Mind Matters Natural and Artificial Intelligence News and Analysis

TagOmega double prime

The “Jump” of Chaitin’s Omega Number

Gregory Chaitin explains, “For any infinity, there’s a bigger infinity, which is the infinity of all subsets of the previous step”

In last week’s podcast, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks asked mathematician Gregory Chaitin (best known for Chaitin’s unknowable number) if the unknowable number could prove (or disprove) Goldbach’s Conjecture that every even number can be expressed as the sum of two primes. This task is harder than it first appears because even numbers go on indefinitely. A proof that Christian Goldbach (1690–1764) was right or wrong must show that even numbers must be like that, no matter how big they are or how many of them there are. This time out, Dr. Marks and Dr. Chaitin discuss what we can know about Omega numbers — and where famous mathematicians are buried. This Read More ›

Could Chaitin’s Number Prove Goldbach’s Conjecture At Last?

Chaitin notes that the problem grows exponentially and the calculations get quite horrendous

In last week’s podcast, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks continued his conversation with mathematician Gregory Chaitin, best known for Chaitin’s unknowable number. One thing they discussed was the usefulness of philosophy, with Chaitin saying that if he had had to do practical work 60 years ago, there wouldn’t be practical research today based on the Omega number. But then they turned to the question of whether the unknowable number could prove Goldbach’s famous Conjecture: This portion begins at 17:17 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks (pictured): The poster problem for the Turing halting problem, is Goldbach’s Conjecture, which says that every even number can be Read More ›