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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.
Inside This Book(Learn More)
Most Helpful Customer Reviews on Amazon.com (beta)
- 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.
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.
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.
"(T)he more precise the transmission of an idea, the more opaque the language." from page 105 of the Unimaginable Mathematics of Borges' Library of Babel.
For those unfamiliar with either Jorge Luis Borges' 1941 story Library of Babel or mathematics the language of this book can be very opaque indeed.
Probably the best way to begin is with the short story itself. In 1941 Jorge Luis Borges wrote a story called Library of Babel. This story was later republished in both his 1944 Ficciones and also in an English language translation from 1964 called Labyrinths. The story is also reprinted in this book. In the main the story talks of the librarians who work a great library of babel which spans the entire universe and is made up hexagonal rooms wherein all possible books (according to Borges) are stored. These books feature all possible letter combinations including books consisting of every possible letter combination from a...a to z...z. In a concluding footnote Borges imagines that a book of infinitely thin pages could also accomodate the storage of the same information.
For someone who wasn't a mathematician the story certainly raised a lot mathemtical issues, albeit perhaps inadvertantly. It's Bloch's obvious function in writing this book to follow those main implications from the Borges story which most fascinate Bloch and in so doing provides Bloch's best estimate as to what mathematics would say as to the resolution of any issues raised by the nonmathematician Borges.
The first and perhaps most interesting one is whether such a library could even be housed within the physical confines of our universe. To answer this question, Bloch goes back to Borges' story and Borges' descriptions of the books themselves. Using mathematics Bloch determines that if you follow Borges' instructions you will come up with a total 25 raised to the 1,312,000th power number of books. Converted to a base ten figure Borges' total number of books would equal 10 raised to the 1,834,097th power. Either number easily dwarfs the size of the visible universe's power to even house Borges' books. On this score, Bloch's numbers say that the universe's storage capacity would "only" equal 10 raised to the 90th power number of books.
In other words, and obviously beknownst to Borges' his library was not physically possible.
In his second chapter Bloch uses information theory to tackle the question of just how one would go about cataloging Borges' library. For his part, Borges' himself imagined that his librarians would be spending a good portion of their time searching the library itself for its own catalogue. However, as pointed out by Bloch and given the logic of Borges' story, that search would invariably be more fruitless than a search of the library itself for any book in question. As noted by Bloch: "Every plausible entry from any possible candidate catalogue volume would have to be tracked down, including scavenger hunts. An immortal librarian would spend a lot of time traversing the Library, ping ponging back and forth between different books purporting to be volumes of a true catalogue." From pages 31 and 31. A true mathematician Bloch ran the numbers supporting his assertions and concluded that the library would have to be its own catalogue. With a bow to the Galileo quotation listed above and also the fact that mathetical reality does so often ordain the nature of physical reality I believe Bloch's information theory assertion as to Borges' library has interesting ultimate implications for those wishing to propound a complete description of the universe. Those interested in further pursuing the implications raised here might well also read Roger Penrose's excellent Road to Reality (though indeed that book also mirrors other issues raised in this volume as well).
Here again though Borges' intuitive insights (viz: that a catalogue could be meaningful found and used) does not correspond with physical reality, it does raise interesting issues outside the scope of his story.
In his third chapter, Bloch uses real analysis as a basis for reviewing the Borges story. To do this Bloch focuses on Borges' footnote that instead of an infinite library, one could conceive of a single book of infinitely thin pages. Borges fans will remember that this idea of a book with infinitely thin pages was featured in another Borges' short story, "The Book of Sand." Bloch attempts to develop the implications of what Borges proposed in three different ways but all fail because a book comprised of infinitely thin pages would require that the book itself be infinitely thin. In other words, the information contained within would be inaccessible.
Here again a thorough going mathematical analysis reveals a disconnect between the story and the reality in a way that Borges' didn't contemplate but still allowed for some interesting speculations.
In his fourth chapter Bloch discusses topology. Even those familiar with mathematics and Borges may find themselves contemplating the first words quoted by Bloch in this review (viz: that the most precise idea transmissions are also the most opaque ones). Here Bloch tries to reflect off certain ideas raised by Borges concerning the physical layout of his library of babel. It's to Bloch's credit that he quickly goes past the litteral wording of what Borges' actually said and quickly focuses on an extended and fascinating discussion of Klein bottles. Named after Oscar Klein, Klein bottles are four dimensional constructs that have the unique property of being able to empty inside of themselves. A more intuitively comprehensible example -- a three dimension Klein figure, if you will -- is the famous Mobius strip which is litterally a one sided object that can be completely traversed without lifting off the plane of the strip. In a similar way one traversing a Klein bottle could continue through a three dimensional object back to a point of origin. A very interesting connection concerning Klein bottles and their real world application was suggested by physicist J Richard Gott in his excellent Time Travel in Einstein's Universe. According to Gott in his book, our universe created itself by pinching off at some point and traveling back in time. For me personally Gott's theory of universal origins has always been the most intuitively satisfying one owing to its use of mathematical paradigm to explain the real world phenomenon of creation itself. Of course, well read math readers will also like Bloch's discussion of Edwin Abbott Abbott's book Flatland wherein Abbott discussed life in a mythical two dimension world. (Experienced math readers may also be interested in knowing that there are not one but two Flatlands movies that have been along with countless books inspired by the Abbott tale including Sphereland, Plainiverse and my personal favorate Flatterland by mathemtician Ian Stewart.)
But again as to the Borges' tale itself Bloch's mathematics shows a disconnect between author Borges' vision and what mathematics would suggest as being the more likely reality.
In his fifth chapter Bloch examines the Borges' tale using geometry and graph theory. Here Bloch discusses Borges' hexagonal layout of his library and possible paths through it. In this way Bloch shows how different layouts would differently affect the lives of Borges' librarians. In positing that disorder might be order Bloch gets about as close to writing a zen koan as he does in this work. Thereafter Bloch speculates on just what Borges' may and may not have been aware of in writing his story.
For me, however, a repeated comparison between what Borges' wrote and what mathematics suggests shows a repeated disconnect between the two...not that such a disconnect matters mind you. In many ways, great literature can be like a diving board in that it helps propel you to a place that the object itself can never go.
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