Abstract
“Entrance” is a marvelous example of a heteronym, a word endowed with (at least) two separate pronunciations, each of which has a meaning distinct from the others. In this case, in the context of what I am writing about, the two pronunciations and meanings complement each other very well: Entrance, a place to enter, and: Entrance, to delight and fill with wonder.
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- 1.
If time is unlimited, and the Universe is bounded, Nietzsche argued that given the existence of only a finite number of atoms, all events must eventually recur infinitely often. A similar argument has been made by those who postulate that if the Universe is unlimited spatially, then infinitely many exact replicas of this moment of you reading this footnote are simultaneously distributed throughout the Universe.
- 2.
Zeno claims that the fastest, Achilles, may never catch the slowest, the Tortoise, for by the time Achilles has caught up to where the Tortoise was, to Achilles’ dismay, the Tortoise has moved on, and Achilles must chase him further yet.
- 3.
There is a whole Universe of approaches I am not taking with this article, and while it may be an interesting exercise to catalogue more of them, including the one in which I misunderstand him to be a South African writer who mysteriously writes in Spanish and avoids discussion of serious racial and ethnic identity issues, there are only so many footnotes available to me.
- 4.
From “The Library of Babel,” pages 112–113, as translated by Andrew Hurley in Collected Fictions.
- 5.
251,312,000 books, enough to completely fill 101,834,013 universes the size of our own (using the current best estimate). To gain intuition about these numbers, and for many other insights and perspectives, see: The Unimaginable Mathematics of Borges’ Library of Babel [1].
- 6.
Ibid, p. 113.
- 7.
Ibid, p. 118.
- 8.
The spherical “volume slices” from figure 6 encourage the viewpoint that a 3-sphere is a collection of two points and infinitely many 2-spheres, which is, perhaps, the easiest way to visualize it. However, in 1931 the great mathematical theorist Heinz Hopf developed a way to fiber the 3-sphere into a collection of infinitely many 1-spheres (circles); that is, every point of the 3-sphere lies on one of infinitely many unit circles. There are no isolated poles in this decomposition of 3-sphere.
References
A.M. Barrenechea, Borges: the Labyrinth Maker. Translated by Robert Lima. New York University Press, 1965.
W.G. Bloch, The Unimaginable Mathematics of Borges’ Library of Babel. Oxford University Press, New York, 2008.
J.L. Borges, Ficciones. Emecé Editores, Buenos Aires, 1944.
J.L. Borges, Collected Fictions. Translated by Andrew Hurley. Penguin Classics, New York, 1998.
K. Lasswitz, The Universal Library. Translated by W. Ley in: C. Fadiman (ed.), Fantasia Mathematica. Copernicus, New York, 1997.
J. Munkres, Topology. Prentice-Hall, New Jersey, 1975.
J. Weeks, The Shape of Space: How to Visualize Surfaces and Three-Dimensional, Manifolds. Dekker, New York, 1985.
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© 2012 Springer-Verlag Italia
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Bloch, W.G. (2012). Lost in a Good Book: Jorge Borges’ Inescapable Labyrinth. In: Emmer, M. (eds) Imagine Math. Springer, Milano. https://doi.org/10.1007/978-88-470-2427-4_15
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