"The Hellman guy, of course, had been explaining public key crypto-systems that heavily embarrassed the NSA and, really, essentially put it out of business for its stated mission, is smiling. As I recall, he had blond hair long, nearly to his waist. "
Turing proved the existence of non-computable reals, so the two are not the same. Also Chaitin's constant is a non-computable real number with a precise mathematical definition.
See: http://en.wikipedia.org/wiki/Chaitins_constant