The Limits of Mathematics---Alternative Version

Abstract

This is an alternative version of the course notes in chao-dyn/9407003. The previous version is based on measuring the size of lisp s-expressions. This version is based on measuring the size of what I call lisp m-expressions, which are lisp s-expressions with most parentheses omitted. This formulation of algorithmic information theory is harder to understand than the one that was presented in chao-dyn/9407003, but the constants obtained in all theorems are now less than half the size that they were before. It is not clear to me which version of algorithmic information theory is to be preferred.