The Library of Babel
From Prep08Wiki
This is another example of infinity in literature, rather than visual art. Jorge Luis Borges was an Argentinian writer, several of whose stories dealt with notions of the infinite. One of these was "The Library of Babel" (1941, translated into English in 1962). You can read the story online here (it's short, and very good). Briefly, the story describes a library containing every possible book, organized into hexagonal rooms. Borges' narrator precisely describes the rooms and the books:
"Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase....There are five shelves for each of the hexagon's walls; each shelf contains thirty-five books of uniform format; each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color."
The narrator postulates that the Library contains every possible book, but that no book appears more than once. He also rejects the idea that the library has a boundary, concluding at the end that the Library is "unlimited and cyclical".
This can lead to an interesting discussion of infinity versus very large, and some good counting problems.
Questions
1. How many books are in the library?
2. How many rooms are in the library?
3. Estimate the volume of the library.
4. Borges' narrator says that the library is "unlimited and cyclical". What does this mean? Can you describe geometric figures that have this property?
5. Instead, is it possible that the library DOES repeat - that copies of the library are repeated ad infinitum to tesselate 3-dimensional space? Could an inhabitant of the library ever distinguish this possibility from the narrator's claim, even theoretically? If so, would they be able to do so in practice?
