Chaitin's Omega

Chaitin's Omega is a number that represents the exact probability that a randomly constructed computer program will halt or finish its task. It encapsulates the inherent unpredictability in whether certain programs will stop or run forever. The value of Omega is extremely mysterious: it’s a well-defined number, but individual digits are uncomputable and contain deep mathematical information about the limits of knowledge and computation. Essentially, Omega highlights the fundamental unpredictability in complex systems and the limits of what we can know through algorithms.