The Unimaginable Mathematics of Borges' Library of Babel (45 page)

Today's notation looks
different, and the formulation of the ideas is simpler and cleaner, but it's
wonderful to seize the opportunity to read, albeit in translation, the seminal
work on infinity from the creator of set theory and the first imaginer of
different sizes of infinity

To Infinity and Beyond,
by Eli Maor.

A user-friendly introduction
to many forms of infinity, including Cantor's notions.

The Divine Proportion,
by H. E. Huntley.

Huntley's work is an
accessible reference which rewards a patient reader with a multiplicity of
extrapolations from Fibonacci's sequence to the real world.

Mathematics and the
Imagination,
by Edward Kasner and James Newman.

A gift from Bioy Casares to
Borges, this book is still surprisingly readable. Today, perhaps most notable
for being the introduction of the word "googol" into the English
language. It was coined by Kasner's nine-year-old nephew.

Fixed Points,
by Yu. A. Shashkin.

Aimed at bright
high-schoolers, this is the most elementary exposition of fixed points and
Brouwer's theorem of which I am aware.

In sum, about all we can
really say in paper's favor is that it's lighter than clay, less awkward than
papyrus, and cheaper than parchment.

—Gregory
Rawlins,
Moths to the Flame

Abbott, Edward A.
Flatland: A Romance of Many Dimensions.
1884. Reprint, New York: Dover, 1992.

Adam, David.
"Give six monkeys a computer, and what do you get? Certainly not the
Bard."
The Guardian,
9 May 2003.
http://www.guardian.co.uk/arts/news/story/0,11711,952259,00.html
(accessed 26 February 2008).

Alazraki,
Jaime.
Borges and the Kaballah: and Other Essays
on his Fiction and Poetry.
New York: Cambridge
University Press, 1988.

Amaral,
Pedro. "Borges, Babel y las matematicas."
Revista Iberoamericana
37(1971): 421-28.

Ammon, Ted.
"A Note on a Note in 'The Library of Babel.' "
Romance Notes
33(1993): 265-69.

Apostol,
Tom.
Calculus, Volume II.
2nd ed. New York: John Wiley & Sons, 1969.

Archimedes.
The Works of Archimedes.
Translated by T. L. Heath. New York: Dover Publications, 1950.

Babel,
Isaac.
The Complete Works of Isaac Babel.
Edited by Nathalie Babel, translated by Peter Constantine. New
York: Norton, 2002.

Barrenechea,
Ana Maria.
Borges: the Labyrinth Maker.
Translated by Robert Lima. New York: New York University Press,
1965.

Barth, John.
Further Fridays.
Boston: Little,
Brown and Co., 1995.

Bell-Villada,
Gene.
Borges and His Fiction.
Rev. ed. Austin: University of Texas Press, 1999.

Benardete,
Jose.
Infinity: An Essay in Metaphysics.
Oxford: Clarendon Press, 1964.

Bioy
Casares, Adolfo, and Jorge Luis Borges.
Chronicles
of Bustos Domecq.
Translated by Norman Thomas di
Giovanni. New York: Dutton, 1976. Bioy Casares, Adolfo, and Jorge Luis Borges.
Six Problems for Don Isidro Parodi.
Translated by Norman Thomas di Giovanni. New York: Dutton, 1981.

Borges,
Jorge Luis, and Norman Thomas di Giovanni.
The
Aleph and Other Stories.

New York:
Dutton, 1978. Borges, Jorge Luis.
Collected
Fictions.
Translated by Andrew Hurley. New York:
Viking, 1998.

__Ficciones.
1944. Rev. ed. 1956. Reprint: Buenos Aires: Emece, 2001.

__Ficciones.
Edited by Anthony Kerrigan, translated by Anthony Bonner.

New York:
Grove, 1999.

__Labyrinths:
Selected Stories and Other Writings.
Edited by
Donald A. Yates

and James E.
Irby. London: The Folio Society, 2007.

__Labyrinths:
Selected Stories and Other Writings.
Edited by
Donald A. Yates

and James E.
Irby. New York: New Directions, 1964.

__The
Library of Babel.
Translated by Andrew Hurley,
illustrated by Erik

Desmazieres.
Boston: David R. Godine, 2000.

__Selected
Non-Fictions.
Edited by Eliot Weinberger. New
York: Penguin

Books, 1999.

Burger,
Edward, and Michael Starbird.
The Heart of
Mathematics.
Emeryville: Key

College
Publishing, 2005. Burton, Robert.
The Anatomy
ofMelancholy.
Introduction by Holbrook Jackson.

New York:
New York Review Books Classics, 2001. Campbell, Jeremy.
Grammatical Man: Information, Entropy, Language, and Life.
New

York: Simon
and Schuster, 1982. Cantor, Georg.
Contributions
to the Founding of the Theory of Transfinite Numbers.

New York:
Dover Publications, 1952. Capobianco, Michael. "Mathematics in the
Ficciones
of Jorge Luis
Borges."
The

International
Fiction Review
9(1982): 51—54. Christensen, James
J.
The Structure of an Atom.
London: Wiley, 1990. Coutinho, S. C.
The Mathematics of Ciphers.
Natick: A. K. Peters,
1999. Delsemme, Armand.
Our Cosmic Origins: From
the Big Bang to the Emergence of Life

and
Intelligence.
Cambridge: Cambridge University
Press, 1998. Descartes, Rene.
Discourse on Method
and the Meditations.
Translated by F. E.

Sutcliffe.
New York: Penguin Books, 1983. Eco, Umberto. "Between La Mancha and
Babel."
Variaciones Borges
4(1997): 51— 62.

