## The Unimaginable Mathematics of Borges’ Library of Babel [book review]

**T**his is a book I carried away from JSM in Boston as the Oxford University Press representative kindly provided my with a copy at the end of the meeting. After I asked for it, as I was quite excited to see a book linking Jorge Luis Borges’ great Library of Babel short story with mathematical concepts. Even though many other short stories by Borges have a mathematical flavour and are bound to fascinate mathematicians, the Library of Babel is particularly prone to mathemati-sation as it deals with the notions of infinite, periodicity, permutation, randomness… As it happens, William Goldbloom Bloch [a patronym that would surely have inspired Borges!], professor of mathematics at Wheaton College, Mass., published the unimaginable mathematics of Borges’ Library of Babel in 2008, so this is not a recent publication. But I had managed to miss through the several conferences where I stopped at OUP exhibit booth. (Interestingly William Bloch has also published a mathematical paper on Neil Stephenson’s Cryptonomicon.)

**N**ow, what is unimaginable in the maths behind Borges’ great Library of Babel??? The obvious line of entry to the mathematical aspects of the book is combinatorics: how many different books are there in total? [Ans. 10¹⁸³⁴⁰⁹⁷…] how many hexagons are needed to shelf that many books? [Ans. 10⁶⁸¹⁵³¹…] how long would it take to visit all those hexagons? how many librarians are needed for a Library containing all volumes once and only once? how many different libraries are there [Ans. 10^{10⁶}…] Then the book embarks upon some cohomology, Cavalieri’s infinitesimals (mentioned by Borges in a footnote), Zeno’s paradox, topology (with Klein’s bottle), graph theory (and the important question as to whether or not each hexagon has one or two stairs), information theory, Turing’s machine. The concluding chapters are comments about other mathematical analysis of Borges’ Grand Œuvre and a discussion on how much maths Borges knew.

**S**o a nice escapade through some mathematical landscapes with more or less connection with the original masterpiece. I am not convinced it brings any further dimension or insight about it, or even that one should try to dissect it that way, because it kills the poetry in the story, especially the play around the notion(s) of infinite. The fact that the short story is incomplete [and short on details] makes its beauty: if one starts wondering at the possibility of the Library or at the daily life of the librarians [like, what do they eat? why are they there? where are the readers? what happens when they die? &tc.] the intrusion of realism closes the enchantment! Nonetheless, the unimaginable mathematics of Borges’ Library of Babel provides a pleasant entry into some mathematical concepts and as such may initiate a layperson not too shy of maths formulas to the beauty of mathematics.

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