How Much Information Can There Be in a Real Number?

摘要

This note gives some information about the magical number Ω and why it is of interest. Our purpose is to explain the significance of recent work by Calude and Dinneen attempting to compute Ω. Furthermore, we propose measuring human intellectual progress (not scientific progress) via the number of bits of Ω that can be determined at any given moment in time using the current mathematical theories.