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Title: Everything and More: A Compact History of Infinity (Great Discoveries)
ISBN: 0393003388
Author:
David Foster Wallace
Publicate Date: 2003-10
Publish: 2003-10
List Price: $23.95
Average Customer Rating: 3.0
Format: Hardcover
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Amazon Lowest New Price: $6.50
Amazon Lowest Used Price: $2.29
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1: Worst-written book I have ever read.
I was expecting an exciting book.
I was disappointed.
This book has no chapters, lots of text message abbreviations, and many phrases ending in a period.
Three-quarters of this book is background information.
When the payoff comes, actually talking about infinities,
the reationship among alelf null, cardinality c, and alef 1
is left as a "problem for the reader" for 20 pages!
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2: Everything and Less.
I (and many of my professional scientist colleagues) thought Gleick's "Chaos" was one of the worst books ever written on math - so confusing and uninstructive it called the whole subject into question. So it is not surprising Gleick praises this book: it is worse than "Chaos". The grammar, punctuation, and style are so tangled I found myself rereading passage after passage to sort out Wallace's meaning. He uses dozens of obscure, undefined, unusual, and unobvious abbreviations, with the index to them lost in the text, and no index at all to the book as a whole, which is very negligent for a technical work. There is no organization into chapters, just numbered sections which do not coincide with any natural divisions in the material. "Stream-of-consciousness" writing may do for Joyce (though he was not known for lucidity), but it is hopeless for presenting technical material. Many of Wallace's explanations explain nothing: "Fourier Series is vital to understanding transfinite math", he writes, and then blows the subject off with a jest (p 115). And there are plain errors: "when n<0, (p+q)^n becomes the Binomial Theorem" (p 117). Finally, the subject-matter itself is questionable: modern mathematicians still regard infinity as an intractable concept that leads to preposterous contradictions, as Archimedes and Galileo found and as Wallace's own examples demonstrate. "Is the area of an infinitely-long and wide sheet of paper infinity squared?" "Are some infinities bigger than others?" If questions like these have cogent answers at all, it is going to take someone more coherent than Wallace to explain them.
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3: Poorly written and with some serious error(s)
I suppose this might just be his style of writing but I just can't stand it. Having read 9 other math related books over the past month, this was a huge disappointment. He uses all sorts of acronyms and idiosyncrasies that just go too far. I got half way through it and then decided to skim seeing if I could find anything that caught my eye. Thinking maybe his discussion of the Continuum Hypothesis should be good, I read that. Of course, he misstated it, confusing which equality was known and which was hypothesized. This doesn't seem huge, but its just silly that in a book about infinity, DFW states one of the most important undecidable hypotheses in all of math incorrectly and actually presents something that is easily provable (c=2^N0). Why not just one star? He did get me to read 100 pages...
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4: Please enter a title for your review
this book offers no recommendation for what mathematical principles a reader should be familiar with before starting it but any claim of it being accessable to an average reader would be misleading.
if seems not only like no attempt was made to relate most of what is being described to any commonsense foundation, but that it was academically overwritten into a code that even someone who already knew all the information contained in the book would have trouble following. in my ironic experience the "emergency glossary" definitions themselves contain more undefined or ambiguous terms than any other part of the text.
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5: How not to write a book on math
It was Isaac Asimov who once pointed out that to be a great science fiction writer, you must first be a great writer, but the converse doesn't necessarily hold true: you can be a great writer but a poor science fiction writer. The same is true for other genres as well as David Foster Wallace's Everything and More illustrates: he may be a great novelist (though I can't even be positive of that, as I've never read any of his books prior to this one), but he is a mediocre science/math writer.
What is Everything and More about? It is a history of the mathematic concept "infinity". From ancient times, the concept of infinity was troublesome and often worked around. Paradoxes such as Achilles and the Tortoise demonstrated the seeming contradictions of the infinite; for example, this ancient paradox pointed out that to go from point A to point B, you must first go to the halfway point, but to get to that point C, you need to first go to the halfway point between A and C, and so on, ad infinitum. Since there is always another midpoint standing between you and your destination, you can never reach it, but, as anyone who has walked from A to B knows, this seeming impossibility is really possible.
Infinity would be a concept more or less ignored or danced around until the development of calculus made it essential. Even then, for a while, infinity (and the related concept, the infinitesimal) was a shaky idea. Yes, calculus worked, but the foundation it was built on was of uncertain strength. It would take the work of Cantor to finally give infinity its strong theoretical basis; indeed, Cantor is the hero of Everything and More, though he really only appears in the end to clean things up.
Wallace is something of a literary writer, which is not a quality that really fits a math history. He is an occasionally witty and generally wordy writer who is often clever but more often too clever. His constant asides and footnotes are distracting and diminish the clarity that this subject requires. He enjoys abbreviations to the point of annoyance. In addition, a book of this type demands a table of contents or at least an index, but neither are provided.
Reading Everything and More is like going diamond mining. You know there is a gem somewhere, but you need to a lot of work to get to it. In the end, I don't think it is worth the effort. Wallace may be a good writer in other contexts, and certainly this is an interesting concept, but he is not the right man for the job. If you want to see what good math or science writing is like, read Martin Gardener, Isaac Asimov, Carl Sagan, Brian Greene or a dozen others; if you want to see how not to write on such subjects, Everything and More is an ideal example.
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