as if i didn’t have enough to worry about, i just read this new scientist article,The Omega Man, and my head is now about to explode. enjoy, and pass it along. basically about gregory chaitin’s extension of turing’s halting problem, and the discovery of omega and super-omega number, which defy calculation.
the randomness of the digits of Omega imposes limits on what can be known from number theory–the most elementary of mathematical fields. “If randomness is even in something as basic as number theory, where else is it?” asks Chaitin. He thinks he knows the answer. “My hunch is it’s everywhere,” he says. “Randomness is the true foundation of mathematics.”