The phrase mystic fictions immediately brings to mind Jorge Luis Borges. On the subject of infinity, Jorge Luis Borges opined, “there is one concept that corrupts and deranges the others. I speak not of Evil, whose limited domain is Ethics; I refer to the Infinite.” He went on to say it would take him seven years of metaphysical, theological, and mathematical study to begin to broach the topic. Borges was conversant with mathematics, certainly being familiar with Cantor’s set theory, as he named ‘The Aleph’ after Cantor’s transfinite numbers. He reviewed a mathematics book, in which he amusingly referred to the “mildly obscene” Möbius strip. (The Möbius strip was the inspiration for a story ‘The Disk’ about a one-sided coin.)
As a mathematician, I have always enjoyed his stories regarding the infinite. Most famous of these are ‘The Library of Babel’ and ‘The Aleph’. Less well-known, but a particular favorite of mine, is ‘The Book of Sand’. Four short pages encapsulate the magic of Borges’ fictions. A mysterious man shows up at the door of the narrator, a collector of rare books, with a book containing an infinite number of pages. Upon reading a page in this Book of Books and then closing it, one will never encounter that page again. The pages are like grains of sand and are metonymic of the moments in our lives, which can never be recaptured except through the vagaries of memory. Our narrator acquires the book and becomes obsessed with it. Soon he realizes, echoing the quote from Borges, that it is monstrous. “I felt it was a nightmare thing, an obscene thing, and that it defiled and corrupted reality.” It always gave me pleasure to show students that if this Book of Sand had countably many infinite, infinitely thin pages, then it can be proven that if you held it vertically and looked at the spine, you would not see it, since it would have what is called measure 0.
First published in Spanish in El libro de arena in 1975; first published in English in a translation by Norman Thomas di Giovanni in The New Yorker, 1977; now available in Collected Fictions, Penguin Books, 1998
A Personal Anthology 