mrsmith
06-17-2008, 07:08 PM
I'm trying to understand Gregory Chaitin's Omega Number in computational theory, reading his article in Scientific American has me a bit lost on his reasoning. He seems to use self referential logic to prove that Omega cannot be calculated and thus a solution to Turing's halting problem doesnt exist. But then again, based on other theories of compulational complexity a simple program can create irreducible states. (Stephen Wolfram) Which contradicts each other.
If such simple rules as aperiodic tiling and other mathematical systems exists to create truely random patterns why is Chaitin's argument valid?
Perhaps im just not understanding the relationship between all these ideas. Any help would be great.
If such simple rules as aperiodic tiling and other mathematical systems exists to create truely random patterns why is Chaitin's argument valid?
Perhaps im just not understanding the relationship between all these ideas. Any help would be great.