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THE UNIMAGINABLE MATHEMATICS OF BORGES' LIBRARY OF BABEL by William Goldbloom Bloch Oxford University Press, 2008, 192 pp. ISBN: 978-0-19-533457-9
Jorge Luis Borges' "Library of Babel" is a captivating short story about a library that, using 25 orthographic symbols, including the blank space, printed 80 symbols per line, 40 lines per page, and 410 pages per book, contains every possible book that can be made. An easy combinatorial calculation shows that Borges' library contains 25!'3i2'000 distinct books. The Unimaginable Mathematics of Borges ' Library of Babel explores a variety of mathematical issues arising from the premise of Borges' library.
Bloch begins with the complete text of Borges' story. The rest of his book is structured as an interweaving of mathematical reflection on the Library of Babel followed by a technical exposition of the mathematics he brings to bear on this reflection. These numbered expositions are each called "Math Aftermath".
Chapter One addresses the very natural question concerning the number of books in Borges' fictional library. This is, of course, an unimaginably large number, so Bloch spends some time trying to get a handle on 251'312'000. He concludes that the...