Chaitin’s number

He offers some here: When I teach a course, I too like to sell the sizzle at the beginning of each lecture. For a graduate course in information theory I teach, the students are told that they will learn why their cell phones use recently discovered coding that pushes the boundaries of what is mathematically possible in communication speed. I also tell them that we will prove that some things exist that we can also prove are unknowable. And there are numbers that a computer can’t compute. There also exists a single number, Chaitin’s number, that we know lies between zero and one. If we knew Chaitin’s number to finite precision, we could prove or disprove numerous open problems in Read More ›