Decades later, in the 1960s, Chaitin took up where Turing left off. Fascinated by Turing's work, he began to investigate the halting problem. He considered all the possible programs that Turing's hypothetical computer could run, and then looked for the probability that a program, chosen at random from among all the possible programs, will halt. Chaitin named this number Omega. And he showed that, just as there are no computable instructions for determining in advance whether a computer will halt, there are also no instructions for determining the digits of Omega.
Omega is uncomputable.
Another example of a computable number might be one that comprises 200 repeats of the sequence 0101. It's a string of 0s and 1s in which each digit is as unrelated to its predecessor as one coin toss is from the next. The same process that led Turing to conclude that the halting problem is undecidable also led Chaitin to the discovery of an unknowable number. An unknowable number wouldn't be a problem if it never reared its head. But once Chaitin had discovered Omega, he began to wonder whether it might have implications in the real world.