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solipsist comments on Yet More "Stupid" Questions - Less Wrong Discussion
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Short answer to your questions: No. They aren't related.
Pedantic answer to your questions: Yes.
If you knew the value of Chaitin's Omega you could calculate the incalculable. You would know the results of computations that should take an infinite amount of time to calculate. You could summon the proofs of any conjecture. You could simulate AIXI. You would have the knowledge of a demigod. Being a demigod has strong bearing on the subjects you bring up, and many others.
Chaitin's Omega and LW's Omega share the same name (I suspect) because they both refer to something superhuman. They are different sort of superhumans, however.