While researching a possible monograph on various mutant, blood-thirsty species of killer bees native to Argentina, I chanced across the name Borget, an expatriated Parisian who had done some seminal work in the area. It was the end of a long day, I was tired, and the resultant loose associations of my weary mind led me to thinking of Borges, the famous Argentine writer. Realizing I was at an impasse in my research, I retired to the parlor for a smoke and the leisure of letting my mind go where it would.
But my mind remained stuck on Borges, or, rather, the name “Borges”. I knew little of the man, himself, or his work. I had seen his name in a letter at my grandparents’ house when I was quite young and the name had stuck with me simply because I wondered how it was pronounced. A few years later, I took a class in world literature in college and Borges was covered. The class was taught by two excellent professors, but they both pronounced “Borges” differently, and, to make things worse, neither pronounced it the way I had guessed it should be pronounced! But that’s neither here nor there.
The letter was written by my maternal great-uncle Gunnar Erfjord, a sailor born in Lofoten, Norway, who had emigrated to the United States, sailed both the Atlantic and the Great Lakes, and put in at the ports of Mar del Plata, Hamburg, and Duluth among others. As my uncle was quite learned (mostly self-taught, although he had mastered Greek and Latin in grade school) and a good conversationalist who seemed to be fluent in almost every European language (although curiously not Spanish), he had made many friends around the world. Including Borges.
This letter was contained in a box of letters and documents that had belonged to my great-uncle (who had died a few years before I was born) that was kept at my grandparents’ house in Green Town, Illinois. I used to go through this box as a young child (the box was called an “ant-proof case” by my older relatives—that alone made it fascinating to me). I later inherited the box and its contents from my maternal grandmother (the only sister of my great-uncle). The box contained, among other things,
* some monographs my great-uncle had written on celestial navigation,
* all the Sherlock Holmes novels and stories in Norwegian translation,
* a book titled “Die Philosophie des Unvollendbar” by someone named Emanuel Lasker,
* a 15 puzzle, which I got quite good at,
* and some letters to and from Borges.
The letters written to Borges I have are in Norwegian. I have inferred from some of their contents that they were fair copies that were then translated into Spanish by a friend of my great-uncle, with the Spanish translations being sent to Borges and the Norwegian originals being saved by my great-uncle.
I have translated one of the letters from my great-uncle from Norwegian to English. Some of the words are technical and I hope that my translation is accurate (my Norwegian is fair, but not great). Here is my translation of the letter:
Port of New York City
Aboard the Mary Celeste
Señor Jorge Luis Borges
Buenos Aires, Argentina
6 November, 1872
I visited our mutual friend, Professor Cantor, while I was recently in port in Germany. He asked me to relay some advice to you regarding the story “The Library of Babel”, which I know you are currently working on. He said that he has discussed the story with you and that you have three versions, the finite version, the countable version, and the uncountable version. His advice is:
* finite version: Cantor said that you should feel free to publish this version, although he said he thinks it lacks “daring”.
* countable version: Cantor said that this is a variation he suggested in which the number of pages in each book in the library is unbounded (but finite) and not restricted to four hundred and ten. Hence there is an infinite number of books in the library with no duplicates. He further said that this was a more “audacious” version of the story and he preferred it to the first.
* uncountable version: Cantor said this was an extended variation of the countable version of the story. In this third version, each of the books has an infinite number of pages and, hence, an infinite number of characters (although many of these books may end in an infinite number of spaces). He said some sort of “diagonal argument” can be used on the individual letters in these books. He said this proved that this version of the library somehow contained more books than the preceding version. It wasn’t clear to me whether this third version was his idea or your idea. I asked him how the librarians could hold one of these endless books in his hands. He said something about how perhaps each leaf of the book could be half as thick as the preceding leaf while waving his hand in a strange manner.
Then Cantor told me very explicitly that you should not pursue work on the “uncountable” version. He said that “like the ‘Matilda Briggs’ and the giant rat of Sumatra, the world is not yet prepared for this story”. He said that he did not want you to follow him in his “descent into the Maelström”. He said that pursuing this version of the story could lead you to professional ruin as happened to him. I thought at the time that the statement seemed a bit melodramatic, but, out of respect for his great intellect, I held my tongue.
I hope this all makes sense to you. He said that it would from your previous discussions and some “personal tutoring” he gave you in “the theory of sets”.
Of our mutual friend’s health, I am sad to report that he has been hospitalized with melancholia. I think that his perhaps exaggerated doubts on the wisdom of publishing the “uncountable version” of your story (not to mention his strange hand waving) were but a symptom of his illness. I tried to discuss this further with him, but he became greatly agitated, so I dropped the discussion.
We set sail for Genoa tomorrow. Assuming the Mary Celeste can successfully navigate the doldrums, I hope to see you in person next year for our annual game of chess.
That is the entirety of the letter. For the most part, I don’t understand it. I don’t know what “uncountable” means nor I do know what a “diagonal argument” is. (I am a professor of entomology and I hope to widen my knowledge of other subjects after I retire.)
However, I do know about the tale of the giant rat of Sumatra. It was published as the thirteenth story in “The Case-Book of Sherlock Holmes” by Sir Arthur Conan Doyle. I have my great-uncle’s copy of a Norwegian translation of this book. “The Adventure of the Giant Rat of Sumatra” is the thirteenth story in the collection. I’ve read the story, but, unfortunately, the title is the best thing about it. Curiously, the story doesn’t appear in the English edition I have.
[Editor: I requested from the author a Wikipedia-style article, but was given instead these random reminiscences, with no references and I believe many inaccuracies and inconsistencies. Here are a few links to Wikipedia entries that might help the reader understand the contents of the letter, since the author seems to be too lazy to do any research himself:
* [Countable set](https://en.wikipedia.org/wiki/Countable_set)
* [Uncountable set](https://en.wikipedia.org/wiki/Uncountable_set)
* [Cantor’s diagonal argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument)
Unlike the author, I know enough of set theory to understand what the letter is about. I leave it as an exercise to the reader to use Cantor’s diagonal argument to prove that the library in the third version of the story contains more books than the library in the second version of the story (although each contains an infinite number of books).]