Escher, M.
C.
The Graphic Work.
Translated by John Brigham. Berlin: B. Taschen, 1990.

Ferrero,
Jose Maria, and Alfredo Raul Palacios.
Borges
algunas veces matematiza.

Buenos
Aires: Ediciones del 80, 1986. Faucher, Kane X. "A Few Ruminations on
Borges' Notions of Library and Metaphor."
Variaciones Borges
12(2001): 126—37.

Foucault,
Michel.
Discipline and Punish.
Translated by Alan Sheridan. New York: Pantheon, 1977.

Fraenkel,
Abraham A.
Abstract Set Theory.
Amsterdam: North-Holland, 1953.

Franzen,
Torkel.
Gödel's theorem: an incomplete guide to
its uses and abuses.
Wellesley: A. K. Peters,
2005.

Gallian,
Joseph.
Contemporary Abstract Algebra.
5th ed. Boston: Houghton Mifflin, 2002.

Gamow,
George.
One, Two, Three. . . Infinity.
1947. Reprint, New York: Viking, 1954.

Grau,
Christina.
Borges y la arquitectura.
Madrid: Catedra, 1989.

Hausdorff,
Felix.
Grundzuge der Mengenlehre.
1914. Reprint, New York: Chelsea, 1949.

Hayles, N.
Katherine.
The Cosmic Web: Scientific Field Models
and Literary Strategies in the Twentieth Century.
Ithaca: Cornell University Press, 1984.

Hernandez,
Juan Antonio.
Biografia del infinito: la nocion de
transfinitud en George Cantor y su presencia en la prosa de Jorge Luis Borges.
Caracas: Comala.com, 2001.

Hofstader, Douglas.
Gödel, Escher, Bach: an Eternal Golden Braid.
New York: Basic Books, 1979.

Huntley, H.
E.
The Divine Proportion: A Study in Mathematical
Beauty.
New York: Dover, 1970.

Kasner,
Edward, and James Newman.
Mathematics and the
Imagination.
New York: Simon and Schuster, 1940.

Keiser,
Graciela. "Modernism/Postmodernism in 'The Library of Babel': Jorge Luis
Borges's Fiction as Borderland."
Hispanofila
115(1995): 39—48.

Keisler, H.
Jerome.
Elementary Calculus: An Infinitesimal
Approach.
Boston: Prindle, Weber & Schmidt,
1986.

Kesten,
Hermann.
Copernicus and his World.
Translated by E. B. Ashton and Norbert Guterman. New York: Roy
Publishers, 1945.

Khinchin, A.
I.
Mathematical Foundations of Information Theory.
New York: Dover Publications, 1957.

Kirk, G. S.,
J. E. Raven, and M. Schofield.
The Presocratic
Philosophers, A Critical History with a selection of texts.
2nd ed. Cambridge: Cambridge University Press, 1995.

Korner, T.
W.
The Pleasures of Counting.
Cambridge: Cambridge University Press, 2000.

Lasswitz,
Kurd. "The Universal Library." Translated by Willy Ley. In
Fantasia Mathematica,
edited by
Clifton Fadiman. New York: Copernicus, 1997.

Lofting,
Hugh.
The Story of Doctor Dolittle.
1920. Reprint, Philadelphia: Lippin-cott, 1948.

Luminet,
Jean-Pierre, Glenn D. Starkman, and Jeffrey Weeks. "Is Space Finite?"
Scientific American,
April 1999: 90-97.

Maor, Eli.
To Infinity and Beyond.
Boston:
Birkhauser, 1987.

McKinzie,
Mark, and Curtis D. Tuckey. "Higher Trigonometry, Hyperreal Numbers, and
Euler's Analysis of Infinities."
Mathematics
Magazine
74(2001): 339— 68.

Merrell,
Floyd.
Unthinking Thinking: Borges, Mathematics
and the New Physics.
West Lafayette: Purdue
University Press, 1991.

Miller, Lynn
F., and Sally S. Swenson,
Lives and Works: Talks
with Women Artists.
Metuchen: Scarecrow Press,
1981.

Nagel,
Ernest.
Gödel's Proof.
New York: New York University Press, 2001.

Nicolas,
Laurent. "Borges et l'infini."
Variaciones Borges
7
(1999): 88—146.

0stergaard,
Svend.
The Mathematics of Meaning.
Aarhus: Aarhus University Press, 1997.

Oxford
English Dictionary.
2nd ed. Oxford: Clarendon
Press, 1989.

Oxtoby,
John.
Measure and Category.
New York: Springer-Verlag, 1971.

Peters, John
Durham. "Resemblance Made Absolutely Extact: Borges and Royce on Maps and
Media."
Variaciones Borges
25(2008): 1—24.

Pierce, John
R.
An Introduction to Information Theory.
New York: Dover Publications, 1980.

Poincaré,
Henri.
The Foundations of Science.
Translated by George Halstead. Lancaster: Science Press, 1946.

Rawlins,
Gregory.
Moths to the Flame: The Seductions of
Computer Technology.
Cambridge: MIT Press, 1996.

Robinson,
Abraham.
Non-standard Analysis.
Rev. ed. Princeton: Princeton University Press, 1996.

Rodriguez
Monegal, Emir.
Jorge Luis Borges: a Literary
Biography.
Dutton: New York, 1978.

Rucker,
Rudolph v. B.
Geometry, Relativity, and the Fourth
Dimension.
New York: Dover, 1977.

__Infinity
and the Mind.
Princeton: Princeton University
Press, 1995.

Russell,
Bertrand.
Human Knowledge: Its Scope and Limits.
London: Routledge, 1948.

__Principles
of Mathematics
. Cambridge: Cambridge University
Press, 1903.