Updated at 3:27 p.m. ET on February 9, 2021.
In Jorge Luis Borges’s story “The Book of Sand,” a mysterious Bible peddler knocks on the narrator’s door and offers to sell him a sacred book he came by in a small village in India. The book shows the wear of many hands. The stranger says that the illiterate peasant who gave it to him called it The Book of Sand, “because neither sand nor this book has a beginning or an end.” Opening the volume, the narrator finds that its pages are rumpled and badly set, with an unpredictable Arabic numeral in the upper corner of each page. The stranger suggests that the narrator try to find the first page. It is impossible. No matter how close to the beginning he explores, several pages always remain between the cover and his hand: “It was as though they grew from the very book.” The stranger then asks the narrator to find the end of the book. Again, he fails. “This can’t be,” says the narrator. “It can’t be, but it is,” says the Bible peddler. “The number of pages in this book is literally infinite. No page is the first page; no page is the last.” The stranger pauses and reflects. “If space is infinite, we are anywhere, at any point in space. If time is infinite, we are at any point in time.”
Thoughts of the infinite have mesmerized and confounded human beings through the millennia. For mathematicians, infinity is an intellectual playground, where an endless string of fractions can add up to 1. For astronomers, the question is whether outer space goes on and on and on. And if it does, as most cosmologists now believe, unsettling consequences abound. For one, there should be an infinite number of copies of each of us somewhere out there in the cosmos. Because even a situation of minuscule probability—like the creation of a particular individual’s exact arrangement of atoms—when multiplied by an infinite number of trials, repeats itself an infinite number of times. Infinity multiplied by any number (except 0) equals infinity.