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The Unimaginable Mathematics of Borges' Library of Babel
by
William Goldbloom Bloch
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 With 74 figures
 Includes the text of Borges' The Library of Babel
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Our Assessment:
B : decent mathematical overview, if not quite Borgesian enough
See our review for fuller assessment.
From the Reviews:
 "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. (...) Though I confess that my mathematical illiteracy made it difficult for me to follow many of his formulas and graphs, the lucidity of Mr. Bloch's arguments enlightened me nevertheless (.....) I was delighted and instructed by the book's wit and wisdom, and grateful for the guided tour through the mathematical foundations on which both the Library of Babel and its mirror, our universe, are so delicately balanced."  Alberto Manguel, The New York Sun
Please note that these ratings solely represent the complete review's biased interpretation and subjective opinion of the actual reviews and do not claim to accurately reflect or represent the views of the reviewers.
Similarly the illustrative quotes chosen here are merely those the complete review subjectively believes represent the tenor and judgment of the review as a whole. We acknowledge (and remind and warn you) that they may, in fact, be entirely unrepresentative of the actual reviews by any other measure.
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The complete review's Review:
Jorge Luis Borges' The Library of Babel is a classic story of an allencompassing library, and because it deals with everything from the infinite to geometric patterns it lends itself to mathematical analysis.
William Goldbloom Bloch's book is an attempt to consider the mathematics behind (and in) the story, as well as to use the story as a sort of springboard to briefly discuss some of these concepts.
Fortunately, the story itself is also printed in the book, for a refresher, and easy reference.
Bloch usefully brings a variety of mathematical concepts to bear on the story.
The first point is the amusingly obvious one: that no matter how small the books in the Library, there isn't nearly enough room in the actual universe to contain the library Borges envisioned (and that's just taking into account the books, not the structure that houses them ...).
From the very large, Bloch moves to the infinitely small (well, thin), addressing the footnote that suggests a single volume could contain all that the Library holds  if it had "an infinite number of infinitely thin pages")  and demonstrating the somewhat surprising (mathematical) dimensions of such a volume
.
The description of the Library (as a whole) as: "a sphere whose exact center is any hexagon and whose circumference is unattainable" allows for an interesting excursion into topology (and cosmology), while the arrangement of the hexagons  the buildingblock rooms of the Library  raises some geometric issues (and graph theory).
It's actually quite a lot of mathematics that's covered here.
The examples (and many accompanying diagrams) are fairly straightforward, though those with a limited maths background may be a bit intimidated.
If anything, however, one would wish for more: this approach, of tying together math and a piece of literature, seems a particularly fruitful (and enjoyable) exercise, and Bloch could well have elaborated more.
The attempts to tie in Borges more generally aren't always that successful, as there seems some hesitancy to play that out as fully as he might have.
So, for example, Bloch's hope that "H. Bustos Domecq, Borges and Bioy Casares fictional antidetective, would admire" the 'lockedroom detective story'example he offers, or the suggestion that: "Pierre Menard may as well be credited with authorship of all the books in the Library "
(a notion that has to be taken in context), seem too tentative, hesitating nods to the master where it might have been better just to go all out and drag H. Bustos Domecq and Menard right into the thick of things (or otherwise leave them truly on the sidelines).
There's a bit of overexplanation to parts of the text  Bloch's explanation of why Umberto Eco would be the ideal reader of the book, or about the shift from "I" to "we" in the text  but it does give the book a bit more of an approachable feel.
And Bloch seems to mean it when tries to get the reader involved, going so far as to provide not only an 'Annotated Suggested Readings'list, but inviting readers to email him for "more personalized recommendations" (include: "your math background and the things you'd like to learn").
The Unimaginable Mathematics of Borges' Library of Babel is clearly a labour of love, which makes the whole thing more endearing too; great care has been taken with everything from the epigraphs (even the table of Contents and the Index have epigraphs !) to the Glossary and Notes (where one can even forgive him the too cute and predictable first one), and while the cover is hardly eyecatching, the inclusion of reproductions of the first and last pages of the autograph manuscript is a nice touch.
Both as a gloss on Borges' story and in its presentation of a variety of mathematical concepts The Unimaginable Mathematics of Borges' Library of Babel is certainly of interest, and should appeal to Borgesfans with any mathematical interest.
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Links:
The Unimaginable Mathematics of Borges' Library of Babel:
Reviews:
Jorge Luis Borges:
William Goldbloom Bloch:
Other books of interest under review:
 By Jorge Luis Borges:
 About Jorge Luis Borges:
 Featuring Jorge Luis Borges:
 See Index of books dealing with Mathematics
 See Index of Literary Essays
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About the Author:
William Goldbloom Bloch teaches Maths at Wheatin College.
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