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The Unimaginable Mathematics of Borges' Library of Babel Hardcover – Sep 15 2008


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"Mr. Bloch, professor of mathematics at Wheaton College, has woven an elegant, ingenious, scholarly interpretation of Borges's text that contradicts the disingenuous 'unimaginable' of his title."--New York Sun


"For the reader of Borges, some of Bloch's observations may offer a useful new way of engaging with the themes of the fiction." -- American Scientist


"You need no advanced mathematics to understand 'The Library of Babel' but chances are good that if you like the story, you'll enjoy Professor Bloch's excursions." -- Mathematical Association of America Review


"Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature, but also exposes the reader - including those more inclined to the literary world - to many intriguing and entrancing mathematical ideas."--Mathematical Reviews


About the Author

William Goldbloom Bloch is Professor of Mathematics at Wheaton College.

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Amazon.com: 9 reviews
28 of 29 people found the following review helpful
Astounding and beautiful Oct. 20 2008
By Lady Ash - Published on Amazon.com
Format: Hardcover
I am team-teaching a class on literature and math this year, and my mathematician colleague and I are reading this book together. We are both seriously impressed by it. I'm going to convince him to write his own review, but I can say this:
- the book is *beautifully* written, a profound joy to read in a way that few books are
- I last took any math in high school, and I find the discussions clear and fascinating. If you think that you "hate math" or are "bad at math," don't be too sure. Bloch takes such care and pleasure in explaining mathematical concepts that I could follow them without much difficulty, and with much enjoyment.

I would recommend this book with wild enthusiasm to anyone who finds thinking pleasurable. And I can't stress enough how excellent the writing is.
8 of 8 people found the following review helpful
It is best to familiarize yourself with the short story, "The Library of Babel" by Jorge Luis Borges before you read it Dec 2 2009
By Charles Ashbacher - Published on Amazon.com
Format: Hardcover
If you read this book without doing a little bit of familiarizing yourself with the short story, "The Library of Babel" by Jorge Luis Borges, you will be starting the process from a weak position. The story describes a universe composed of an immense library of all books of 410 pages having a specified format. The library is constructed from a series of hexagonally shaped rooms, with four walls covered by books and each room contains the necessities for human survival. The order and content of the books is random, so the vast majority contains nothing but gibberish and there is no labeling by content. There are librarians, but the disorder has put them into a mood of despair, for librarians desire order in the stacks.
The structure of this library forms the database for the mathematics described in this book. It begins with the combinatorial computations needed to fathom, if that is possible, the enormous number of rooms and books that must be in the library. While it is possible to compute the number of possibilities, the number is so large that it justifies the use of "unimaginable" in the title. Other aspects of mathematics demonstrated based on the parameters of the library are information theory, the topology of the library and the universe it is, graph theory is used to explain the complexity of accessing the books and the probability of finding a book that you care about.
It is written in a conversational style, while mathematical formulas are used when necessary, the bulk of the text is expository in nature with an emphasis on general understanding. Writing a math book where the starting point is an item of literature is an interesting process and Bloch performs the task very well.
12 of 14 people found the following review helpful
A treat if you already like Borges March 10 2009
By Alatriste - Published on Amazon.com
Format: Hardcover Verified Purchase
Bloch is not only a mathematician, he's also a critic who has reviewed a lot of the literature on the Library of Babel and the life of Borges. So there is a lot in the book besides working out some of the mathematical implications of Borges' inspirations.

If you got as far as calculus in your math studies then you can probably follow most of the math without too much trouble. If you are a fan of Borges, there is a lot here about his math background and interests that you probably didn't know and which affected other works of his too.

If you are neither, pass this by. Go read some Borges and if you like him, then come back and read this.
5 of 5 people found the following review helpful
While doomed to appeal only to a small crowd of Borges nerds, this is a fun text, even if it sometimes gets away from itself Jan. 5 2011
By Christopher Culver - Published on Amazon.com
Format: Hardcover
Of all the short stories in Argentinian writer Jorge Luis Borges' masterpiece collection FICCIONES, "The Library of Babel" is one of the most peculiar. This weary narration by an aged caretaker of a library of seemingly infinite expanse involves several exotic mathematical principles, yet ones fairly easily graspable by the layman. The mathematician Bloch has written a fine book about all the thought-provoking concepts in Borges' story.

The complete text of "The Library of Babel" is included here, so if you like the intersection of maths and literature, you have all you need here to explore Borges' vision. Still, I'd recommend neophytes read this story first in FICCIONES, as there you'll also find some other enjoyable and influential short stories.

Each chapter discusses the relevant concepts in accessible prose, followed by a "Math Aftermath" for those who want to see rigorous figures and calculations. First we have combinatorics, namely how to calculate the number of possible books in the library. Bloch A remarkable conclusion is drawn, perhaps unrealized by Borges himself. If the library contained every possible book, even if only a single copy of each, then its contents would still be exponentially too large to fit in our universe. The second chapter concerns information theory, namely the (im)possibility of creating a catalogue for the Library.

In Chapter 3, Bloch discusses real analysis, with the springboard being Borges' footnote that instead of an infinite library, one could conceive of a single book of infinitely thin pages. A trip through non-standard analysis reveals a complication that Borges evidently didn't realize.

The fourth chapter discusses topology. The idea of the Library as a Pascal sphere is well-known to Borges fans, but Bloch also describes how a 4-dimensional sphere could meet Borges' description of an infinite but periodic universe. This is the most challenging of all the chapters, especially the Math Aftermath which talks about klein bottles and the like. You'll find this chapter much easier if you've read Edwin Abbott's FLATLAND.

Chapter 5, devoted to Geometry and Graph Theory, examines the honeycomb layout of the Library and possible paths through it, presenting multiple possible interpretations of Borges' text that have quite different ramifications for the inhabitants. The following chapter introduces more combinatorics to ponder how the disorder of the Library might be the Grand Order.

So as you can see, Borges' little story, that many people have no doubt read, thought "How cute", and moved on straightaway, touches on an immense amount of mathematical concepts. The final chapter is dedicated to informed speculation on just how much of the mathematical ramifications of the text Borges was conscious of.

My maths skills have seriously atrophied since I left school, but this was a friendly, approachable text, a catalyst for the all too rare utterance "Who knew maths could be fun!"

My only complaint is that Bloch occasionally goes off on flights of fancy that depart far from Borges' work, when a discussion rooted in the text is already more than enough to satisfy or overwhelm the layman. Also, there is a chapter dedicated to critics that he doesn't like, where he suggests that people stop looking at the text from certain literary criticism perspectives instead of venerating its mathematics.
3 of 3 people found the following review helpful
A Masterpiece March 24 2010
By miriam1025 - Published on Amazon.com
Format: Hardcover
I can't put it down! This is a fascinating concept - taking what is essentially a literary piece with mathematical overtones and extracting the mathematical concepts for analysis. I am a total novice at math and even I can follow the reasoning which means that it is a masterfully written book. I can't recommend it highly enough. If you're not a math enthusiast (as I was not when I picked it up) you will be after reading this. I eagerly anticipate Mr. Bloch's next book - thank you so much you have opened my mind to so many new and exciting ideas that I never would have contemplated had I not given this book a try.


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