Chaitin's constant

Chaitin's constant is a real number that represents the likelihood of a randomly chosen computer program halting—essentially, whether it will finish running. It embodies the limits of what can be known in computer science, indicating that there are problems we cannot predict or solve. Specifically, it shows that there are certain truths about algorithms that are inherently unprovable, emphasizing a fundamental randomness in computation. Thus, Chaitin's constant highlights the intersection of mathematics, computer science, and philosophy, showcasing the complexities of understanding information and limits of computation.