Abstract: Borges’ short story "The Library of Babel" is a classic literary exploration of the idea of a combinatorial library that contains all possible books of a certain format. However, this idea can be expanded into a theoretical enumeration over all possible recordable attempts by humans to communicate. From this we can deduce that the fidelity with which humans can refer is ‘only’ countably infinite, which is the smallest infinity known as aleph-zero. This paper constructs this enumeration and explores two consequences of it. Firstly, it is at least possible that the size of the set of ‘true’ things in the universe is a ‘larger’ infinite, such as aleph-one (as suggested by the diagonal arguments by Cantor, Gödel, Turing). If this is the case, then it would be impossible for even the full extent of our theoretically possible recordable discourse to explicitly refer to each thing that is ‘true’ about the universe. Maybe there are unquantifiable and indefinable aspects of the world that we cannot capture in any recordable discourse, let alone in the specialised discourse of programming. However, such an expressibility gap would be between humans and the universe, not humans and computers. Secondly, this paper looks at how this enumeration gives theoretical support for certain uses of unique identifiers in programming languages, such as Semprola.
PPIG 2018 - 29th Annual Workshop
All recordable human discourse is trapped in aleph-zero