reference to the text (finite though the 305 well ordered pages may be, the philosophical foundation of mathematics is revealed to be a quagmire of contradictions, gaps and logical difficulties, and it all begins back where the history o ...more
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
E. C. Koch
I think maybe I didn't quite get this one. Given how hyper-aware DFW is of audience and readership, and how hard he tried to strike a balance between writing for the expert and the layman, it's surprising to me that he seemed to fail to make anyone happy. The critical response that Everything and More received more or less harangued him for making so many technical mistakes or for oversimplifying really complex mathematical concepts, which he constantly tells the reader he's doing (oversimplifyi ...more
Pierre Menard
May 27, 2014 Pierre Menard rated it 1 of 5 stars  ·  review of another edition
Recommends it for: Who likes teachers like John Keating
Shelves: mathematics
L’eclettico romanziere americano David Foster Wallace si cimenta in un ambizioso progetto di “scrittura tecnica popolare”: raccontare la genesi storica e scientifica della teoria matematica dell’infinito elaborata nella seconda metà dell’Ottocento, con annessi e connessi (dai paradossi zenoniani al dualismo aristotelico fra infinito potenziale e infinito attuale, dai lavori di Bolzano, Weierstrass, Dedekind fino alla definitiva sistemazione cantoriana, sconfinando nel Novecento con i risultati o ...more
Adesso che sono quasi alla fine devo dire che: DFW sei un grande narratore, ma non un grande espositore di argomenti matematici. L'argomento non è dei più facili, eppure non è detto che debba essere per forza incomprensibile. Tu DFW l'hai voluto rendere così, incomprensibile.
Quello che potrebbe aiutare a renderlo comprensibile a chi non ne è già a conoscenza per studi precedenti è l'uso di una terminologia appropriata e univoca. Ovvero: tu DFW vuoi evitare le ripetizioni, giocare con gli acroni
Armineh Nouri
Not all infinities are created equal, and neither are books written about them. Everything and More is not a technical examination of the concept of infinity and transfinites and their implications for mathematical analysis, calculus and set theory; nor is it a philosophical account of their history. In DFW's engaging, sharp and yet down-to-earth-to-the-point-of-somewhat-insecure style, the book delves into the lives and struggles of those among us who dared to ponder what lay beyond the mortal ...more
Chris Packham
Cantorian sets are hard! But this is also an awesome exploration of how uncomfortable it is to deal with abstract ideas.
Thinking warm thoughts about my high school calc teacher, who undoubtedly would understand this book a lot better than I do.

ho appena iniziato e mi pare che sul Principio di Induzione ci sia qualcosa che non va:

"... in realt�� noi agiamo per ���fiducia��� nel ripetersi di eventi dei quali abbiamo esperienza, secondo il Principio di Induzione per cui se un fatto x si �� ripetuto n volte in passato in determinate circostanze specifiche, possiamo ragionevolmente supporre** che le stesse circostanze produrranno il fatto x, la formazione dell���azione non risulta pertanto che essere una applicazione di tale principi
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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
More about David Foster Wallace...
Infinite Jest Consider the Lobster and Other Essays A Supposedly Fun Thing I'll Never Do Again:  Essays and Arguments Brief Interviews with Hideous Men This Is Water: Some Thoughts, Delivered on a Significant Occasion, about Living a Compassionate Life

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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 likes
“What exactly do ‘motion’ and ‘existence’ denote? We know that concrete particular things exist, and that sometimes they move. Does motion per se exist? In what way? In what way do abstractions exist? Of course, that last question is itself very abstract. Now you can probably feel the headache starting. There’s a special sort of unease or impatience with stuff like this. Like ‘What exactly is existence?’ or ‘What exactly do we mean when we talk about motion?’ The unease is very distinctive and sets in only at a certain level in the abstraction process—because abstraction proceeds in levels, rather like exponents or dimensions. Let’s say ‘man’ meaning some particular man is Level One. ‘Man’ meaning the species is Level Two. Something like ‘humanity’ or ‘humanness’ is Level Three; now we’re talking about the abstract criteria for something qualifying as human. And so forth. Thinking this way can be dangerous, weird. Thinking abstractly enough about anything … surely we’ve all had the experience of thinking about a word—‘pen,’ say—and of sort of saying the word over and over to ourselves until it ceases to denote; the very strangeness of calling something a pen begins to obtrude on the consciousness in a creepy way, like an epileptic aura.” 0 likes
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