Catalogue

There is an interesting issue of the catalogue for the library. How would you summarize which book you are referring to? Is a title enough? What would the title of the book be? One starts to run into difficulty because every possible book is in this library. Since titles are generally at most a couple of lines long, you'll end with many of the books with the same title. In fact is there a way to uniquely identify books in this library? Beyond reproducing the whole text, probably not. Some books you will be able to write a short programme which will reproduce the whole text. For example the book with MCV repeated continuously has a short programme which can be used to reconstruct the book: just keep repeating MCV.

This gets into interesting issues of measures of randomness and complexity. There are ways to measure randomness by looking at the shortest programme that can reproduce the sequence. I wrote an article on issues related to this and Memory in the recent issue of Drawbridge. It raises the question of which books do you pick out as having meaning and which are just random nonsense. The issue of music and noise obviously relate to this. But equally which mathematical proofs do we mark out as special and worthy of note and which are boring and tautological? There is a aesthetic judgement being made in the choice of mathematical pathways. I could get a computer to churn out theorems for me but which are worthy of me sending off to be published? The monkey and the mathematical typewriter.

Here is a link to the Infinite Monkey Theorem