Infinity in computable probability
Logic
2020-06-04 v3 Computation and Language
Logic in Computer Science
Abstract
Does combining a finite collection of objects infinitely many times guarantee the construction of a particular object? Here we use recursive function theory to examine the popular scenario of an infinite collection of typing monkeys reproducing the works of Shakespeare. Our main result is to show that it is possible to assign typing probabilities in such a way that while it is impossible that no monkey reproduces Shakespeare's works, the probability of any finite collection of monkeys doing so is arbitrarily small. We extend our results to target-free writing, and end with a broad discussion and pointers to future work.
Keywords
Cite
@article{arxiv.1101.3578,
title = {Infinity in computable probability},
author = {Maarten McKubre-Jordens and Phillip L. Wilson},
journal= {arXiv preprint arXiv:1101.3578},
year = {2020}
}