Brooke Santy
Dr. Schulteis
History of Infinity
24 October 2017
Jorge Luis Borges on Infinity
Jorge Luis Borges was born on August 24, 1899 and died on June 14, 1986. He was an
Argentinian poet, short-story writer, and essayist whose works became classics of 20th century literature. Borges concerns himself with several mathematical concepts by writing multiple short stories involving infinite processes. One of Borges’ strongest links to mathematics is through
Georg Cantor’s theory of infinite sets. One of the short stories Borges wrote is called, “The Book of Sand” or “El libro de arena.” He wrote this short story in 1975. This short story deals with an infinity whose elements are a dense set, that is, for any two elements, we can always find
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In the story, the narrator describes the book as having pages that are “infinitely thin” which can be interpreted either as referring to a set of measure zero, or of having infinitesimal length, in the sense of second order logic.
The story begins with an unnamed narrator being visited by a tall, Scots Bible-seller. This
Bible-seller presents the narrator with a very old, cloth-bound book that he bought in India from an Untouchable. The book is entitled, “Holy Writ” and underneath this title, it reads, “Bombay.”
However, it is to be called “The Book of Sand” because “neither the book nor the sand has any beginning or end.” When the narrator opens the book, he discovers that this book is infinite-- it is written in an unknown language and is occasionally punctuated by illustrations. Once one page turns, more pages seem to grow out of the front and back covers. The narrator trades a month of his pension and a prized Wiclif Bible for “The Book of Sand” and hides it on his bookshelf. The
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Santy narrator obsesses over the book over the summer, to the point where he refuses to go outside in fear of it being stolen. In the end, the narrator realizes that the book is monstrous and
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The sand in the story may symbolize infinity. As Borges suggests in this story, the sand, like the infinite, has neither a beginning nor an end. Also, the pages in “The Book of Sand” have measure zero. A set has measure zero if the sum of the lengths of a countable collection of intervals enclosing the points can be made arbitrarily small. Therefore, the infinite pages and infinite sand suggest that
Borges believed in an infinity.
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Works Cited
Gouhin, Sophia. “The Book of Sand.” Prezi.com, 2 June 2014, prezi.com/vr5sfhbmws7a/the- book-of- sand/.
“Jorge Luis Borges and mathematics.” Wikipedia, Wikimedia Foundation, 10 Oct. 2017, en.wikipedia.org/wiki/Jorge_Luis_Borges_and_mathematics. Monegal, Emir Rodriguez. “Jorge Luis Borges.” Encyclopædia Britannica, Encyclopædia
Britannica, inc., 23 Aug. 2017, www.britannica.com/biography/Jorge-Luis- Borges.
“The Book of Sand.” Gchamp's Blog, 6 Nov. 2009, gchamp.wordpress.com/2009/10/10/the- book-of- sands/.
“The Book of Sand.” Wikipedia, Wikimedia Foundation, 17 Oct. 2017,